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BETA DECAY STUDIES IN NEUTRON RICH Tc, Ru, Rh and
Pd ISOTOPES AND THE WEAK R-PROCESS

presented by

Fernando Montes

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BETA DECAY STUDIES IN NEUTRON RICH Tc, Ru, Rh AND Pd
ISOTOPES AND THE WEAK R-PROCESS
By

Fernando Montes

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Physics and Astronomy

2005

ABSTRACT

BETA DECAY STUDIES IN NEUTRON RICH Tc, Ru, Rh AND Pd ISOTOPES
AND THE WEAK R—PROCESS

By

Fernando Montes

The r-process is responsible for the creation of more than half of the existing
elements heavier than iron in the universe. Because most of the isotopes involved in
its proposed path have not been reached experimentally, most of the nuclear physics
required to successfully model the r-process has been derived using theoretical models.
Among the most important nuclear properties necessary to model the r—process are 3-
decay half-lives T1/2 and fi-delayed neutron emission probabilities P". The mass region
around the shell closure N = 82 has been of considerable theoretical and experimental
interest since nuclear physics in that region is responsible for the creation of elements
in the onset and A z 130 peak of the solar r-process abundance pattern.

fl-decay studies were performed at the National Superconducting Cyclotron Labo-
ratory. A new technique at the NSCL to measure the kinetic energy of the implanting
fragments was used to distinguish charge states of the fragments in the particle identi-
fication. fl-delayed neutron branchings for neutron-rich “6‘120Rh, 120422 Pd and 124Ag
have been measured and they are direct inputs in r-process calculations. Half-lives for
neutron-rich 114‘11"’Tc, 114“118Ru, 116‘mRh and 119‘de have also been measured.

The results agree reasonably well with theoretical QRPA calculations within model
uncertainties and the only exception is the neutron branching of 12"Rh. The measured
Pn values are direct inputs in r-process network calculations. The isotopic solar r-
process abundance ratio 12oSn/ 119Sn increases by 40% when using the experimental
values instead of the prediction by the ETFSI—Q mass model. Although it is not

possible to draw definite conclusions about the shell structure in this mass region

based on the measured T1/2 and P" values alone, it was found that the absolute values
of the quadrupole deformation 62 have to be maintained or slightly reduced from
the predicted FRDM and ETFSI-Q models values to have agreement with measured
116“mRh T1,; and Pn values. Furthermore, a systematic increase in Q5 values best
reproduces the experimental values of the 121'123Pd isotopes. A relative weakening of
the neutron shell closure at N = 82 is consistent with an increase in the Q5 values
for the exotic Pd isotopes but because the predicted fl-strength functions may have
systematic problems, such increase might be compensating for other nuclear structure
deficiencies.

The region Sr-Ag is not only of particular interest due the challenges in obtaining
the observed solar r-process abundance pattern when modeling the r-process but also
because there are some discrepancies between elemental abundances from r-process
rich metal-poor and solar system r-process abundances. Even though there are ambi-
guities in the contribution of the s-process that is used to calculate the solar r-process
abundance pattern, elements 423 Z 347 seem to be less abundant than the so-
lar abundance. These observations suggest that an additional mechanism besides the
strong r-process is required to create the missing or residual abundances in the region
Z s 47. Since the astrophysical scenario and conditions necessary for such a process
were not known, a network calculation with classical neutron exposures from s-process
to r-process type was used to find the astrophysical conditions (an, 7') in which a
neutron capture process would produce the necessary residual abundance pattern.
Neutron density and temperature were spanned from 107 (s-process) to 1022 cm—3
(r-process) and from 0.09 to 1.5 GK, respectively. Neutron densities and temper-
atures that resemble a r-process-like scenario were found to better fit the residual
abundance pattern. An overabundance of Pd was calculated and it may be due to

incorrect nuclear structure properties when modeling the neutron capture process.

to Monica, my inspiration and my light

iv

ACKNOWLEDGMENTS

I would like to thank my advisor Hendrik Schatz who always was enthusiastic
and willing to help me through my time at the NSCL. He was extremely supportive
and made me realize how the most daunting tasks can actually be pretty easy. I will
always remember how everything can be done in 30 minutes.

I would like to thank Paul Mantica for answering all my questions and explaining
even the most trivial things.

I would like to thank all the people in the Schatz group; Peter Santi for his help
during the setup and running of the experiment and because he was always there
when I had a problem; Paul Hosmer for all the discussions and for making my stay
at the lab really enjoyable; Thom Elliot for being my personal Google, helping me
with network calculations and proof-reading of the manuscript; Alfredo Estrade and
Michelle Ouellette for the mate and ice cream meetings.

I would like to thank Colin Morton, Sean Liddick and Bryan Tomlin for all their
help during the experiment and for valuable physics discussions.

I would like to thank my collaborators at the University of Mainz, Bernd Pfeiffer
and K.-L. Kratz for reminding me multiple times of previous work pertinent to mine
and their help with theoretical calculations.

I would like to thank my collaborators at the University of Maryland and Notre
Dame, Bill Walters and Andreas Woehr for having the time to discuss my results.

I would like to thank the members of my guidance committee, Vladimir Zelevin—
sky, Carl Schmidt, Thomas Glasmacher, Ed Brown and Tim Beers for answering my
occasional questions.

I would like to thank the staff of the NSCL for their help and advice; the computer
department, especially Barbara Pollack, for help with my multiple software and disk-
space requests; the A1900 group for being extremely helpful in the preparation of and

during the experiment.

I would like to thank those who supported and believed in me. To fellow graduate
students, Jorge Benitez, Mark Wallace, Eric Pellegrini, Divya Singh and Mustafa
al-HajDarwhish. To Shruti Tewari and Jennifer Nichols for their friendship.

Finally, I would like to thank my wife and family. I always had their understanding

and constant encouragement through my years in graduate school. Thank you Monica

for always being there.

vi

Contents

vii

l Astrophysics 1
1.1 Introduction ................................ 1
1.2 s-process .................................. 5
1.3 r-process .................................. 10

1.3.1 Stellar Observations ....................... 15
1.3.2 Proposed sites of the r-process .................. 19

2 Nuclear Physics 23
2.1 Relevant nuclear physics properties ................... 23
2.2 A=112-123 mass region .......................... 24
2.3 Sr-Pd region ................................ 32

3 fl-decay studies in the Tc-Ag region near to the N=82 shell closure 33
3.1 Experimental setup ............................ 33

3.1.1 Isotope Production ........................ 33
3.1.2 Detector Setup .......................... 35
3.1.3 Electronics ............................. 39
3.2 Particle Identification ........................... 42
3.2.1 Implants and B Decay ...................... 51
3.3 Fitting and Maximum likelihood methods ............... 52
3.3.1 6 detection efficiency ....................... 53
3.3.2 ,8 Background ........................... 57
3.3.3 Neutron detection and background ............... 61
3.4 P,, determination ............................. 63
3.5 Error analysis ............................... 66
3.6 Results ................................... 69
Analysis and discussion 73
4.1 Theoretical calculations ......................... 73
4.2 Discussion ................................. 76
4.3 Astrophysical impact ........................... 90
4.4 Conclusions and outlook ......................... 93
Is there a weak 1' — process? 95
5.1 Abundances ................................ 95
5.2 Different processes ............................ 97

5.3 Residuals ................................. 98

5.4 Reaction Network ............................. 100
5.5 Results ................................... 101
5.6 Analysis .................................. 106
5.7 Conclusions and outlook ......................... 112
A Abundances 114
Bibliography 115

viii

List of Figures

1.1 Elemental abundance composition right after the Big Bang and current
solar elemental abundance composition. Images in this thesis / dissertation
are presented in color. .......................... 2
1.2 Proposed path of different nucleosynthesis processes in the nuclei chart.
Black squares represent isotopes in the valley of stability, dark-green
squares are isotOpes with known mass, light-green squares are isotopes
with unknown mass but with known half-life, and squares with yellow
color are isotopes predicted to exist within theoretical proton and drip
lines but with no known experimental information. .......... 3
1.3 Solar abundance curves [8] (black dots) and different contributions.
Dotted line is the s-process contribution from the sum of the weak [9]
and main [10] component, dashed line is the p—process contribution
from p-only isotopes in [8] and solid line is the r-process contribution

obtained by subtracting p- and s— contributions from solar. ...... 4
1.4 Solar s-process abundance (solid line) obtained from the sum of the
weak [9] (dashed line) and main [10] component(dotted line). ..... 8

1.5 Abundance curves derived from two different s-process models. a) Solid

and dashed lines are main s-process abundance curves from [10] and

[14], respectively. b) Difference in the s-process abundance curves from

[10] and [14]. c) Solid line is the r-process abundance curve obtained by

subtracting p- and s- (from [10]) contributions from solar [8]. Dashed

line results from using [14] instead. (1) Difference in the r-process abun-

dance curves that result using [10] and [14]. .............. 9
1.6 a) and b) Theoretical neutron separation energy as a function of neu-

tron number for Tc and Ru, respectively. The solid and dashed lines

show predictions based on the ETFSI-l [16] and ETFSI-Q [17] mass

models, respectively. c) and d) Normalized abundance Y as a function

of neutron number for Tc and Ru, respectively. Solid and dashed line

are obtained using Eq. 1.2 with [CT = 130 keV and the predicted S,,

from the ETFSI-l and ETFSI-Q mass models, respectively ...... 11
1.7 Solar r-process abundances (dots) and abundances predicted using the

classical r-process model. The solid line shows the predictions based

on the ETFSI-Q mass model assuming quenching of the neutron shell

gaps far from stability. The dashed line shows the predictions based on

the ETFSI-l mass model without such shell quenching. Figure taken

from [15]. ................................. 13

ix

1.8

1.9

2.1

2.2
2.3

2.4

3.1
3.2

3.3

3.4

3.5

3.6

3.7

Elemental abundance pattern of r-process rich stars CS 22892-052, HD
155444, BD +17°3248 and CS 31082-001 compared with solar r-process
abundance derived using the s-process contribution from Travaglio et
a1. [14]. Abundances have been shifted for all stars for display purposes.
Adapted from [18]. ............................
Elemental abundance pattern of r-process rich stars CS 22892-052, HD
155444, BD +17°3248 and CS 31082—001 compared with solar r-process
abundance derived using the s-process contribution from Arlandini et
a1. [10]. Abundances have been shifted for all stars for display purposes.
Adapted from [18]. ............................

“OZI to 133Sn mass region. Isotopes with previously known half-lives
are shown to the left of the dashed line. Isotopes mentioned in the
text are also shown. The r-process waiting points predicted with the
ETFSI—Q mass model in the classical r-process model [43] are framed
with black thick lines. ..........................

Experimental level scheme of 133Sn and assigned single-particle states.

Difference of two-neutron separation energy as a function of proton
number at the N =82 shell closure. Solid circles represent direct mass
measurements. Open circles are results obtained by an indirect mea-
surement such as a Qfl value. Solid and dashed lines are theoretical
predictions from different models. Courtesy of K.-L. Kratz .......
110Zr to 133Sn mass region showing the region of interest. Isotopes with
previously known half-lives are shown to the left of the dashed line.
A half-life measurement for the isotopes colored in gray was obtained
and for isotopes with open circles a new P" value was measured. The
r-process waiting points predicted with the ETFSI-Q mass model in
the classical r-process model [43] are framed with black thick lines. . .

Schematic diagram of the NSCL. ....................
Schematic of the fl-decay endstation. Silicon detector serial numbers
are given below the name of the detector. Distances between detectors
are also given. Courtesy of S. Liddick ...................
Schematic diagram of the fl-decay endstation surrounded by the Neu-
tron Emission Ratio Observer NERO. Distances between concentric
rings are also given. Drawing not to scale. ...............
Electronics setup during experiment 02032. Numbers within circles cor-
respond to delays in nanoseconds. ....................
Particle identification using energy loss in the first PIN detector versus
time-of-flight of all nuclei reaching PINl. Examples of gates used in
the identification are shown. .......................
Energy loss in the first PIN detector versus time-of-flight of only im-
planted nuclei in the DSSD. Examples of gates used in the identification
are shown ..................................

17

18

29

31
34

36

40

42

43

Calibrated versus theoretical total kinetic energy for isotopes of interest. 44

3.8 Total kinetic energy versus time-of-fiight for isotopes of interest. The

mass number and approximate location of each isotope is shown. . . 45
3.9 Histograms of the total kinetic energy for Tc isotopes. The name of

the gate applied in Fig. 3.6 is shown and each graph includes only the

fragments within that gate. Gaussian fits and a constant background

are also shown. .............................. 46
3.10 Histograms of the total kinetic energy for Ru isotopes. The name of

the gate applied in Fig. 3.6 is shown and each graph includes only the

fragments within that gate. Gaussian fits and a constant background

are also shown. .............................. 47
3.11 Histograms of the total kinetic energy for Rh isotopes. The name of

the gate applied in Fig. 3.6 is shown and each graph includes only the

fragments within that gate. Gaussian fits and a constant background

are also shown. .............................. 48
3.12 Histograms of the total kinetic energy for Pd isotopes. The name of

the gate applied in Fig. 3.6 is shown and each graph includes only the

fragments within that gate. Gaussian fits and a constant background

are also shown. .............................. 49
3.13 Histograms of the total kinetic energy for Ag isotopes. The name of

the gate applied in Fig. 3.6 is shown and each graph includes only the

fragments within that gate. Gaussian fits and a constant background

are also shown. .............................. 50
3.14 Isomeric 7-ray spectrum collected within 20 us following the arrival of

a particle. Known 7-1ines used in the identification are shown. . . . . 51
3.15 Decay curves of rhodium isotopes. Contributions from the parent, daugh-

ter, granddaughter and background are shown .............. 54
3.16 Decay curves of palladium isotopes. Contributions from the parent,

daughter, granddaughter and background are shown. ......... 55
3.17 Decay curves of silver isotopes. Contributions from the parent, daugh-

ter, granddaughter and background are shown .............. 56
3.18 13 efficiency of the [i-decay endstation as a function of mass number for

Rh, Pd and Ag isotopes. ......................... 57

3.19 a.) ,B-background of the 40 pixels in the strip channel 15 of the back
of the DSSD during one typical data run. b.) ,B-background of the 40
pixels in the strip channel 15 of the back of the DSSD averaged over
all the data runs. ............................. 59
3.20 Average 6 background per second for a given isotope. Results from
three different methods are shown. For an explanation of the methods

read text. ................................. 60
3.21 fl-n background of the 40 pixels in the strip channel 15 of the back of
the DSSD averaged over all the data runs. ............... 63

xi

3.22

3.23

3.24

4.1

4.2

4.3

4.4

4.5

4.6

Error bars from Monte Carlo simulations of 10000 event sets. a.) num-
ber of times the input half-life was inside the MLH error bars in percent
as a function of the confidence interval chosen for the MLH error bars
when each event set had 50 decay chains. b.) Histogram of the differ-
ences between the MLH result and the input MC parent T1/2 normal-
ized to one a when each event set had 50 decay chains. c.) Same as a.)
but each event set had 8 decay chains. d.) Same as b.) but each event
set had 8 decay chains. ..........................
Relevant energy levels and decay scheme of neutron-rich Ru isotopes.
Known microsecond or longer transitions are shown in gray color. The
position and assignment of the energy levels in 11"'Ru is arbitrary be-
cause only the 7 energy is known [83] ...................
Relevant energy levels of neutron-rich Pd isotopes. Known microsecond
or longer transitions are shown. The position and assignment of the

67

69

energy levels in de is arbitrary because only the 7 energy is known [83]. 71

Experimental half-lives from this work and from literature compared
with QRPA calculations using mass extrapolations and the FRDM and
ETFSI-Q ground state deformation predictions. ............
Experimental ,B-delayed neutron emission probabilities from this work
and from literature compared with QRPA calculations using mass ex-
trapolations and the FRDM and ET FSI-Q ground state deformation
predictions. ................................
Theoretical deformations that predict the measured half-lives (black
squares) and the measured Pu values (black circles) in this work (with
the exceptions of 115Ru, 116Rh and 122Ag where the known ground state
T1/2 was used, and of 121Ag where the known P,, value was used).
Predicted deformations from the FRDM and ETFSI-Q mass models
are also shown. Thick lines going from top to bottom correspond to
cases in which any deformation in the range —0.3 S 62 S 0.3 predicts
the measured Pu. Dotted lines going from top to bottom correspond
to cases in which no deformation in the range —0.3 S 62 S 0.3 predicts
the measured half-life. ..........................
Theoretical half-lives of Ru isotopes as a function of quadrupole defor-
mation 62 with 64 = 0. Shaded regions correspond to the experimental
T1/2 in this work. .............................
Theoretical half-lives of 116‘1"th isotopes as a function of quadrupole
deformation £2 with 64 = 0. Shaded regions correspond to the experi-
mental T1/2 or P” in this work. .....................
Theoretical half-lives of “9,1201% isotopes as a function of quadrupole
deformation 62 with 54 = 0. Shaded regions correspond to the experi-
mental T1/2 or Pa in this work. .....................

xii

77

81

83

84

4.7

4.8

4.9

4.10

4.11

4.12

5.1

5.2

5.3

5.4

5.5

5.6
5.7

Theoretical 12"Rh T1 /2 and P" values calculated as a function of qua-
drupole deformation 62 with 64 = 0 using a QRPA model. The two
lines correspond to the upper and lower limit of the Qp [MeV] input
value in the QRPA calculation. The shaded region correspond to the
experimental T1/2 or P” obtained in this work ..............
Theoretical half-lives of Pd isotopes as a function of quadrupole defor-
mation 62 with 64 = 0. Shaded region correspond to the experimental
T1 /2 or Pa in this work. .........................
Experimental half-lives from this work and from literature compared
with QRPA calculations using FRDM and ETFSI-Q ground state de-
formation, Q-value and S,, predictions. .................
Theoretical half-lives and Pn values of Ag isotopes as a function of
quadrupole deformation 62 with 64 = 0. Shaded region correspond to
the experimental T1/2 or P,, in this work (with the exception of the P“
of 121Ag where a previously known value was used). ..........
Solar and calculated r-process abundances using a one component
(nn=5x 1023 cm‘3, T=1.35 GK, 7:2 s) classical r-process code. Exper-
imental information available before this work was used in the classical
r-process calculations (blue line). Red triangles represent a simulation
that also included the half-lives and Pa values measured in this work.
The ETFSI-Q and QRPA models were used to obtain theoretical values
necessary for the simulation ........................
Mass region showing the calculated isotopic abundances just before
freezeout. Largest abundances were normalized to 1. Stable isotopes
are shown in gray. The most important fl-decay rates that affect the
120Sn/ 119Sn abundance ratio are also shown. The B—decay rate in red
represents the 12"Rh Pn value measured in this work. .........

Differences between CS 22892-052, HD 155444, BD +17°3248 and CS
31082-001 abundances and scaled solar r-process abundance pattern
derived using Travaglio et al. [14]. The difference has been normalized
such that the mean difference for elements in the range 56_<_ Z 579 is
equal to zero. ...............................
Differences between CS 22892-052, HD 155444, BD +17°3248 and CS
31082—001 abundances and scaled solar r-process abundance pattern
derived using Arlandini et at. [10]. The difference has been normalized
such that the mean difference for elements in the range 563 Z 379 is
equal to zero. ...............................
Average residual and solar r-process distributions as a function of
atomic number derived using the Travaglio et at. [14] model. .....
Average residual and solar r-process distributions as a function of
atomic number derived using the Arlandini et al. [10] model ......
f (an , t) as a function of time for different astrophysical conditions
when using the Arlandini et al. [10] model ................
f (nu, T) in the parameter space when using Arlandini et at. residuals.
f (nu, T) in the parameter space when using Travaglio et al. residuals.

xiii

85

86

88

89

91

92

96

96
99
99
101

103
103

5.8

5.9

5.10

5.11

5.12

5.13

5.14

Abundances obtained using different astrophysical conditions. The de-
sired residual distribution as a function of atomic number using the
Travaglio et al. [14] model is also shown. ................
Abundances obtained using different astrophysical conditions. The de-
sired residual distribution as a function of atomic number using the
Arlandini et al. [10] model is also shown. ................
Sum of the elemental abundance pattern of r-process rich stars CS
22892-052, HD 155444, BD +17°3248 and CS 31082-001 with the result
of a network calculation using nn 2 1021 cm‘3, T = 0.09 GK and 7' =
0.8 3 (red symbols), compared with solar r-process abundance (black
lines) derived using the s-process contribution from Travaglio et al. [14].
Also shown are the star’s abundances (blue symbols). Abundances have
been shifted for all stars for display purposes. .............
Sum of the elemental abundance pattern of r-process rich stars CS
22892-052, HD 155444, BD +17°3248 and CS 31082-001 with the result
of a network calculation using nn 2 1021 cm‘3, T = 0.09 GK and 'r =
1.2 3 (red symbols), compared with solar r—process abundance (black
lines) derived using the s-process contribution from Arlandini et al.
[10]. Also shown are the star’s abundances (blue symbols). Abundances
have been shifted for all stars for display purposes. ..........
Differences between the sum of CS 22892-052, HD 155444, BD +17°3248
and CS 31082—001 abundances with the result of a network calculation
using 12,, = 1021 cm‘3, T = 0.09 GK and 7' = 0.8 s, and scaled solar
system abundance pattern derived using Travaglio et al. [14]. The dif-
ference has been normalized such that the mean difference for elements
in the range 565 Z 379 is equal to zero. ................
Differences between the sum of CS 22892-052, HD 155444, BD +17°3248
and CS 31082-001 abundances with the result of a network calculation
using 12,, = 1021 cm‘3, T = 0.09 GK and 'r := 1.2 s, and scaled solar
system abundance pattern derived using Arlandini et al. [10]. The dif-
ference has been normalized such that the mean difference for elements
in the range 563 Z 379 is equal to zero. ................
Mass region showing the calculated isotopic abundances just before
freezeout using a network calculation with n" = 1021 cm‘3, T =
0.09 GK and T = 1.2 s. Largest abundances were normalized to 1.
Squares with black thick lines represent stable isotopes. The most im-
portant fi-delayed neutron emission branchings that reduce the final
Pd abundance are also shown. ......................

xiv

104

105

109

110

111

List of Tables

1.1

3.1

3.2

Contributions in percent from different models to s-process only solar
system abundances. ...........................

Neutron statistics. N )3 is the number of parent decays, Nfl is the total
number of correlated fl-n coincidences, and B is the number of fl-n
background coincidences ..........................
Experimental fl-decay half-lives (T1 )2) and ,B-delayed neutron emission
probabilities (Pn) measured in this work. Previously known data is
shown when available. ..........................

XV

13

65

Chapter 1

Astr0physics

1.1 Introduction

We are interested in the creation of elements. Elements have been created since the
Big Bang occurred some 13 Gyr ago. Almost all the H and He along with some of the
Li currently existing in the universe was created a few minutes after the Big Bang.
As shown in Fig. 1.1, the elemental composition after those few minutes consisted
of 76% H and 24% He by mass and only negligible amounts of heavier isotopes [1].
Since then, the H abundance is being depleted and it is being converted into He and
heavier elements. Nucleosynthesis in stars is the dominant process responsible for
the creation of elements from He up to Fe, except for Be and B which are mainly
created in collisions between interstellar gas nuclei and cosmic rays. The amount of
material heavier than He (which from now on are going to be called metals, following
astronomers nomenclature) created during the evolution of the universe after the big
bang correspond to ~ 1 — 3% by mass fraction [2].

Stars create metals in a variety of different ways. During most of a star’s life,
the principal fusion reaction is the conversion of H into He (p—p chain, CNO cycle
[3]). These exothermic fusion reactions inside the star release energy that prevent its

collapse due to gravitational energy. If the star is sufficiently massive, once all the

 

    

 

 

80
I After Big Bang
I in solar system
60 ‘ ‘
s:
0
IE
U}
8
E 40 —
o
0
I—
0
2::
M
2
g 20 ~
0 _

 

 

 

 

Figure 1.1: Elemental abundance composition right after the Big Bang and current so-
lar elemental abundance composition. Images in this thesis/dissertation are presented
in color.

H in the star’s core has been transformed into He, the He material starts to burn
into C in what is called the triple-a reaction. This process of transforming nuclei into
heavier elements continues until Fe and Ni are reached and it is usually referred as
stellar burning. No further fusion reactions occur after Fe because the production of
any heavier elements by fusion are endothermic. Besides consuming energy, fusion
into heavier elements requires a high kinetic energy due to the rise of the coulomb
barrier with increasing proton number.

There are other processes contributing to the creation of elements as shown
in Fig. 1.2. To produce elements heavier than Fe, two dominant mechanisms take
place [4]. These mechanisms involve capture of neutrons which is not affected by an
increasing coulomb barrier due to the absence of coulomb barrier to overcome. They
are called the 5- (slow) and r- (rapid) processes.

Even though the r-process and s-process create the majority of elements heavier

than Fe, there are other nucleosynthesis processes contributing. The p—process cre-

rp-proce .

protons

 

neutrons

Figure 1.2: Proposed path of different nucleosynthesis processes in the nuclei chart.
Black squares represent isotopes in the valley of stability, dark-green squares are
isotopes with known mass, light-green squares are isotopes with unknown mass but
with known half-life, and squares with yellow color are isotopes predicted to exist
within theoretical proton and drip lines but with no known experimental information.

 

 

 

 

 

 

 

 

 

 

log a

 

 

 

 

 

*r—process
Ba +8-pl’0C088
o . ”Pp-process
:1 ‘\ ' Q l
1 t I ' 1" " .
a I l 1“ ‘ .. "i x
c U U ‘ H Fl 1‘ H In 1'!
—' (pg-q U V n) '
\
\ U "‘
-1 ~ 1: ~
I: ‘
.. x .
-2 1 1 A 1 149‘ 1 11
50 55 60 65 70 75 80
Z

 

(a) (b)

Figure 1.3: Solar abundance curves [8] (black dots) and different contributions. Dot-
ted line is the s-process contribution from the sum of the weak [9] and main [10]
component, dashed line is the p-process contribution from p-only isotopes in [8] and
solid line is the r-process contribution obtained by subtracting p- and s- contributions
from solar.

ates nuclei by photodisintegration of heavy seed nuclei by a series of ('y,n), (mp)
or (7,01) reactions. The new unstable material then decays back to stability and a
new abundance pattern is obtained. A possible site of the p-process is the supernova
shock passing through O-Ne layers of the progenitor star. The rp-process, on the
other hand, synthesizes matter through a sequence of proton captures and ,B-decays
along the proton-drip line. Possible astrophysical scenarios are nova explosions on
accreting white dwarfs [5], X-ray bursts on accreting neutron stars in close binary
systems [6] and the early neutrino driven wind in core collapse supernovae [7]. The
p- and rp- processes proceed through the proton-rich side of the chart of the nuclides
and therefore specific signatures of such processes can be obtained from rare p-rich
nuclei.

The contributions of the major processes to the solar system abundance pattern

are shown in Fig. 1.3. The s- and r- processes are the dominant source of elements
heavier than Fe and the p—process only has a significant contribution in specific cases
such as Mo. It is observed that Ba is predominantly an s-process element (@8096
in solar system material) while Eu is predominantly an r-process element (295% in
solar system material). These two elements are traditionally used as signatures of the

respective process.

1.2 s-process

Heavy elements can be synthesized by exposing light nuclei to a flux of neutrons. When
a nucleus (Z,A) captures a neutron, the new formed nucleus (Z,A+1) may be stable
or unstable. If the nucleus (Z,A+1) is stable, it has to wait until it captures another
neutron for the process to proceed. If it is unstable, it can ,B-decay to (Z+1,A+1) or
capture a second neutron to (Z,A+2). Whichever happens faster determines what step
follows. Close to stability, B-decay half-lives are typically of the order of hours or days.
For very neutron rich isotopes the fl-decay half-lives can go down to milliseconds. If
the neutron captures are slow compared to the B-decays, the resulting path proceeds
close to the valley of stability. This type of process is called the s-process. Nuclei with
small neutron capture cross sections can be expected to have a larger abundance
relative to those with high cross sections because the latter will be destroyed faster
through neutron captures. Peaks in the s-process elemental solar abundance shown
in Fig. 1.5(a) are due to neutron closed shells. At closed shells, the cross section to
capture a neutron is reduced because the next neutron would have to occupy another
energy level less bound. The Sr-Y—Zr, Ba—La—Ce-Pr—Nd and Pb peaks are due to the
N=50, 82 and 126 shell closures, respectively.

In the classical s-process picture, any abundance as a function of mass number can

only change by neutron captures. fl-decays do not change mass number and therefore

do not appear in the equation,

dN
T: = _0'ANA+0A—1NA—1, (1.1)

where 0,, is an average neutron-capture cross section, the neutron exposure is defined
as 7' = f nandt and Up is the thermal velocity of the neutrons. In steady-state,
dNA/d'r -> 0 and JANA = constant. Clayton and collaborators [11] showed that a
single neutron density exposure has to be replaced by exponential distributions of
exposures to correctly reproduce the solar system abundance of s-only nuclei.

The classical picture breaks down for nuclei that have comparable probabilities
of undergoing fl-decay or neutron captures such as 134Cs, 148Pm, 151Sm, 154Eu, 170Yb
and 185W [12]. They are called branching points, and because isotopic abundances
resulting from those branchings are temperature and neutron density dependent, the
abundances of nuclei along the different branches serve as signatures of the conditions
at the site of the s-process. To fully include the effect of those branching nuclei and
the possibility of time dependent neutron fluxes, it is necessary to use a full network
of nuclei coupled with a realistic stellar model instead of the classical picture.

It has been recognized that to correctly reproduce the solar system s-process
distribution at least two different components are required [13]. The weak component
of the s-process, which likely occurs in the core of massive stars (2 15 M0) at the
He burning and to some extent, C burning stages, is responsible for the creation
of elements with A390. From stellar models the expected temperature and neutron
density are in the range T = 0.18 -0.3 GK and nn = 0.8— 1.9 x 1080m‘3, respectively
[13]. The temperature in this scenario is high enough for the reaction 22Ne(a,n)25Mg
to liberate the necessary neutrons.

The so—called strong or main component of the s-process occurs in He burning
shells in asymptotic giant branch (AGB) stars. The main component is responsible

for creating elements with A2 90 [10,14]. When the intershell between the He and

H shells in AGB stars becomes convective, protons are captured by 12C forming
13C via the reaction sequence 1"’C+p—> 13N—> 6+ —+ 13C. The dominant reaction
liberating neutrons is then 13C(a,n)160. In addition, after H burning in a shell has
built up enough He, a He shell flash occurs expanding the star and shutting off the
H burning. In the convective intershell, the reaction 22Ne(a,n)25Mg is also activated
and a second neutron flux may occur. This neutron flux affects the final abundances
of isotopes that are branching points, even though due to its low neutron production
it does not contribute much to the overall element production. After the shell settles
and compresses, H starts burning again and the process repeats. Such a sequence of
mixing and burning in different pulses explains the overall success of the exponential
distribution of neutron exposures in the classical picture. From stellar models, the
13C(oz,n)160 reaction contributes a neutron flux of around nu = 7 x 107 cm‘3 for a
duration of 20000 years at T =0.09 GK. The 22Ne(a,n)"’5Mg reaction, on the other
hand, contributes with a more intense neutron burst nn =10lo cm“3 for a shorter
period of time (a few years) in a hotter environment T 20.27 GK.

Traditionally the s-process pattern had been modeled using the classical approach
but as the nuclear physics of more s-process branchings has been measured, more
sophisticated methods have been developed. Arlandini et al. [10] obtained an s-process
abundance pattern for the main s-process component based upon nucleosynthesis in
low mass AGB stars (2 MG and metallicity Z = é-ZG). This stellar model is not
completely parameter-free and the final abundance in their stellar model still depends
on the choice of parameters such as the amount of 13C. In addition, uncertainties
in the neutron-capture cross sections create uncertainties in the predicted s-process
abundances (6Y,). The weak s-process has been modeled by Raiteri and collaborators
[9] by core burning of massive stars and the subsequent supernovae explosions included
in a sequence of stellar models representing the expected range of stellar masses.

Figure 1.4 shows the total s-process contribution to the solar system abundance

pattern with the contributions from the main component using the Arlandini et al.

 

 

 

 

 

log 8

 

 

 

026 2’s 3?) 312 3‘4 3‘6 3‘8 4’0 4‘2

 

Z

Figure 1.4: Solar s-process abundance (solid line) obtained from the sum of the weak
[9] (dashed line) and main [10] component(dotted line).

approach and the weak component using the Raiteri et al. approach.

More recently, Travaglio and collaborators [14] obtained a much improved predic-
tion of the main component in the s-process by taking into account the contributions
from a range of low to intermediate stellar masses and different metallicities. They
also studied the galactic chemical evolution and predicted the s-process abundance
pattern at the time of the solar system formation.

Figure 1.5(a) shows the solar s-process abundance pattern derived using the two
different s-process models ( [10] and [14]). The weak component is the same in both
models [9]. The relative differences of both models is shown in Fig. 1.5(b). Discrep-
ancies between the two models are observed for elements below Z 5 50. While, for
elements with Z 5 37, the Travaglio et al. model creates more material, for elements
in the range 38 3 Z s 49 it creates less material than the Arlandini et al. model.

Isotopic deficiencies in this mass region are specially problematic in the ’Ifavaglio

s-process s-process

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 I I f I I I I
—Travaglio et al. 04 _
----- Arlandini et al.
‘ Sr-Y-Zr
La-Ce-Pr Pb "'2 ‘ \ . ~..
co l :0 | .
s 2 0~ I
—' <
. -0.2 P [
'0'4‘ I—Arlandinietal. -Travaglioetal.]
-1 1 1 1 1 1 4 _ 1 1 1 1 1
30 40 50 60 70 80 30 40 50 60 70 80
Z Z
(a) (b)
r-process r-process
7 77 I I I l I I I I I
6 r —Travaglio ct 111 f
5 ..... Mandi,“- c, ,1: 0.5 [ F—Arimdini et al. - Travaglio et al.]
4
w 2"»
3 3- 2
2 _ <
1 .
0

 

 

 

 

 

l
y—s

 

 

(C) (d)

Figure 1.5: Abundance curves derived from two different s-process models. a) Solid
and dashed lines are main s-process abundance curves from [10] and [14], respectively.
b) Difference in the s-process abundance curves from [10] and [14]. c) Solid line is the
r-process abundance curve obtained by subtracting p- and s- (from [10]) contributions
from solar [8]. Dashed line results from using [14] instead. (1) Difference in the r-process
abundance curves that result using [10] and [14].

9

model because solar abundances of s—process only isotopes should come entirely from
contributions from the main component of the s-process. Table 1.1 shows the contri-
butions of the Arlandini, Travaglio and Raiteri models to some s-process only isotopic
abundances. Either a third s-process component has to be included to account for such
deficiencies or there is a problem in the Travaglio model. For elements with Z 2 50

both models agree within the error bars and no major discrepancies are found.

1 .3 r-process

The rapid neutron-capture process (r-process) is responsible for the creation of more
than half the elements heavier than iron in the universe [4]. For the r-process to hap-
pen, a scenario is necessary with sufficiently high neutron density such that neutron
captures occur faster than fl-decays.

In the classical r-process picture, this scenario involves seed nuclei in the Fe region
being bombarded with a constant neutron flux (nu) for a fixed amount of time (1')
so that heavier nuclei are formed. Kratz et al. [15] showed that a single neutron
exposure is not enough and that at least three components are needed to successfully
reproduce the solar r-process pattern. In classical r-process calculations usually the
waiting point approximation is employed. In this approximation, it is assumed that for
each element Z there is a (n,'7)-——‘('y,n) equilibrium between isotopes. This equilibrium
entirely determines the abundances of the different isotopes of the same element. The
equilibrium abundances depend on temperature and neutron density. When equating

the chemical potential of neighbor isotopes, one obtains

 

Y(Z,A+ 1) __ G(Z,A+ 1) [(A+ 1)27rh2

3/2
Y(Z,A) ‘7'" G(Z,A) AmukT ] ervzv(Sn/kT), (1.2)

where Y(Z, A) is the abundance defined in A, G(Z, A) is the partition function, nn

is the neutron density and 5,, is the neutron separation energy.

10

 

 

 

      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7 r I t r Y 7
6 6 J
5 5 -
% 4 7 % 4 - J
a 3 2
a " 3 7 7
VJ -e-ETFSI-1 5
2 “ '8- ETFSLQ ‘ 2 7 —e—ETFSI-1 ‘1
9 6- ETFSl-Q j]
1 z=43 " 1 - z=44 .
0 J l l 1 i l 1 I 1 1 I 1
7o 72 74 76 78 so 82 84 “70 72 74. 76 78 so 82 84
II n
100 "---‘r—-- “‘T‘ 7 r— 7 1 ’<}—- — 100 I 1 r 17 A
, w Y
2:73:29. :1 ~
L ‘ ' 'I 4 . -e-EFTSI-I ! ' 1
10 II I‘ I... 10 +3_ ETFSI-Q] i I‘ I
I | , , I I II
I I , | g ‘I I
"" l P i I :< I ‘ '— 1 ” 'I ‘8' ll 1
°\° I II " g\° ' l
h‘ Z=43 : ‘I I _‘ Z=44 w : I
>‘ 0.1 » [i I I! II >' 0.1 ~ [I , I
II I [I l I
|\ I | I I I
l | l I \ g I
“-017 'H - 0.01- I \I I -
l | I | \| I
I H l | El I
i :1 \‘t‘ i i k I
. l I L l l l J 0.0 l 1 g l l
0 00 70 72 74 76 78 80 82 84 0170 72 74 76 78 80 82 84
II I]

Figure 1.6: a) and b) Theoretical neutron separation energy as a function of neutron
number for Tc and Ru, respectively. The solid and dashed lines show predictions
based on the ETFSI-l [16] and ETFSI-Q [17] mass models, respectively. c) and (1)
Normalized abundance Y as a function of neutron number for Tc and Ru, respectively.
Solid and dashed line are obtained using Eq. 1.2 with [CT = 130 keV and the predicted
8,, from the ETFSI-l and ETFSI-Q mass models, respectively

11

Figure 1.6 shows the theoretical neutron separation energies and the resulting
normalized abundances Y as a function of neutron number for Tc and Ru isotopes
when kT = 130 keV, which is typical for a r-process [15]. It is observed that almost
all the elemental abundance is accumulated into just one or two isotopes, which are
called waiting points since the half-lives of those isotopes determine how fast the
material moves via fl-decay to the next element. The theoretical neutron separation
energies Sn used in Fig. 1.6 are predicted using the ETFSI-l [16] and ETFSI-Q [17]
mass models. These mass models are further explained in Section 4.1 but among
other differences, the ETFSI-Q model predicts a smaller neutron separation energy
for the most neutron-rich isotopes than the EFT SI-l model. This difference in S7,
results in different isotopes being waiting points. For Tc, the most abundant isotope
changes from 125Tc using the EFT SI-l model to 121Tc and 123Tc using the ETFSI-
Q model. A similar change occurs for Ru. This reduction in the neutron separation
energy therefore has an effect on the final abundance pattern because the material
that has been waiting to fl-decay when the neutron flux is exhausted (refered as
freeze-out) would fi-decay to different stable isotopes depending on which mass model
is used. The r—process path is defined as the collection of isotopes with the largest
abundances for every element. Because during the r-process, the neutron density and
the temperature are expected to change as a function of time, the waiting points also
change. Waiting points have an 8,, that correspond to a value from 0 to ~5 MeV.
This change in neutron density and temperature produces a “widening” of the most
abundant isotope per element, and it is modeled using different components (nn,T,'r)
in a classical r-process calculation.

Solid and dashed lines in Fig. 1.7 are the predicted abundance patterns using a
classical r-process calculation with a combination of different components (nn,T,'r)
best fitted to reproduce the solar system r-process abundance pattern (how to obtain
this abundance is explained in Section 1.3.1) while using two different mass models.

Solar r-process abundances are shown as dots in the figure. The same stellar condi-

12

Table 1.1: Contributions in percent from different models to s-process only solar sys-
tem abundances.

 

 

 

 

 

 

 

 

 

 

 

 

s-only Main component Weak component
isotope Arlandini et al. [10] [ Travaglio et al. [14] Raiteri et al. [9]
W31. 47% 52% 24%
93Nb 85% 67%
96M0 106% 78%
l(”Ru 95% 73%
104Pd 106% 78%
110Cd 97% 71%
101 T I I I I I I I I I I I I l I I I r I I I I I I I
3 10 J ‘ -
a - I \’ ' I
N 10]} J "V 1: AM“ 3." ~fi,’ \ \_\[
‘a ‘l ' ’ i "” " 'v . ’
3 III-“I “\ If." I. 'I ‘t I I I
i ‘V' I ,7" U
10" l I l l I J I l L l I l l l l 1 1‘5: 1 l I I __ I l l I
100 120 140 160 180 200 220

A

Figure 1.7: Solar r-process abundances (dots) and abundances predicted using the
classical r-process model. The solid line shows the predictions based on the ETFSI-
Q mass model assuming quenching of the neutron shell gaps far from stability. The
dashed line shows the predictions based on the ETFSI-l mass model without such
shell quenching. Figure taken from [15].

13

tions were used while using the ETFSI-l and the ETFSI-Q mass models. As it can
be seen in the graph, while there is a successful reproduction of the positions and
relative heights of the abundance peaks, there are also some deficiencies or abun-
dance troughs at A z 115 and A w 175. These features have been interpreted as
signatures of nuclear structure for extremely neutron-rich nuclei [15]. In this frame-
work, the observed troughs have their origin in an overestimation of the N=82 and
the N=126 shell gap strengths far from stability. This gap size of the shell closures is
embedded in the predicted neutron separation energies and thus it is reflected into the
predicted abundances. The solid line in Fig. 1.7 is the result of the calculation using
the ETFSI-Q mass model and it shows an improvement to the overall fit compared to
the ETFSI-l masses. The ETFSI-Q mass model includes a phenomenological weak-
ening of the neutron shells. In particular, the abundance trough around A z 115 and
A z 175 are eliminated to a large extent when using the ETFSI-Q mass model. It
has been suggested [15] that this result may indicate such weakening of the neutron
shell closures for nuclei far away from stability. Nuclear structure properties of nuclei
in this region indicating such weakening are mentioned in Section 2.2.

As noticed before, the fi-decays from one isotopic chain to the next allow the r-
process to create heavier elements and determine the speed at which the heavy nuclei
are formed. Of particular importance within the r-process are the so—called bottle-
necks, or isotopes with particularly long half-lives. These bottle-neck isotopes are
typically located at shell closures where the sudden drop in the neutron separation
energy makes photodisintegration more favorable. Because the neutron-rich isotOpe
cannot capture anymore neutrons before it photodisintegrates, it has to wait to 6-
decay to capture another neutron. If the neutron shell closure is strong, the same
process repeats and the ensuing isotopes are driven closer to stability. As the path
gets closer to stability, the half-lives get longer and those isotopes become the longest
waiting points in the r-process. Between waiting points at closed shells, the timescales

of fl-decays along the r-process path are one or two orders of magnitude shorter.

14

The ratio of neutron-to—seed nuclei has to be around 100 to 150 in order to produce
elements up to Pt, Th or U. When the neutron flux is exhausted, nuclei in the r-process
path decay back to stability through a series of B-decays, sometimes accompanied by

B-delayed neutron emission.

1.3.1 Stellar Observations

As it has been mentioned before, elements above Fe are created mainly in the r-, s-
and, to a lesser degree, in the p—process. The r-process is one of the least understood
processes because it involves extremely neutron-rich isotopes which are difficult to
study experimentally and because it requires the most extreme astrophysical con-
ditions. Because of that, any calculation has to rely on theoretical models that are
based on our knowledge of nuclear structure properties of known nuclei. How nuclear
structure properties change from nuclei close to stability to extremely neutron-rich
nuclei is not well understood. Furthermore, the astrophysical scenarios in which a
r-process may occur are still a matter of debate. Since the s-process is relatively well
understood compared to the r-process, its calculated abundance pattern is used to
obtain the solar system r-process abundance pattern by subtracting it from the total
solar abundance Y, = Y0 — Y, — Yp.

Fig. 1.5(c) shows the solar r-process abundance pattern after subtraction of the
s- and p— components from the solar system abundance. Because of the mentioned
discrepancy in the calculated s—process abundance pattern, two different r-process
abundance distributions are obtained. The relative differences of the solar r-process
abundance derived using both models is shown in Fig. 1.5(d). The main difference in
the solar r-process contributions are in the predictions of Sr, Y and Zr elements. Using
the s-process contribution from Arlandini et al. [10], the solar r-process contribution
has smaller amounts of Sr, Y and Zr material than using the s-process calculations
from Travaglio et al. [14].

Recently r-process-enhanced metal-poor stars have been discovered that allow

15

one to directly observe the r-process elemental abundance pattern. Because metal-
poor stars ([Fe/ H] <1) are believed to be old stars formed from material not yet
mixed and processed as much as in our solar system (therefore the low metallicity),
their abundance patterns reflect the matter composition of just a few nucleosynthesis
events. The interstellar material from which the star was formed is reflected in the
unburned star’s surface material. High resolution spectroscopy observations from stars
allow us to know the composition of the surface. In addition, the main component of
the s-process occurs in low or intermediate stars of 1-8 solar masses. These stars have
long evolutionary time scales of the order of billion of years. Because it is believed
than the r-process is related to stars heavier than 8 solar masses which live only a
million years, the products of the s-process take longer to be created and ejected into
the interstellar medium. For these reasons, there are metal-poor stars that formed out
of material exposed mainly to an r-process event. Detailed abundance patterns of r-
process enhanced metal-poor stars are therefore extremely useful to identify signatures
of the r-process.

Recent comprehensive studies of the metal-poor stars CS 22892-052 [19] ([Fe/H]=-
3.1), HD 155444 [20], BD +17°3248 [21] and CS 31082-001 [22] are shown in Fig. 1.8
and Fig. 1.9. The scaled solar system r-process abundances are also shown for com-
parison. While CS 22892-052 and 31082-001 belong to the subclass of highly r-process
enhanced stars (r-II) for which [Eu/Fe]>+1.0 and [Ba/Eu]<0, HD 155444 and BD
+17°3248 belong to the subclass of moderately r-process enhanced stars (r-I) for
which 0.3g[Eu/Fe]$+1.0 and [Ba/Eu]<0. Metal poor r-process enhanced stars r-I
and r-II exhibit abundance ratios of r-process elements such as Eu, Os and Pt much
larger than observed in the sun in spite of their relative low Fe abundance. The fact
that r-process elements are enriched, allow astronomers to observe their absorption
lines because otherwise those lines would be too weak to detect for most elements.

For Ba (2:56) and heavier elements, the scaled solar r-process abundances agree

very well with the abundances in metal poor stars as shown in Fig. 1.8 and Fig. 1.9.

16

 

 

 

 

 

 

 

 

4IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII‘IIIIIIIIIIIIIIIIIIIIIIII
—Solarr-process
o C822892-052
2.. I HDllS444 —
o BD+173248
I CS31082-001 -
w ‘7,
u 0” A
c I .( ‘
'23 I ‘
~E -2- . . i
.2. I
0 H I l ‘
m ,1,
’4’ I -‘
I
_6_ '5‘ -- ‘ 7 I 17» _
‘ .> .
. I I .
I
.8lllllllLLLlilllllllllllllllllllllllllllllllllll LlllJlll
30 40 50 60 70 80

Z

Figure 1.8: Elemental abundance pattern of r-process rich stars CS 22892-052, HD
155444, BD +17°3248 and CS 31082—001 compared with solar r-process abundance
derived using the s-process contribution from Travaglio et al. [14]. Abundances have
been shifted for all stars for display purposes. Adapted from [18].

17

 

 

 

 

 

 

 

4[VIII'UTTI'II'ITIYIIIIlrIIUIIIIII‘IITIIIIUII'U'IIIrIIIII'I
— Solar-process «
0 CS 22892-052
2_ I HD 115444 ‘
o BD+173248
1' CS31082-001 -
w ,
OD 0'- n1
.2 _. _ I ~ -
3 ‘ -
.5 -2_ "ll .
s y 1- -
a 4" . n, ‘
i, v. I
-6— ’ l
r
.8
3| 80

 

Figure 1.9: Elemental abundance pattern of r-process rich stars CS 22892—052, HD
155444, BD +17°3248 and CS 31082-001 compared with solar r-process abundance
derived using the s-process contribution from Arlandini et al. [10]. Abundances have
been shifted for all stars for display purposes. Adapted from [18].

18

Even though the absolute values differ, the relative abundances are pretty similar.
For lighter elements in the Z=40-50 range, abundances from the metal-poor stars do
not agree as well as for the heavier elements compared with the solar abundances.
Chapter 5 discusses these discrepancies and possible astrophysical scenarios in which

a different nucleosynthesis process may produce them.

1.3.2 Proposed sites of the r-process

Possible sites where the r-process may happen require a high density of free neutrons.
This condition is satisfied in supernovae and neutron star mergers, which are the most
accepted candidates for possible sites. Within the supernova site, two possible sce-
narios have been discussed in literature, the neutrino-driven wind model and prompt
explosions.

The neutrino-driven wind model in supernovae has been studied widely in the
literature [23—26]. When a supernova occurs, the stellar core collapses into a neutron
star. The gravitational binding energy that the neutron star liberates is ~ 1053 erg,
most of which is released by the emission of 14,, 178, u”, 17,, and 17., neutrinos. Near the
newly forming proto-neutron star, matter is completely dissociated into neutrons and
protons. When some of the energy released from the neutron star in the form of
neutrinos passes through this material, some of the neutrinos are captured by the

neutrons and protons by the reactions,

ue+n—>p+e‘ (1.3)

17e+p—>n+e+. (1.4)

These reactions transfer energy to the material which leads to heating and pro-
duces a mass outflow. Besides depositing energy, the neutrino captures change the
neutron-richness of the material. Because the antineutrinos come from deeper re-

gions in the neutron star, they are more numerous than the neutrinos, and have a

19

higher average energy and higher luminosity, equation 1.4 dominates and the ma-
terial becomes more neutron-rich [27]. The outflow of material is usually referred
as the neutrino-driven wind [28]. As the wind expands, its temperature and density
change producing new reactions that change its composition. When the temperature
drops to ~0.5 MeV, protons and neutrons assemble into a-particles; eventually, when
the temperature drops further, an a—process starts in which neutrons and a—particles
are captured into heavier nuclei [29]. When the temperature reaches kT ~0.25 MeV,
the coulomb barrier prevents charge-particle reactions. At this point, nuclei up to
A ~ 90 have been produced. The remaining neutrons start to be captured by the
newly formed heavy nuclei during the subsequent r-process.

One way to parametrize such r-process is using the entropy of the system, the
ratio of neutrons to protons, and the expansion timescale. If the entropy is low, a
very neutron-rich environment is needed for the r-process to happen. Conversely, if
the entropy is high enough, even a small excess of neutrons over protons allows the
process to happen. Current models however do not achieve sufficiently high entropy
for the expected neutron richness for an r-process to reach the heaviest nuclei.

Another suggested scenario in the same site are prompt supernova explosion mod-
els. During the core collapse, high densities allow the creation of neutrons by elec-
tron capture thus decreasing the electron pressure. Infalling material interacts with
those neutrons close to the resulting proto—neutron star resulting in a r-process. Even
though the collapse of O-Ne-Mg cores of stars in the 8-10 M9 seemed promising
candidates [30], recent calculations do not reach the low entropies and high neutron
density necessary to produce an r-process [31].

A second suggested r-process site is a neutron star merging with another neutron
star or a black hole [32—37]. The basic idea is that after the neutron stars have come
into contact, a rapidly spinning object with mass of around 3 M0 forms surrounded
by a thick disk of a few times 0.1 MG and a low density region. Besides the cooling

due to an expansion caused by angular momentum, the temperature changes due

20

to nucleosynthesis releasing nuclear binding energy and heating up the material. An
r-process proceeds inside this neutron-rich material. Due to the material being so
neutron-rich, the required entropy does not have to be as high as in the supernova
site scenario. Due to angular momentum conservation, some of the material avoids
collapse and matter from the neutron star is ejected. Neutron star mergers occur at a
rate ~ 103 lower than supernovae and therefore there are fewer events to create heavy
elements. Argast et al. [38] showed that the amount of r-process material generated
in neutron star mergers would lead to a scatter in the [Eu / Fe] ratio that is too large
compared to the one observed.

As pointed out in [39], comparing Eu and Ge abundances in halo stars of different
iron abundances suggests different production sites for Eu and Ge. The ratio [Eu / Fe]
seems to decrease over time and it shows a large scatter for very old stars that reduces
over time. On the other hand, the [Ge/ Fe] ratio shows little scatter suggesting it
does not change much over time. The large chemical inhomogeneity at early times
in the galaxy when some of these stars were formed explains the large scatter. As
more material went through r—process events, chemical abundances were homogenized
resulting in less abundance scatter. Because Ge has not changed its relative abundance
over time, maybe it has been produced in a large number of r-process events, while
Eu has only been produced in some of those events and that is why more time is
required to smooth out the inhomogeneities. A possibility is that perhaps the r-
process occurs in more than one scenario resulting in different abundance yields and
rates of production.

Recently, prospects of obtaining an r-process from gamma ray burst disk winds
has been discussed in the literature [40]. Gamma ray bursts occur in rare supernovae
(collapsars) or in some neutron star mergers. In both cases, an accretion disk forms
around a black hole. The key to obtain the necessary neutron-rich material are neu-
trinos emitted from the disk. To make the outflow material have the right neutron

excess, electron capture and electron antineutrino capture must dominate. Depend-

21

ing on the accretion rate, the viscosity and the angular momentum of the material a
r-process may proceed if the entropy is low.

It is difficult to pinpoint an exact location of the r-process due to our insufficient
understanding of how supernovae explode and the properties of neutron stars. Among
the problems with the supernovae scenario is the incomplete understanding in the role
of neutrinos, the hydrodynamics of the material in 3D simulations, the equation of
state and the explosion mechanism. Therefore, how the process happens in either

scenario is still an unresolved question.

22

Chapter 2

Nuclear Physics

2.1 Relevant nuclear physics properties

As mentioned in the previous chapter, the r-process path is determined by neutron
separation energies (Sn) and partition functions. The location of the solar r-process
abundance peaks are determined by the r-process path and therefore depend on the
underlying nuclear structure.

fl-decay half-lives (T1 ,2) determine the speed of the process toward heavier ele-
ments for a given set of astrophysical conditions. In addition, waiting points with long
T1/2 serve as bottlenecks where material accumulates. The height of the peaks in the
r-process elemental solar abundance distribution can therefore be explained by the
long half-lives of some of the involved nuclei at the magic numbers N = 50, 82 and
126.

Once the neutron freeze-out occurs, very neutron-rich nuclei decay back to stability
through a series of fl-decays with branchings for fl-delayed neutron emission (Pu)
further affecting the final abundance pattern. In addition, the fl—delayed neutron
emission releases neutrons which increase the neutron abundance during freezeout.

Besides the neutron separation energies, partition functions, fi—decay half-lives

(T1 /2) and B-delayed neutron emission probabilities (Pu), individual neutron capture

23

cross sections may be important while the neutron flux is disappearing and there is a
breakdown of the equilibrium conditions. Depending on the site where the r-process
takes place, neutrino interactions may also play a role [41].

Fission occurs for very heavy nuclei produced in the r-process. Decays may oc-
cur through spontaneous fission or neutron capture induced fission when nuclei are
produced at excitations energies above their fission barriers. Fission of heavy nuclei
prevents the creation of nuclei heavier than A>256. Besides depleting the heaviest
isotopes produced in the process, fission increases the abundance of the light isotopes

that serve as seed nuclei and the amount of available neutrons.

2.2 A=112-123 mass region

The A=112-l23 mass region is of considerable importance for r-process studies. In this
region, r-process models do not produce suflicient amounts of nuclei to explain the
solar system elemental abundances as shown in Fig. 1.7. As mentioned in Section 1.3,
it has been suggested that this problem may be due to the incorrect strength of the
shell closure used in theoretical mass models because the problem can be alleviated
to some extent by assuming a reduction of the N =82 shell gap far from stability [42].

Since the region around N=82 is responsible for the formation of the A z 130 peak
in the solar r-process abundance pattern, this mass region has been of considerable
theoretical and experimental interest. Figure 2.1 shows the limit where experimental
information had been obtained before this work in the region below the N=82 shell
closure. Isotopes with at least an experimentally known half-life are shown to the left
of the dashed line in Fig. 2.1. A ,B-decay half-life is a global quantity and it is one of
the “easiest” nuclear structure properties to measure.

In section 2.1 the relevant nuclear properties necessary to correctly model the r-
process were mentioned. Because the progenitors of only a few nuclei in the r-process

path have been studied experimentally in the A=112-130 mass region, theoretical

24

 

S"(Sm-Z-

In (49) 131
Cd (48)
Ag (47)
Pd (46)

Rb (45)
Ru (44)
Te (43)

Mo (42)
Nb (41)
Zr (40)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Proton number Z

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

70 71 72 73 74 7s 76 77 78 79 80 81 82 83
Neutron number N

Figure 2.1: 110Zr to 133Sn mass region. Isotopes with previously known half-lives are
shown to the left of the dashed line. Isotopes mentioned in the text are also shown.
The r-process waiting points predicted with the ET FSI-Q mass model in the classical
r—process model [43] are framed with black thick lines.

models are required. Theoretical models are based on nuclear properties of experi-
mentally known nuclei. In this section relevant experimental properties in this mass
region are discussed.

Particularly important are properties from the neutron-rich double-magic nucleus

35231150, proton single-particle §§3Sb5h neutron single particle §§3Sn5o, proton single-

hole 33111149 and neutron single-hole gi‘ISnm. Their properties are needed to constrain
single particle energies in shell model calculations and other microscopic nuclear struc-
ture calculations. I

Experimental information for very neutron-rich Ag to Sb isotopes has been ob-
tained mainly through ,B-decay spectroscopy mainly at OSIRIS and CERN-ISOLDE.
Among the 1p or 1h isotopes, the structure of the closest isotopes to stability 318nm

(u—hole) and §S3Sb51 (w-particle) have been known for more than a decade. Energy

25

1h“, z3700 keV

1i,,,2 2694 keV

2f5/2 2005 keV
3pm 1655 keV

lh,,,2 1561 keV
3pm 854 keV

 

me

133
Sn

Figure 2.2: Experimental level scheme of 133Sn and assigned single-particle states.

26

levels in u-particle §§3Sn50 have been identified more recently [44] and they are shown
in Fig. 2.2. Using a Nilsson model, Pfeiffer and collaborators [42] showed that by
reducing the spin—orbit interaction from the standard value, the correct energy of the
1423/2 and ”PI/2 levels in §§3Sn5o is obtained; otherwise, those energy levels are located
more than 2 MeV higher than the measured values.

For 7r-hole 35111149 only the half-life and the energy of the first two excited states
are known and more experimental information is needed. Recently, spectroscopy be-
came available for 130In [45]. The high measured energy of the [7rg97], ® @7712] 2QP
1+ state is determined by the difference in the strength of the proton-neutron in—
teraction between 779872 and 1197712 relative to “997; and Vhl‘ll/2. The location of the
orbitals 1197/2 and ugn/z is also important when determining the location of the 2QP
1+ state. The proton-neutron interaction was artificially changed in the shell-model
code OXBASH [46] to calculate the correct energy placement, and if that interac-
tion is maintained at the shell closure down to Zr, the half-lives of 128Pd to 122Zr
become longer [45]. However, the reason for such change is not understood and more
experimental information is required.

For §§°Cd43 only the ground state half-life and energy of the first excited state
is known. At N=83, the measured half-life of 131Cd (682t3 ms) is short compared
to global theoretical predictions from QRPA calculations [47] (943 ms) that use the
FRDM [48] mass model. In addition, the experimental Pn value (3.411%) is smaller
than predicted (99%) when using the same theoretical calculation. Hannawald et
al. [49] using the Q5 value predicted in the Audi et al. mass evaluation [50], which
agrees with the ETFSI—Q mass model [17] but not the FRDM mass model, as inputs
of the QRPA calculation and including first forbidden transitions correctly calculated
the experimental T1/2 and P7, value.

Level systematics of Cd isotopes up to N=82 have been obtained [42] and in
particular E(2+) and E(4+) (energy of the first 2+ and 4+ states in even-even nuclei,

respectively) level systematics have been measured up to 128Cd. The behavior of

27

E(2+) is a good indication of nuclear structure and of collective properties when
compared systematically between even-even isotopes of the same element. Away from
shell closures, collective behavior prevails and the nucleus displays features that can be
described as the rotation of a statically deformed shape. Due to collective interactions
among many nucleons the energy of the first 2+ state is lowered in comparison with
the value at the shell closures where single particle excitations can usually explain
the low energy level structure of the nucleus. Similarly, the ratio E(4+)/E(2+) is a
good indication of deformation. Away from shell closures, this ratio is almost constant
and close to shell closures sharply decreases The experimental ratio E(4+)/E(2+) of
neutron-rich Cd isotopes is almost unchanged (z 2.25) up to 126Cd. There is a small
decrease of that ratio in 128Cd which contrasts with the more dramatic decrease in
neighboring even-even Sn and Te isotopes. Such a reduction would be consistent with
a weakening of the shell strength seen by the Cd isotopes [42].

Dillmann et al. [45] studied the r—process waiting point 130Cd and pointed out that
the measured Q3 value agrees with recent mass models that include a reduction of the
shell strength at N=82, usually referred as shell quenching. The measured Qfi value
is higher than the predictions from models with a strong N =82 shell closure such as
the finite range droplet model (FRDM) [48], ETFSI-l [16] and the Duflo—Zuker mass
formula [51]. However, even though “shell quenching” models as the Hartree—Fock-
Bogoliubov Skyrme force P HFB-SkP [52] and the ETFSI-Q [17] are in much better
agreement, others as the most recent microscopic HF models [53, 54] predict a lower
Q5 value than measured by up to 1 MeV.

The observations of the mentioned low-lying up3/2 and 1491/2 single-particle levels
in £1,338n50, the experimental systematics of the ratio E(4+)/ E (2“) of neutron-rich Cd
isotopes, the observation and explanation of the short T1/2 and Pn value of 131Cd and
the large 130Cd Qp are evidence of shell quenching for Cd, In and Sn isotopes.

Figure 2.3 shows the difference 5,,(82) — 3,,(84) as a function of proton num-

ber. Such difference can be interpreted as the strength of the shell closure because

28

N= 82 Shell (3(le N= 82 Shell Gap

 

 

    

6.54 nnnnnnnnnnnnnnnnnnn AALL 6.5‘
:FRDM aExp : :
> : \ : > .
g 5.5: .— § 5.5:
H a] - K—‘
A 1 A
V ‘ fi‘
(D C no
\Ig r- ‘14s4
(I) 4'5: : (I) _
' 3. __ M.- -r '
’0? E Groote . \'~—-’E {Q
33-51 r 83.51
a : : a I
(I) ‘1 : U) ‘
E ,EFTss-o ;
25‘.I .......................

 

 

 

 

 

 

 

2.5 ‘
4O 45 50 525 60 65 70 4O 45 50 525 60 65 70

Figure 2.3: Difference of two-neutron separation energy as a function of proton num-
ber at the N=82 shell closure. Solid circles represent direct mass measurements. Open
circles are results obtained by an indirect measurement such as 3 Q5 value. Solid and
dashed lines are theoretical predictions from different models. Courtesy of K.-L. Kratz.
it represents the steepness of the slope of the neutron separation energy as a func-
tion of neutron number after N=82 as shown in Fig. 1.6 a) and b). Coming from
the “proton-rich” side, the experimental values show a sharp peak with a maximum
around Z250. In principle, one should expect a close to symmetric decrease on the
“neutron-rich” side and the two experimental values seem to be in agreement. If the
notion of symmetry is maintained as the proton number is decreased, one could ex-
pect the experimental values to follow a path close to the ETFSI-Q predictions at
least until the difference flattens out as it did on the “proton-rich” side. This may be
further indication of a weakening of the shell closure at N =82.

So far, most of the experimental studias in the very-neutron rich Tc-Pd region
have been done at the IGISOL facility in Jyvfiskyla, with spectroscopic and fl-decay
information having been obtained for nuclei up to 114Tc [55], 115Ru [56], 118Rh [57]
and 120Pd [58]. More recently, Walters et al. [59] reported the measurement of the
energy of E(2+) in 120Pd resulting from the ,B-decay of 120Rh at the NSCL at MSU.

29

In this region, the dominant fl-decay transition takes place via the transformation of
a g7/2 neutron into a 99/2 proton. In even-even nuclei, decay typically occurs through
0" —+ [7rg9/2 (8 1197712] 2QP 1+ fl transitions. The GT fi-strength is distributed over
several states due to deformations.

Comparing the known low-energy structure of N374 Pd isotopes and the isotonic
Xe isotopes, Walters and collaborators concluded that Pd and Xe isotopes share the
same N =82 shell structure. If shell quenching is defined as a reduction of the shell
gap compared to the largest gap (2:50 in the difference 8,,(82) — 3,,(84) shown in
Fig. 2.3), then Walters’ conclusion suggests the existence of shell quenching for both
Pd and Xe isotopes. On the other hand, if shell quenching is defined as the existence
of an additional shell gap reduction far from stability on top of the shell gap reduction
observed on the “proton-rich” side in Fig. 2.3, Walters’ conclusion would indicate no
shell quenching for the Pd isotopes.

All these observations make the need of nuclear experiments extending the bound-
ary of known nuclei crucial for our understanding of nuclear structure in this mass
region. In this work, we extend the limit of known ,B-decay half-lives and ,B-delayed
neutron emission probabilities Pn further toward the r-process path by measuring ,8-
decay half-lives Tug of very neutron-rich 114"115Tc, 114“llaRu, 116“121Rh and 119"12“Pd
and Pn values (or upper limits) for 116‘120Rh, 120-122 Pd and 122‘124Ag isotopes. Fig. 2.4
shows the region of interest. Chapter 3 discusses the experiment and results. Analysis
and implications in the r-process are discussed in Chapter 4.

The measured Pn values are direct inputs of r-process models and even though T1/2
and P7, values are global quantities they provide first experimental clues on masses,
shapes, and fi-decay strength functions far from stability. The half-life measurement
contains information about low-lying ,B-decay strength while the P” value is sensitive
to the strength just above the neutron separation energy. These measurements also
provide an important test for the theoretical predictions used for the majority of the

nuclear physics calculations in r-process models.

30

 

In (49)
Cd (48)
Ag (47)
PdMQ
Rh (45)

Ru (44)
Tc (43)

Mo (42)
Nb (41)
Zr (40)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Proton number Z

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

70 71 72 73 74 75 76 77 78 79 80 81 82 83
Neutron number N

Figure 2.4: 110Zr to 133Sn mass region showing the region of interest. Isotopes with
previously known half-lives are shown to the left of the dashed line. A half-life mea-
surement for the isotopes colored in gray was obtained and for isotopes with open
circles a new Pn value was measured. The r-process waiting points predicted with
the ETFSI—Q mass model in the classical r-process model [43] are framed with black
thick lines.

31

2.3 Sr-Pd region

The presence of discrepancies between the abundance pattern of the r—process solar
abundances and the metal-poor stars in the Z 2 38 — 47 region hints at an additional
process contributing in this region. The need of nuclear data to correctly model the r-
process in order to correctly disentangle the various contributions of neutron-capture
processes makes experimental information essential.

In Chapter 5 the need of an additional neutron-capture process is discussed and
the necessary astrophysical conditions are studied. Network calculations used in that
chapter required the use of theoretical models. Of particular importance in the results
is the possible doubly semi-magic number 110Zr. A strongly quenched model may
result in almost no deformation around Z 2 40 and N 2 70 [60]. Due to the interplay
of collective and single-particle excitations, the region around the Zr isotOpes has a
concentration of rapidly evolving shapes and excitation modes within a small mass
range. As the classical neutron shell closure at N250 is filled, a sudden increase in
deformation is observed near N258. In this region, reducing pairing correlations by
exciting particles into higher-lying orbitals still results in an increase in the binding
energy through a gain in the proton-neutron interaction. When the radial overlap
between the neutrons and the protons is maximal, this gain in binding energy is
maximized.

Most of these studies up to N2 66 took place at small ISOL facilities and by using
GAMMASPHERE or EUROGAM. As the neutron number is increased this strong
deformation must change to a spherical shape at N 282. Recent calculations on shape
deformations [61,62] have shown complex energy landscapes with several minima and
the presence of tetrahedral symmetry has been suggested. More experiments are to
come and we will have a more through understanding of the nuclear structure in this

mass region.

32

Chapter 3

fl-decay studies in the Tc—Ag region

near to the N282 shell closure

3. 1 Experimental setup

3.1.1 Isotope Production

Radioactive isotopes are produced at the National Superconducting Cyclotron Lab-
oratory (NSCL) at Michigan State University using projectile fragmentation. In this
technique, a primary ion beam is accelerated to relativistic energies before hitting a
target. Some of the primary beam nuclei continue as degraded primary beam while
some interact with the target creating new fragments. Because of their high velocities,
the resulting fragments proceed with forward momenta to a fragment separator. At
the focal plane of the fragment separator, nuclei are physically separated depending
on their nuclear charge Z and ratio of atomic number over atomic charge (A / Q). This
method, referred as B p — AE - Bp, makes use of a degrader located at the dispersive
plane of the separator where beam particles lose difl'erent amounts of energy depend-
ing mainly on Z. Once the nuclei of interest has been isolated, the selected isotopes

are sent to an experimental vault were nuclear properties can be further studied. A

33

NSCL [ii-decay
endstation and

Cocktail beam , ~95 MeV/u / NERO

 

Primary beam: 136Xe, 120 MeV/u, 2 pnA

 

 

0

 

 

 

 

 

 

 

Target: Be, 206 mg/cm2 IPM
Momentum acceptance: 0.5%

Plastic scintillator
IPM Equivalent Al 56 mg/cmz

Figure 3.1: Schematic diagram of the NSCL.

schematic layout of N SCL is shown in Fig. 3.1.

In the current experiment (NSCL 02032), nuclei of interest consisted of neutron-
rich Tc, Ru, Rh, Pd and Ag isotopes. A 1.4 pnA average intensity 136Xe beam (primary
beam) with an energy of 121.8 Mev / nucleon was produced using the coupled cyclotron
facility at the NSCL. The primary beam impinged onto a 206 mg/cm2 Be target where
an assortment of nuclei were produced (secondary beam) by fragmentation reactions.
The A1900 fragment separator [63] was used to separate and isolate the nuclei of
interest.

Degraded primary beam is the most abundant isotope after the target. Because
of charge exchange reactions between the projectile and the target, the 136Xe beam
could become fully stripped of electrons or pick up electrons from the target while
going through the target. The charge exchange reaction between target and projectile
is a stochastic process. Once an average depth inside the target has been reached, the

charge state distribution of the ions does not depend on the initial charge state but the

34

initial projectile’s energy, and target and projectile atomic numbers. In the current
experiment, fully stripped 136Xe54+ to lithium-like 136Xe51+ degraded primary beam
charge states were more abundant than all the nuclei of interest combined by at least
two orders of magnitude. The intensity of other degraded primary beam charge states
is less or comparable to secondary beam fragment intensities. To avoid transmitting
degraded primary beam charge states to the implantation and decay endstation, the
momentum acceptance was set to :l:0.5% at the dispersive plane of the fragment
separator. The magnetic rigidity Bp in the first part of the A1900 was set to 3.96
Tm. This value of magnetic rigidity corresponds to a setting between the degraded
primary beam fragments 136Xe51+ and 136Xe""’+.The second part of the A1900 had a
magnetic rigidity of Bp 2 3.8515 during the production setting so that 120Rh ions

were centered.

3.1.2 Detector Setup

At the dispersive plane of the A1900, the beam hit an equivalent effective thickness
of 56 mg/cm2 Al material which was used as a degrader. The equivalent Al material
corresponds to a PPAC detector, which was not used during the experiment, and a
plastic scintillator which was used to obtain a position measurement in the horizontal
plane of each isotope. Among ions of the same species there is a linear correlation (to
1“ order) between their momentum and their horizontal position at the dispersive
plane. This position information was used to correct the spread in detected energy loss
and time-of-flight (TOF) measurements of the same species further downstream that
is induced by the i0.5% momentum spread of the fragments. The same scintillator
was also used to obtain one of the signals of a TOF measurement for each isotope. The
second signal of the TOF measurement was obtained from a second plastic scintillator
in the experimental vault. The approximate distance between the signals of the TOF
measurement was 38 m.

In the experimental N3 vault, the radioactive beam was implanted into the fi-

35

Drawing not to scale Beta Calorimeter

 

   
 

 

  

PIN 1 PINZa ] $381) 1 SSSD3 SSSD5 P1N3 ]
1061-16 2007-8 2194-1 2186-5 2194-14 2103-14
PIN2 SSSDZ SSSD4 SSSD6 PIN4
2095-23 2194-12 2186-10 2194-4 2103-12
‘1 1 DSSD v\ 1 l l v 1
] W582: ‘ \K
j w

l

i x

J .. ~ H
”21 mm 41—27 mm / K [13 mm| \
9 mm 9 mm 1 mm 1 mm

\ 7 ‘1 \P P -

 

 

 

 

 

 

 

 

 

 

 

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

I
1]...

Figure 3.2: Schematic of the fi-decay endstation. Silicon detector serial numbers are

given below the name of the detector. Distances between detectors are also given.
Courtesy of S. Liddick.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4L

decay endstation where the subsequent fl-decay was studied. The N SCL fl-decay
endstation [64] was surrounded by the Neutron Emission Ratio Observer (NERO) [65]
to study the fi—decay properties of the selected nuclei.

A schematic diagram of the ,B-decay endstation is shown in Figure 3.2. The ,6-
decay endstation consists of a stack of three Si detectors (PINl, PIN2 and PIN2a)
followed by a double-sided Si strip detector (DSSD) and a stack of single-sided Si
strip detectors (SSSD). The first three PIN detectors had thicknesses of 488, 992 and
966 pm respectively and their electronics was set up to detect beam energy losses up
to 10 GeV. The PIN thicknesses were selected so that nuclei of interest would slow
down in the PINs and be stopped inside the DSSD.

A cooling system surrounding the PINs and DSSD detectors was used trying

36

to improve their energy resolution. Inside the B-decay endstation the cooling system
consisted of a copper pipe in contact with copper frames located near each detector at
25 mm. A mixture of ethylene glycol and water was used as coolant at a temperature
of 0° C. The energy resolution of each detector was measured at room temperature
and during cooling. Leakage currents were reduced but no appreciable gain in the
resolution was observed

The DSSD consists of 40 1-mm strips in the front (y-direction) and 40 l-mm strips
in the back (:c-direction) resulting in 1600 individual pixels in the xy-plane. Each
strip was connected to a dual gain amplifier to detect the energies of the secondary
beam fragments being implanted (0—3 GeV, low gain) and the energies that the ,8
particles deposit (0-400 keV, high gain) when the implanted isotopes fl-decay. To
take advantage of the number of pixels the beam was defocused to illuminate as much
area of the detector as possible. For each isotope reaching the DSSD, the specific pixel
location of the implantation, a time stamp of when the event took place, and front
and back energies were recorded.

The first SSSD detector had a thickness of 990 pm and it was used as an additional
mechanism to detect 5 particles and to identify isotopes that do not stop inside the
DSSD. The SSSD detectors used were segmented into sixteen strips and they were
mounted so that the strip orientation alternated between the x and y directions.

The fl-decay endstation was surrounded by the Neutron Emission Ratio Observer
(NERO) [65] to detect fl-delayed neutron emission as shown in Fig. 3.3.

NERO consists of 60 proportional counters containing 3He or BF3 placed in con-
centric rings embedded in a polyethylene matrix surrounding the implantation cham-
ber. Once a decay event had been observed in the ,B-decay endstation, a hardware gate
was Opened for 200us to allow NERO to detect neutrons. The gate time was chosen
to allow time for the neutrons to become thermalized inside the NERO moderator
matrix to maximize detection efficiency. Each proportional counter was individually

read out and time and energy were recorded. Since the energy of the neutrons is not

37

BF, Proportional
Counters

   
  

B-decay endstation

-—1

 

Polyethylene ’He Proportional
Moderator Counter

Figure 3.3: Schematic diagram of the fl—decay endstation surrounded by the Neutron

Emission Ratio Observer NERO. Distances between concentric rings are also given.
Drawing not to scale.

38

directly measured because of the moderation, the measured energy is simply the Q
value of the reaction inside the proportional material plus the typically small residual

energies of the neutrons.

3.1 .3 Electronics

A schematic diagram of the signal processing system is shown in Fig. 3.4. The event
trigger was either a PINl signal (particle arriving with the beam) or a master gate
DSSD signal (fl-decay). The master gate live signal resulted from an AND between
a master gate and a not-busy signal from the computer. The live signal triggered the
computer acquisition to read the detectors and created gates for the VME ADCs and
coincidence registers.

The 80 signals from the DSSD (40 back and 40 front strips) were grouped in
blocks 1-16, 17—32 and 33-40 for both back and front strips. Because it is necessary
to distinguish between implantation of particles, which roughly deposit 22 GeV, and
emission of fi-decays, which leave energies around 2150 keV, those blocks of signals
were sent into Multi Channel System (MOS) pre—amplifiers. These pre-amplifiers pro—
vide low- and high- gain outputs. The low-gain output signals were used to detect
ion implantations and they were sent into VME ADCs. The high-gain signals were
used to detect ,B-decays and they were sent into a Pico Systems shaper -discriminator.
After shaping, the high-gain signals were then sent into VME ADCs. An OR signal
of the timing signals of each Pico systems module went into a coincidence register
bit. In software, this bit in the coincidence register was used to decide if there was
information in the corresponding VME ADC that had to be read-out. In that way,
the DSSD information was read in blocks of 16 low and high channels even if there
was only one strip within that block registering an event, but only the VME ADCs
that had experimental data were read-out. The DSSD master gate signal consisted of
an OR signal between all the 6 ORs of all the Pico system modules. The individual

timing signals of each module were also sent into a scaler module.

39

IM2NSci

1M2 S Sci
SeGa

Pin 2a, ‘
24

Pin]

Pink——

 

Figure 3.4: Electronics setup during experiment 02032. Numbers within circles corre-
spond to delays in nanoseconds.

40

Signals of the PIN detectors were sent into pre-ampliflers and then to amplifiers
that provided fast and slow signals. The slow or energy signals were then sent into
a VME ADC while the fast or timing signal (PIN master gate) were sent into a
coincidence register and a scaler module. The electronics of the 12 Ge detectors in
SEGA were similar to the PIN ’3. While the particle identification was being confirmed
with 'y-rays from microsecond isomers, the trigger was switched to an OR of the timing
signals out of the SEGA amplifiers.

Three scintillator signals were used to obtain the TOF of incoming particles. A
scintillator in the experimental vault was used as the TOF start signal and two delayed
signals from photomultipliers at both ends of the scintillator in the dispersive plane of
A1900 (1 M 2N and I M 28) were used as the T OF st0p signals in two TAC modules.
The TAC’s gate was triggered by an AND between PINl master gate and the master
gate live signal to only receive data when an incoming particle arrived to PINl.

NERO has 60 proportional counter signals that were grouped into A, B, C and
D quadrants. Each quadrant has 15 signals that went into a Pico System shaper
-discrirninator. Following shaping, signals were sent into a Phillips ADC. The fast
signals from the discriminator were sent into coincidence registers, scalers and VME
multi-hit TDC modules. In software, only ADC channels with signals in the coinci-
dence register were read. The timing signals were OR’ed together to obtain a NERO
master gate signal. The NERO master gate live was the result of an AND between
the NERO master gate, a computer not-busy signal and a latch signal that was ON
for 200 as after the master gate live signal was created. The NERO live signal created
gates for the NERO ADCs and coincidence registers. Times of all neutron events in
all NERO channels that occur within 200 ps after a decay trigger were recorded. The
ADCs used for the energies were single-hit and therefore in each channel, only the
first of the energy signals of neutron events within the 200 as window were recorded.
NERO readout came last in software and a bit set by the end of the 200 as latch gate

was used to make sure the time for NERO to detect neutrons was over.

41

 

Energy loss [a.u.]

    

 

 

= 52.4%. ‘
ToF [a.u.]
Figure 3.5: Particle identification using energy loss in the first PIN detector versus

time—of-flight of all nuclei reaching PIN 1. Examples of gates used in the identification
are shown.

3.2 Particle Identification

Particle identification was first obtained at the extended focal plane of the A1900
through a combination of the information of the energy losses in a stack of Si detectors
and a TOF measurement. A plastic scintillator at the extended focal place of the
A1900 provided the start signal while a delayed signal from the scintillator at the
dispersive plane was the stop of the TOF measurement. A Ge detector was used to
obtain ’y—rays of known microsecond isomers to verify the identification.

In the experimental vault, the particle identification was obtained using a similar
procedure with the energy losses of the PIN and DSSD detectors and the start signal
of the time-of-flight from the scintillator in the experimental vault. As a first step,
each nucleus was identified by the momentum-corrected energy loss in PIN1 and the
momentum-corrected TOF measurement as shown in Fig. 3.5. Due to the presence of
secondary-beam charge states, additional information is needed because fully stripped
isotopes with mass number A have a similar PIN1 energy and TOF as hydrogen-like

isotopes with mass number A-3. To identify the charge states, the total kinetic energy

42

 

.2.
m In .
m .

    

 

 

21:.- ~ ‘i.' .
ToF [a.u.]

Figure 3.6: Energy loss in the first PIN detector versus time-of-flight of only implanted
nuclei in the DSSD. Examples of gates used in the identification are shown.

..7

 

of each isotope was obtained by summing up the calibrated energies of the first three
PINS and the DSSD. The particle identification of nuclei reaching the DSSD is shown
in Fig. 3.6. Within the selected fragments, the majority of the In, Cd isotopes and
unfortunately the very exotic Rh, Pd and Ag isotopes were stopped before they
reached the DSSD and no final identification was obtained.

The energy calibration of the first three PIN detectors and the DSSD was done
using degraded primary beam at different energies (13140, 14505, 14717 and 14762
MeV). The program LISE [66] was used to theoretically calculate the energy loss of
the Xe particles passing through the Si material in the PIN and DSSD detectors.
The LISE program has the option of using AT IMA [67] or Ziegler et al. [68] methods
to calculate the stopping and range of ions into matter. As mentioned before, in
the current experiment In, Cd isotopes and very exotic Rh, Pd and Ag isotopes are
stopped before they reach the DSSD. Because ATIMA mistakenly predicted that all
of those isotopes would reach the DSSD while Ziegler et al. was more accurate in their
predictions, it was decided to use the theoretical energy losses calculated by Ziegler et

al. The reason of the disagreement however, is not well understood. Figure 3.7 shows

43

 

l l I

119Pdm§ 122 Aié'fi;

12000 — .«f' a
lzoPdm‘I) , ff 123A Ag47+
1211, (146+ x" 124 A 47+

'0

118 R1149;

121
'0 dAgm
1171, 451545122

11’Rh'flwil') Q1181, d45+
"5Rh4*@§' @1191, (145+
. 12 45+
11200 _ '11;th

Wm: . .
11200 11600 12000

TKE Theory [MeV]

11600 —

TKE Experiment [MeV]

 

 

 

Figure 3.7: Calibrated versus theoretical total kinetic energy for isotopes of interest.

the resulting calibrated versus theoretical total kinetic energy for isotopes of interest.

The total kinetic energies (TKE) versus time-of-flights (TOF) for Tc, Ru, Rh, Pd
and Ag isotopes are shown in Fig. 3.8. The hydrogen-like charge states with mass
number A—3 can be distinguished from the fully stripped isotopes with mass number
A due to the difference in TKE and to some extent TOF.

To better understand the contamination of charge states in the particle identifi-
cation, it was decided to obtain a total kinetic energy histogram after the energy has
been corrected by the TOF measurement. This is equivalent to a rotation in Fig. 3.8

so the “distance” between charge state and fully stripped state is maximized. Figures

44

Technetium Ruthenium
' _.' ‘f‘:‘.ll4-,. “1.5-ctr;

 

 

  
      

..‘_o"n .

TKE [a.u.]
1?».
l :

TKE [a.u.]

 

 

 

 

 

 

 

.ToF [a.u.]
Rhodium

‘L' " T°C 3’21.

 

 

Palladium

       

[12,

"m Ia-u-I

“cl ' ToF [a.u.]
er

‘

 

 

   

 

 

Tor ta.
Silv
X”:

 

    
   

 

FM

ToF [a.u.]

min“:-

Figure 3.8: Total kinetic energy versus time-of-flight for isotopes of interest. The mass
number and approximate location of each isotope is shown.

45

 

 

 

 

 

Counts [a.u.]
counts [a.u.]

 

 

 

    

' E 2595 2610
Total kinetic energy [a.u.] Total kinetic energy [a.u.]

Figure 3.9: Histograms of the total kinetic energy for Tc isotopes. The name of the
gate applied in Fig. 3.6 is shown and each graph includes only the fragments within
that gate. Gaussian fits and a constant background are also shown.

3.9, 3.10, 3.11, 3.12 and 3.13 correspond to histograms of the rotated total kinetic
energy for Tc, Ru, Rh, Pd and Ag fragments respectively. Each fragment must be
within a gate defined in Fig. 3.6 to be included in the histogram.

Particle misidentification is gate-dependent and different gates in the TKE vs
TOF graphs and TKE histograms were used to study the background contamination.
In cases where the contamination was higher than average a contamination-induced
error was included in the results. Particle misidentification due to the resolution and
spread of the energy of the isotopes was calculated to be on average less than 3%.

The particle identification was confirmed at the beginning of the experiment by
detecting 7—rays from the decay of known microsecond isomers in 130Sn and 126'mln
at a temporary and separate implantation station upstream. In addition, 7—rays from
the decay of a well known 164 ns isomer of 134Te, which is the most abundant fragment
being implanted, were also observed. For these measurements, the NSCL Segmented

Germanium Array (SEGA) [69] with 11 Ge detectors was used to detect 7—rays in

46

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    
 

l - Z0 A2
60 0° -
__ so __ 80—
:i =3
.2. 40- 2'.
5 8
5 3° 5
G O
U 29 _ U
10 _ 20 ~
2530 2505 2610 0+ 2575 2588 2600 2612
Total kinetic energy [a.u.] TOW kinetic energy [NI-l
40 I +
0 Counts
35 —Fit 20_A3
—Backgro1md
—115R
30 —118R: ‘

 

 

 

=3 25.
.2.
3 20»
a 15+
0
10»
5-

 
 

 

s", ‘ .____vm
2590 2600 2610 2620 263
Total kinetic energy [a.u.]

Figure 3.10: Histograms of the total kinetic energy for Ru isotopes. The name of the
gate applied in Fig. 3.6 is shown and each graph includes only the fragments within
that gate. Gaussian fits and a constant background are also shown.

47

600

 

 

 

 

 

 

 

 

 

0Com *1
500 » ‘
g “g 400.
a a
300—
% 2
:1 :1
a a zoo-
100~

        

 

 

      
   

 

         

 

 

 

 

 

 

 

 

 

 

 

7 ——~ ————;‘ ‘k k ' ' ,
° ' 555 2573 2590 2608 3 | 2580 2600 2620 . -0
Total kinetic energy [a.u.] T0131 kinetic energy [ML]
200
0 Count:
—Fit
: ‘ Z1_A3
150 —llfi ~ _
=i =3
3. .3.
a 100 - 3
a a
U U
50—
01 2592 2608 2624 264 2 ‘ .5 "'1 .
Total kinetic energy [a.u.] Total kinetic energy [a.u.]

Figure 3.11: Histograms of the total kinetic energy for Rh isotopes. The name of the
gate applied in Fig. 3.6 is shown and each graph includes only the fragments within
that gate. Gaussian fits and a constant background are also shown.

48

Counts [a.u.] Counts [a.u.]

Counts [a.u.]

 

 

 

 

 

 

 

 

 

 

 

 

 

    
  
 
 

 

 

 

  
 

   
      

 

 

 

 

 

_ —ll9Pd
2580 .
Total kinetic energy [a.u.]
2000 . . . .
0 Counts fl
:ggckgmlmd ” '1"
1500 ~ ——118Pd
—121Pd
1000 r
500 —
0.. ____ __._;“ .
2580 2595 261 2625
Total kinetic energy [a.u.]
80 . ,, A-..
0 Count:
70 ,_ _ . a
l ___m ”H zz A5
so —120Pd
40
30

 

  

2595

 
 

 

 
     

 

2610 2625 2640 "
Total kinetic energy [a.u.]

Counts [a.u.]

Counts [a.u.]

 

 

 

 

 

 

 

 

 

 
   

 

 

 

 

 

 

 

 

 

 

  
   
  
 

 

 

 

    

 

1000 ~
800 ~
600 ~
400 ~
200 ~
0« ' 1 . ' L
2565 2580 2595 2610
Total kinetic energy [a.u.]
700 n - 4
600 . Lg,” .
—Background
—ll9P
500 " —122Pd
400 ~
300 ~
200 ~
100 ~
2’ : 2595 2610 2625 2640
Total kinetic energy [a.u.]

Figure 3.12: Histograms of the total kinetic energy for Pd isotopes. The name of the
gate applied in Fig. 3.6 is shown and each graph includes only the fragments within
that gate. Gaussian fits and a constant background are also shown.

49

 

 

 

 
   
  
  
    

 

    
   

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 
  
 
  
 
   

 

 

 

 

 

   

I T V I l 2500 1 I 1 i l
5°“ 009m ' Law“ 8 .
400 :gldckgroun d Z3_A1 I 2000 - —-Background ~
_ - —120A
'2' —122Ag ' ': —123A§ Z3—A2
' ' 1500 ~ «
3 300 - - .2.
i "a
c 200 _ q a 1000 ~ ~
0 U
100 _ « 500 - -, ~
04.. ‘1’; ‘ ‘ H” .. "D 00::;;;W I ‘ K ' ".‘p
2573 2590 2608 2 576 2590 2604 2618 2632
Total kinetic energy [a.u.] Total kinetic energy [a.u.]
1000 — 0 Counts J
—Fit
—Background Z3_A3
300 - —121Ag -
E —124Ag
~— 600 »
i
c 400 ~
U
200 —
04 ————- ~——-=“~=I-- -
2590 2608 2625 2643
Total kinetic energy [a.u.]

Figure 3.13: Histograms of the total kinetic energy for Ag isotopes. The name of the
gate applied in Fig. 3.6 is shown and each graph includes only the fragments within
that gate. Gaussian fits and a constant background are also shown.

50

100 .

 

 

 

V0 VIE
«9 $2
80 3 -
.5 N
% 23
60 —~ 9 _
é a a ,8
*a a =2
T a
g 40 g (I; -
U M F!
20 - 1 -
l l‘; Ilr‘ I
l l ‘ I
0 * * ‘

 

 

200 400 600 800 1000 12100 1400
Energy [keV]

Figure 3.14: Isomeric 7—ray spectrum collected within 20 us following the arrival of a
particle. Known cy—lines used in the identification are shown.

coincidence with beam particles. Observed 'y-rays collected during ~9 hours are shown

Fig. 3.14.

3.2.1 Implants and B Decay

Once the isotope had been identified, it was considered to be implanted into the DSSD
if the event had a valid signal in PIN 1, a signal in the low gain channel in at least
one front strip in the DSSD, a signal in the low gain channel in at least one back
strip in the DSSD and the absence of a valid signal in the first SSSD (the isotope
went through the first three PIN detectors and it stopped in the DSSD). On the other
hand, an event was defined as as a decay if the event did not have valid signals in

PIN1, PIN2 and PIN 23 and valid signals in the high gain channel in at least one front

51

strip in the DSSD and in the high gain channel in at least one back strip in the DSSD
(it was not a particle coming with the beam and the ,6 particle was detected in the
DSSD). Because some light energy events may be light particles that deposit small
energies in the first three PINs, software thresholds were set appr0priately to identify
and discard them.

Correlations between implants and decays were obtained in software on an event-
by-event basis using time and pixel locations. To be correlated, a decay had to take
place within a given correlation time of an implantation in the same pixel or the 8
pixels adjacent to it. Up to three decays within the correlation time window were
considered in the analysis (parent, daughter and granddaughter decay). The corre-
lation time window was chosen isotope-dependent so decays of a fourth generation
were minimal. It was typically 10 s and for the very exotic Pd and Rh isotopes was
reduced to 1-3 s. If there were two or more implants correlated to the decay, the
decay was discarded. The total implantation rate in the DSSD was 0.4 Hz. Because
the average implantation rate per 9—pixels was only 0.002 Hz, the number of multiple

implantation events correlated to a decay event were negligible.

3.3 Fitting and Maximum likelihood methods

Differences between the time stamps of implants and correlated decays were used
to obtain the fl-decay half-lives of implanted nuclei. One method to obtain them is
based on a histogram of such differences which is then fit with a Bateman [70] equation
that takes into account the decay of the parent, daughter and granddaughter nuclei.
The fitting procedure involves a least-squares minimization which finds a constant
background level and the decay constant for the parent decay. Although this method
has been widely used in the past and its highly effective in cases with a large number of
statistics, the binning procedure that is used to obtain the histogram leads to some loss

of decay information. Also, the fitting procedure requires enough statistics to satisfy

52

the requirements of Gaussian statistics of the individual histogram bins. Because some
of the isotopes of interest had a small amount of statistics, it was decided to use a
maximum-likelihood (MLH) calculation where all the available information is used.
This method has been used in the past in experiments with low statistics [71, 72].
The maximum-likelihood method finds the parent decay half-life which maximizes
a joint probability density called the likelihood function. The likelihood function is
calculated considering the probabilities of all the possible scenarios that may result in
the observed sequence of decays, including parent, daughter and granddaughter decays
as well as background. The ,B-delayed neutron emission probabilities effectively change
the event chain that a given nucleus may follow in its decay and they were included in
the analysis. For each decay chain, a probability as a function of parent decay half-life
can be calculated if the daughter and granddaughter half-lives, background rate and
fi-detection efficiency 6,3 are known. They have to be calculated independently because
taking into account a second free parameter (5 background for example) leads to a
large number of maxima in the likelihood function for the typical experimental data
in this work. This high number of maxima was found using Monte Carlo simulations
that created “decay data” with expected experimental values of parent, daughter and
granddaughter T1/2, 6,3 and )3 background. Even though three decay generations were
included, the only free parameter (after other “free” parameters were found using

alternate methods) in our maximum likelihood analysis is the parent decay half-life.

3.3.1 6 detection efliciency

In the cases of 116"12"Rh, 121‘m’Pd and 121“124Ag, there was sufficient statistics to
also fit histograms as shown in Fig. 3.15, Fig. 3.16 and Fig. 3.17, respectively. Those
cases were used to find the ,B-decay efficiency (6,3) of the NSCL fi-decay endstation

by comparing the total number of fitted parent decays N1 with the total number of

53

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

116Rh
a 100. T,,,= 6883‘52 ms
_ 50
(g: :
E
5 +
5 101+ +ll+ MA
10: l l Ti+ll , I
100
g :
E
5.
U 10:
3100:
§ :
g u, M + +
Q 10
1000 A H 119R,l ‘ ‘
T,,,=17l:l:18ms
8
§
3
E
U
120m;
a 100_ T...= 136313 ms
g .
g l
3.x- .\ . . .\. .Ig.

 

 

 

 

0 2000 4000 6000 8000" 10000
Time [ms]

Figure 3.15: Decay curves of rhodium isotopes. Contributions from the parent, daugh-
ter, granddaughter and background are shown.

54

 

 

 

 

 

 

 

 

 

10’
a lZlPd
§ T,,2 =285i24ms
E
810’ N”
_ . +4» 44—2—4
h. .\_/ x. . . I . m
122Pd
g _ T,,,=175i16ms
§1o§
E
5 +++i+++++++ ++++ +++
10f \\

 

 

 

2000 4000 6000 8000 10000
Time [ms]

Figure 3.16: Decay curves of palladium isotopes. Contributions from the parent,
daughter, granddaughter and background are shown.

55

 

l22 Ag

.I

g 2 Tm: 357i24 ms
o 10 L—

53 E *4

E Z +

g _

O

U

.. Junk... 2‘. '1 .V’ l ..
l + ++l+ M"

 

 

107
”..1...1...1..

103 123Ag
T,,,= 272 i 24 ms

 

 

1 I'll

Counts/ 100 ms

 

 

 

 

 

 

Counts/100 ms
)—
Q.
111]
l .
O
‘
u.
+
D
+
+

 

 

 

10" ,\1 . 1\1 ..1.\

J

0 2000 4000 6000 8000 10000
Time [ms]

 

Figure 3.17: Decay curves of silver isotopes. Contributions from the parent, daughter,
granddaughter and background are shown.

56

_M

B efficiency

I I I I I I I T I

 

 

 

 

 

36 — l, —e—Rh ~
'EJ-Pd
[3‘ ..)(..Ag
32 — \ -
\
l \

 

28_ It ~

\\
;.I---[---1 _
2(ils l 1i7 71i9 A 121 I 123 L 125
A

Efficiency [%]

 

 

 

Figure 3.18: 6 efficiency of the fl-decay endstation as a function of mass number for
Rh, Pd and Ag isotopes.

implanted isotopes N into the DSSD using the equation,

N1 _ AoTi/z

5‘9 = N ‘ Athnz’

 

(3.1)

where A0 is the number of counts in the first bin, T1/2 is the fitted parent half-life
and At is the bin size. The efficiencies range from 23% to 27% for different isotopes
with no systematic trends as shown in Fig. 3.18. The average B—decay efficiency was

taken to be 6 = 25% :l: 2%.

3.3.2 ,8 Background

Due to the nature of the experimental setup, decays of long-lived late generations

outside the correlation time may be correlated to a more recent uncorrelated implant

57

occurred within the same or adjacent pixels. They correspond to decays assigned to
the wrong implant and those cases constitute 5 background. Other potential back-
ground sources are light fragments that pass through the Si detectors and mimic the
energy loss of electrons and are not entirely rejected by software gates. Because of
the low implantation rate, the background is constant over the correlation time af-
ter an implantation. The background rate was determined by counting decay events
that occurred outside a 10 s correlation window after an implantation. If there was
an implantation, the pixel where it happened along with the 24 adjacent pixels were
“blocked” for 10 seconds. If a fl-decay type event occurs, it is counted as background
in the nine adjacent pixels if they are not “blocked”. The background rate for an
implantation pixel is then the number of counted background decays divided by the
total “unblocked” time at this location. The time the pixels were blocked was varied
from 10 to 100 s and no noticeable changes were observed.

Because fragments in the beam do not hit uniformly over the face of the DSSD,
there are more fragments being implanted at the center of the DSSD than close to the
edges. This results in a )6 background that is pixel-dependent as shown in Fig. 3.19.

Because the implantation profile in the DSSD may change for different isotopes,
the decay background (which is calculated pixel by pixel) may change. For each
isotope, a background was calculated by taking the average of the pixel-dependent
background of all the pixels where an implantation of the specific isotope occurred.
This way of calculating background is represented by black triangles in Fig. 3.20.

As mentioned before, the fitting procedure also finds a background level. The B
background found in this way for cases with high statistics is represented in Fig. 3.20
with black squares. A third method of finding the ,6 background (black diamonds
in Fig. 3.20) uses the maximum likelihood method itself and it can be used as a
consistency check when compared to the results of the other methods. The method
outlined in Ref. [73] was followed, where the total number of implantation events N is

the sum of those implantations that were followed by up to three observed decays N123

58

 

 

3 8

1:. 0.04. i .

“U

a 003. 48 .

E0 . flag a5

3(4) 0.02, gag §§ .

N

g; 0.01» 5 W555,
. t

'7.“

a 0.03- .W..

“G 0.025» 4’ "4

a 002. 4‘. I‘

Eb ° 0’ .0 1

{4, 0.015- M ”’04...

33 0.01». 1

on.

 

 

 

5 1‘0 1‘5 20 25 30 35
Strip front

Figure 3.19: a.) fl-background of the 40 pixels in the strip channel 15 of the back of
the DSSD during one typical data run. b.) B-background of the 40 pixels in the strip
channel 15 of the back of the DSSD averaged over all the data runs.

59

0.035 ;

Rhodium

 

 

.6

3

U
_r_

 

s:
E

B—background [1/8]

6

e .9
1— 6
u: N

 

I

v ’ '
I

l

0 Po method
I Fitting method
A Counting method

 

 

 

ll

 

 

0.0215 116 117 118 119 120 121

0.03

B-background [1/8]

A
Silver

 

0.025 ~

.6
€
N

0.015 -

 

I I

0 Po method
I Fitting method
3 A Counting method

 

 

A A

II +
l

.4

 

 

0.01

20

121 122 123 124 125

A

0.04

0.035 ~

B-background [1/8]

0.01

Palladium

 

0.03 -
0.025 »
0.02 .
0.015 ~

' 0 Po method '
- Fitting method Q
A Counting method

 

 

 

 

 

 

 

 

““118 119 120 121 122 123

A

Figure 3.20: Average 13 background per second for a given isotope. Results from three
different methods are shown. For an explanation of the methods read text.

60

plus the number of implantations that did not have any observed decay event within
the correlation time No, N = N0 + N123. If P0 is the probability of the observation of

no decay event within the correlation time, No and N123 can be expressed as,

Nolb) = NPolb)

N123 = N (1 - Po(b)) and therefore,

N0(b) = W. (3.2)

P0 is a function of different parameters, one of them being the B background b. No
calculated using Eq. 3.2 thus depends on the background which is then chosen such
that the experimental and calculated No were equal, N5” = No(b).

The fitting method and No method of finding the 6 background were found to be
consistent, but because they are indirect methods that have the uncertainties of other
parameters (daughter and granddaughter T1 /2, 3 detection efficiencies) entangled in
the result and they are based on less statistics as they require real implantation
events, it was decided to use instead the background found by counting decay events
occurred outside a 10 s correlation window after an implantation (counting method in
Fig. 3.20). The total average background rate of decay-type events was 0.023 i 0.002
Hz.

3.3.3 Neutron detection and background

An event with a valid energy signal in one or more of the NERO preportional counters
was considered a neutron event. Using appropriate energy gates in software, neutrons
can be distinguished from electronic “noise” or from low energy gamma rays which
may also interact with the detector gas. Background neutrons may originate from
cosmic rays or fragmentation reactions of the radioactive beam.

To determine the background of fl-n coincidences, a procedure similar to the one

used to obtain the ,8 background in the DSSD was used. Instead of counting just

61

fi-decays, the same procedure was followed for fl-neutron coincidences. Pixel and
run information of all events that include neutrons and fl-decays that are considered
uncorrelated and background-like were counted. Because of the low total fi-decay rate
in the DSSD (2.8 Hz), the probability of detecting a neutron correlated to more than
one decay within the 200115 time gate is less than 10’4%.

The background is position and time dependant. The neutron background varies
randomly as a function of time and because of the low number of background neutron
events, it was decided to average all background events as a function of time to obtain
a background rate per pixel. A typical pixel-dependent fl-n background is shown in
Fig. 3.21. As it was shown in Fig. 3.19, the fl-background is larger at the center than
at the edges of the DSSD. The dip in Fig. 3.21 at the center of the DSSD is due to that
increase in fl-decay background because neutron background alone does not depend
as much on pixel location. Because of the pixel dependency, the fl-n background
rate (bp_,,) was calculated averaging only the pixels that had a given isotope being
implanted. Comparing the average rate for all isotopes with the 13 background rate, it
was found that the probability for detecting a background neutron within 200128 after
a fl-decay was on average 0.78:t0.11%. The expected number of B-n coincidences per
implant was tc x bfi_,,. The average b5-" is 0.18 :I: 0.02 mHz and the total number of
background neutrons per isotope are shown in Table 3.1.

The total cosmic ray-related neutron event rate is just z 5 Hz. Because NERO de-
tects neutrons only for 200ps after PIN 1 triggers, the cosmic ray-related background
was calculated to contribute only ~15% of the total measured fl-n background. Be-
cause no long-lived B-delayed neutron emitters are implanted, the largest contributor
must have had a different origin. Most likely this additional 6 — n comes from “light
beam particles that are indistinguishable from ,B-decays and are accompanied by neu-
trons.

As mentioned before, neutrons may result from heavy ions fragmenting inside the

fl-decay endstation before stopping in the DSSD. Those neutrons were not considered

62

 

 

 

 

E 2, 7 .
» I:
E} . ii ff .
m 0.75 g 2 2;

8 §§§§§§§§§§§ 5

g; (L25»

:1

5 108 15 20 25‘ 30 35‘
Strip front

Figure 3.21: ,B-n background of the 40 pixels in the strip channel 15 of the back of
the DSSD averaged over all the data runs.

in the fl-n background because they were not triggered by decay events but by PIN l
signals and therefore those events were not included in the neutron analysis. Never-
theless, to determine the likelihood of neutrons produced by fragmentation of beam
particles, we took the ratio of the number of PIN1 valid energy signals accompanied
with a neutron detection versus only PIN1 valid energy signals. The number of neu-
trons detected associated with implantation events is approximately 16 times higher
than what is expected from only random coincidences with cosmic-ray related neu-
trons. Less than 3% of the PIN1 triggers have an associated neutron and because of

the low beam rate (~1-2 Hz), the contribution to the overall neutron rate is minimal.

3.4 Pn determination
Pn values were calculated using

Nn—B

P =
n NpXCN,

 

(33)

where N,, is the total number of correlated fi-n coincidences, B is the calculated

number of fl-n background coincidences, N 5 is the number of parent decays and EN

63

is the NERO efficiency. Neutron statistics are shown in Table 3.1. All the isotopes
where the P,, values could be measured have sufficient fl-decay statistics to determine
the number of parent decays N ,9 from decay curve fits. Because fl-delayed neutron
emission from daughter and granddaughter decays are expected to be zero they were
not considered in the analysis.

As a consistency check, it can be observed in Table 3.1 that for cases with expected
Pn=0, the number of measured neutron matches closely the number of expected
background neutrons.

In all cases, the minimum number of fl-n coincidences that would be necessary to
have a one sigma confidence (using gaussian statistics) of having at least one coinci-
dence above the expected number of B-n background coincidences was calculated. If
the number of measured ,B-n coincidences was less than that minimum, the minimum
of ,B-n coincidences was used to calculate the upper limit in the P,, value. In such a
way, the resulting upper limit is the interval in which there is a one sigma confidence
of not measuring at least one B-n coincidence above background.

The NERO neutron detection efficiency decreases slightly as a function of neutron
energy from a value of 37% at 0.1 MeV to 32.4% at 1 MeV. For more energetic
neutrons the drop off is more dramatic and for a neutron energy of 5 MeV the efficiency
has fallen to 17% [65]. QRPA [47] calculations were performed to obtain the expected
neutron energies corresponding to decays from the ground state of the parent nucleus
to excited daughter states just above the neutron separation energy Sn in nuclei of
interest. The expected neutrons had energies ~ 0.1 - 1.0 MeV which are in the range
where the NERO efficiency is roughly constant. A NERO efficiency of e = 34.71: 2.3%

was used.

64

Table 3.1: Neutron statistics. N ,9 is the number of parent decays, N" is the total
number of correlated fi-n coincidences, and B is the number of fl-n background coin-

cidences.

 

l Isotope I Implants I N ,3 j N,, l B ]

 

 

 

 

 

 

 

 

 

 

 

121Ag 1672 399 3 3.2
122Ag 4859 1229 8 9.7
123Ag 18836 4756 45 31.2
124Ag 4848 1247 14 8.7
W9Pd 945 259 3 1.3
12°Pd 8802 2577 13 14.7
121Pd 11646 2950 22 21.7
122P6 2626 669 8 5.3
123Pd 293 1 0.5
mm 30 0 0.1
“613.11 2421 591 3 3.9
“711.11 759 189 1 1.2
“811.11 3173 868 14 5.9
11912.11 4700 1256 35 7.9
120Rh 982 245 2 1.6
12112.11 118 1 0.2
1141111 661 1 1.2
“51111 129 0 0.2
“6Ru 419 0 0.8
117Ru 572 2 1.0
118Ru 144 2 2.7
11"Te 55 1 0.1
115TC 81 0 0.1

 

65

 

3.5 Error analysis

Experimental daughter and granddaughter half-lives were taken from Ref. [74] except
when measured in this work. When a literature value and a result from our experiment
was available, a weighted average was used.

The uncertainties in our results include statistical and systematic errors. The
half-lives statistical error is directly obtained from the maximum likelihood analy-
sis, where we have taken an approach explained in Ref. [75] to obtain a confidence
interval for cases with low rates. Because the maximum probability density is in gen-
eral asymmetric around the maximum, it was decided to use the highest probability
density interval with the minimal length interval and the highest probability density
corresponding to 68% of the area under the likelihood curve. For this interval, no
value outside has a higher probability than any value inside.

To verify that the quoted interval corresponds to a one a error, Monte Carlo
simulations of two different physical situations were run and “decay data” was created.
Fig. 3.22(a) and 3.22(b) are the results of a simulation of 10000 event sets with 50
decay chains each. Fig. 3.22(c) and 3.22(d) are the results of a simulation of 10000
event sets with 8 decay chains each. Typical expected experimental values of parent,
daughter and granddaughter T 1 ,2, (Ep and 6 background were used.

Figures 3.22(a) and 3.22(c) show the number of times the input half-life was inside
the MLH error bars in percent as a function of the confidence interval chosen for the
MLH error bars. A confidence interval of 68% for the error bar correctly predicts the
input half-life within the MLH error bar 68% of the time or more. Only in the case
with very low statistics (8 decay chains), the confidence interval chosen for the MLH
error bars overestimates the uncertainty. Figures 3.22(b) and 3.22(d) show histograms
of the difference between the MLH half-life and the input MC half-life. One a error
correspond to a 68% confidence interval when selecting the MLH error bars. The

asymmetry in the histograms is due to the asymmetry in the likelihood function as a

66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

$100» 500»
g 801 400.
E 60 8E 300
g 40» 8 200
D

g 20 100’
8 0 . i . i . 0

20 40 60 80 100

Confidence interval [%]
(a)

23100 800*
g 80 -
8 60 g: 600
E a
:52 40 1 8
.3 _ / 200’
g 20
8 0 / . i . . . 0

20 40 60 80 100

 

Confidence interval [%]
(C) ((0

Figure 3.22: Error bars from Monte Carlo simulations of 10000 event sets. a.) number
of times the input half-life was inside the MLH error bars in percent as a function
of the confidence interval chosen for the MLH error bars when each event set had 50
decay chains. b.) Histogram of the differences between the MLH result and the input
MC parent T1/2 normalized to one a when each event set had 50 decay chains. c.)
Same as a.) but each event set had 8 decay chains. (1.) Same as b.) but each event set
had 8 decay chains.

67

function of parent T1/2.

Uncertainties in the daughter and granddaughter half-lives, efficiency and back-
ground were included in the systematic error. The fl-delayed neutron emission prob-
abilities were taken from theoretical predictions [74] or, if measured, from this work.
The largest contribution to the error among the P,, values come from the parent, but
their effect is rather small and they do not have a major impact in the T1/2 results.
To obtain the total error, all the analysis parameters were varied within their un-
certainties. An average error for each parameter resulting from its uncertainty was
found, and then those errors were added in quadrature together with the average sta
tistical error. The 6 detection efficiency of the parent decay is the largest systematic
uncertainty and it contributes up to 70% of the total error. The uncertainty in the 13
background and daughter T1/2 had similar contributions to the total error and they
were usually smaller than 15%. The statistical error is usually larger than individual
systematic errors and for cases with low statistics, it has the largest contribution to
the total uncertainty.

Uncertainties in the total number of correlated fl-n coincidences N,,, total number
of fl-n background coincidences B, number of parent decays Nfl and NERO efficiency
6N affect the total uncertainty of the measured P,, values. The statistical error of
N, was assumed to follow gaussian statistics and it contributes to m50—70% of the
total error. The uncertainty in B contributes to less than 30% of the total and it
was calculated using N x tc x A05-" where N is the number of implanted isotopes
and tc is the correlation time. The value of Abp_,, was calculated to be 0.02 mHz.
The uncertainty in N ,3 is isotope dependent and it is calculated from the intrinsic
uncertainty in the fitting procedure that is used to obtain the number of parent decays
in Figs. 3.15, 3.16 and 3.17. Uncertainty in the NERO efficiency was calculated to

contribute z 5% to the total error.

68

Ru

 

 

 

 

 

 

 

 

 

 

 

400 . . —.
-- 11/2-
350 _ .......... 9/ -
--- 7/2-
300 _ — _ ..... 5,2_
5 _ 22 ------- 7/2+
3.1 25" GS 5/2+
9 200 — T—
0 _ 1
a 150 J!!!
100 t .
50 _ -
0

 

 

 

 

 

 

 

 

 

vi 7 g . .
109 111 113 115 117
A

Figure 3.23: Relevant energy levels and decay scheme of neutron-rich Ru isotopes.
Known microsecond or longer transitions are shown in gray color. The position and

assignment of the energy levels in 117Ru is arbitrary because only the 7 energy is
known [83].

3.6 Results

Table 3.2 shows the resulting measured half-lives in this work. All the measured
half-lives in this work agree with values found in literature within one a with the
exception of 121Ag and 115Ru. 121Ag is within two a of the known value. For 115Ru
one possible explanation of the discrepancy is the possible presence of an isomeric
state. Odd 109‘115Pd isotopes are known to have an isomeric 11/2‘ state with an
excitation energy of less than 200 keV as shown in Fig. 3.24 and a half-life longer
than 50 8. Such an isomeric state is also known in 113Ru [82] (Fig. 3.23) with a half-
life of 051(3) s. Tomlin et al. [83] also reported the presence of a microsecond isomer
in 117Ru. Therefore it seems possible that the discrepancy of our 115Ru half-life to the
previous value could be due to an unobserved similar isomer.

The existence of an isomeric state that would lead to a mixture of the measured

69

Table 3.2: Experimental fl-decay half-lives (T1 p) and B-delayed neutron emission
probabilities (Pu) measured in this work. Previously known data is shown when avail-

able.

 

 

 

 

 

 

 

 

 

Isotope Half-life (ms) Pn (%)
This Work ] Previous This Work ] Previous

mAg 6613 780(10) [76]

122Ag 357(24) 550(50) 5 1.3 0.186(10) [76]

200(50) IM [74]

123Ag 272(24) 293(7) [77] 1.0(5) 055(5) [76]
124Ag 1871: 172(5) [77] 1.3(9)

“9Pd 918(111) 920(130) [78]

12°Pd 492(33) 500(100) [58] _<_ 0.7

121 Pd 285(24) g 0.8

12"’Pd 175(16) 5 2.5

mp6 174::

de 38:33

116Rh 68823 680(60) 5 2.1

570(50) IM [79]

1171111 3943; 440(40) [80] g 7.6

with 2663? 300(60) [57] 3.1(14)

1191211 171(18) 6.4(16)

120m: 136}; g 5.4

121Rh 1513;

man 5103', 570(50) [81]

“51111 4053?, 740(80) [56]

116Ru 204%

117Ru 142]?

118Ru 12343§

“4'11: 913: 150(30) [55]

“5'16 733%

 

 

 

 

 

70

 

 

 

 

 

 

 

 

 

 

250 g . g , m , , .
200 h __ ......
E 150 — 3 ‘15- M2 M2 —
g 100 "I33 _ M2 .11..“ GS 5/2+
H 0.. B-
50 — E3 [ J
i l L .... E3 ...l.

 

0 107 109 111 113 115 117 119 121
A

Figure 3.24: Relevant energy levels of neutron-rich Pd isotopes. Known microsecond
or longer transitions are shown. The position and assignment of the energy levels in
de is arbitrary because only the 7 energy is known [83].

ground state and isomer half-lives in 123Pd is also possible. As mentioned before, odd
109““5Pd isotopes have a long-lived 11/2’ isomer that decays through either a E3
transition to the 5 / 2+ ground state or through beta decay as shown in Fig. 3.24. For
117Pd, the 7/2+ energy level drops below the 11/2‘ energy level and 3 M2 transition
occurs to that intermediate state with T1/2=l9.1(7) ms [80]. Tomlin et al. [83] re-
ported the existence of a microsecond E72135 keV 7—ray from de that may be due
to the 11/2—_7/2+ M2 transition. A Weisskopf estimate for a 50 keV M2 transition
in 1"""Pd gives a half-life of the order of milliseconds. Therefore, it seems plausible
that an unobserved long-lived isomer exists in 123Pd corresponding to a similar tran-
sition. The current reported T1/2 value would then be a mixture of the decay of the
long-lived isomer and the ground state since it would not be possible to distinguish
between them.

The measured 1”Ag and 116Rh half-lives in this work correspond to a mixture of

h _.1

the half-lives of the ground state and a known isomer for each case.
The resulting P,, values are shown in Table 3.2. The current results agree well

with previously measured values for 122Ag and 123Ag.

72

Chapter 4

Analysis and discussion

4.1 Theoretical calculations

To model astrophysical processes such as the r-process requires knowledge of 6 decay
properties of nuclei far from stability. In addition, because such process proceeds
through elements from Fe to U, a complete and consistent understanding of nuclear
structure through a large mass range is needed. Because the majority of nuclei involved
in the r-process have not been studied experimentally, the need for such knowledge
has stimulated the development of theoretical models.

There are different types of theoretical models: some start from basic microsc0pic
principles and include nuclear correlations (shell model), some attempt to achieve self-
consistency (HFB+QRPA) and other emphasize global applicability (macro / microsc0pic
mass model+QRPA). Modeling an r-process requires a global knowledge of nuclear
properties and because it is generally used in self-consistent r-process calculations,
the macro/microsc0pic mass model+QRPA was used in this work.

The macro / microsc0pic mass model+QRPA model divides the problem into three
steps. First of all, ground state masses and deformation parameters of nuclei are cal-
culated in a macroscopic description that includes microsc0pic effects based on the

Strutinski method of adding shell effects plus a pairing correction. We have used the

73

finite-range droplet model (FRDM) [48] and the extended Thomas-Fermi with Struti-
nsky integral (ETFSI-Q) model [16] to obtain the ground state masses and deforma-
tion parameters. The ETFSI formalism is based on a Skyrme-type force Hartree-Fock
approach and BCS pairing. The basic idea behind the FRDM and ETFSI-Q methods
involves calculating the total potential energy as a function of proton and neutron
numbers. The potential energy is the sum of a macroscopic term plus a microscopic
term representing the shell plus pairing corrections. Because some aspects of the
FRDM are later used in the calculation of the B-decay rates, only the FRDM method
is going to be explained with some detail.

The macroscopic term of the FRDM mass model is based on the dr0plet model,
which accounts for the finite range of the nuclear force and includes higher order terms
in A‘l/3 and (N — Z) /A in order to add nuclear compressibility and variations in the
proton and neutron radii, respectively. The microscopic term is divided into the shell
and pairing corrections calculated from a set of single-particle levels. Wave functions
were obtained using a potential which included a spin-independent nuclear part in
the form a folded-Yukawa potential, 8. spin-orbit part and the coulomb potential felt
by the protons.

The shape of the nuclear surface depends on the quadrupole deformation 62, hex-
adecapole deformation E4 and higher terms. To use this parameterization of the shape
of a nucleus, a procedure motivated by the Nilsson modified-oscillator model was used.
Starting from a deformed harmonic oscillator potential (Nilsson modified-oscillator
model), the shape of the nuclear surface is found by equating it to an equipoten-
tial surface. Because the single-particle potential is dependent on the shape of the
nucleus, 62 and 64 become free parameters that are to be calculated. To introduce
pairing effects, the Lipkin-Nogami pairing model is used with a constant pairing in-
teraction acting between doubly-degenerate single-particle levels starting below the
Fermi surface. In this approach, a set of coupled nonlinear equations are solved and

quasi-particle energies and occupation probabilities are found.

74

Shell effects were included using the Strutinsky method. In this method, the shell
correction is calculated by subtracting the energy of a “uniform” distribution of states
(gaussian shape for each state) from the sum of the energies of single-particle levels
weighted by their occupation probabilities.

Potential energy surfaces are calculated as a function of quadrupole £2 and hex-
adecapole 64 deformation. The ground state of a nucleus corresponds to the minimum
of this surface.

The second step in the macro / microsc0pic mass model+QRPA calculation consists
in taking either the FRDM or ETFSI-Q mass models’ ground-state shapes to find
single-particle levels using the same folded-Yukawa potential with the Lipkin-Nogami
pairing model used in the FRDM calculation. In a third and final step, the Gamow-

Teller component of the [ii-decay is calculated using the operator
A
131i = GA 2(0’Tih, (4.1)
t'

where G A is a coupling constant, the operator t" changes a neutron into a proton
and a is the spin operator. The ,B-strength function 5,3 which contains the nuclear
structure information of the decay is proportional to < ¢;|)61+|¢,- >2. This type of
decay is the dominant form of decay on the neutron-rich side due to the discrepancy
in the number of neutrons and protons.

In terms of the strength function, the half-life T1/2 using Fermi’s golden rule is

given by,
Et'SQs
1
_T = Z Sp(E,-) x f(Z,Qp _Ei)7 (4-2)
1/2 13.20

where Q5 is the Q value of the decay and f (Z, Q5 — E.) is the Fermi function. The
energy dependent phase space factor f z (Qp — E05 strongly weighs the low-energy
part of the excitation spectrum and therefore T1/2 is dominated by the lowest energy

resonances in the strength function.

75

The B-delayed neutron emission probability is calculated as the ratio of the tran-

sition probability to states above the neutron separation energy Sn,

___ 23358412.) x “2,9. — E.)
23?.” 84E.) x 172.62. — E.)

 

(4.3)

n

This method neglects possible *7 decays from states above the neutron separation

energy. This simplification is justified in most, but not all cases [74].

4.2 Discussion

In Fig. 4.1 our measured experimental half-lives values are compared with theoretical
predictions. The Q5 value and S,, were taken from extrapolations from measured
values [84], and the deformations 62 and 64 from the FRDM or the ETFSI-Q mass
models. The predictions and the experimental values agree within a factor of 3, which
is well within the expected model uncertainties [47]. The only exceptions are the half-
lives of 119Pd and 124Pd. Closer examination reveals a trend for the models to over-
predict the half-lives for ruthenium and palladium isotOpes. On the other hand, while
the rhodium predictions using the FRDM deformations reveal a trend to under-predict
the half-lives, the predictions using ETFSI-Q deformations indicate no systematic
trend for the more neutron-rich isotopes.

The neutron emission probabilities Pn values provide additional nuclear structure
constraints as they probe the fl-strength distribution above the neutron separation
energy. The experimental neutron emission probabilities are compared in Fig. 4.2
with theoretical predictions. In general, the comparisons agree very well, and the
only surprise is the low measured P,, value of 120Rh.

As mentioned before, the QRPA model is a microscopic-macrosc0pic approach
and as such, it lacks a complete description of the inner workings at the microsc0pic

level. Phrthermore, it was designed as a unified approach to predict nuclear structure

76

Technetium Ruthenium
200 — .9— -5-

 

 

r I __T—_" T

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+FRDM+QRPA +FRDM+QRPA ’
'3' ETFSIQ'I'QRPA '9' ETFSIQ-I-QRPA
]' 0 Nubase 1000 _ O Nubase
X Monteeetal. X Montesetal.
1: 1:
El 100. h-~"‘9" £1 £5
3 8° 5
} i
:1: 7° :1:
6o .1
50
100-
4113 114 115 116 113 114 ft; 116 117 :ufiill9
A A
(a) (b)
Rhodium Palladium
1000 I I I T J I I I I I I I
+FRDM+QRPA
e- ETFSthQRPA 1000 . -
f o Nubase
X Montes ct al.
1: 1:
£1 £1
0 0
g; E; 100. ,
+FRDM+QRPA
I: II: €-BTFSIQ+QRPA
<> Nubase
[ x Montes et al.
100.

 

 

 

 

 

 

 

115 116 1i7 118 119 120 121 122 11.18 119 120 121 122 123 124 125
A A

(C) ((1)

Figure 4.1: Experimental half-lives from this work and from literature compared with
QRPA calculations using mass extrapolations and the FRDM and ETFSI-Q, ground
state deformation predictions.

77

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

Rhodium Palladium
20 [— - "I" I I I - ___[pI "_‘fi 3 I F I
+FRDM RPA
:gggggggA I 2.5_ .a—mmafsm
15L 0 Montcsetal. I fl . MonwsetJl
2 h
3' 1"
a. l 9.. 1 5 r
E E
n. m
1 _
121 123
A
(a) (b)
Silver
2.4 a ,
+FRDM+QRPA
2.1 ~ ‘B-E'I‘FSIQ+QRPA
I Nubasc
1.3. O Montactal.
,_ 1.5 ~ 4
\’
9— 1.2 -
fl
9* 0.9 _
0.6 P- 4
0.3 P
in 1&3 125

A

(C)
Figure 4.2: Experimental fl-delayed neutron emission probabilities from this work and

from literature compared with QRPA calculations using mass extrapolations and the
FRDM and ETFSI-Q ground state deformation predictions.

78

quantities of any given nucleus. Free parameters of the model were chosen based
on known nuclear properties. In addition to the underlying uncertainties within the
model, input parameters as deformation values 62 or 64, level order, or Q5 value have
a direct bearing in the B—decay rates and P” values. Uncertainties in those input
parameters are therefore entangled in the quoted expected uncertainty of the model.

As the neutron number is increased from mid-shell to a closed shell, the shape of
the nucleus is expected to change from deformed to spherical at the shell closure. For
the case of Tc, Ru and Rh, both FRDM and ETFSI-Q models predict oblate shapes
that become less deformed with increasing neutron number as shown in Fig. 4.3. For
some of the Pd and Ag isotopes, both models predict different shapes (prolate and
oblate) and even within the same model, jumps between an oblate and prolate shape
occur as the number of neutrons is increased. In addition, the FRDM mass model
predicts for 121’12‘1‘Pd and 120“12“Ag isotopes two mass minima within 200 keV. This
is less than the typical mass model uncertainty of 680 keV [48]. In those cases, the
two mass minima also have quadrupole shape parameters with opposite signs.

Due to the uncertainty in the predicted shape deformation from the theoretical
models, it was decided to study systematically the effect of changing the deformation
from an oblate shape (52 = —0.3) to a prolate shape (62 = 0.3) for all the isotopes of
interest. In addition, both half-life and P” can serve as probes of the nuclear shape by
finding the “correct” quadrupole deformation that would result in the experimentally
measured value. In cases where measured half-lives and Pn are available, the system is
further constrained by deformations that would “correctly” predict both. The results
are summarized in Fig. 4.3 where theoretical deformations used in the QRPA that
predict experimental half-lives and P" values are shown.

Figure 4.4 shows theoretical Ru half-lives as a function of quadrupole deformation
£2 keeping 64:0. Shaded regions correspond to the experimental value. The absolute
minimum from the FRDM or ETFSI-Q mass models predict some hexadecapole defor-

mation 64, but its influence on the half-life is smaller by at least an order of magnitude

79

0)

Figure 4.3: Theoretical deformations that predict the measured half-lives (black
squares) and the measured P" values (black circles) in this work (with the excep-
tions of 11"’Ru, 116Rh and 1”Ag where the known ground state T1/2 was used, and of
121Ag where the known P" value was used). Predicted deformations from the FRDM
and ETFSI-Q mass models are also shown. Thick lines going from t0p to bottom
correspond to cases in which any deformation in the range —O.3 S 62 S 0.3 predicts
the measured P". Dotted lines going from top to bottom correspond to cases in which

0.3

Technetium

 

0.2

0.1 I

-o.1 .

-o.2 .

 

A): I-.. _ -_

0.3

 

 

 

 

-0.3

 

0.2 .

0.1 ~

 

 

 

o FRDM
o mer
I rm

0 Pu

 

-o.3

O

 

69 70

0.3

 

71L

 

0.3

0.2

 

 

0.2—

0.1

 

 

4.1 H

-0.2 ~

 

 

 

 

 

 

‘0'371 72 73 7; N75 76

L.

Ruthenium

 

 

-0.1 ~

-0.2 ~

 

 

.+ '-

 

O
O

T
l

 

 

O
f i 1; o
70 72 “is

69

N
Palladium

i4 75

 

 

 

 

 

 

 

 

 

 

no defamation in the range —0.3 _<_ 62 5 0.3 predicts the measured half-life.

80

200

250

Tm [m]
N
s

150

100

-o.4"-o.3 -o.z 41.1 o 0.1 oii’oi'a

 

1 HR“

T1 n [ms]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8

2

 

 

t M I

 

§§§§§§§§

 

 

 

 

50

m
Ru

1

 

 

.o

.4 .63 -o'.2 -o‘.1

s2

0 oil 012 013

0.4

Figure 4.4: Theoretical half-lives of Ru isotopes as a function of quadrupole defor-
mation £2 with 64 = 0. Shaded regions correspond to the experimental T1/2 in this

work.

81

than the quadrupole deformation 52. For the even-even 114’116Ru isotopes, there is no
deformation that would predict the correct half-life, while for 11‘-°’Ru a spherical or
slightly prolate shape would predict the measured value. For 115’117Ru the situation is
not as clear as either an oblate or prolate shape predict the experimental half-lives.

In the case of Rh isotopes both T1/2 and P" are shown in Fig. 4.5 and Fig. 4.6 as a
function of quadrupole deformation. Shaded regions correspond to the experimental
value. There are deformations that predict the experimental T1/2 and P" values of
all Rh isotopes. For 116-119ml a deformation value around 6 #01 — 0.15 (prolate
shape) is consistent with the half-life and the P“. The theoretical models on the
other hand, predict a value of e z-0.3 - -0.2 (oblate shape). For l2"Rh, while the
FRDM prediction agrees with the measured value, the ETFSI-Q model overpredicts
the P" value of 120Rh by almost a factor of 4. Because of this overprediction, it was
decided to study systematically the effect of the uncertainty in the Q5 value and in
the quadrupole deformation.

From the mass extrapolation taken from [84], Q5210.92:t0.61 MeV for the decay
of 12"Rh into 120Pd. Figure 4.7 shows the dependence of the half-lives and P" as a func-
tion of quadrupole deformation using the upper and lower limit of the extrapolated
Qfi value. As before, the shaded region corresponds to the experimental values in this
work. Uncertainties in the quadrupole deformation and in the Q3 values explain the
discrepancy of the predicted P" value with the current experimental result as shown
in Fig. 4.7. The discrepancy may also be due to the incorrect energy placement of
the dominant GT feeding (1197/2 —> 7rgg/2) above the neutron separation energy to
120Pd. Such an energy shift would produce a lowering of the predicted T1/2 bringing
the predicted ETFSI-Q value closer to the measured one but it would increase the
disagreement with the FRDM prediction. Spectrosc0pic information is needed and a
definitive conclusion is beyond the scope of the current work.

Theoretical half-lives of Pd isotopes are shown in Fig. 4.8 as a function of qua-

drupole deformation. Again, shaded regions correspond to the measured value in this

82

 

 

 

 

 

 

 

035
“6
1500 . - 03 Rh
._ u _ 0.25
a ‘R” .\°
11000 - . E 0.2
E- I 1 0.15
500 - L . 0.1
0.05
1000 . ,
7 [Wm 7 6
E o:
S :E 4
E" 500. .

 

 

 

 

 

Pn [%]
U

N

 

 

500. r 4 .
I—4u"r I ‘
£300-11,” a
S
h h a

E
_ m... y.

-0.4 -0.3 -0L.2 -0‘.1 0 011 012 013 0.4 90.4 -0'.3 -0‘.2 .011 0 0:1 012 013 0.4

 

 

 

 

 

 

Figure 4.5: Theoretical half-lives of 116‘m‘Rh isotopes as a function of quadrupole
deformation £2 with 64 = 0. Shaded regions correspond to the experimental T1/2 or
P" in this work.

83

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

600 I . 35 * ‘
30 ~ .
500 - “th I
-~ ___. 25 ~ mm:
a 40" ~ - .\°
—- —- 20 ~
00 L -
[_S 3 g 15 _ 4
2°" W “ “’ " *
300 - a 20 L. g
250 -
a 113R]! S; 15 ~ mRh
-- 200 - - '—
513 E 10 ~ .
100 _ I) - 5 ’
50 1 1 1 1 1 1 1 o ‘ ‘ ‘ ‘ ‘ ‘
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
8 2 82

Figure 4.6: Theoretical half-lives of ll9'12°R.h isotopes as a function of quadrupole
deformation £2 with 64 = 0. Shaded regions correspond to the experimental T1/2 or
P“ in this work.

84

 

 

 

 

 

 

 

 

 

 

 

 

 

 

600 I I I I
+1153 .h‘
500 +1031 I! ‘\
400 . I b
E -’ 1 '3
—- 300 1 . 9..
a l a
p." Q"- , \ ha
200 “1....-.4‘ ,.-.1 N
‘ F
IMH I I w
0 L 1 1 1 1 0 1 1 1 1 #
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 -0.3 -0.2 -0.1 0 0.1 0.2 0.3
8 82

Figure 4.7: Theoretical 12"Rh T1/2 and Pn values calculated as a function of quadru-
pole deformation 62 with 64 = 0 using a QRPA model. The two lines correspond to
the upper and lower limit of the Q5 [MeV] input value in the QRPA calculation. The
shaded region correspond to the experimental T1/2 or Pn obtained in this work.

85

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3000 _ .
2000- .
250M
E" 2000 . . g 1500 ~ *
S1500 " “ ‘-
l- [- 1000 ‘ 120 ‘
Pd
1000 v. .
500 U 500
ll9Pd
800 _ 300 - _
7 600 - '7; 600 _ .
E. E
S 400 S 400
[- V1.2 [— 122P d
200 - . 200
lZlPd K
300 ~ « 400 _
7 250 - . 7 300 _ .
a I) _a.
sf 200* II. + [.5- 2oo~ '“Pd «
150 I 100 . ~
123p d
100 1 1 1 1 1 1 1 o 1 1 L 1 1 1 1
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 -0.4 .03 -0.2 -0,1 0 0,1 0.2 0,3 0,4
8 8
2 2

Figure 4.8: Theoretical half-lives of Pd isotopes as a function of quadrupole deforma-
tion 62 with 64 = 0. Shaded region correspond to the experimental T1/2 or P" in this
work.

86

work. Pn values are not shown for 120‘de because in those cases any defamation
in the range —0.3 S 62 5 0.3 predicts the measured value within the error bars and
no new information is gained. For the even-even 120'122'124Pd isotopes there is nei-
ther an oblate nor a prolate deformation that predict the experimental value. For the
even-odd 119’121'123Pd isotopes there is, on the other hand, both oblate and prolate
shapes that match the experimental value. The absolute values of the deformations
for 121’123Pd are higher than the predicted quadrupole deformations either from the
FRDM or the ETFSI-Q mass model as shown in Fig. 4.3. We did not, however, found
any systematic trend that would explain the theoretical over-prediction of the ex-
perimental half-lives. In the case of 119Pd, it is seen that the half-life value is very
sensitive to the quadrupole deformation used, which could explain the discrepancy
between prediction and experiment.

Because the predicted half-life is the combination of different parameters, another
possibility to explain the over-prediction of the Pd isotopes’ half-lives is that the Q5
values of the fl-decay from the extrapolations are systematically too low for the Pd
isotopes. To further explore this possibility, Fig. 4.9 shows theoretical half-lives using
the Q5 value, Sn and deformations £2 and 64 from the FRDM and ETFSI-Q mass
models instead of from mass extrapolations. While the Q5 values are lower for the
FRDM than either extrapolations or ETFSI-Q mass models, the ETFSI-Q Q5 are
higher than the values from the mass extrapolations. The difference in Q5 between
ETFSI-Q and FRDM mass models is in the range 0.5-1.4 MeV. Even though the
ETFSI-Q predictions are still higher than the measured T1/2 for N _>_76, they do a
better job than the FRDM results except for 119Pd. An increase in the Q5 value to
better reproduce the experimental results would be consistent with a weakening of
the neutron shell closure observed by the Pd isotopes. Systematic problems in the
predicted fl-strength functions in principle could also play a role and therefore, a
definite conclusion based solely on the basis of the half-lives cannot be drawn.

Figure 4.10 shows theoretical half-lives and Pn values of Ag isotopes as a func-

87

Palladium

1000 » m

 

 

'5' 5
E a, ‘EX/ \L‘ _g
o -’ X I
g; 100». d/ .
II: -0-FRDM+QRPA 7
+3- ETFSIQFQRPA
0 Nubase
X Montes et al.

 

 

 

 

 

 

Ills 1i9 120 121 122 123 124 125
A

Figure 4.9: Experimental half-lives from this work and from literature compared with
QRPA calculations using FRDM and ETFSI-Q ground state deformation, Q-value

and S,, predictions.

88

8000 1 T A7 1 I ‘h‘ 0.3 r T I 1? T T 7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i
121 0.25 _
6000 _ A8 mAg
_ 1 ..
E S
-—-s4ooo . 1 9— 0 15 L 1
1.. ‘ 5
0.1
2000 — (
0.05 ~ «
i S J
2500 ~ 1 0.8 .
2000 _ mAg
E '7 0.6 » I
\
115001 9—
15 0.4 ,
h 1000 -
m >4 A 002
1 < x
3000 - I
123 I 8 "3A8
2500 » Ag (
_ 6 ~ +
i 2000 ~ -‘ a
515M " -4
1— E 4 .
2 L4
K 7 I 4
I 6 >- “‘Ag
7 1000 I 124 Ag — _ 5 _
.3. E 4 _ .
{-5 a 3 ~
500
A 2
l 1 \l
’ k ,
1 l 1 l l i 1 0 J l .L _L l L 1
90.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 -0-4 4’3 -0-2 -0-1 0 0.1 0.2 0.3 0-4
s2 82

Figure 4.10: Theoretical half-lives and Pn values of Ag isotopes as a function of qua-
drupole deformation £2 with 64 = 0. Shaded region correspond to the experimental
T1/2 or Pa in this work (with the exception of the Pa of 121Ag where a previously
known value was used).

89

tion of quadrupole deformation. From N =73 to more neutron-rich, the FRDM mass
model predicts two minima within 200 keV with about the same absolute value of
62, one oblate and the other prolate. Even though the predicted deformations that
would agree with experimental values are consistent in general for the half-lives and
P" values, those deformations may be oblate and prolate and a conclusion is not

straightforward.

4.3 Astrophysical impact

To study the impact of the new experimental P" values, a classical r-process calcu-
lation was used. Isotopic abundances were determined assuming that a (n,'y)=('y,n)
equilibrium is quickly obtained before any B-decay occurs. At every time step, iso-
tOpic abundances were first calculated using Eq. 4.4 neglecting differences in the
ratios of the partition functions. Each isotopic chain had a total abundance equal to
Y(Z) = 2A Y(Z, A). Once the isotOpic abundances were calculated assuming equi-
librium in an isotopic chain, their sum was normalized to Y(Z). The final isotopic
abundances in the time step were obtained taking into account only the fl-decay flow.
The abundance flow from each isotope to the next by B—decay is determined by the

expression,

dY(Z, A)

_ Z—1,A (Z-IIA)
dt _ Y(Z—1,A)(1—P,(, 0A,,

+Y(Z — 1, A + 1)P,SZ‘1’A+1),\§,Z"1’A+1) — Y(Z, A)).§’A, (4.4)

where A5 is the fl-decay rate. This process repeats for the time T to be determined
by the fit to solar r-process abundances. After the time T, freeze-out occurs and only
B-decays were considered.

The solar r-process abundance pattern is shown in Fig. 4.11 along with two simu-

lated classical r-process patterns. In both classical calculations, existing experimental

90

100

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 
  

 

 

 

 

 

7 __f I ”__I—-— "j
-°-Solar '
Fit before experiment
10 I ‘ Fit after experiment -
l- ’ 1 ~
<
>‘
0.1'ifurJ' . 4
J It ' I i
0.01— ’
o“001001A’40 T 180
0 14P+Sour I V
—Fit before experiment
0.12? A Fit after experiment 4
0.1 ~
< 0.08 ~
>.
0.06 P
0.04 . ‘
0.02 ~ ‘ I1
117 1is 1i9 120 121 122 123
A

Figure 4.11: Solar and calculated r-process abundances using a one component
(n,,=5><1023 cm‘3, T=1.35 GK, 7:2 8) classical r-process code. Experimental in-
formation available before this work was used in the classical r-process calculations
(blue line). Red triangles represent a simulation that also included the half-lives and
Pn values measured in this work. The ETFSI-Q and QRPA models were used to
obtain theoretical values necessary for the simulation.

91

Sn (50)
In (49)
Cd (48)
Ag (47)
Pd (46)
Rh (45)
Ru (44)
Te (43)
Mo

Nb (41)
Zr (40)

Abundance

 

Proton number Z

 

7o 71 72 73 74 75 76 77 78 79 so 81 82 83
Neutron number N

Figure 4.12: Mass region showing the calculated isotopic abundances just before
freezeout. Largest abundances were normalized to 11. Stable isotopes are shown in
gray. The most important fl-decay rates that affect the 120Sn/ 119Sn abundance ratio
are also shown. The B—decay rate in red represents the 120Rh P" value measured in
this work.

data available before this work was used. The simulation represented with red trian-
gles included the half-lives and Pfl values measured in this work. The ET FSI—Q mass
model was used to calculate theoretical masses and the QRPA+ETFSI—Q model was
used to calculated unknown T1/2 and Pn values. A neutron density 5x1023 cm‘a,
temperature 1.35 GK and a 7' time of 2 s were chosen to best reproduce the solar
r-process A z 130 abundance peak.

Fig. 4.12 shows the isotopic abundances just before freezeout. Even though in
principle all the half-lives of participating isotopes are used in Eq. 4.4, only the ones
belonging to isotopes with high abundance Y(Z, A) are important for the calculation.
Because the proposed r-process path before freezeout is further out from stability as
shown in Fig. 4.12, the measured Tc, Ru, Rh and Pd half-lives do not directly affect
the final abundance pattern. The measured Pfl values, on the other hand, are direct

inputs in the calculation and they directly affect the final abundance pattern.

92

“itwi'mJ

Since, with the exception of 12oRh, there is good agreement between theory and
experimental values, the only noticeable effect in the final abundance pattern is due
to the low experimental Pn of 12“Rh. It is found that it strongly affects the abundance
ratio of 12oSn/119Sn produced in the r-process. With the low measured P" value in-
stead of the QRPA prediction using the ETFSI-Q mass model, the 120Sn/ 11“’Sn ratio
increases by 40% from 1.22 to 1.66, still inside the value of 1.3(5) deduced from solar
system abundances and s-process models [10]. The large error in the solar r-process
isotopic abundances is due to the 21% and 10% uncertainties in the s-process contri-
bution of 119Sn and 120Sn, respectively. This ratio is dependent on the predictions of
P1, values of the more neutron rich isobars as shown in Fig. 4.12, onthe predictions
for the half-lives of the progenitors in the r-process path, and on the astrophysical

assumptions.

4.4 Conclusions and outlook

New or improved half-lives of very neutron-rich 114—115TC, 114‘lmRu, 116—121%, 119—124Pd,
and P0 values (or upper limits) for 116-120%, l2”‘1'”Pd and 122‘mAg isotopes have
been measured. In general, there is reasonable agreement between measurements and
the QRPA results within the expected model uncertainties. The only surprise is the
low measured value of the 12"Rb P,, value. Because of this discrepancy, and because the
measured neutron branchings are direct inputs in r-process models, current r-process
calculations have somewhat modified final abundance pattern.

A correct understanding of the nuclear structure from mid-shell to the N=82 shell
closure is desired in this mass region because of its relevance in the r-process. Even
though it is not possible to make definite statements about shell structure in the very
neutron-rich Tc—Pd region based on the measured T1/2 and P" values, comparison
with theoretical QRPA predictions provide insight into this region. Systematic trends

in the T1/2 and Pa values can be used to disentangle uncertainties from the QRPA

93

lltl‘lf- IL. n (I;

model itself and uncertainties in the input parameters such as Q3 value and qua-
drupole deformation 62. It was found that for 116—“9% isotopes, the absolute values
of 62 deformations have to be maintained or slightly reduced from predicted FRDM
and ETFSI-Q models to agree with measured T1/2 and Pa values. For the 121’123Pd
isotopes, a systematic increase in Q5 values best reproduces the experimental values.
Such an increase in the Q5 values for the exotic Pd isotopes would be consistent with
a relative weakening of the neutron shell closure seen for N 275 Pd isotopes. In section
1.3, it was pointed out that sufficient amounts of nuclei are created in the mass region
A=112-123 in r-process calculations if one assumes the ETFSI-Q mass model. Because
this mass model assumes a weakening of the N =82 shell closure, one is tempted to
assume that the possible large Q3 value of the Pd isotopes is an additional signature
of nuclear structure for extremely neutron-rich nuclei. However, because systematic
problems in the predicted fl-strength functions could in principle also play a role,
the ETFSI-Q model might be compensating for other nuclear structure deficiencies.
Measurements and spectroscopic data are needed before definite conclusions can be
reached.

The measured P” values are direct inputs in r-process network calculations. The
isotopic abundance ratio 120Sn/ 119Sn increases by 40% when using the experimental
values instead of the prediction by the ETFSI-Q mass model. Further fl-decay mea
surements in this mass region would affect final abundances precisely where the theo-
retical models with a strong shell-closure predict an abundance through at A z 115.

The current experiment made use of a new technique at the N SCL to measure
the kinetic energy of the implanting fragments. Such a measurement is necessary for
distinguishing charge states of the fragments in the particle identification. This paves
the way for more experiments to study more very neutron-rich nuclei in this mass
region. This is necessary to finally disentangle nuclear from astrophysical effects when

studying the r-process.

94

Chapter 5

Is there a weak 7“ — process?

5.1 Abundances

In Section 1.3.1, discrepancies between elemental abundances from recently observed
r-process rich metal-poor stars and solar system r-process abundances were shown.
While for Ba and heavier elements the abundances agree within error bars, there are
noticeable differences for lighter elements 383 Z 547.

To better observe the discrepancies between solar and the r-process rich metal-
poor star abundances, the difference A1096 2 1096”“r — loge"‘°‘°' (for a definition
see Appendix A) is shown in Fig. 5.1 and Fig. 5.2, where r — solar refers to the
solar r-process abundance. Two different r-process solar abundances are used because
of ambiguities in the main component s-process contributions. Two s-process models
(Travaglio et al. [14] and Arlandini et al. [10]), explained in Section 1.2, were used. The
resulting two different patterns of solar r-process abundances are shown in Fig. 1.5.
The difference Alogc shows that in the Travaglio case, the lighter elemental metal-poor
star abundances are lower than the solar r- abundances. Using the Arlandini model,
such observation is still valid for 423 Z 347. The abundance pattern below Ba seems
to be consistent from star to star and the discrepancies are within the observational

uncertainties. The average of the differences for all the stellar abundances are also

95

 

 

CS 22892-052

0

BD +173248
0,5 _ CS 31082-001
Average '

DD

 

 

 

 

 

 

 

60 70 80

Z

Figure 5.1: Differences between CS 22892-052, HD 155444, BD +17°3248 and CS
31082—001 abundances and scaled solar r-process abundance pattern derived using
rIi'avaglio et al. [14]. The difference has been normalized such that the mean difference
for elements in the range 563 Z S79 is equal to zero.

 

 

   
   

 

 

1 l I T
0 CS 22892-052
0 BD +173248
0,5 _ e CS 31082-001
Average

 

 

 

 

.L.

4o 3?) 6T 70 80
2

Figure 5.2: Differences between CS 22892-052, HD 155444, BD +17°3248 and CS
31082—001 abundances and scaled solar r-process abundance pattern derived using
Arlandini et al. [10]. The difference has been normalized such that the mean difference
for elements in the range 563 Z 579 is equal to zero.

96

shown for both models.

5.2 Different processes

Because isotopic abundances are much harder to obtain from spectroscopic data, only
very limited information is available. Two stable isotopes of Eu have been observed
[85,86] in metal-poor stars and their proportions agree with the solar system r-process
proportion. Since the sun is only 4.6 billion years old, this isot0pic agreement together
with the good agreement of heavy elemental abundances (2256) between metal-poor
and solar r-, suggests that the r-process creating these heavy elements has been pretty
robust and uniform through time. It appears that conditions such as temperature,
density and neutron flux vary only in a small range and that the r-process has been
operating in the same way since it first started. The r-process responsible for the
creation of the majority of r-process abundances has been referred in literature as the
strong r-process [42].

It is generally believed that metal-poor stars are old stars that reflect the matter
composition of just one or a few r-process nucleosynthesis events. Spectroscopic ob-
servations reflect the unburned material composition of the interstellar material from
which those stars were formed. The difference Alogc then would simply reflect the
ratio of what had already been produced and was mixed in the interstellar medium
where the r-process rich metal-poor stars were formed, over the composition of inter-
stellar material produced by many r-process events at the time of the solar system

formation,

 

 

Aloge, = loge?” —loge£"’°""
ystar _r—solar
= l ' 12 — l ' — 12
09 Y” + 09 YH
YJtar
= log—:——. (5.1)
Yir solar

97

Elements for which Alogc < 1 are elements that had less abundance when the star
formed than when the sun formed. The observed Ag abundance in the metal-poor stars
is only z30% (Aloge z -—0.5) of the solar r-process abundance regardless of the model.
For Ru, Rh and Pd, the observed abundance is between 50 and 90% of the solar r-
process abundance. Because of the discrepancies for Z<56, another process responsible
of creating the residual differences that the strong r-process cannot produce has
been called the weak r-process [42] even though the astrophysical site and conditions
in which a neutron-capture process would create the residual abundances are not
yet known. The study of nucleosynthesis conditions that would create the missing
abundances is the subject of this chapter.

For Sr, Y and Zr, the picture is not as clear due to the uncertainties in the 8-
process contribution. Also, the galactic chemical history as observed in their scaling

with Fe and Eu indicates a different origin of those elements.

5.3 Residuals

To find the actual amount of material that is missing in these metal-poor stars, the r-
process-rich star elemental abundance was subtracted from the r-process solar system

abundance,
An = lar—solar _ Kstar : YH (lologez—N’Olar _ lologcftar) . (52)

In a logarithmic scale the abundance residuals become

 

AY
1096335 = 10910 t +12
YH
= loglo (10'0-9'53‘“r —10‘°9‘?“") + 12.0. (5.3)

Figures 5.3 and 5.4 show the average amount of material that still would have to

be produced in nucleosynthesis events in addition to the strong r-process to reach the

98

 

 

 

 

 

 

l — Solar r-process
0 Residuals
005 ’- "
o
0 ~ .
w l I
ED '0 5 r I l r
_2 o
'1 h 1 I “

 

 

 

 

 

 

:3 I . , llnlil- j

'35 40 45 50 55 60 65 70 75
Z

 

 

Figure 5.3: Average residual and solar r-process distributions as a function of atomic
number derived using the Travaglio et al. [14] model.

 

 

 

 

 

 

 

105 T I l 1 I T I
ll
—Solarr-process
0,5 L. 0 Residuals
0 L.
w
Elf-0.5 - l l’ ' l
-1 t i .. .
-1.s - l’ I -
0
"1 [HI ‘
-25 * . 1 -

 

 

 

 

 

 

 

Figure 5.4: Average residual and solar r-process distributions as a function of atomic
number derived using the Arlandini et al. [10] model.

99

solar system abundance pattern. The solar r-process abundance pattern is also shown
for comparison. The average abundance for each element was obtained using the
weighted average from Eq. 5.3 of the metal-poor star abundances. The total number

of residual abundances that were considered was 21.

5.4 Reaction Network

To find the astrophysical conditions (nn, T, r) in which a neutron-capture process
would produce the necessary residual abundance and pattern, a network calculation
with classical neutron exposures from s-process to r-process type was used. Instead of
a waiting point approximation, an abundance network containing 2026 nuclei from H
to Ta was used. Nuclear reactions affected isotopic abundances for every time step. A
range of different neutron densities and temperatures were chosen to simulate different
astrophysical environments.

Nuclear reaction rates were taken from experiment and statistical model calcu-
lations. The Hauser-Feschbach code NON-SMOKER [87] was used to calculate the
theoretical rates using the FRDM [48] mass model to calculate the Q values of the
reaction. Theoretical B-decay rates were taken from [47] or when available from un-
published calculations by Kratz [88].

The initial abundance composition consisted of just neutrons and 56Fe. While in
principle neutron density could change due to neutron captures, the neutron to 56Fe
ratio was chosen so that nn did not change by more than 5% of the initial value. The
Ag abundance is generally believed to be the most accurate stellar observation of these
r-process—rich stars. The abundances found in the reaction network were normalized
to the residual Ag abundance. For this reason, only time steps with a silver abundance

different than zero were studied.

100

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T1 Irmlt [1rfiflll lrnfltll l ”mill l Infill Int"!!!
1000 / _
.1
l
\/ ~ .

Ca: ‘J -

["1 ‘

d: 100 _ ““1823 $411?qu
v ....... nn: = . _
‘H — nn=10"18 T=0.09 GK 3
------- nn=10"18 T=l.5 GK _
—- nn=10"15 T=0.09 GK ~
....... nn=10"15 T=1.5 GK .
_ —— nn=10"12 T=0.09 GK ‘

nn=10"12 T=l.5 GK
- ~w nn=10"7 T=0.09 GK -
10| 1111“]- llllufl- Inim- Ilium. lingu- l 114m
1 100 10000 1606 1e+08 16+10 16+12
Time [s]

Figure 5.5: f (nu, T, t) as a function of time for different astrophysical conditions when
using the Arlandini et al. [10] model.

5.5 Results

In order to find the right conditions that would create the residual abundance pattern,

a chi-square function f (nu, T, t) defined as,

 

(YiCAL _ YiRES ) 2

f(ana t) = Z Ayfis

iERES

(5.4)

was used. The residual abundance uncertainties depend on the metal-poor star obser-
vation uncertainties and the solar r-process uncertainties. The solar r-process abun-
dances uncertainties depend mainly on the s-process uncertainties. Because in princi-
ple all the uncertainties are independent, the use of a chi-square function is justified.

The closer the value of f (nu, T, t) to the number of residuals is, the better the
agreement between the abundance pattern calculation and the desired residual pat-

tern.

101

Because the observed abundance pattern is the composition after the neutron flux
is exhausted and nuclei had time to decay back toward stable nuclei, two consecu-
tive steps were included in the network calculation. In the initial step, nn was kept
approximately constant as explained before. The temperature was kept constant as a
function of time. For every time step, a stable abundance pattern was approximated
by assuming an abrupt neutron exhaustion and a decay back to stability due only to
fl-decays. This “fast” decay back to stability was used because of the impracticality
of running a decay network calculation for every time step. The “fast” decay stable
pattern was compared to the desired residual abundance pattern by the function
f (nu, T, t)-

Typical f (an, t) curves are shown in Fig. 5.5. The average atomic number of
heavy nuclei, which starts at Fe, increases as a function of time. As the material
becomes heavier, some of it reaches the region 383 Z 547 resulting in a decrease of the
function f (nu, T, t). The final increase in f (nu, T, t) is due to more and more material
increasing its atomic number while the abundance in the region 383 Z 547 decreases.
For a given set of astrophysical conditions (an), an increase in the temperature
causes an increase in photodisintegration and the moving of the neutron—capture
process path closer to stability, where the B—decay half-lives are longer. This increase
in T1/2 reduces the speed of the process but the overall pattern of decrease and
then increase of f (nu, T, t) is conserved. The half-lives of the progenitor isotopes
that produce the 38_<_ Z 347 abundance also affect the time-width of the dip in the
f (nu, T, t) curve. For high neutron density, the involved half-lives are short and the
material spends less time passing through this region than when there is less neutron
density. Because the isotopes involved when there is a low neutron density are closer
to stability and therefore have longer half-lives, the time-width of the dip in the curve
is larger.

Fig. 5.5 also shows that deeper minima exist for high nn and low T. To better

observe this, a new function was defined as f (nu, T) = f (nn, T, r). The ideal neutron

102

200

100

   

log nu [cm'3]

    

0.2 ' . Tuo’K]

Figure 5.6: f (n,., T) in the parameter space when using Arlandini et al. residuals.

 

Figure 5.7: f (n,,, T) in the parameter space when using Travaglio et al. residuals.

103

1000 l

 

100

10

 

 

 

     

Ye

o Residuals

0.1 .__. nn=10"7 T=0. 09 GK t.2.70 10"11 s
H nn=10"14 T=0. 09 GK t=7.01 10"4
-—- nn=10"21 T=0.09 GK t=0.809 s

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.01 ‘
0.001 =3
0.0001 1 1 l 1 l 1 l 1 l 1 l 1 l 1 v v v vv
20 25 30 35 40 45 50 55 60 65 70 75
Z

Figure 5.8: Abundances obtained using different astrophysical conditions. The desired
residual distribution as a function of atomic number using the Ti'avaglio et al. [14]
model is also shown.

flux duration 7 for each set of astrophysical conditions (an) was the time that
minimized f (an , t).

Figures 5.6 and 5.7 show f (nn, T) for different astrophysical conditions. Neutron-
capture processes with a high neutron density n,, 2 1016 seem to reproduce the
residual abundance pattern better. Regardless of the s-process contribution used, the
abundance patterns that best fit the respective residual patterns were obtained with
a r-process-like scenario. For high neutron densities, f (an) stabilizes close to a
minimum value. The absolute value of the function f (nn, T) is dependent upon the
model used. In the Travaglio et al. model, f (nu, T) has a value around 20 — 50 which
corresponds to a normalized chi-square value of 1 — 2.5 (the total number of residuals
is 21). In the Arlandini et al. model, the normalized chi-square is around 2 — 4.

Abundance patterns obtained using a sample of different astrophysical conditions
are shown in Fig. 5.8 and 5.9. As mentioned before the residual pattern is better

reproduced using a high neutron density. Low neutron densities do not reproduce

104

 

IOOOIII]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100
10 a
1 :l
D
>..
0.1
0'01 o Residuals * 7 ”ML ‘
-—-nn=10"7 T=0.09GK t=2.710"lls 1
o—onn=10"l4 r=0.09 GK t=7.2610"4s ‘l
0.001 -—-nn=10"21 T=0.09 GK F1223
00001 1 l 1 l 1 ll 1 l 1 J ' vv ‘l

 

20 25 30 35 40 45 50 55 60 65 70 75

Z

Figure 5.9: Abundances obtained using different astrophysical conditions. The desired
residual distribution as a function of atomic number using the Arlandini et al. [10]
model is also shown.

the residual abundance pattern due to the shell closure at N=82. To satisfactorily
reproduce the residual abundance pattern most of the abundance has to go into
38_<_ Z 547. For Z 256, the amount of created material has to be at least an order of
magnitude less than the average abundance of the light heavy elements. At the shell
closure, material tends to accumulate resulting in a peak in the abundance pattern.
For processes with a relatively small neutron density, the shell closure produces pro-
genitor bottleneck abundances that decay back to stability in the region 565 Z 560
resulting in an overabundance of Ba. The high abundance in this region therefore
prevents the correct residual pattern of low abundance for Z 256. For processes with
a large neutron density, the final abundance peak occurs around 52_<_ Z 556 and
therefore the residual pattern may still be reproduced. It is unfortunate that there is
no observational data to constrain the 523 Z 356 abundances.

To better simulate the decay back to stability, another network calculation was

run once the set of astrophysical conditions n", T and r that minimizes f(nn, T, t) had

105

been obtained. The initial abundance pattern of such calculation was the abundance
at time T (just before freezeout). The initial neutron density is set to zero to simulate
a sudden freezeout. Using a full network allows the possibility of not only B-decays
but other nuclear reactions such as captures of the emitted fl-delayed neutrons while
the system decays back to stability. The final abundance patterns shown in Fig. 5.10
and 5.11 are the result of such calculations.

Even though specific sets of astrophysical conditions were used in Fig. 5.10 and

5.11, similar r-process-like scenarios produced similar results.

5.6 Analysis

Generally there is good agreement between the solar r-process abundances and the
sum of the observed main r—process abundances in metal-poor stars plus the here
calculated weak r-process abundances from Section 5.5 as shown in Figs. 5.12 and 5.13.
While the Z 256 elements are produced in negligible quantities, the right abundance
and pattern is obtained for the majority of the light heavy elements. Clearly, the
residuals are drastically reduced from 0.5-1 (Figs. 5.1 and 5.2) to less than 0.25 when
adding a high neutron density weak r-process component. This demostrates that the
discrepancies between observed abundances and solar r-process abundances can be
explained by a late weak r-process.

Exceptions are the abundances of Sr (only for the Arlandini case), Y and Pd. The
Pd abundance is always overproduced, in the Arlandini et al. case by almost a factor
of 3 compared to the expected solar r-process abundance. The abundance of no Pd and
105Pd correspond to 35% of the final abundance in that case. Increasing the fi-delayed
neutron emission branchings (Pu) of 110Sr, 110Y, 110Zr, 105Kr, 105Rb, 105Sr and 105Y
decreases the final abundance of 110Pd and 105Pd as shown in Fig. 5.14. However, the
overabundance of Pd still would be a factor of #2 even if the mentioned Pas were

increased to 100%. Another possible explanation to the high Pd abundance would

106

 

 

T

 

 

Relative log a

 

.09....-

Solar r-process

CS 22892-052

CS 22892-052 + process
HD 115444

111) 115444 + process
BD +173248

BD +173248 + process
CS 31082-001

CS 31082-001 + process

 

 

 

Figure 5.10: Sum of the elemental abundance pattern of r-process rich stars CS 22892—
052, HD 155444, BD +17°3248 and CS 31082-001 with the result of a network calcu-
lation using nn 2 1021 cm‘3, T = 0.09 GK and r = 0.8 3 (red symbols), compared
with solar r—process abundance (black lines) derived using the s-process contribu-
tion from Travaglio et al. [14]. Also shown are the star’s abundances (blue symbols).

Abundances have been shifted for all stars for display purposes.

107

 

  

 

 

Solar
CS 22892-052

 

 

 

 

 

 

 

- CS 22892-052 + process
0 HD 115444
4 , I , I r 0 HD 115444 + process
c BD +173248 T
3 o BD +173248 + process —4
- CS 31082-001
2 . cs 310232-001 + process 1
I
o: 1 _
DD 0 I =
G I _
'_‘ I
0 _1 _
.>
5 _2 I _
2 .I I .
SE '3 I ‘
'4.” I I i
-5 _ .. _
. I E
-6 3: —
l I l I l l l l l
30 40 50 60 70 80

Figure 5.11: Sum of the elemental abundance pattern of r—process rich stars CS 22892-
052, HD 155444, BD +17°3248 and CS 31082—001 with the result of a network calcu—
lation using nfl = 1021 cm‘a, T = 0.09 GK and r = 1.2 3 (red symbols), compared
with solar r-process abundance (black lines) derived using the s—process contribu-
tion from Arlandini et al. [10]. Also shown are the star’s abundances (blue symbols).
Abundances have been shifted for all stars for display purposes.

108

 

 

 

 

 

 

 

 

 

1 ' 1 ' I ' l 1 I I
. CS 22892-052 + process
r - HD115444+ rocess
0 BD +173248 rocess
0 5 _ I 1 CS 31082-001 process _
I -—- Average
w p i |.
'1 I;
W .' if. E'. "
o 0 - _, - ' ' 1 | . _ _.
"‘ (“I 111 if llll
< " I l i 4
i l l
-0.5 — ' —
_1 l 1 l 1 I 1 I 1
40 50 60 70 80
Z

Figure 5.12: Differences between the sum of CS 22892-052, HD 155444, BD +17°3248
and CS 31082-001 abundances with the result of a network calculation using nn =
1021 cm”, T = 0.09 GK and r = 0.8 s, and scaled solar system abundance pattern
derived using Travaglio et al. [14]. The difference has been normalized such that the
mean difference for elements in the range 565 Z 579 is equal to zero.

109

 

_ I .
0.5— l -
n! e

 

. CS 22892-052 + process
- HD 115444 + rocess ;
-0-5r . BD +173248 rocess ' ‘

. CS 31082-001 process
._. Average

 

 

 

 

 

 

l l l l l l l l l
'1 4o 50 60 70 80
Z

Figure 5.13: Differences between the sum of CS 22892-052, HD 155444, BD +17°3248
and CS 31082-001 abundances with the result of a network calculation using nu =
1021 cm‘3, T = 0.09 GK and r = 1.2 s, and scaled solar system abundance pattern
derived using Arlandini et al. [10]. The difference has been normalized such that the
mean difference for elements in the range 563 Z S79 is equal to zero.

110

  
  

Proton number Z

 

76 78 Abundance
36 1
34
32 0.1
30 0.01
28 0.001
25 54 Neutron number N 0.0001

Figure 5.14: Mass region showing the calculated isotopic abundances just before
freezeout using a network calculation with nfl = 1021 cm“3, T = 0.09 GK and
r = 1.2 s. Largest abundances were normalized to 1. Squares with black thick lines
represent stable isotopes. The most important fl-delayed neutron emission branchings
that reduce the final Pd abundance are also shown.
be an incorrect nuclear structure around N=70. Changing the neutron separation
energy 8,. would shift the progenitor abundances before freezeout affecting the final
Pd abundance. As mentioned in section 2.3, a new magic number at N=70 may create
new “waiting” points in a neutron-capture process. Depending on the strength of the
new shell closure, the progenitor abundances could be shifted “upward” increasing
the final abundance of Ag and Cd and thus reducing the relative Pd abundance.
The abundances of Y, Sr and Zr observed in the metal-poor stars exceed the so-
lar r-process abundances when using the Arlandini model. The large scatter of the

abundance ratios of these elements to heavier r-process elements may indicate an as-

111

trophysical origin different from the strong r-process. The observed overabundances
could be just a reflection of this scatter. To decrease their abundance a process would
have to destroy such elements and increase the abundance of the other light heavy
elements. Such process was not observed, and the most promising scenario still in-
creases the Sr and Y abundance by a small amount. However, because the s-process
contribution for Sr and Y differ between the Arlandini and Travaglio models, it is not

straightforward to reach any conclusion.

5.7 Conclusions and outlook

Astrophysical observation indicate that an additional mechanism besides the strong
r- processes is necessary to account for the observed solar r-process abundance in the
region Z s 47. Even though this mechanism had been referred as the weak r-process,
the astrophysical scenario and conditions necessary for such a process were not known.
There is however some ambiguity in the amount of material such a process creates
due to the discrepancies in the solar r-process abundances between the Arlandini et
al. and Travaglio et al. models. The calculations and results presented in this chapter
are the first step toward determining the conditions that would result in the creation
of these residual abundances.

To find a set of astrophysical conditions (neutron density, temperature and neu-
tron flux duration) that would allow a neutron-capture process to produce the cor-
rect abundance pattern, a network calculation with different neutron densities and
temperatures was used. Neutron densities were spanned from a s-process—like (nu z
107 era—3) to a r-process-like (72,, z 1021 cm‘3) scenario. Temperature was also
spanned from 0.09 to 1.5 GK.

In general, the neutron densities and temperatures that better fit the missing
material resemble an r-process like scenario regardless of which solar r-process abun-

dances are used. This result justifies the name, weak r — process, as the process

112

responsible of creating such residuals.

Discrepancies such as the overabundance of Pd may be due to the incorrect nuclear
structure used in the calculation. Changing the theoretical nuclear reaction rates by
using a different mass model would give some clues as in fact, the problem of the Pd
overabundance is due to nuclear structure uncertainties, and it requires further study.
In addition, the abundance of Y and Sr seem to differ from the solar abundance but
the s—process contribution also differ between models.

Supernovae explosions and neutron star mergers are the preferred possible sites
of an r-process. These sites have different astrophysical conditions and the neutron
star mergers reach a neutron density of up to 1030 cm“3. To further constraint the
scenario responsible for creating the residual abundance, the calculations presented
here should be extended to more neutron-rich densities to account for the possibility
of neutron star mergers producing the residual abundances.

Recent results form the Hamburg/ESQ R—process Enhanced Star survey (HERES)
[89-91] extended the number of r-I and r-II stars for which elemental abundances have
been measured. Elemental abundances exist now for Sr, Y, Zr, Ba, La, Ce, Nd, Sm
and Eu for 8 new r-II stars and 35 r-II stars. Among the light r-process elements,
Y, Sr and Zr show scatter that is larger than explained by error in the observational
analysis. These new observations should be included in the future in the current
analysis to better constraint the contribution of a weak r-process to their observed
abundances. In the next few years, the Sloan Extension for Galactic Understanding
and Exploration (SEGUE) should extend the number of observed r-process enhanced
stars to a minimum of 100-150 r—II stars and 300-500 r-I stars [92]. Such amount of
spectroscopic data would put the r-process into solid observational ground and put
further constraints in the modeling of the astrophysical production of weak r-process

elements.

113

Appendix A

Abundances

Abundance is defined as

(A.1)

where X, is the mass fraction of a given element or isotope. It is a standard definition
independent of density when dealing with how much material exist in a given envi-
ronment. The number density of a given element or isotope can also be expressed in

terms of abundance with

 

 

711': . =CGS . =Y1'PNA, (A.2)

if CGS units are used. Because differences between elements vary by orders of mag-

nitude, a commonly used definition is

Y
Ac; 2 loglo (Y—Z) + 12.0 2 loge. (A.3)

The elemental abundance can also be expressed as

Ye, = Y310‘09“12. (AA)

114

 

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