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ABSTRACT

PROPERTIES OF GAMMA-RAY TRANSITIONS IN 55Co

FROM 55m DECAY AND 56Fe(p,ny)55Co

By

Lawrence Edward Samuelson

The 56Ni beta decay and the 56Fe(p,ny)56Co reaction with beam
energies between 5.5 and 8.4 MeV have been used with Ge(Li) spectrom-
eters to study properties of y rays from states of 56Co below 2.85
MeV of excitation. The 55Ni decay y-ray spectrum and y-y coincidences
were studied. y-y coincidences, y-ray excitation functions, y-ray
angular distributions, and absolute cross sections were measured for
the 56Fe(p,ny)55Co reaction. A beta-decay scheme for 56Ni, which
includes six y rays, and an energy-level diagram for 56Co, which
includes 35 y rays (14 of which are reported for the first time)
from 20 excited states, are presented. Comparisons of the data
from 56Fe(p,ny)55Co with predictions of the statistical compound
nuclear model have resulted in spin assignments (in parentheses)
for the following states (energies in keV) 0f 56CO: 158.4 (3), 576.6
(5), 829.7 (4), 970.3 (2), 1009.2 (5), 1114.6 (3), 1450.8 (0), and
1720.3 (1). Branching ratios are presented for 14 y rays from these
eight states and multipole mixing ratios are given for 12 of these

y rays (10 are predominantly M1). The data are consistent with a

Lawrence Edward Samuelson

spin 4 assignment to the ground state. Contrary to previous sug-
gestions, evidence from all experiments indicates that only one state
exists in 56Co in the neighborhood of 1451 keV of excitation. The
level energies, y-ray multipole mixing ratios and y-ray branching

ratios agree, in general, with shell-model predictions of McGrory.

PROPERTIES OF GAMMA-RAY TRANSITIONS IN 55Co

FROM 56Ni DECAY AND 56Fe(p,ny)56Co

By

Lawrence Edward Samuelson

A THESIS

Submitted to

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

DOCTOR OF PHILOSOPHY

Department of Physics

1972

0‘3‘

51
6%,] ACKNOWLEDGMENTS

I wish to thank Dr. W. M. Kelly for suggesting this area of study.
His encouragement and constant interest during the experimental work
and his guidance and patience during the preparation of this thesis
are deeply appreciated.

I also wish to thank most sincerely Dr. R. A. Warner for his in—
valuable assistance and encouragement in all phases of this work. Many
fruitful discussions led to solutions of apparently insurmountable problems.

Drs. Wm. C. McHarris, F. M. Bernthal and B. H. Wildenthal have
contributed to various phases of this investigation through informal
discussion. Dr. J. B. McGrory was very kind to send shell-model calcula-
tions on 5600. Their generous cooperation is gratefully acknowledged.

Dr. H. G. Blosser and Mr. H. Hilbert have assisted with the operation
of the Michigan State University sector-focused cyclotron.

Dr. E. M. Bernstein, Dr. R. Shamu and Mr. Eric Warren assisted
considerably with the operation of the Western Michigan University tandem
Van de Graaff. Their unselfish generosity is gratefully appreciated.

Dr. R. E. Doebler, Dr. R. R. Todd, Dr. R. W. Goles, Mr. C. B.

Morgan and Mr. W. B. Chaffee aided in data collection and interpretation.

Mrs. Carol VanderMeer and Mrs. Peri-Anne Warstler aided greatly
by typing the various versions of this manuscript.

Much of the financial assistance for this research has been provided
by the National Science Foundation, the U.S. Atomic Energy Commission,

and Michigan State University.

ii

TABLE

ACKNOWLEDGMENTS . . . . . . .

LIST OF TABLES. . . . . . . .

LIST OF FIGURES . . . . . . .

I. INTRODUCTION. . . . . .

II. THE

A.

III. THE
A.
B.
C.

D.

BETA DECAY OF 56M.
Source Preparation
The y-ray Spectrum

y-y Coincidences .

OF CONTENTS

The 55Ni Beta-Decay Scheme

56Fe(p,ny)56Co REACTION . .

Y-y Coincidences . . . . .

y-ray Excitation Functions

y-ray Angular Distributions. . .

Total Absolute Cross Sections at Ep=7.30

IV. DISCUSSIONS 0F INDIVIDUAL

A.

Ground State, Jfl=4+

Ex-158.4 keV, 3+ .

Ex=576.6 keV, 5+ .
Ex=829.7 Rev, 4 .
EX=970.3 keV, 2 .
Ex-1009.2 keV, 5+.
EX-lll4.6 Rev, 3*.
Ex-1450.8 keV, 0+.

Ex-l720.3 keV, 1+.

LEVELS.

Higher Excited States.

111

Page

ii

vii

12
16
18
32
46
61
65
65
66
67
67
69
69
70
71
74

77

Page
V. COMPARISONS WITH SHELL MODEL
CALCULATIONS FOR 56Co. . . . . . . . . . . . . . . . . 79
VI. SUMMARY AND CONCLUSIONS . . . . . . . . . . . . . . . . . 88
BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . 91
APPENDICES. . . . . . . . . . . . . . . . . . . . . . . . . . . 96
A. Separation of Nickel from Irradiated Iron
Shimstock. . . . . . . . . . . . . . . . . . . . . . 96
B. Integral Coincidence and Gated Spectra from the
56Fe(p,ny-y)56CO Reaction at Ep-7.38 and 8.36 MeV. . 97
C. y-ray Angular Distributions from the 56Fe(p,ny)56Co
Reaction at Ep=5.77, 6.65, 7.03, 7.05, 7.30, and
7.40 MeV . . . . . . . . . . . . . . . . . . . . . . 106
D. The Experimental and Theoretical Values of the

* k
A and A 56Co y-ray Angular Distribution Co—

2 4
efficients as a Function of the y—ray Mixing
Ratio 6 .. . . . . . . . . . . . . . . . . . . . . . 120
E. Relative x2 as a Function of Arctan 6 for the

5600 y-ray Angular Distributions . . . . . . . . . . 130

iv

 

‘4‘.

Table

II.

III.

IV.

VI.

VII ,

LIST OF TABLES
Page

Energies and relative intensities of the y rays

in 5500 from the beta decay of 56Ni. . . . . . . . . . . 7
Summary of two-parameter y—y coincidence results

for the 56Ni 5 56Co decay. . . . . . . . . . . . . . . . ll
Energies of y rays found in 56Co at excitations

up to 2.86 MeV from 56Fe(p,ny)55Co. Unless

otherwise indicated, the identification of 56Co

y rays are based upon both y-ray excitation

functions and y—y coincidences . . . . . . . . . . . . . 24
Results of two parameter y—y coincidence

experiments from 56Fe(p,ny-y)5500. . . . . . . . . . . . 25
y-ray energy standards used as calibrations

in the determination of 56Co y-ray energies

from 55Fe(p,ny)55Co. Those y rays listed for

the isotope 55Fe appeared in the spectra from

55Fe(p,p'y). . . . . . . . . . . . . . . . . . . . . . . 27
Form of the optical-model potential and

parameters used in the calculations of trans-

mission coefficients. The Coulomb potential,

Vc(r), is that due to a uniformly charged sphere

1/3

of radius 1.25A [F]. The parameter E is the

center-of-mass energy of the nucleon in MeV. . . . . . . 43

Experimental y—ray angular distribution fitting

* *

parameters A2 and A4 and the associated y-ray

 

 

 

 

all
A

 

WI

Table

VIII.

IX.

Page

multipole mixing ratio, 6. The fitting
parameters and mixing ratio are defined in
the text. The errors assigned to both the

* *
A and A coefficients represent plus or

2 4
minus one standard deviation. The ranges
of 6 were determined from these coefficients
as described in the text . . . . . . . . . . . . . . . . 53
56Fe(p,n)56Co total cross sections at
Ep = 7.30 MeV. . . . . . . . . . . . . . . . . . . . . . 63
Reduced transition probabilities, B(Ml)
and B(E2), calculated by McGrorya and
comparisons of the shell-model results
with experimental y-ray multipole mixing
ratios, 6, and y-ray branching ratios
from 56Fe(p,ny)55Co. The experimental
transition energies were used when calculat-
ing the theoretical mixing and branching
ratios (necessary formulas are presented
in the text).. . . . . . . . . . . . . . . . . . . . . . 83
Shell-model predictions by McGrorya of the
half lives of the first eight excited states
of 56Co. Only observed transitions were
included in these calculations. Internal—

conversion effects were not included . . . . . . . . . . 85

vi

Figure

LIST OF FIGURES

Page

Typical 56Ni singles spectrum taken with the

2.SZ-efficient Ge(Li) spectrometer . . . . . . . . . . . 5
Integral coincidence and gated spectra from

the 56Ni ydy coincidence experiment. Peaks

labeled with a 2 were identified as triple

coincidences where two of the three coincident

y rays have been summed in one detector. Peaks

labeled in parentheses are believed to be from

chance coincidences or insufficient background

subtraction. . . . . . . . . . . . . . . . . . . . . . . 9
Decay scheme of 56Ni. The y-ray energies were

measured using the 56Ni decay. The intensities

have been rounded off and are normalized to 100

for the 158.4-keV transition strength. The 56N1

decay half life and the half lives of the 158.4—,

970.2-, and 1450.7-keV states are from Ref. 1.

The 5500 ground-state half life is from Ref. 5.

The Q: value is from Ref. 42. The spin and parity
assignments are from 56Fe(p,ny)56Co and are dis-

cussed in the text. Log ft values are also dis—

cussed in the text.. . . . . . . . . . . . . . . . . . . l3
Geometry for the in-beam y-Y coincidence measure-

ments. The squares are not meant to represent the

actual size of the Ge(Li) detectors, but only the

approximate location of their cryostat caps. . . . . . . l9

vii

Figure

Page

Integral coincidence and representative gated

spectra from the 55Fe(p,ny-7)55CO y-y coincidence

experiment at Ep = 8.36 MeV. y-rays labeled with

a question mark, although they appear to be in

coincidence, could not be placed in the decay

scheme. Peaks labeled in parenthesis are

believed to be from chance coincidences or

insufficient background subtraction. . . . . . . . . . . 21
The y-ray decay scheme for excitations of 5500.

The y-ray energies and branching ratios were

measured using 55Fe(p,ny)55Co. The arrows on

the right indicate the maximum possible excita-

tions for the proton energies of the y-y coincidence

and y-ray angular distribution experiments. The

spins, parities, and level energies labeled with

an asterisk are from Ref. 15, while the remaining

values were determined from 56Fer,ny)56Co. Dots

denote observed coincidence relationships between

y-ray transitions entering and leaving a state . . . . . 29
Typical y-ray spectra from the excitation function
measurements. The first appearances of the various

56CO y rays are labeled. . . . . . . . . . . . . . . . . 33
Excitation functions for the first eight excited

states of 56Co. The units of the ordinate are

arbitrary but are proportional to the absolute

cross section. The data were taken at 125°, a

viii

Figure

10.

11.

Page

zero of P2(cose), in order to minimize angular

distribution effects. Neutron feedings were computed

for each level from the y-ray intensity imbalances,

and then were normalized from run to run (as described

in the text) to obtain the relative cross sections.

The thresholds were calculated using Q = -5.357 MeV

for the ground state (Ref. 48) and are connected to

the first non-zero data points with dotted lines.

Solid lines connect the data to guide the eye. Where

not visible, error bars are smaller than the data-

point symbol . . . . . . . . . . . . . . . 36
Experimental and theoretical cross-section ratios.

The ratios are taken with respect to the 158.4-keV
first excited state. Error bars identify the data
(lines connecting the data are to guide the eye).
MANDY predictions for selected beam energies are

shown for JTr = 0+,...,6+. A J1T = 3+ for the 158.4

keV state was used as explained in the text. Straight
lines connecting the theoretical points approximate
expected smooth curves . . . . . . . . . . . . . . . . . 40
Geometry for the in—beam y-ray angular distribution
measurements. The monitor and target angles were

held fixed throughout all of the measurements. . . . . . 47
Angular distributions of 56Co y rays taken at Ep = 5.77,

6.65, 7.05, 7.30, and 7.40 MeV. The solid lines

through the data represent least squares fits using

ix

Figure

12.

l3.

14.

Page

the equation for W(e) given in the text. W(6)
has been normalized to 1 at 90°. Except for
the Ep - 7.40 MeV case, two experimental points
were taken at each angle; only their weighted

average is presented . . . . . . . . . . . . . . . . . . 51

*

Representative plot of MANDY predictions for the A2

and A: coefficients as a function of y-ray mixing

ratio, 5. (Definitions are presented in the text.)

This plot is for the case of the 158.4-keV y ray

at Ep - 5.77 MeV. A spin of 4 for the final state

was assumed; the spins and parities of the initial

state label their appropriate 6-ellipses. Represen-

tative values of 5 are also labeled. The experi-

mental A: and A: coefficients including uncertainties

are shown as a rectangle in approximately the center

of the plot. . . . . . . . . . . . . . . . . . . . . . . 55
Representative relative X2 versus arctan 6 plots for

angular distributions of each of the 56Co y rays.

J" values for the initial states label each curve.

The J value assumed for the final state was that

previously assigned in this work . . . . . . . . . . . . 58
Comparisons of level spins, parities, and energies

of the present experiment and from Ref. 15 (asterisked
values), with the predictions of McGrory (Ref. 30).

Dashed lines indicate tentative correlations. For

excitations above 3 MeV, see Ref. 15. . . . . . . . . . 80

Figure

15.

l6.

17.

Page
Integral coincidence and gated spectra from the
55Fe(p,ny)55Co reaction at Ep = 7.38 and 8.36 MeV.
The x-axis is from the 2.5% detector while the y—
axis is from the 7.4% detector. Background sub-
traction using the adjacent continuum has been
included. Peaks labeled in parenthesis are be-
lieved to be from chance coincidences or insuf-
ficient background subtraction. More details
are given in the text. . . . . . . . . . . . . . . . . . 97
y-ray angular distributions from the 56Fe(p,rzy)56Co
reaction at Ep = 5.77, 6.65, 7.03, 7.05, 7.30, and
7.40 MeV. The solid lines through the data repre-
sent least squares fits using the equation for
W(e) given in the text. W(6) has been normalized
to 1 at 90°. Except for the Ep = 7.40 MeV case,
two experimental points were taken at each angle;
only their weighted average is presented. The
assignment of errors is outlined in the text. . . . . . 106
Plots of the experimental and theoretical values
of the A: and A2 56C0 y-ray angular distribution
coefficients as a function of y-ray mixing ratio 6.
(Definitions and descriptions for the calculations
are presented in the text.) Only those cases are
shown where y-ray feeding from above was judged

to be insignificant. In each case the spin used

xi

 

Figure

18.

Page

for the final state was that determined from this
experiment; the possible initial state spins and
parities label their appropriate O-ellipses. Ap-
proximate locations for the values of 6 can be
found by comparison with Fig. 12. In each case

the l+ "ellipse" is a short straight vertical
* *

line passing through the point A2 = 0.0, A4 0.0.
* *
The experimental A2 and A4 coefficients including

uncertainties are shown on each plot as a rec-
tangle . . . . . . . . . . . . . . . . . . . . . . . . . 120
Plots of relative x2 versus arctan 6 for 56Co

y-ray angular distributions. Only those cases are
shown where y-ray feeding from above was judged to
be insignificant. Assignment of errors necessary
for the determination of x2 is outlined in the text.
In each case the spin used for the final state was
that determined from this experiment; the possible
initial state spins and parities label their ap-
propriate curves. It is instructive to compare
these plots with the corresponding plot of Fig.

17 . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

xii

I. INTRODUCTION

The earliest investigationsl_6 of the low-lying excited states
of 5500 began with the beta decay of 56Ni. These studies, which in-
cluded measurements of the 56Ni half life,1 the y-ray spectrum,1’3’”
y-y angular-correlations,1’3 the internal-conversion electron spec—
trum,2 and lifetimes of some 56Co states,1 produced valuable informa-
tion. However, only selected states below 1.8 MeV could be populated
and unambiguous spin assignments for these states could not be made.

More recently, experiments involving the two-particle trans-
fer reactions 5”Fe(3He,p)55Co,7-1° 5I+Fe(a,d)55Co,11 58Ni(p,3He)5500,12
and 58Ni(d,a)55C08:9:13‘15 and the charge-exchange reactions 56Fe(p,n)--
55C015’17 and 55Fe(3He,t)56C018-21 have increased the knowledge of
the properties of these and additional states. However, the interpre-
tations of these experiments depend strongly upon assumed 56Co wave
functions and reaction mechanisms. Neither is well-known.

In particular, the J1T of a state in 56Co at 1451 keV has been
somewhat controversial. In the early 55Ni decay work, 1- or 2i seemed
most consistent with the data, with 1—(2’) being favored by Ohnuma
et aZ.,3 and 2+ by Jenkins et al.2 and Wells.22 Later, Belote
et aZ.,8 Observing 2 = 0 transfers in (3He,p) and (d,o) and a weak
Gi.u) cross section, chose 0+. Belote et all.8 then conjectured that
this state was an anti-analog of the 56Fe ground state (JTr = 0+).
Subsequent particle transfer work has confirmed J1r - 0+ (e.g. see

Ref. 12 and 15). However, R003 and Goodman19 reported an I -= l trans-
far in the (3He,t) reaction, implying J1T = 1-; they then suggested

thiit: possibly a 0+ and a 1. state occur within a few keV of each

other at this energy.

The 56Fe(p,ny)56Co reaction23’2“ near threshold was chosen
for the present study because the reaction should be well described
by the statistical compound nuclear (CN) theories of Wolfenstein,25
Hauser and Feshbach,26 Biedenharn and Rose,27 Satchler,28 and Sheldon

29 Since all states for which there are sufficient

and Van Patter.
energy and angular momentum are excited in this type Of reaction,
both members of the doublet (if they exist) at 1451 keV should be
populated quite strongly because of their expected low spins. Com—
parisons of the results Of the present work with the predictions of
the statistical CN theory and with previously measured.56Co y-ray
characteristics have lead to unambiguous spin assignments for all
5600 states below 1.8 MeV. In addition, y-ray multipole mixing ratios,
precise level energies and y-ray branching ratios are obtained.
This experimental information is compared with shelldmodel level
energies and B(Ml) and B(EZ) values for 56Co calculated recently
by McGrory.30

As a supplement to the (p,ny) work, the y-ray spectrum accom-
panying the 56Ni beta decay was reinvestigated. These experiments
corrOborated the previous 56Ni decay work and the energies of some

56CO y-rays. In particular, the 1451 keV state was examined very

carefully in the decay study for any evidence of it being a doublet.

II. THE BETA DECAY OF 56Ni

Ge(Li) detectors were used to measure the y-ray spectrum and
y-v coincidences accompanying the 56Ni beta decay. These experi—
ments yielded y-ray energies and intensities and confirmed the place-

ment Of y-rays in the 56Ni decay scheme.

A. Source Preparation

 

The 6.1—day 56Ni activities were produced via the 56Fe(3He,3n)56Ni
reaction (Q = -16.3 MeV) by bombarding 0.02 gm/cm2 iron foils with
45-MeV 3He particles from the Michigan State University sector-focused
cyclotron. After allowing about 10 days for the undesired 1.5—day
s7N1 activity to decay, chemical separations were performed.

The iron foils were first dissolved in hot 15N HCl, evaporated
to dryness, and redissolved in lON HCl. The samples were then passed
through a column of Dowex l—X8 anion exchange resin previously brought
into equilibrium with lON HCl. This procedure31 removed all detect-
able contaminant cobalt activities such as 56CO and 58CO. The desired
$6Ni activities were then separated from the remaining contaminant
radioisotopes such as 51Cr, 52Mn, and 5“Mn by the standard procedure
of precipitation of nickel dimethylglyoxime (Ni-DMG).32 The Ni-DMG
was finally dissolved in 15N HCl and placed in thin-walled plastic

vials for counting.

B. The 1:Ray Spectrum

 

Three different Ge(Li) detectors were used to take y-ray singles
spectra: (1) a 2.52-efficient (compared to a 7.6 cm x 7.6 cm NaI(T1)
detector at 25 cm and at a y-ray energy of 1332 keV) Ge(Li) detector
with a 15:1 peak-to-Compton ratio and a FWHM resolution of 2.34 keV
at a y-ray energy of 1332 keV; (2) a 4.52-efficient Ge(Li) detector
with a 22:1 peak-to-Compton ratio and a FWHM resolution of 2.10 keV;
and (3) a 10.4Z-efficient Ge(Li) detector with a 30:1 peak-to-Compton
ratio and a FWHM resolution of 2.28 keV. A typical 56Ni decay y-ray
singles spectrum is shown in Fig. 1. Optimum resolution and the most
symmetric peaks were Obtained using an ORTEC model #450 Research
Amplifier direct-coupled into a Northern Scientific 504MHz analog-
to-digital converter. The data were accumulated in either the MSU
Cyclotron Laboratory's Xerox Data System 2-7 time-sharing computer
using a pulse-height analysis routine,33 or in a Digital Equipment
Corporation PDP-9 computer loaded with another pulse-height analysis
routine. Peak centroids and areas were determined off-line by the
peak-fitting code SAMPO,3“ which was especially useful in stripping
unresolved multiplets.

Since it offered the best over-all resolution, the 4.5%-efficient
Ge(Li) detector was used to take the spectra for the y-ray energy
measurements. For these measurements, spectra from a 55Ni source
were taken in the presence of various combinations of such well-known
y-ray energy standards as 57Co, 139Ce, 203Hg, 51Cr, 20781, 137Cs, 5“Mn,
5500, 88Y, 652n, 60Co, 22Na, 1”K, and 192Ir. The calibration energies

assumed can be found elsewhere.5:35’36 Care was taken so that standard

.eeueeoneeeen Agaveo senseseee un.~ man sees ensue antennae nesween Azem Heeenss .H enemas

mmeDZ nEZZ<Io

 

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peaks and the 56Ni decay peaks grewhinto the spectra at roughly equal
rates. A quadratic fit was then made to the calibration energies
versus measured centroids in two energy regions (100-800 keV and 700-
2000 keV). The 56Co y-ray energies were then calculated by computer
using this calibration and are listed in Table I.

The 2.5%- and 10.4Z-efficient Ge(Li) detectors were both used
for y-ray intensity determinations. Separate singles spectra were
taken using each detector with the 56Ni source placed both at 5 cm
and at 25 cm from the face of the detector. The use of two detectors
with highly different efficiencies and of two source—to-detector
distances allowed for sumrpeak identification. Background spectra
(with the source removed) were also taken with each detector. The
relative efficiency curves were determined using the y-ray intensity
standards 160-11), 203118, isomuf’ 110mg, 177m“, 5600, say, soCo, and
2"Na. The relative intensities of the v-rays from these standards
can be found elsewhere.5’37'39 The intensities presented in Table

I were obtained by averaging the four sets of data.

Table I. Energies and relative intensities of the Y rays
in 5600 from the beta decay of 56Ni.

 

 

 

EY(keV) IY
Present Piluso Present Piluso
work at aZ.a work et al.
158.4i0.l 158.3t0.2 5100. 5100.
269.5iO.1 269.6i0.1 36.0il.4 40.0i0.7
480.5iO.1 480.7i0.l 36.0il.5 41.4i1.4
749.9tO.1 750.6iO.l 50.5:2.5 54.3:3.5
811.8i0.l 812.2i0.2 88.5:4.4 91.3:3.5
1562.0i0.2 1562.5i0.2 14.3il.4 12.8il.4

 

 

aSee Ref. 4.

bThe relative y-ray intensities presented by Piluso et al. (Ref. 4)
have been renormalized here to 100 for the intensity of the 158.4-

keV transition.

C. y—Y Coincidences

 

Prompt v-ray coincidences in the 56Ni beta decay were determined
with a Ge(Li)-Ge(Li) spectrometer using the 4.52- and 10.4Z-efficient
detectors arranged in 150° geometry with a graded (Pb-Sn—Cu) absorber
placed between them to minimize Compton scattering from one detector
into the other. A typical two-parameter, fast—slow coincidence arrange-
ment (resolving time 2TSE 100 nsec) was used. Addresses corresponding
to the energies of coincident v-rays were listed in pairs on magnetic
tape."0 This listing yielded a 4096X4096-channe1 array of prompt
coincidence events which were later sorted Off-line in gated slices.1+1
The gated slices included careful subtraction of background coincidences
which were determined from the adjacent continuum.

The integral coincidence spectrum from each detector is shown
at the tap of Fig. 2. Each spectrum represents 330,000 coincidences.
Beneath each integral spectrum in Fig. 2 are shown spectra in coinci-

dence with the various 56Co peaks. The results are summarized in

Table II.

Figure 2.

Integral coincidence and gated
spectra from the 56Ni y-Y coinci-
dence experiment. Peaks labeled
with a 2 were identified as triple
coincidences where two of the three
coincident Y rays have been summed
in one detector. Peaks labeled in
parentheses are believed to be from
chance coincidences or insufficient
background subtraction.

 

 

 

 

   

  

 

 

 

 

 

         

 

 

   

 

 

 

 

 

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11

Table II. Summary of two-parameter y-Y coincidence

6
results for the 56Ni + 56Co decay.

 

 

 

EY/EY

(keV) 158 270 481 511(yi) 750 312 1562
158 -—- yes yes no yes yes yes
270 yes --- yes no no yes no
481 yes yes -—— no no yes no
511(Yi) no no no --- no no no
750‘ yes no no no --- yes no
812 yes yes yes no yes --- no

1562 yes no no no no no ---

 

 

12

D. The 55Ni Beta-Decay Scheme

 

The 56Ni beta-decay scheme is shown in Fig. 3. Corrections
for internal conversion are included using coefficients measured by
Jenkins and Meyerhof.2 The intensities are normalized to 100 for
the 158.4-keV transition strength. The values shown for the half
life of 56Ni and the half lives of the 158.4-, 970.2- and 1450.7-
keV states of 56Co are those measured by Wells et al.1 The Qe value
of 2.134i0.011 MeV is from mass differences recently calculated by
Ewbank and Raman.“2 The spin and parity assignments shown are based
on 56Fe(p,ny)5500 experiments and will be discussed in detail later.

The limits on the beta-feeding intensities and associated log
ft values shown in Fig. 3 were computed using the experimental un-
certainties in the imbalances of the electromagnetic decay intensities.
A minimum.of 922 and a maximum of 1002 for beta feeding to the 1720.2-
keV state, results in a log fE between 4.38 and 4.42. A recent shell-
model calculation by Goode and Zamick1+3 predicts log ft = 5.8 for this
0+ to 1+ allowed transition. A maximum of 4% beta feeding to the
1450.7-keV state yields log f% > 6.3. The 0+ to 0+ transition to
this state is an isospin forbidden (AT = l) Fermi transition“+ for
which one might expect“5 log ft 37.8. The lower limits of 6.5 and
7.1 on the log ft values for the 0+ to 2+ transition to the 970.2-

Rev state and the 0+ to 3+ transition to the 158.3-keV state, respec-
tively, are very small compared to log ft =12 expected“5 for these
second-forbidden transitions. These discrepancies indicate the
difficulty of measuring log ft values to high precision.

The 06 value of 2.134 MeV allows the possibility of positron

Figure 3.

l3

Decay scheme of 56Ni. The y-ray
energies were measured using the
56Ni decay. The intensities have
been rounded off and are normalized
to 100 for the 158.4-keV transition
strength. The 56Ni decay half life
and the half lives of the 158.4-,
970.2-, and 1450.7-keV states are
from Ref. 1. The 56Co ground-state
half life is from Ref. 5. The Q
value is from Ref. 42. The spine
and parity assignments are from
56Fe(p,ny)56Co and are discussed

in the text. Log ft values are
also discussed in the text.

14

n 0%.:

 

 

 

 

 

 

 

 

 

 

 

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15

decay to the ground state and the 158.4- and 970.2-keV states. How-
ever, no coincidences with the 511.0—keV annihilation radiation (other
than chance) were observed in the 56Ni decay (see Fig. 2). This fact
supports the upper limit of 0.01 per decay for the relative intensity
of positron emission reported by Sheline and Stoughton.”6

Weak peaks seen at 427.9, 908.3, and 970.2 keV in the singles
spectra taken with the 56Ni sources at 5 cm and weak peaks seen at
428, 639, 908, 970, 1081, and 1292 keV in the y—y coincidence spectra,
were concluded to be sum-coincidence peaks since they were only found
to be in coincidence with appropriate members of the same y-ray cas-
cade and they all disappeared in singles spectra taken with the sources
at 25 cm. (Observable intensities would have been expected if the
peaks had been real.) Unfortunately, because of the longer counting
time required, the possible 970.2-keV ground-state transition was
masked somewhat in the 25 cm measurements by a 968.9-keV background
7 radiation from the negatron decay of 228Ac (from the 232Th a—decay
chain). However, the 970.2-keV peak apparently disappeared at the
larger distance, since the centroid shifted between the 5 cm and the
25 cm measurements by the entire 1.3-keV difference between these
two y rays, and since the peak area at 25 cm was completely accounted
for by taking the ratio (measured in the background spectrum) of the
areas of the 968.9-keV peak and the slightly more intense 911.1-keV
peak which branch from the same excited state in the 228Th daughter.5’L’7
There was no evidence to suggest changing the upper limits of 0.01
out Of 100 55Ni decays reported by Piluso et aZ.1+ for the intensities
of possible 970.2-, 1292.3-, 1450.7-, and 1720.2-keV y rays.

A discussion of the 1451—keV excitation region is given in

Section IV-H.

III. THE 56Fe(p,nv)56Co REACTION

Four types of experiments were performed using the 55Fe(p,ny)56Co
reaction (Q = -5.357 MeV).1+8 In the first type, y-v coincidences were
measured with a Ge(Li)—Ge(Li) spectrometer for 56CO excitations up to
2.85 MeV. These coincidences identified 56Co y rays and allowed place-
ment in the excited-state decay scheme. Except for the special cases
of ground-state transitions with no coincidences, this method was
very powerful. In the second type of experiment, excitatiOn functions
of the various 56CO y rays were measured from below the (p,n) threshold
up to 2.26 MeV of excitation. Individual spectra provided y-ray branch-
ing ratios, while the excitation functions provided threshold informa-
tion (and hence, evidence for y—ray placement in the excited-state
decay scheme), information on relative cross sections as a function
of proton energy (and hence, evidence for spin assignments), and an
indication of the level density and the degree of statistical averaging
in the compound nucleus. In the third type of experiment, angular
distributions of the various Co y rays were measured for excitations
up to 1.91 MeV. Beam energies were chosen, where possible, such that
the state in question was not fed from above by y-ray transitions.

The y-ray angular distributions provided information on spins, y-ray
multipole mixing ratios, and y-ray branching ratios. In the fourth

type of experiment, absolute cross sections for excitations of the first
eight excited states of 5600 were measured at a beam energy of 7.30

MeV. The experimental absolute cross sections offer direct comparisons
with theoretical cross-section predictions of the statistical CN theory.

In the following discussions, 56Co y rays and excited states are

16

17

referred to with energies measured using 56Fe(p,ny)56Co. In a few
instances these energies are slightly different from 56Ni decay

values. The adopted energies appear in Section VI.

18

A. ydy Coincidences

 

Proton beams (all beam energies quoted in this paper are in the
laboratory system) of 7.38 and 8.36 MeV (corresponding to excitations
in 5600 of about 1.89 and 2.85 MeV, respectively) were obtained from
the MSU Cyclotron for the in—beam y-y coincidence measurements. The
target was a 0.90 mg/cm2 iron foil enriched to 99.4% 56Fe. The 2.5%-
efficient Ge(Li) detector (previously described) and a 7.4%-efficient
Ge(Li) detector with a peak-to-Compton ratio of 25:1 and FWHM resolu—
tion of 3.5 keV were positioned as shown in Fig. 4. The lead block
between the detectors has a 1.3 cm diameter hole drilled almost
through it and served as a shielded beam stop as well as an attenuator
for photons Compton scattered from one detector toward the other.

A typical two-parameter, fast-slow coincidence arrangement with
constant-fraction timing discrimination was used. The single-channel
analyzer window (2T 2550 nsec) set on the output from a time-to-
amplitude converter was a few nanoseconds less than the interval
between cyclotron beam bursts. The 77-day half life of the 5600 ground
state resulted in minimal radioactivity build-up in the target, and
insured that most detected y rays were from beam induced reactions.
The coincidence events were stored on magnetic tape and later sorted
off-line using background subtraction as described previously for the
beta decay work. The 7.38—MeV spectra contain about 1 million coinci-
dence events accumulated in 12 hours of counting, while the 8.36-MeV
spectra contain close to 7 million coincidence events accumulated
in 31 hours. Typical singles counting rates for both experiments

were 7000 cts/sec in the 2.5%-efficient detector and 20,000 cts/sec

19

7‘7 COINC
GEOMETRY

BEAM

 

g ”/’,TARGET

 

 

 

7.4% = g 2.5%
Ge(Li) Li-JJ Ge(Li)

 

 

 

 

 

 

 

 

 

 

Pb BEAM STOP and

,,,,,, "COMPTON SUPPRESSOR"
O I Z 3 4 5
SCALE (cm)

 

Figure 4. Geometry for the in-beam y-y
coincidence measurements. The
squares are not meant to repre-
sent the actual size Of the Ge(Li)

detectors, but only the approximate
location of their cryostat caps.

20

in the 7.4%-efficient detector. The average beam current was about
7 nA.

The two integral spectra and some representative gated spectra
from the experiment with Ep = 8.36 MeV are shown in Fig. 5. Thirty-
five y rays were definitely identified to be from 56Co, and 6 others
are possibly from the same nucleus. These include 21 Y rays previously
reported by Del Vecchio et 611.21+ to be in coincidence with neutrons
from the same reaction. The energies (as determined below) of the
56Co y rays are listed in Table III; the coincidence relationships
between these y rays are listed in Table IV. (For brevity, the coinci-
dence data taken at Ep = 7.38 MeV and many gated spectra taken at Ep =
8.36 MeV are not shown here. All the gated coincidence spectra from
which the coincidence relationships were derived and from which energy
calibrations were determined, can be found in an Appendix to Ref. 49.)

As a supplement to the coincidence experiments, the energies
of those y rays from the excited states of 56Co up to and including
the 1720.3-keV state (excluding the 1561.7-keV y ray) were determined
by taking a y—ray singles spectrum of 56Fe(p,ny)56Co at E1) = 7.30
MeV in the presence of the well-known v-ray energy standards 22Na,
7SSe, 88Y, 118Sn, and 137C3. The calibration energies assumed are
presented in Table V. The remaining energies of the 1561.7-keV y ray
and the y rays from the excited states of 1930.4 keV and above, were
determined from the various y—y coincidence gated spectra. In both
cases, prominent 56Fe y rays from the 56Fe(p,p'y) reaction (see Table
V) were used as sons of the energy standards. For the y-ray energy
determinations from the y-ray singles data, a quadratic fit was made

to the measured centroids (analyzed by SAMPO3“) versus calibration

Figure 5.

21

Integral coincidence and
representative gated s ectra

from the 56Fe(p,ny-v)5 Co y-v
coincidence experiment at EE =
8.36 MeV. y-rays labeled w th a
question mark, although they ap-
pear to be in coincidence, could
not be placed in the decay scheme.
Peaks labeled in parenthesis are
believed to be from chance coinci-
dences or insufficient background
subtraction.

22

 

 

 

             

                             

       

 

 

     
  

 

 

 

 

 

     

 

 

 

 

 

 

 

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CHANNEL NUMBER
Figure 5

23

 

 

N
J

CClNI'S PER CHANNEL

F:

 

ZII-

 

 

 

IIIII II

 

 

 

(d) 8| l.9-keV GATE

   

(D
8 f’=_ (e) mo.o- e |||4.6- keV GATE
5": /

 

 

 

 

(f) |77|.4-8 |772.|- keV GATE

I238.3 (55a)

 

 

2000

CHANNEL MMBER
Figure 5 Continued

 

 

 

24

Table III. Energies of y rays found in 56CO at excitations
up to 2.86 MeV from 55Fe(p,ny)5500. Unless otherwise
indicated, the identification of 56Co y rays are
based upon both y-ray excitation functions and

y-y coincidences.

 

 

Transition energies (keV)

 

Presegt n-y coincidegce Present n—v coincidegce
work (Ref. 22) worka (Ref. 22)
158.4so.1 158.5 1254.4:0.3c
269.5:O.1 269.7 1319.8:0.3° 1317.9
285.0:0.l 284.7 1334.710.3C
(424.7102)C ' 1387.3103c 1387.1
432.8:0.2 (1459.1:0.6)°
480.5:0.1 480.4 1561.7:O.4
576.6:O.1 576.4 (1641.110.7)c
671.3:0.1 671.3 1760.1:O.5°
750.1:0.1 750.0 1772.1:0.4c 1771.5
811.9:O.1 812.0 (l782.4:0.6)°
829.8so.1 830.0 1892.7:0.4°
945.510.2 945.4 1901.5so.4 1901.3
956.1:0.3 2066.1:O.4° 2066.5
960.1:0.2 959.6 2131.1so.5C 2129.5
1009.210.1d 1009.3 2146.4:O.5° 2145.0
(1046.6:0.5)° 2198.7:O.5°
1090.1:O.4° (2313.3so.9)c
1101.1:0.5c 2451.110.7c
1110.0:0.2 2488.8:0.7C
1114.6:O.l 1114.6 2506.7:0.7°
1184.9:0.2°

 

 

aThose y-ray energies presented in parentheses are from weak transitions
believed to belong to 56CO but which could not be placed in the decay scheme.

bThe energy errors of all y rays listed are $0.5 keV.
cIdentification was based upon v-y coincidences only.

dIdentification was based upon y-ray excitation functions only.

25

Table IV. Results of two parameter v-y coincidence experiments

from 56Fe(p ,nv-y)560o.

 

 

 

Gated y ray Coincident y raysa
(keV) (REV)
158.4 269.5(4.9), 285.0(1.8),(424.7)b(0.45), 480.5

(20.), 671.3(21.), 750.1(12.), 811.9(3100.),
945.5(0.74), 956.1(1.6), 960.1(5.3), (1046.6)b
(0.97), 1090.1(2.1), 1101.1(1.1), 1110.0(1.1),
1184.9(4.7), 1254.4(2.1), 13%9.8(3.0), 1334.7
(3.3), 1387.3(6.3), (1459.1) (1.2), 1561.7

(4.0), (1641.1)b(1.1), 1760.1(2.7), 1772.1(8.O),
(1782.4) (1.3), 1901.5(10.), 2066.1(7.0), 2131.1
(4.0), 2146.4(9.4), 2198.7(7.1), (2313.3)b(0.89),
2451.1(2.7), 2488.8(1.0), 2506.7(3.1)

269.5 158.4(16.), 480.5(85.), 811.9(5100.)

285.0 158.4(13.), 671.3(2100.), 829.8(32.), 945.5(16.),
1110.0(23.)

480.5 158.4(16.), 269.5(17.), 811.9(5100.), 1184.9(16.)

576.6 432.8(11.0), 1892.7(5100.)

671.3 158.4(2100.), 285.0(51.), (945.5)C(24.)

750.1 158.4, 811.9

811.9 158.4(73 ), 269.5(23.), 480.5(2100.), 750.1(66.),

960.1(32.), (1090.1)C, 1184.9(26.), (1254.4)C,
1319.8(10.), 1334.7(13.), 1387.3(33.), (1641.1)C,

(1760.1)c
829.8 285.0
945.5 158.4(5.2), 285.0(12.), 671.3(23.), lll4.6(3100.)
956.1 & 960.1 158.4, 811.9
1110.0 8 1114.6 285.0(7.1), 945.5(7o.), 1110.0(2100.), 1114.6(84.)
1090.1 158.4, 811.9
1184.9 158.4(65.), 480.5(2100.), 811.9(67.)
1254.4 158.4, 811.9
1319.8 158.4, 811.9

1334.7 158.4, 811.9

 

26

Table IV (continued)

 

 

 

Gated y ray Coincident Y raysa
(keV) (keV)

1387.3 158.4, 811.9

1561.7 158.4

1760.1 158.4, (811.9)C

1772.1 158.4

1782.4 (158.4)°

1901.5 158.4

2066.1 158.4

2131.1 158.4

2146.4 158.4

2198.7 158.4

 

 

aNumbers in parentheses following the y-ray energies represent the y-ray relative
intensities (normalized to 100. for the most intense peak) observed in that
particular gated spectrum. It should be carefully noted that since these
numbers are highly geometry dependent (because of angular correlation effects),
they are presented solely as a crude indication of the peak intensities that
one might expect to observe in a similar experiment.

bThese y rays seem to be in coincidence with the gated y ray but could not be
placed explicitly in the excited—state decay scheme.

cThese v-ray peaks did not have sufficient statistics to warrant the claim of
a definite coincidence.

27

Table V. Y-ray energy standards used as calibrations in the determination
of 56Co Y-ray energies from 56Fe(p,nY)56Co. Those Y rays listed
for the isotope 56Fe appeared in the spectra from 56Fe(p,p'Y).

 

 

 

Calibration Calibration
energy energy

Isotope (keV) Reference Isotope (keV) Reference
758s 121.113t0.010 a 56Fe 1175.13:0.05 c
135.998:0.010 a 1238.30:0.02 c
264.651s0.015 a 1360.22i0.03 c
279.525i0.012 a 1810.44to.58 c
400.640i0.015 a 2034.9210.03 C
1138n 391.689:0.010 a 2113.81i0.15 c
1370s 661.635:0.O76 b 2273.6 i1.5 d
881 898.04 10.04 b 2523.8 10.08 c
22Na 1274.55 :0.04 b 2598.58i0.03 c
56Pe 846.79 £0.08 c 2758.7 12.1 d
1037.91 t0.03 c 2983.5 i1.6 d

 

 

aSee Ref. 36.

bSee Ref. 35.

cSee Ref. 39; these calibration energies were determined in Ref. 39, using
the decay of 56Co.

dSee Ref. 57; these calibration energies were determined in Ref. 57, using
56Fe(n,n'Y).

28

energies in one energy region (120-1300 keV). For the Y-ray energy
determinations from the y-Y coincidence data, a similar quadratic fit
was made in one energy region (800-3000 keV). In the latter, the
55Fe calibration peak centroids were determined from a spectrum gated
on the intense 846.8—keV 56Fe y—ray peak. The 56Co Y-ray energies
were then calculated by computer using the appropriate calibration
curve. The energies of six Y rays found in both the 56Ni decay and
the 56Fe(p,nY)55Co reaction, agree to within the experimental errors
(see Tables I and III). The adopted energies of these six Y rays are
listed in Section VI.

The excited-state decay scheme in Fig. 6 is consistent with the
coincidence data and the excitation function data (next section).

Dots denote observed coincidence relationships between Y-ray transitions
entering and leaving a state. The beam energies (and the correspond-
ing maximum possible 56Co excitations) at which the coincidence and
angular distribution data were taken are shown on the right. The

spin assignments for states up to and including the 1720.3-keV state,
are based on the present experiments and will be discussed in detail
later in Section IV. The spin and parity assignments to the states

at 1930.4 keV and above are those of Schneider and Daehnik15 and are
consistent with these and other experiments.

The positive parities shown in Fig. 6, up to and including that
for the 1720.3-keV state, could not be determined in the present work
and are therefore assumed. This assumption is supported, however, by
the even 2 transfers observed in the (d,o) experiment of Schneider
and Daehnik15 and in the (p,3He) experiment of Bruge and Leonard,12

and by shell-model considerations”,50 In its simplest shell-model

Figure 6.

29

The Y-ray decay scheme for excita-
tions of 57Co. The Y-ray energies
and branching ratios were measured
using 57Fe(p,rzy)56Co. The arrows
on the right indicate the maximum
possible excitations for the proton
energies of the Y-Y coincidence and
Y-ray angular distribution experi-
ments. The spins, parities, and
level energies labeled with an
asterisk are from Ref. 15, while
the remainin values were deter-
mined from 5 Fe(p,ny)56Co. Dots
denote observed coincidence rela-
tionships between Y-ray transitions
entering and leaving a state.

Ep (MeV)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

30
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DIST COINC
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2399' 2060.0
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3.12"? 1930.4 74
<—-—9 4.15.6
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1 4%»? 1720.1
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Figure 6

31

configuration, 56Co has two valence nucleons: a proton hole in the

fb/z orbit and a neutron in the p3/2 orbit. Since the three nearest
orbits available for particle excitations (p3/2, fg/z, and p1/2) have
odd parities, all states formed with the required even number of valence
nucleons will necessarily have a total even parity. The simplest shell-
model states having odd parities that can be formed, have particle
configurations [(ud3/2)'1(vp3/2)] and [(nf7/2)'l(vgg/2)]. Because of
the energy required for formation, such states would be expected at
considerably higher excitations.

Because of the high Compton continuum and the large number of
56Fe Y rays from the 56Fe(p,p'Y) reaction that occur in all singles
spectra, ground-state transitions in 5600 having no coincidences and
having energies greater than 2 MeV are difficult to identify. Thus,
although some such ground-state transitions would be expected from
states excited in the present experiments, none were positively
identified. Also, because of these same reasons, branching ratios

for those states above 1.8 MeV of excitation could not be determined.

32

B. Y-Ray Excitation Functions

 

The Y—ray excitation functions were obtained with proton beams
having energies ranging from 5.55 to 7.75 MeV. These beams were
stepped in 100 keV intervals with the Western Michigan University
Tandem Van de Graaff. The target was the same 56Fe foil used in the
coincidence studies and contributed approximately 40 keV to the energy
spread of the proton beams. The Y rays from the 56Fer,nY)56Co reaction
were detected with the 2.5%-efficient Ge(Li) detector (previously
described) at approximately 125° from the beam direction (to minimize
angular distribution effects) and at 5 cm from the target.

Dead-time and amplifier pile-up corrections, as well as run-to-
run normalizations, were made by using the digitized output from a
beam current integrator to trigger a Berkley Nucleonics Corporation
model #BHrl Tail Pulse Generator. The pulser was in turn connected
to the test input of the detector's preamplifier. The resulting
pulser peak in the Y—ray spectrum was placed so as not to interfere
with Y-ray peaks. Again, to preserve optimum resolution and sym-
metric peak shapes, an ORTEC model #450 Research Amplifier was
direct coupled to a Northern Scientific 100-MHz ADC. The y—ray spectra
were stored in 4096 channels with approximately 0.5 keV per channel
in the WMU on-line PDP-lS computer. Typical run times were 50 minutes
with counting rates of less than 6000 cts/sec.

Typical Y—ray spectra which show the appearance and growth of
the various 56Co Y rays are shown in Fig. 7. In addition to seventeen
56Co y rays previously identified from the coincidence experiments,

a 1009.2-keV ground-state transition was identified. The approximate

33

Figure 7. Typical Y—ray spectra from the
excitation function measurements.
the first appearances of the
various 56Co Y rays are labeled.

 

 

34

 

                      

 

 

 

    

 

 

 

 

5 4 2 2 3 2 3
m o .0 .0 .0 O .0 .0 w .0 .0 .0 . . .0 .0 .0 O p p m
mum? I A
88... 4
O A .¢.O_w_
C ammo _.N\IN_I\
x $313»:
I v
n7. W mess- m m m m m M w m m
m m n s m n s. s s w s 5 .m
e. .., 7. 7. .. s s s s .4. A... w
x p I I I I I I I 8 I I
E
$31 88.
6.3:
N89. m
2
E8138 one...
1- 6.63..
none. .m
88.
saw. «.8.
CI P d\ L {nL I\ p \- L \ I} p I . 1\nIL {\nIp - u
.0 .0 .0 0 0 .0 1 .0 0 .0 .0 .0 0 .0 .0 .0 0 .0 .0 .0 .0 .0 .0 .0

492410 mud 9.2300

CHANNEL NUMBER
Figure 7

35

thresholds of the 56Co y rays were completely in agreement with their
placement in the excited-state decay scheme.

The excitation functions for the first eight excited states
of 5600, measured to a maximum excitation of 2.26 MeV, are shown in
Fig. 8. For each data point the total neutron population of the
state was determined by subtracting the intensities of all the y
rays feeding the state (where appropriate) from the intensities of
all the y rays deexciting the state. Internal-conversion corrections
were neglected since they were small in comparison to other errors.
(The largest correction would be 1% for the 158.4-keV Ml transition.2)
The y-ray intensities were determined from the peak areas obtained
using SAMPO3'+ and the detector's relative efficiency curve. The
neutron papulation of each state at each beam energy was normalized
by dividing by the pulser peak area.

The most noticeable features of the excitation functions are
the large fluctuations. The maximum experimental error associated
with any given point is 12% whereas the point-to-point fluctuations
average 15% and some are as high as 100%. Since the fluctuations do
not correlate in sign and magnitude from state to state, it is unlikely
that they originate from an incorrect experimental technique. Hausman
et al.51 observed this same phenomenon in their low energy ”8Ti(p,p'y)
experiment (there, a CN excitation of 211.7 MeV was achieved). Since
their fluctuations persisted from angle to angle and were approximately
loo-keV wide, they suggested that the peaks were neither due to Ericson—
type fluctuations nor due to isolated resonances, but instead were
caused by several overlapping resonances. Since the statistical CN

excitation-function predictions agreed well, both in shape and in

Figure 8.

36

Excitation functions for the first
eight excited states of 56Co. The
units of the ordinate are arbitrary
but are proportional to the absolute
cross section. The data were taken
at 125°, a zero of P2(cose), in order
to minimize angular distribution
effects. Neutron feedings were
computed for each level from the
y-ray intensity imbalances, and
then were normalized from run to
run (as described in the text) to
obtain the relative cross sections.
The thresholds were calculated
using Q = -S.357 MeV for the

ground state (Ref. 48) and are
connected to the first non-zero
data points with dotted lines.
Solid lines connect the data

to guide the eye. Where not
visible, error bars are smaller
than the data-point symbol.

37

fl

[1111]

[11111 I

l

 

+_ >3 ONE II

+0 >mx mOO_ ..|
+0 >9. 050 I:

+m >9. 9: II

+N >3 00m II
+m >9. mm. II:

 

.'

w unawam

i>mé am

---—----
~
‘
~~~

l l

l

[1:111

l

l

11 11 l l

l

111 1 l

_-o_

 

 

NOIlOES 88083 BALLV—BH

38

absolute magnitude with their data averaged over ZOO-keV energy inter—
vals, they further concluded that an experimental energy spread of
200 keV would have resulted in good statistical averaging whereas their
actual 50-keV spread was too small.
In similar experiments with A =60 and ON excitations of 10-15
MeV, Lee at aZ-52 observed fluctuations on the order of 2-3 times the
experimental resolution. They suggested that the assumption of com—
plete randomness of the statistical CN theory may be invalid and
that some residual interactions may cause clustering of strong levels
which give rise to the gross fluctuations. No conclusions can be
drawn from the present experiment concerning the above suggestions
other than to say that similar gross fluctuations have been observed.
From level-density studies by Huizenga and Katsonos,53 the
average level spacing in 57Co (assuming similarity to 57Fe for which
empirical parameters are known) at a CN excitation of about 12 MeV
(corresponding to a beam energy of about 6 MeV) is expected to be
0.03 keV. Thus, the energy spread of 40 keV is predicted to overlap
=1300 CN states of mixed spin and parity in the present experiment.
The overlap predicted for ”9V in the experiment of Hausman et al.,51
was 21800 CN states Thus, the conclusion here is similar to that of
Hausman gt aZ-.51 namely, that since the agreement between experi-
mental and theoretical cross-section ratios and Y—ray angular distribu-
tions is so good (see below), the statistical CN theory reasonably
describes the situation even though complete statistical averaging
is not achieved.

In order to compare the excitation functions with the predictions

39

of the statistical CN theory, experimental and theoretical cross
sections for the various excited states of 56Co are plotted in Fig.

9 as ratios with respect to those for the 158.4-keV first excited state.
As is shown in Fig. 9 the theoretically predicted cross sections vary
as a function of the spin and parity of the final excited state.

This fact can be seen most easily from the following expression for

the total cross section:

)‘2
O = _8? (2.] +l)’l‘

j19j2

where A is the wavelength of the incoming proton, J1 is the spin of the
intermediate state in the compound nucleus, and T is the penetrability

term. The penetrability T is determined from the following expression:

T 1(E1)T (Ez)

1232

2TH (E)

 

where the T2 (E)'s are the various particle transmission coefficients

J
which depend upon the particle's center-of-mass energy, E, and orbital
and total angular momentum, l and j, respectively. The sum in the
denominator extends over all open channels by which the intermediate
CN state can decay.

The sum in the total cross-section expression is made over all
possible values of jl and jz, which are the total angular momentum of
the incoming protons and outgoing neutrons, respectively. Since this

sum involves the spin of the intermediate compound-nuclear state,

parity conservation and the angular momentum coupling rules require

Figure 9.

40

Experimental and theoretical cross-
section ratios. The ratios are
taken with respect to the 158.4-
keV first excited state. Error
bars identify the data (lines
connecting the data are to guide
the eye). MANDY predictions for
selected beam energies are shown
for J1T = 0+,..,6+. A J1T = 3* for
the 158.4 keV state was used as
explained in the text. Straight
lines connecting the theoretical
points approximate expected
smooth curves.

O—E/OTSS keV

41

 

 

0.8 r
<16"
<14-

(er

C18-
(16*
(14-
(12*

Oil

0.8L
0.6b

(l4

 

 

rY'I'TVVY'Tjuyv

q

(a) 577 keV -z’ ‘

-30.;

 

 

(b) 830 keV 7

 

 

 

 

 

 

(14

(12

 

 

(10

ED (MeV)

Figure 9

' I

7 I ' 1

(d) IOO9 keV

 

(e) |l|5 keV

   
 
   
 
    

V rT f r I V

 

42

a different sum over the numerical T-values for each possible final
excited-state spin and parity. Since the target has in a 0+ and since
the outgoing neutrons are mostly 2 = 0, low (high) spin final states
are reached predominantly through low (high) spin intermediate states
which are in turn reached by low (high) angular momentum protons.
At these bombarding energies (5.5 - 7.5 MeV), the incoming protons
are predominantly i=2. Thus, the cross sections are expected to be
largest for J values of 1, 2, or 3. The division of the cross section
to each final state by that to the 158.4-keV state at the same proton
energy, removes the absolute normalization and thus makes the com-
parison of the experimental and theoretical values quantitative.
The interpretation of Fig. 9 in regard to spin assignments is dis-
cussed in Section IV.

The theoretical cross sections used above and the theoretical

* *
angular distribution parameters A and A were calculated using the

2 4

statistical CN computer code MANDY written by Sheldon, Gantenbein,
and Strang.5“ MANDY requires as input the transmission coefficients
T£j(E) for all open entrance and exit channels. These coefficients
were computed with a modified version of the optical-model code
ABACUS - 11.55 For the real spin-independent pair of the nuclear
potential, the usual Wood-Saxon form was used; for the imaginary part,
the derivative of the Wood-Saxon form was used; and for the spin-
orbit part, the Thomas form was used.

The proton transmission coefficients were calculated using the
local optical-model parameters listed in Table VI. These parameters

were determined by Perey56 from elastic scattering data in the 9-22

MeV range. It was assumed that the explicit energy dependence would

43

.mm .mmm Eoum mum om> ocuoua map can mumumamumo oouuooc ones

.qn .wmm Boom mum .om> unmoxo .mumuoamuma oououa oxen

 

 

 

 

 

 

 

<0. I m . <ou I m
m\H . u . m\H .
m
m m\Hm-uvm + H .wm o H umr. ops + .m\H.m-uVo + H .ww a: H + «\Hmuuv + H o> u Auvo> u >
H a . om> N ; .mq a H
m.k sq.o mo.o mN.H mN.H OH mmN.o I o.mq acouusmz
n.n sq.o mo.o mN.H mN.H HH M\H-<N + m~m.ou~.oq mucuoum
A>mzv Ame Ame Hmv Ame H>mzv H>mzv comHusz

 

 

.>mz ca comaoac mnu mo hwumom mamaIMOIHmuaoo one ma m umumamumm one .HmH M\H<m~.a msavmu
mo oumnam wowumsu maauomwcs m on map umnu ma .Auvo> .Hmwucouoo naoaaoo one .wucoaofiummoo

dogmmwamamuu mo maoaumflsoamo mnu ca vow: mumumamuma mam Hmfiuamuoa Hovoalamuwuno man mo Show .H> manna

44

allow the use of these parameters at energies as low as 4 MeV. These
same parameters were used quite successfully by Hausman et al.51 in
their l”3T1 study.

The neutron transmission coefficients were calculated using the
local-equivalent optical model parameters of Perey and Buck57 listed
in Table VI. Again it was assumed that the explicit energy dependence
would allow the use of these parameters at energies as low as 40 keV
and as high as 1.8 MeV. These neutron and proton parameters were also
used by Sheldon.58 The depth of the real spin-orbit potential for both
neutrons and protons was taken as 7.5 MeV which is the local equivalent
to the non-local value used by Perey and Buck.

Fourteen inelastic proton channels and all known Open neutron
channels were included in each of the MANDY calculations. The spins
and energies for the proton channels are from 55Fe(n,n'y) work by
Armitage et al.59 There are many more open proton channels than were
included; however, it was felt that they could be safely ignored, as
the exit proton energies involved are well below the 5.354MeV Coulomb
barrier. These low energy protons also have much less phase space
available to them. A comparison of predicted and measured absolute
cross sections is made later in Section III-D.

Since the theoretical cross-section predictions involve the use
of estimated opticaldmodel parameters (in determining the penetrabilities),
systematic errors in these predictions are possible. The internal con-
sistency of the present experimental results and the agreement of some
of the results with previously known quantities, indicate that these
possible systematic errors are minimal. No attempt was made to vary

any of the optical-model parameters in the theoretical calculations.

45

The errors assigned to the experimental points of Figs. 8 and 9
arise from uncertainties in three different quantities: (l) the y-ray
peak areas, (2) the detector relative y—ray efficiency corrections, and
(3) the run-to-run normalizations. The y-ray peak area uncertainties
result from the inherent statistical error associated with a nuclear
decay process as well as from systematic analysis errors particularly
in the determination of background. The latter is felt to be an
often neglected but very important source of error. An estimate of
the combined error (for each peak) was made by comparison with the
y-ray angular distribution data as described in the next section.
(The y-ray spectra of both experiments were quite similar.) The
resulting estimated peak-area errors varied from 1.5 to 10% and in
all cases were larger than the statistical errors. The uncertainties
in the relative efficiency corrections were estimated to be between
3 and 52 (depending upon the y-ray energy) by comparing graphically
several possible fits to the experimental detector relative efficiency
curve. Although systematic errors could enter here, they would be
difficult to estimate. The uncertainties in the run-to-run normaliza-
tions were estimated to be between 0.5 and 1% (depending upon the
pulser-peak area). Special care was taken to arrange the geometry
to insure against any additional systematic errors associated with

beam loss or secondary electron emission.

46

C. y—Ray Angular Distributions

 

Proton beams of 5.77, 6.65, 7.03, 7.05, 7.30, and 7.40 MeV from
the MSU cyclotron were used to bombard a piece of the previously des-
cribed enriched 56Fe foil. A thin strip of foil measuring 1 mm by 10
mm was carefully positioned on the axis of rotation of a high angular
precision goniometer.60 Thus, only when the beam passed through the
axis of rotation could 56Co y rays be produced. A diagram of the
scattering chamber geometry is shown in Fig. 10.

The 2.52-efficient Ge(Li) detector was rigidly mounted on the
goniometer arm with the face of the detector 12.7 cm from the target.
The detector subtended approximately 10° of arc. A semicircle of
99.999Z pure lead with a thickness of 0.419:0.013 mm was placed 5 cm
from the target. Since this thickness of lead was capable of stapping
lZ-MeV protons, angular distributions all the way to 0° could be taken
for all bombarding energies. Also, y rays from reactions with the
lead, although present, were minimal since the beam energies used
were considerably below the 11.85-MeV Coulomb barrier for lead. As
a precaution, all of the beam line near the detector was carefully
lined with clean lead to eliminate any y rays from beam-induced re—
actions with the aluminum beam pipe.

An electronic set-up similar to that used to take the excitation-
function data was used to compensate for pile—up and dead-time
effects caused by changing y-ray counting rates due to beam current
fluctuations and an increase of y—ray and x-ray intensities from the
lead beam stop as 0° was approached. Here the pulse generator was

triggered by elastically scattered proton counts provided by a properly

Figure 10.

47

Geometry for the in-beam y-ray
angular distribution measurements.
The monitor and target angles were
held fixed throughout all of the
measurement.

48

oH uuamHm

.5898 865 2202.8 Sada
cotton 88.3 _m :3va «EN

, w .

\

I

/\ , 3853

. OR. 859. .5586

_ an. 3:8 :9;

a 66.0.0 « N00
8665

 

mac-a .693

 

 

49

collimated silicon surface-barrier detector held rigidly in place
at -45° with respect to the beam direction. Since the total number
of protons scattered into a given solid angle is directly proportional
to the total integrated beam current that has passed through the
target, correct normalization for the distributions taken at 5.77,
6.65, 7.05, and 7.40 MeV was then provided by simply dividing y—ray
peak areas by the pulser peak area. Once isotropy of the 480.5-keV
y-ray transition was well established in the 7.05- and 7.40-MeV angular
distributions, this transition was used as an internal normalization
for the angular distributions taken at 7.03 and 7.30 MeV (the tail
pulse generator was not available).

The data were stored in 4096 channels with approximately 0.5
keV per channel through a Northern Scientific 50-MHz ADC interfaced
to the MSU cyclotron's XDS 2-7 computer.33 The spectra (at the ap-
propriate beam energies) are very similar to those presented in
Fig. 7. Typically, spectra were accumulated for one hour between
changes of angle and usually angular distributions contained 20 points
in 10° intervals taken in random order over the angular range of 0°
to 90°. Duplication of most points increased confidence in the data.

The spectra were analyzed off—line using the computer code SAMPO3“
which allowed y-ray peaks of interest to be stripped from adjacent
background peaks. After normalization of y-ray peak areas, least
squares fits to the experimental y-ray angular distributions using the

computer code GADFIT61 were made to the equation:

k i:

W(6) = A0[l + A2 P2(cose) + AA P4 (cose)].

* *
The parameters extracted from the fit are A0, A2, and A4 where A0 is

50

the intensity integrated over all solid angles. By correcting these
integrated intensities for the relative detector efficiency and absorp-
tion in the lead semicircle, branching ratios having all angular
dependence removed were obtained. These branching ratios agree well
with those obtained from the excitation function data. The branching
ratios presented in Fig. 6 and listed in Table IX are averages of the
two experiments. The effects on the angular distribution of the non—
zero solid angular acceptance of the detector were found to be negligible.
The y-ray angular distributions taken at beam energies of 5.77, 6.65,
7.05, and 7.30 MeV and selected y-ray angular distributions taken at
7.40 MeV are shown in Fig. 11, while the measured A: and A: values for
all beam energies are listed in Table VII.

For each angular distribution measured, theoretical A: and A:
coefficients as functions of the mixing ratio, 6, were generated from
MANDY for a particular final spin, and an assortment of initial spins.
An example of these 6-ellipses is shown in Fig. 12. The functional
form of W(6) using these predicted values of A; and A: (as a function
of 6) was then compared with the experimental data to determine the
chi-square (x2) per degree of freedom (reduced x2) for the fit. For
reduced X2 to be meaningful, however, "accurate" uncertainties must be
assigned to the data. Since two points were taken at each angle it was
found that the purely statistical uncertainties rarely caused over-
lapping error bars. This fact would indicate that these uncertainties
were underestimating the true uncertainties. For the y—ray angular
distribution measurements, the major uncertainties are in the y—ray

peak areas and the angle-to-angle normalizations (pulser peak areas).

As indicated in the previous section, systematic errors (primarily in

51

Figure 11. Angular distributions of 56Co
y rays taken at - 5.77, 6.65,
7.05, 7.30, and 7.40 MeV. The
solid lines through the data
represent least squares fits
using the equation for W(6)
given in the text. W(6) has
been normalized to l at 90°.
Except for the = 7.40 MeV
case, two experimental points
were taken at each angle;
only their weighted average
is presented.

RELATIVE GAMMA -RAY INTENSITY W(9)

 

 

1.2 E9 . 5.77 Mg

1.0— '

.—

I
08f E, -158.4 keV

Ihhd—i—hhfl-h
1.2 lEp - 6.65 MeVl

 

1.

II Er ' 158.4 keV

0.9
i i

0.7 Er ‘ 285.0 REV
1.0 E, - 576.6 keV

0.8

L3

E, - 67L3 kevL

=.8||9 keV

 

 

08 E, - 1009.2 keV

1 L L 1 .1. L A 1

0° 30°60" 90°

 

52

 

 

1.2— Ep = 6.65 MeV
r CONT'D

'0 “W

:-

 

 

 

 

 

08» E7 = 1114.6 keV
{W
[.2 lEp ‘ 7.65 MeVI
I
L! '
Ey ' “58.4 keV
H
0.9
E = 28 k V
0.7 7 5'0 '3
|.| E7 ' 480.5 keV
0.9

1.1 E, - 576.6 keV

0.. M“

0.7

1.2

L

\L
"O E, - 671.3 keV +7

, . 811.9 keV

 

 

 

 

 

l2 Ep ‘ 7.85 MeV
E‘I CiO'NTD I

_ 1
08 E, = 1009.2 keV

,—

 

LO wJHf-kfi

0.8

1 1 1 A 1 1 1 1‘

[Sp - 7.30 1E
9

+1+~4~1
Er ' “58.4 keV

 

  
    

Er ' 269.5 keV

285.0 keV

1.2 ~L Er = 671.3 keV

 

 

 

2.| E m

1.9» Ey " 829.8 keV I0» “#714
_ (>-

"7. 1.26

'5“ E, - 750.1 keV
I.—

ll': \ 0.8"

0.9- J L
1 11-4. ,Llnlltlill
0° 30° 60° 90° 0° 30° 60° 90°

ANGLE 0

Figure 11

 

 

CONT'D

LOW
08» E, . 8|I.9 keV
I.

p ‘ 7.30 MeV]

 

 

E,’ - 829.8 keV

 

1.1 Er ' 009.2 keV

1.1 ~ E, - lll4.6 keV

09°

h

0.7-

J l A 1 A l L 1

 

 

1.3 Ep - 7.40 MeV

1.1 E, - 269.5 keV
I
0.9

1.21-
E, - 480.5 keV

LO EWIW

 

 

53

*
Table VII. Experimental y-ray angular distribution fitting parameters A2
*
and A4 and the associated y-ray multipole mixing ratio, 6. The

fitting parameters and mixing ratio are defined in the text.

* *
The errors assigned to both the A2 and A4 coefficients represent

plus or minus one standard deviation.

The ranges of 6 were

determined from these coefficients as described in the text.

 

 

 

E E
p Y * *
(MeV) (keV) A2 A4 6
5.77 158.4 -0.11010.018 —0.008¢0.020 —0.034:6:-0.006
6.65 158.4 -0.059:0.015 0.01910.019 -0.048<6<-0.010a
285.0 -0.19010.076 0.027:0.092 -0.020282 0.088
576.6 -0.191¢0.042 0.037:0.053 0.022282 0.0728
671.3 0.146:0.060 -0.038i0.067 0.221282 0.3048
811.9 -0.121¢0.010 0.00110.012 0.015283 0.035
829.8 0.673:0.353 0.005:0.432 -0.092282 1.1458
1009.2 —0.002:0.346 0.035:0.410 -0.024282 0.361
1114.6 -0.038:0.025 -0.006:0.030 -0.093§8§-0.056
7.03 158.4 -0.013:0.009 0.01110.009 b
285.0 —0.12210.038 0.02910.047 -0.028<6< 0.039
576.6 -O.178:0.016 0.02310.023 0.041282 0.061a
671.3 0.141:0.023 -0.020¢0.033 0.253282 0.2908
811.9 —0.066:0.010 0.003:0.012 ""
—0.085:0.013C 0.004:0.015c 0.005<6< 0.040c
829.8 0.517:0.055 -0.086:0.068 “d‘
1009.2 —0.08010.072 -0.006:0.089 0.070<6< 0.154
1114.6 -0.014:0.028 0.000:0.034 -o.116§8§-0.064
7.05 158.4 -0.024:o.012 0.012:0.018 b
285.0 —0.12710.075 0.01510.100 -0.047<5< 0.084
-480.5 0.00210.027 0.02010.034 850:09
576.6 -0.158:0.021 0.00910.029 0.050<6< 0.0768
671.3 0.128:0.026 -0.014¢0.031 0.241282 0.282a
811.9 -0.073:0.009 -0.001:0.011 ""
-0.09010.011c -0.001¢0.013c 0.014<5< 0.044c
829.8 0.475:0.043 0.038:0.061 0.337?6?'0.467a
1009.2 -0.082:0.069 0.008:0.088 0.071282‘0.151
1114.6 -0.0l7:0.028 0.009¢0.035 —0.11328§}0.061
7.30 158.4 -0.01510.015 0.002:0.018 b
269.5 -0.296:0.023 0.030:0.031 8=0.0e
285.0 -0.13410.055 -0.025:0.076 -0.022<6< 0.088
576.6 -0.169:0.024 -0.008:0.032 0.0402152’0070a
671.3 0.074:0.030 0.014:0.038 01983530245a

 

 

‘ ~

.n!

.n.

54

Table VII (continued)

 

 

 

E E
p 7 * ,
(MeV) (keV) A2 A4 0
7.30 750.1 -o.053:0.043 0.033:0.055 -22.7 56572.91f or
-0.0415§:_0.251
811.9 -0.060:0.008 0.00010.011 b
829.8 0.453:0.071 -0.086i0.091 0.1425§5_0.715a
1009.2 -0.061:0.106 -0.017:o.144 0.059§§§_0.186
1114.6 -0.027:0.026 0.008:0.034 *0-10259570-047
1561.7 0.082:0.742 -0.070:1.074 g
7.40 158.4 -0.028:0.009 0.016i0.009 b
269.5 -0.018:0.025 0.006t0.029 8=0.0e
285.0 -0.066:0.142 -0.006:0.163 -0.186:§§_0.107
480.5 -0.002:0.006 -0.001:0.007 6=0.0e
576.6 -0.169:0.017 0.01410.021 0.044565_0.065
671.3 0.087t0.021 -0.016:0.025 0.215§§§_0.2483
750.1 -0.006:0.034 0.007:0.040 -4.30 56571.95h or,
—O.187:§§_0.062h
811.9 -0.038:0.010 0.001:0.011 b
829.8 0.504:0.064 -0.011:0.075 d
1009.2 -0.09010.078 0.012i0.096 0-059:§:.0-151
1114.6 -0.014:0.037 0.012:0.043 -0.1275§570.049
1561.7 0.020:0.724 -0.104to.806 g

 

 

8The weak y-ray feedings from higher lying states have been ignored in determining
these mixing ratios.

bThe y-ray feedings from higher lying states for these cases could not be ignored,
hence, no value for the mixing ratio could be determined.

cThe y-ray feeding from the higher lying 0+ state at 1450.8 keV*has be n taken
into account in these cases, hence, the corrected values for A2 and A4 and the
corresponding range of the mixing ratio.
* *
dThe 4+ 6-ellipse lies outside the ranges of A2 and A4 for these cases.

eSee the text for discussion of the pure multipole order.
fThis value is unlikely; see text for explanation.

* *
gThe errors on A2 and A4 for these cases are too large to allow a determination
of the mixing ratio.

hThe y-ray angular distribution for this case has anomalously become isotropic
for possible reasons discussed in the text. The possible ranges of 5 given
may therefore not be valid.

Figure 12.

55

Representative plot of MANDY
predictions for the A3 and AZ
coefficients as a function of
y-ray mixing ratio, 6. (Defini-
tions are presented in the text.)
This plot is for the case of the
158.4-keV Y ray at =5.77 MeV.

A spin of 4 for the inal state
was assumed; the spins and parities
of the initial state label their
appropriate G-ellipses. Repre-
sentative values of 6 are also
labeled. The experimental A;

and AZ coefficients including
uncertainties are shown as a
rectangle in approximately

the center of the plot.

56

 

LG

I

0.8

.0
A
I

I
p
N

I

- 0.8

I

I

-|.0

 

-|.2

I I j I I I

   

Ep = 5.77 MeV
EE)r==IESE314-l(€9/

 

 

 

l

 

 

- 0.8

- 0.6 - 0.4 - 0.2 0.0 0.2 0.4

Figure 12

57

the background determination) are very important in the case of the
y-ray peak areas. Since it was felt that these systematic errors could
not be "accurately" estimated a priori, the following approach was
taken.

The uncertainties for each of the data points were adjusted
during the determination of the experimental A: and A: coefficients to
make the reduced X2 for the best fit to be approximately one. This
condition yields accurate uncertainties provided the form of the
fitting function W(e) is correct. Since direct interaction effects
are expected to be small at the beam energies used, the even-order
Legendre polynomial series used is probably valid. The uncertainties
determined in this manner varied from 1.5 to 102. In all cases these
uncertainties were larger than the combined statistical errors of the
y-ray peak areas and the pulser peak areas.

The values of reduced X2 were determined from the theoretical

* *
A and A4 coefficients, the experimental y-ray angular distribution,

2
and the data uncertainties determined as described above, and were
plotted against arctan 6. Some representative plots are shown in
Fig.1l3. (Again, the remaining plots can be found in Ref. 49.) All
relevant spin and parity values have been included in the plots, al-
though in each caseseveral of them can be eliminated on the basis
of cross-section ratios as discussed in the next section. The ordinate
is labeled "relative x2" instead of "reduced x2" because of the manner
in which the uncertainties were determined. It should be noted that
a pronounced minimum in relative X2 will only be approximately one

if the theoretical 6-ellipse passes through the experimental range of

* *
the A2 and A4 coefficients. It should also be noted that the 0.1%

Figure 13.

58

Representative relative X2
versus arctan 6 plots for
angular distributions of
each of the 56Co y rays.

JTr values for the initial
states label each curve.
The J value assumed for

the final state was that
previously assigned in this
work.

59

 

 

 

E, . 158.4 keV Ey - 671.3 keV E, = 829.8 110v
Ep - 577 Mev '03 E9 . 7.05 am 3 Ep . 7.30 MeV

'03 A \
.02 '11 ». .0.
' J34. ”Q" " V,

‘5)

it

Er ' 285.0 E“

18'

E: . 3 ‘. '° ‘ l1: ”\fi wig/é‘W/f/‘s
‘1 “8° 53...... " 1 3"“,

'00 2'I‘ o‘\3°
'02 f . an '
I
WT)!" .
E 4‘ o: o 0
10° 5 3 2
s . km!
Ep' 6.65 MeV

6.65 MeV

Q.
8
25

\ , - 7 .1 110v 3
“ E9 = 7.30 MeV E, . 1009.2 110v

 

RELATIVE x2
5 01 "‘

«hm

 

 

 

lllll 7 l l l L l
“90"60' ‘30“ 0° 30° 60‘ 90' “90"60' ”30° 0° 30’ 60° 90° ~90'-60'-30’ 0° 30' 60' 90°

 

 

ARCTAN 8

Figure 13

60

confidence limit here is at reduced x2 = 2.27, provided that the
assigned uncertainties are "accurate". Finally the uncertainties of
the A: and A: coefficients were almost independent of the errors
assigned to the individual data points and were therefore essentially
determined by the data-point scatter about the fit. Because the
angular distributions usually included 20 points, these uncertainties
can be assumed to be approximately one standard deviation errors.

The measured mixing ratios are presented in Table VII. The ranges
were determined from the one standard deviation errors in the A* and A*

2 4

coefficients. (In virtually every case, the appropriate 6-ellipse

* *
2 and A4 range to allow

the quoted range of mixing ratio to reflect the experimental error.)

passed through a sufficient portion of the A

When more than one measurement of 6 exists, an average of the several
values was made. More weight was given to those cases with smaller

* *
errors in the A2 and A4 coefficients. The final averaged values

suggested for the mixing ratios of the various 5600 y rays measured

in the present work are given in Table IX.

61

D. Total Absolute Cross Sections at EP = 7.30 MeV

 

A 7.30-MeV proton beam from the MSU cyclotron was used to bom-
bard the 56Fe foil which was placed at 55° with respect to the beam
direction. The 2.5%-efficient Ge(Li) detector was positioned with
its face 12.7 cm from the center of the target and at 90° to the beam.
Dead-time and amplifier pile-up corrections were made as described
for the excitation function measurements. The charge was collected
in a shielded ZOO-cm long, 8.3-cm diameter piece of lead-lined alumin—
um beam pipe and integrated. The 0.90:0.09 mg/cm2 target thickness
was determined by measuring the energy loss of 5.48-MeV alpha particles
from an 2"’lAm source. The target was placed 15 cm in front of the
Faraday cup described above. Since the root-mean—square angle for
beam scattering from the target is approximately 1°, all of the charge
should have entered the charge-collecting section of the beam pipe.
The absolute normalization of the counting efficiency curve was
determined for the geometry used by counting S7Co, 137Cs, 51*Mn, and
60Co intensity standards. The precision quoted for the standards
was 152.52 Care was taken to place the standards as closely as
possible to the position of the beam spot on target. Corrections
for y—ray angular distribution effects were included in the analyses,
but corrections for internal conversion and target self-absorption were
neglected since these were expected to be small in comparison to
experimental errors.

Major experimental uncertainties lie in the target thickness
(estimated uncertain by 110%, including non-uniformities), the inte—

grated charge (estimated at 15%), the absolute normalization for the

62

efficiency curve (approximately 110%, including uncertainty in source
positioning), and the y-ray peak areas (:2 to 17%). The total error
associated with the measurement is then approximately 115%.

The neutron feeding to each state was determined from the
absolute y-ray intensities as described in the excitation function work.
The Qp,n) cross sections were finally calculated using these neutron
feedings. The results are listed in Table VIII. Included in the table
are the total absolute cross-section predictions of MANDY for Ep = 7.30
MeV as well as a comparison of the relative cross sections normalized
to that of the 158.4-keV first excited state. The theoretical total
cross sections listed are for the J1r values suggested by this work.
Because of the fluctuations in the excitation functions, the total
cross sections measured here are expected to deviate randomly from the
theoretically predicted values. However, except for the cross section
to the 1450.8-keV state, which appears to have a maximum in this energy
region (see Fig. 8), the measured total cross sections are on the
average 30% below the theoretically predicted values. Accurate
quantitative comparison cannot be made between these measurements
and the excitation function data because the experiments were per-
formed with different accelerators, and the beam energy of the MSU
cyclotron has not been calibrated precisely at these low energies.

The nominal beam energies of the two accelerators are expected to be
within a few kilovolts, however.

Four possible explanations can be suggested for the 30% dis-
crepancy. First, an unknown systematic error could have caused the
experiment to yield incorrect results. Second, the transmission co-

efficients used in the MANDY calculations, although good enough to

63

.q.me

D\b fl HOMO
n

xuoB was» %A vmummwwSm eh mo mmoam> mmonu you vmusmmmum haco mum mcoauomm mmouo HmuOu Hmowumuomcam

 

 

 

+H ma~.o m.na nn~.o o.~ao.¢a m.o-H
+o HmH~.o n.5H qu.o m.mam.m~ m.om¢H
+m ooq.o H.wm H58.o m.mwm.m~ c.8HHH
+m woa.o m.w NNH.o a.oa~.o ~.¢ooa
+~ qam.o 8.60 mmm.o n.68m.o¢ m.onm
+8 qu.o H.m~ oom.o o.~Hm.mH n.m~w
+m nna.o 8.8H mna.o ~.me.m c.0nm
+m ooo.Hm m.Hm ooo.Hm w.nwm.om <.me
.. a... 9...”. .1... A”... fin...
mamofiuouoona Hmuooafiumaxm noquuHoxm

 

 

a

.>0z om.n n m up macauomm mmouo HmuOu OUmmA:.mvommm .HHH> manna

64

yield reasonable y-ray angular distribution and relative cross-section
predictions, could yield inaccurate absolute cross sections. Third,
the calculations included all open neutron exit channels but were
restricted to 14 proton exit channels. The open proton channels

used corresponded to a maximum excitation in 56Fe of about 4 MeV.

With 7.28 MeV of incident proton energy, an excitation of about 7.15
MeV is expected. Thus, a multitude of open proton channels in this
additional 3-MeV excitation range were not taken into account. Although
inclusion of these additional channels would reduce the predicted

cross sections, the effect could not be large since, as mentioned
earlier, the limited phase space available to such low energy particles
and the 5.39-MeV Coulomb barrier both act to reduce the transmission
coefficients considerably. The absolute cross-section predictions
presented in Table VIII, using 14 open proton exit channels, were on
the average 7% smaller than the results of a similar calculation using
8 open proton exit channels. Finally, the Moldauer level-width fluc-
tuation correction63 was not included in this calculation. This
correction would reduce slightly the magnitude of the total absolute
cross sections but would have a pronounced effect only at much lower

bombarding energies.

IV. DISCUSSION OF INDIVIDUAL LEVELS

Excluding the ground and first excited states, the spin assign-
ments resulting from the present work are based upon cross-section
ratios taken with respect to that of the 158.4-keV first excited state,
upon y-ray angular distributions, and where necessary, upon previous
internal-conversion electron and lifetime measurements. Spins elimin-
ated by the comparisons of the cross-section ratios to the theoretical
predictions of MANDY are not to be considered as choices in the analyses
of the y-ray angular distributions. Other J1t values have been included
in the relative X2 plots in Fig. 13 to emphasize the difficulty of
making J1T assignments to states of 56Co solely on the basis of y-ray
angular distributions. Throughout the following discussions it is
assumed that only even parity states exist below 1.8 MeV of excita-
tion in 5500.

A. Ground StateLJ1r = 4+

 

The ground-state spin is not directly measured in this experi-
ment but is important since it in part determines the A: and A: co-
efficients for the y-ray angular distributions of the five ground-
state transitions. Fortunately, the ground-state J1r has been pre-
viously determined to be 4+ by such diverse methods as y-y angular
correlation}:3 hyperfine structure in paramagnetic resonance,5°
several different particle-transfer and charge-exchange reactions
(references listed earlier), and inference from the log,ft data for its
decay to states in 56Fe.65 It should be noted that consistencies in

the present work support this assignment.

65

66

B. Ex = 158.4 keV, 3+

 

The plot in Fig. 13 for the ground-state transition from this
state shows pronounced minima in relative x2 for the J"T possibilities

+, 3+ and 5+. A less pronounced minimum is exhibited for

of 1+, 2
JTr = 4+ suggesting this choice is less likely. A careful study of

Fig. 12 shows that J1r - 6+ can be eliminated. Since the angular
distribution of the 158.4-keV y ray is not isotropic (see Fig. 11 and
Table VII), J1r =0+ can also be eliminated.

Previous internal-conversion electron measurements by Menti,66
Jenkins and Meyerhof,2 and Ohnuma et aZ.,3 as well as lifetime measure-
ments by Wells at al.,1 have shown that the 158.4-keV transition is
predominately M1 in character. This fact rules out the JTr a 1+ pos-
sibility since either a 45% M3 + 55% E4 or 3% M3 + 97% E4 transition
is required to be consistent with the two minima observed for J1r a 1+
in relative x2. Similarly, the JTr = 2+ possibility is ruled out
since a 93.2% E21+ 6.8% M3 or 7.6% E2 + 92.4% M3 transition is required.

The J1r a 4+ and 5+ possibilities can be eliminated by comparing
the changes in the theoretically predicted cross section as‘a function
of beam energy with the measured excitation function for this state.
(See Fig. 8.) The experimental cross section changes at most by a
factor of 2 from a beam energy of 5.77 to 7.30 MeV, while the change
predicted by MANDY is a factor of 7.4 for J1T = 4+ and 6.0 for JTr = 5+.
The change predicted for JW 8 3+ is 1.4.

Thus, J1r = 3+ is the only value consistent with the known M1

character of the 158.4-keV y ray and with the results of the present

experiment. From its angular distribution, an M1 transition with a

67

0.01 to 0.09% E2 admixture is indicated for the 158.4-keV y ray. A
mixing ratio -0.04 < 6 < -0.06 (see Tables VII and IX) is in excellent
agreement with the value —0.045 < 6 < 0.014 measured by Ohnuma et al.3
and the value -0.33 < 6 < 0.00 measured by Wells at al. ,1 both using
y—y angular correlations in the decay of 56Ni.

The 158.4-keV y-ray angular distribution reported by Menti66
using the (p,ny) reaction is in complete disagreement with the present

* *
experiment. Menti's measurement of A - 0.258:0.027 and A - -0.lZSi

2 4
*
0.028 at Ep - 5.8 MeV is not consistent with our values of A2 a
*
-0.110:0.018 and A4 - -0.008:0.020 at Ep 8 5.77 MeV. This was the

only 56Co y-ray angular distribution reported by Menti. The internal
consistency of our data and their agreement with other types of experi-

ments suggests that the coefficients reported by Menti are in error.

0. Ex . 576.6 keV, 5+

 

The cross-section ratio plot in Fig. 9, shows an unambiguous
choice of J1r a 5+ for this state. A pronounced minimum in relative
X2 is observed for J1r - 5+ in the plot of Fig. 13 for the ground-
state transition from this state. An Ml transition with 0.04 to 0.49%

E2 admixture is indicated for this y ray.

D. Ex = 829.7 keV, 4+

 

The cross-section ratio plot in Fig. 9, shows an unambiguous
choice of JW - 4+ for this state. Both y-ray branches from this state

have analyzable angular distributions. It should be noted that for

68

all of the y-ray angular distribution measurements in which the 829.7-
keV state was excited, it was also fed from above by a weak 285.0-
keV y-ray transition. The feeding intensity was never more than 17%
of the total intensity from the 829.7-keV state and was found to cause
changes in the A: and A: coefficients that were much less than the
quoted errors. The feeding was therefore ignored in the following
analysis.

The angular distribution of the 671.3-keV y ray yields a
pronounced minimum in relative X2 for JTr - 4+ in the plot of Fig.
13. A predominantly Ml transition with 4.6 to 7.8% E2 admixture is

indicated for this y ray.

The 829.8-keV y-ray angular distribution shows somewhat anomalous

*
2

large and positive. Only large error bars in three cases allow inter-

behavior. The experimental A for every beam energy is consistently
section with the 4+ 6-ellipse. (The 6-ellipses for this case are very
similar to those of Fig. 12.) The 6-ellipse is approached more closely
as the beam energy increases, however. A possible explanation is that
since the peak is very weak, systematic errors are allowed to enter
during the critical background subtraction process. The background
exhibits a large anisotropy with A: = 0.26:0.01 and A: - -0.07i0.01

in this region of the y-ray energy spectrum. A diffuse minimum is
observed in relative X2 for JTr = 4+ in the plot of Fig. 13. A pre—

dominantly Ml transition with 1.2 to 37% E2 admixture is possible

for this y ray.

69

E. Ex a 970.3 keV, 2+

 

The choice of JTr from the cross-section ratio plot in Fig. 9
for this state is ambiguous since the points scatter equally as well
about the 1+, 2+ and, less likely, 3+ theoretical lines. A y-ray
transition of 811.9 keV to the 3+ first excited state is the only
y ray observed to deexcite this state. The depths of the minima in
relative X2 in the plot of Fig. 13 for the angular distribution of
this y ray, eliminate the J" = 3+ possibility but leave both the 1+
and 2+ choices. Internal-conversion electron measurements by Ohnuma
et aZ.3 have shown that the 811.9-keV y ray is predominately Ml. This
fact rules out the J1r = l+ possibility since either an 65% E2 + 35% M3
or 0.5% E2 + 99.5% M3 transition is required.

Thus, J1T - 2+ is the only value consistent with the known Ml
character of the 811.9-keV y ray and with the results of the present
experiment. Two pronounced minima in relative X2 are observed for
J" - 2 . One minimum requires a 1.7% Ml + 98.3% E2 transition. Since
this multipole mixing is inconsistent with the M1 character of this
y-ray, it can be discarded. The other minimum requires an M1 transition
with 0.02 to 0.12% E2 admixture. A mixing ratio 0.015 < 6 < 0.035
(see Tables VII and IX) is in excellent agreement with the value
-0.025 < 6 < 0.12 measured by Ohnuma et aZ.3 using y-y angular correla-

tions in the decay of 56Ni.

F. Ex = 1009.2 keV, 5+

 

The cross-section ratio plot in Fig. 9 shows an unambiguous

70

choice of J1T = 5+ for this state. Although two y-ray branches are
observed for this state, only the 1009.2-keV ground-state transition
is strong enough to allow an angular distribution analysis. A pro-
nounced minimum in relative X2 in the plot of Fig. 13, is observed for
the 5+ choice. An Ml transition with a 0.49 to 2.5% E2 admixture is

indicated for the 1009.2-keV y ray.

0. Ex = 1114.6 keV, 3+

 

The cross-section ratios for this state (Fig. 9) are scattered
about the J1T = 3+ theoretical line with other possible, but less
likely, choices being 0+ or 1+. Three y-ray branches are observed
for this state with two, the 285.0— and 1114.6-keV y rays, having
analyzable angular distributions. The asymmetric 285.0-keV y-ray

angular distributions shown in Fig. 11 rule out J1r = 0+. The J1T = l

+
possibility cannot be ruled out on the basis of the y—ray angular distri-
butions, however, since pronounced minima in relative x2 in the plots
of Fig. 13, are observed for J1T = 1+ for both y rays.

This level does not deexcite as would be expected for a 1+
state. The lowest multipole order possible for the y—ray branches to
the two 4+ states fed would be M3. Assuming the B(M3)'s of these
transitions to be comparable in magnitude, the energy dependence of
the transition probability alone would require the 1114.6-keV transi-
tion to be 10“ times as intense as the 285.0-keV transition. The
measured value is only 8.5. Also, the 956.1-keV y-ray branch to the

first excited 3+ state would be an E2 transition. The lifetime against

such an E2 decay is 107 (Weisskopf estimate) times smaller than that

71

for an M3 decay. The fact that this branch is so weak (5% of the
decays) would be inexplicable without a remarkable accidental cancella-
tion of matrix elements.

Finally, a J1r = l+ assignment would open up the possibility of
feeding from the decay of 56Ni, the possibility of y-ray feeding from
both the higher lying 0+ and 1+ states at 1450.8 keV and 1720.3 keV,
respectively, and the possibility of y-ray decay to the lower lying 2+
state at 970.3 keV. None of these phenomena are observed. A J1r = l+
assignment is therefore highly unlikely and only J1r = 3+ remains.

Pronounced minima in relative x2 in the plot of Fig. 13 for
J" = 3+ are observed for both the 285.0— and 1114.6-keV y rays. An
M1 transition with a 0.04 to 0.64% E2 admixture is indicated for the

285.0-keV y ray, and an M1 transition with a 0.01 to 0.25% E2 admixture

is indicated for the 1114.6-keV y ray.

H. Ex = 1450.8 keV, 0+

 

The cross—section ratios for this state (Fig. 9) are scattered
about the J1r = 0+ theoretical line with other choices of 3+or 4+
seemingly possible. A y-ray transition of 480.5 keV to the 2+ fourth
excited state at 970.3 keV is the only y ray observed to deexcite this
state. The angular distribution for this 480.5-keV y ray is isotropic
(see Fig. 11). The isotropy is a necessary (although insufficient) con—
dition for a spin zero assignment. A pronounced minimum in relative
X2 in the plot of Fig. 13 is not observed for J“ = 4+ and clearly
eliminates this possibility. However, a pronounced minimum is ob-

+
served for J1t = 3 . Conversion-electron measurements by Jenkins and

72

Meyerhof,2 and by Ohnuma et aZ.,3 as well as lifetime measurements

by Wells et aZ.,1 have shown that this transition is largely E2. The
necessary mixing ratio for the JTr = 3+ possibility, however, is

0.16 < 6 < 0.20, giving at most a 96.2% Ml + 3.8% E2 transition.

A J1r a 0+ assignment on the other hand requires the 480.5-keV y-ray

w - 0+ is the only value consistent

transition to be pure E2. Thus, J
with the known E2 character of the 480.5-keV y ray and with the results
of the present experiment.

Because of the abnormally long half life of this state (l.6iO.l
nsec),1 a supplementary experiment was performed to investigate pos-
sible nuclear hyperfine interaction effects caused by the expected
large internal magnetic field (2333 koe)67 in the vicinity of the
target nuclei in the 56Fe target. A proton beam of 7.52 MeV was used
to bombard a 0.02 mg/cm2 stainless steel target. In this stainless
steel target the magnetic field in the vicinity of the nuclei is minimal,
thus, angular distribution "wash-out" due to precession of the magnetic
moment should be greatly reduced. Partial angular distributions (10
data points) clearly showed an isotropic distribution for the 480.5-
keV y ray (A: - 0.01:0.02 and A: = 0.00:0.03). Other S6Co y-rays
preserved their previous behavior observed in the 56Fe foil target
2 - -0.30:0.1o and A:

As discussed earlier, JTr assignments of l- and 2t have been

(e.g. the 269.5-keV transition had A = 0.01:0.13).
suggested for this state. These suggestions are incompatible with

the measured cross-section ratios. The odd parity possibilities,

which are not shown on the plot of Fig. 9, require, for example, cross-
section ratios of 0.543 for JTr = l- and 0.573 for JTr - 2- at Ep = 7.68

.1.
MeV. These values are very close to the J1T = 1+ and 2 theoretical

73

points and are about 2.5 times the average of the two closest measured
ratios, 0.198. The J1T = 0+ assignment suggested in this work was
essentially eliminated in the y-y angular correlation analyses by
Wells et aZ.1 and Ohnuma et al. 3(using the decay of 56Ni) on the
basis of their error assignments to the angular correlation coeffi-
cients. An increase to two standard deviations in their reported
errors would have resulted in compatibility with the J1r = O+ assign—
ment.6

The additional suggestion that two states exist in this region
of excitation with J1r - 0+ and l- is also incompatible with the present
work. From the y-ray singles and y-y coincidences measured using the
56Ni decay, no evidence could be found for y rays deexciting a second
state near 1451 keV. The full width at half maximum (FWHM) for both
the 269.5- and 480.5-keV y-ray peaks (exciting and deexciting the
1450.8—keV state, respectively) as determined by SAMPO,3° were pre-
dicted to within 0.9 and 0.4%, respectively, using a least squares
linear fit to the FWHM values and energies of the seven other most
prominent 1~ray peaks (other than the 511.0-keV annihilation radiation
peak) in the spectrum of Fig. 1. Assuming doublet members with ap-
proximately the same intensity, an increase in the FWHM value of 5%
corresponds to a centroid difference of only 0.02 keV. Similarly,
from y-ray singles and y-y coincidences measured using the 56Fe(p,ny)—
56Co reaction, no evidence could be found for y rays deexciting an
additional state in this region. Here, as opposed to the B decay, all
existing states are expected to be excited. Since the additional state
is suggested to have J1T = l-, a large predicted cross section should

produce a reasonably large y-ray peak or peaks. As before, the FWHM

74

for both the 269.5- and 480.5-keV peaks (from a randomly chosen excita—
tion function spectrum) were predicted within 3.2 and 2.2%, respectively.
If the 1450.8-keV state were really a very close-lying doublet with
both members deexciting via a 480.5-keV y ray, the cross-section
ratios should be =3.5 times the measured values. In view of the
internal consistency of the present data, this value is a much larger
inconsistency than would be expected.

Finally, the energies of the 269.5- and 480.5-keV y rays were
measured independently to be the same within the experimental errors
of 10.1 keV using both the 56Ni decay and 56Fe(p,ny)56Co. Thus, it is
concluded that there is strong evidence that only one state exists
in 56Co in the region of 1451 keV of excitation, namely, at 1450.8

keV and the state has J1T = 0+.

I. Ex = 1720.3 keV, 1+

 

The cross-section ratios for this state show a scatter of points
about the J1r = 1+ and 2+ theoretical lines and in close proximity to
the 0+ and 3+ lines. Three y-ray branches are observed for this state
with two, the 269.5- and 750.1-keV y rays, having analyzable angular
distributions. The J = 0 possibility is eliminated by the anisotropic
distributions of both y rays (see Fig. 11). The relative x2 plot for
the 750.1-keV y ray sheds little light on possible J1r assignments since
all the remaining choices have pronounced minima.

The 269.5—keV y-ray angular distribution is more illuminating,
however. Since this transition goes to a spin zero state, the 6 = 0

requirement yields theoretical angular distribution coefficients that

75

are unique (i.e. it must be a pure multipole transition). The co—

*
efficients predicted by MANDY at Ep = 7.30 MeV for J1T = 1+ are A2 =

* n + * *
-0.218 and A4 - 0.000, for J = 2 are A2 - 0.517 and A4 - -0.302, and
* *
for J1r - 3+ are A - 0.842 and A a 0.136. The measured values of

2 4

* *
A2 - -0.296i0.023 and A4 = 0.030:0.03l at EP - 7.30 MeV are compatible

only with JTr = 1+ since J1T - 2+ and 3+ require large positive values

* *
of A2. The measured value of A is, however, still almost four standard

2
deviations more negative than the predicted value. Najam at al.58
observed this same type of behavior for a 1+ state in a 66Zn(p,ny)56Ga
experiment at a proton beam energy of approximately 6.50 MeV. They
attribute this behavior to a direct reaction component for the (p,ny)
reaction.

To further investigate this somewhat anomalous behavior an ad-
ditional y-ray angular-distribution measurement was made with the beam
energy increased by just 100 keV (from 7.30 MeV to 7.40 MeV). The
angular distribution for the 269.5-keV y ray obtained at the new

9:

energy was, very surprisingly, isotropic with A2 - -0.018:0.025 and

A: - 0.016:0.029. The angular distributions for all the other y rays,
except the 750.1-keV y ray which had also become isotropic, remained
virtually unchanged (see Table VII). The following possible explana-
tion, given below, for this strange behavior supports the J1r - l+
assignment.

Anisotropic y-ray angular distributions result from alignment
of the excited residual nuclei with respect to the beam direction. The
addition of angular momentum from the incident proton causes the original

alignment of the compound nucleus which then, after neutron decay,

results in alignment of the excited residual nucleus. Assuming s—wave

76

exit neutrons, 1n = 0 (expected near threshold), a final state with
spin 1 can only be reached with s-, p-, and d-wave protons, 2p = 0,
l, and 2, since the 56Fe target nuclei have J1r = 0+. The parity selec-

tion rule, hf - n for 2p +12n - even, further requires 2p - even only,

1

since flf - n - + l and 2n - 0. This restriction eliminates the par-

1
ticipation of pdwave protons. Thus, the final state of J1r - l+ can
only be reached with sdwave protons going through 1/2+ compound-nuclear
states and d-wave protons going through 3/2+ compound-nuclear states.
No other combinations are allowed.

States of residual nuclei reached with s-wave entrance protons
and s-wave exit neutrons through 1/2+ compound nuclear states can have
no alignment since the proton imparts no orbital angular momentum to
the compound nucleus and the spin of the neutron can be oriented in
any direction. On the other hand, states of residual nuclei reached
through 3/2+ compound nuclear states created by d-wave entrance protons
have some alignment. The exit neutron in this case can "wash out"
the alignment but cannot destroy it. Resulting y-ray angular distribu-
tions in the former case must be isotropic from the lack of nuclear
alignment but in the latter case can be anisotropic. Because of the
extremely restricted number of possibilities, a dominance in the com—
pound nucleus (in either cross section or density of states) of one
spin over the other can greatly affect the magnitude of the subsequent

*
y-ray anisotropy. MANDY predicts a maximum possible value of A2 = -0.5

*
, 2
for the case of only 1/2+ states. This behavior is restricted to spin

for the case of only 3/2+ states in the compound nucleus and A 0.0

1 states since residual states of spin greater than 1 can always be

reached by more than one pathway in which nuclear alignment is preserved,

77

even if only one type of spin state is available in the compound
system.

Thus, JTr a 1+ for the 1720.3-keV state, is the only value
consistent with the results of this experiment and with the above dis-
cussion. The 269.5-keV y ray is thus pure M1 which is consistent with the
internal—conversion electron measurements by Jenkins and Meyerhof2
and Ohnuma et aZ.3 A mixing ratio of -0.04 < 6 < 0.25 or -22.7 < 6 < -2.9
is indicated for the 750.1-keV y ray. The former value (i.e. an M1
transition with a 0.16 to 5.9% E2 admixture) is in reasonable agree-
ment with the value -0.20 < y < 0.09 measured by Ohnuma at 612.3 using
y—y angular correlation in the decay of 56Ni. The mostly Ml character
is further supported by the internal-conversion electron measurements
of Ohnuma at al.3 The 1561.7-keV y-ray branch from this state to the 3+
first excited state at 158.4 keV, must be an E2 transition by virtue

of the angular momentum change between these states.

J. Higher Excited States

Excitation functions and y-ray angular distributions were not
measured for any of the higher states. An increasingly complex y-ray
spectrum and rapidly decreasing detector efficiency with the increasing
energies of newly encountered y-rays, would have made such measure-
ments difficult. In addition, for the case of the y-ray angular
distributions, increasing beam energies resulted in higher levels of
radiation from the lead beam stop. For these same reasons, no ground-
state transitions were identified from these states in singles experi-

ments .

78

Some comments can be made, however, about the y-ray transitions
from these states observed in the y-Y coincidence measurement at
Ep = 8.36 MeV. All of the spins suggested for these higher states by
Schneider and Daehnik15 (marked with asterisks in Fig. 6) from
58Ni(d,01)56Co, are compatible with the assumption that there is at
most a spin change of two between states connected by y—ray transi—
tions. This assumption suggests a spin 1 or 2 for the 2635.7-keV
state by virtue of its 1184.9-keV y-ray transition to the 0+ state at
1450.8 keV. No y-ray transitions from the known states (see Ref. 15)

+, 7+) were observed, presumably

at 2281 keV (7+) and 2371 keV (6+, 5
because the low energy (p,n) cross sections to such high spin states
are very small. Thus, the spin of the 2469.3-keV state must surely be
3, 4, or 5 by virtue of its observable 1892.7-keV y-ray transition to
the 5+ state at 576.6 keV. This 2469.3—keV state may be a 4+ state
predicted in this energy region by McGrory.30 (See Fig. 14.) The
lack of observed y-ray transitions from the known state (see Ref. 15)
at 2791 keV may be simply due to a low cross section caused by low

exit neutron energy and not to high spin. The existence of a state at

2289.8 keV suggested by Del Vecchio et aZ.2° is confirmed.

v. COMPARISONS WITH SHELL MODEL CALCULATIONS FOR 56Co.

The 5600 nucleus has one neutron outside and one proton hole
inside an otherwise closed f7/2 shell. It thus lends itself quite
nicely to shell-model calculations. McGrory3o has recently performed
a calculation in which 56Co was represented as a ”OCa core plus 14
or 15 nucleons in the‘f7/2 orbit and the remainder in the.p3/2,'f5/2,
or P1/2 orbits. He used single-particle energies which best reproduced
the 57Ni spectrum and Kuo-Brown matrix elements for the effective two—
body Hamiltonian. He then used the resulting 5500 wave functions to
calculate the reduced transition probabilities, B(Ml) and B(E2), for
all possible M1 and E2 y-ray decay channels for each of the predicted
states. For the BOMl)'s the bare Ml operator was used while for the
B(E2)'s an effective charge of 0.5 was used.69 These reduced transi-
tion probabilities are compared below with lifetime measurements by
wells et al.1 and with the y-ray multipole mixing ratios and branching
ratios measured in this experiment. The same 56Co wave functions used
in these calculations were quite successful in predicting strengths
for deuteron pickup in a recent 58Ni(d,a)5600 experiment by Schneider
and Daehnik.15

The spins, parities, and energies of the 56Co states predicted
by McGrory and the corresponding experimental assignments of the present
work are shown in Fig. 14. As can be seen, the agreement between theory
and experiment is quite remarkable for the states below 2 MeV of
excitation. Only the second 5+ state and the 0+ state are predicted
too high in energy and even these discrepancies are no more than

450 keV.

79

Figure 14.

80

Comparisons of level spins,
parities, and energies of the
present experiment and from
Ref. 15 (asterisked values),
with the predictions of McGrory
(Ref. 30). Dashed lines in-
dicate tentative correlations.
For excitations above 3 MeV,
see Ref. 15.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

,1” 2999
, ” ’ 5+
(279" ------ 2+ 2870
2730.4 '9' ‘ I ’ 2780
2635.7 2647.2 36651—3532 311::‘1... .1: 2720
2609.5 12:35:11 ‘2 2640
2469.3 14.3 5)" / +
0 ~‘ *
(237I __ 57".} ---~-.. +
2304.9 2357'3——)—:’I§) 5*): s +
2224.5W75 .1.
312*) at
2060.0 + / +
27(3) 1* X3: 2087
'930'4 ‘ 3121‘s 7' 31992
1720.3 1*
1680
1450.8 0°
5’ 1381
||l4.6 3” /3+ “68
1009.2 ,
9703 .f ‘2: 992
5+
576.6 5,,// 649
3+
0.0 - .
141 4. 0
PR
W%SREKNT THEORY
(MCGRORY)

Figure 14

82

For the following discussion, the M1 and E2 transition proba-
bilities, W(Ml) and W(E2), were calculated from the B(M1)'s and B(E2)'s

computed by McGrory and presented in Table IX, according to,70

won) = 1.7588 x 10"13 EY3 B(Ml), [Sec—1]
and W(E2) = 1.2258 x 10+9 8Y5 B(E2), [Sec-l]
where BY = the experimental y-ray energy in MeV,
B(Ml) = the M1 reduced transition probability in
2
nuclear magnetons squared, U0 ,
and B(EZ) = the E2 reduced transition probability in

eZF”.

The predicted half lives are then the reciprocals of the transition
probabilities multiplied by 1n2.

The calculated B(E2)'s range from 0.01 to 100 eZF” and the B(M1)'s
from 0.002 to 2.5 “02' Thus, in light of the above equations, all
y-ray transitions with energies less than 1 MeV should be predominantly
M1 except for the rare case of accidental matrix-element cancellation
or where Ml transitions are not allowed by angular momentum selection
rules.

The latter is the case for the 0+ state at 1450.8 keV. If
this state is 0+, no M1 decay is possible and, in fact, only one E2
channel, that to the 2+ state at 970.3 keV, is open. McGrory's
predicted half life against this E2 decay is 2.12 nsec (see Table X).
The only y-ray decay observed for the 1450.8—keV state is that to the
970.3-keV state and it has a measured half life of 1.6i0.1 nsec.1
Even with the factor of 1.3 discrepancy (completely accountable by

the somewhat arbitrary choice of 0.5 for the effective charge in the

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85

 

 

 

Table X. Shell-model predictions by McGrorya of the half lives of
the first eight excited states of 56Co. Only observed
transitions were included in these calculations. Internal-
conversion effects were not included.

Excitation T1/2tha T1/2epr
energy

(keV) (psec) (psec)

158.4 10.9 <100

576.6 0.586

829.8 6.03

970.3 0.105 <100
1009.2 0.115

1114.6 0.529

1450.8 2.12x103 (1.6:0.1)103
1720.3 0.753

 

 

aSee Ref. 30.

b

See Ref. 1.

86

E2 operator), this is remarkable agreement.

Only two additional states, at 158.4 keV and 970.3 keV, have
previously measured lifetimes.1 Upper limits for the half lives of
these states were set at 100 psec. The half lives predicted by McGrory
for these states are 10.9 and 0.105 psec, respectively. The very short
half life predicted for the 970.3-keV state accounts for the lack of
an observable 970.3-keV E2 y-ray branch to ground.

The predicted multipole mixing ratios presented in Table IX
were calculated from the equation

52 a ngz)
W(Ml) '

The predicted relative phases of 6 presented are those of McGrory.
Except for the 829.8-keV transition whose anomalous behavior was dis-
cussed previously, the agreement between the theoretical and experi-
mental mixing ratios is quite good. A particular case is the 671.3-
keV transition from the first excited 4+ state to the first excited
3+ state. Here, compared to the E2 admixtures of other predominantly
M1 transitions, a sizeable E2 strength (5.9il.4 percent) is both pre-
dicted and observed. The rather small B(Ml) predicted for this transi—
tion causes enhancement of the theoretical E2 strength (5.2 percent).
Some quantitative agreement between theory and experiment is therefore
indicated.

The theoretical and experimental y-ray branching ratios are
presented in Table IX. In general, agreement is very good.

The shell-model calculations show that the predominant y—ray

decay mode for the excited states of 56Co below 2 MeV of excitation is

87

through Ml transitions. This supports those J1T assignments that were

based in part on the prevalence of M1 decay.

VI. SUMMARY AND CONCLUSIONS

The y-ray decays of the excited states of 56Co below 2.85 MeV
of excitation have been studied via the electron-capture decay of
56Ni and the 56Fe(p,ny)56Co reaction. The adopted energies (in keV)
of the six y rays common to both studies are: 158.4:0.1, 269.5:0.1,
480.510.l, 750.010.1, 811.910.1, and 1561.9i0.2. The Ge(Li)-Ge(Li)
y-y coincidence technique used both on and off line, was extremely
useful in the placement of y rays in the decay schemes. In particular,
high—energy y rays (greater than 1500 keV) could be separated in the
in-beam spectra from otherwise overwhelming Compton backgrounds. In
fact, the high Compton background and diminishing detector efficiency
for high energy y rays forced an end to the excitation function and
y—ray angular distribution measurements at about 2 MeV of excitation
in 5500. Since the statistical compound nuclear theory appears still
valid at these excitations, these background problems are the only
hindrance to a continuation of these measurements to higher excitations.

The combined use of cross-section ratios and y-ray angular
distributions proved very potent in determining unique spin assign-
ments. The experimental errors of the y—ray angular distributions
and the experimental errors and fluctuations of the cross-section ratios
were, however, greater than the sensitivities required to make parity
determinations. Thus, it is necessary to assume all parities even
'based upon previous experimental results and shell-model considerations.
53pin and parity assignments (in parenthesis) were thus made for the
following 56Co states (energies in keV): 158.4(3+), 576.6(5+),

829.7(4‘5, 970.3(2+), 1009.264“), 1114.6(3+), 1450.8(0+), and 1720.3(1‘3.

88

89

Comparisons of the experimental cross-section ratios and y—ray
angular distributions with the predictions of the statistical CN
theory (via the code MANDY) showed remarkable agreement, with two
notable exceptions. First, gross fluctuations, often 15% in magnitude
and 40—100 keV in width (roughly 1-3 times the target thickness) were
observed in the excitation function measurements. These fluctuations
also manifested themselves in the cross-section ratios as scattering
about the predicted values. Second, otherwise anisotropic angular
distributions (both predicted and observed) for two y-ray decays of
the 1720.3-keV l+ state became isotropic when the beam energy was
increased by 100 keV to 7.40 MeV. It would be interesting to know
if the same behavior under similar conditions is observed for 1+
states in other nuclei as would be predicted by the possible explana-
tion offered in the text. These two exceptions indicate partial
breakdown in the statistical assumption of large numbers of over-
lapping CN states of random spin and parity. A satisfying explana-
tion for the gross fluctuations would be interesting and useful in—
formation.

No evidence was found in the present work for the existence of
an additional level near the 1450.8-keV state. The cross-section
ratio comparisons and the angular distributions of both the 480.5-
keV y ray deexciting the level and the 269.5-keV y ray feeding it were
uniquely compatible with a J1T = 0+ assignment to a single state.

The shell-model calculations of McGrory30 are in excellent
agreement with the measured level energies and spins. Although spins

were only measured in the present work to 1.8 MeV of excitation, the

90

apparent agreement of the results of other experiments indicates that
his calculations can be extended quite satisfactorily to higher excita-
tions. McGrory's calculations of the B(M1)'s and B(E2)'s agree, in
general, with the y-ray measurements reported here. Lifetime measure-
ments for these states are needed for more direct comparisons with

the predicted transition probabilities.

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11).

2R.

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and Breach Science Publishers Inc., New York, 1963).

57F. Perey and B. Buck, Nucl. Phys. 32, 353 (1962).

58E. Sheldon, Rev. Mod. Phys. 32, 795 (1963).

59B. H. Armitage, A. T. G. Ferguson, G. C. Neilson, and W. D. N.
Pritchard, Nucl. Phys. A133, 241 (1969).

60K. M. Thompson and C. R. Gruhn, Nucl. Inst. and Meth. 14, 309 (1969).

61GADFIT, computer code written by R. A. Warner, Michigan State University
Cyclotron Laboratory, unpublished.

62The absolute intensity standards were obtained from the Radiation
Materials Corporation of Waltham, Massachusetts.

63F. A. Moldauer, Phys. Rev. 123, 968 (1961); 13;, B642 (1964); Rev. Mod.

Phys. 29. 1079 (1964).

95

6“R. V. Jones, W. Dbrowalski, and C. D. Jeffries, Phys. Rev. 192, 738
(1956).

65A. H. Sher and B. D. Pate, Nucl. Phys. 511g, 85 (1968), and references
cited therein.

66Walter Menti, Helv. Phys. Acta,.49, 981 (1967).

67s. 3. Hanna, J. Heberle, c. Littlejohn, c. J. Perlow, R. 3. Preston,
and D. H. Vincent, Phys. Rev. Letters_4, 177 (1960).

68M. R. Najam, W. F. Davidson, W. M. Zuk, L. E. Carlson, and M. A. Awal,
Nucl. Phys. A113, 577 (1971).

69E. C. Halbert, J. B. McGrory, B. H. Wildenthal, and S. P. Pandya, in
Advances in Nuclear Physics, edited by E. Vogt and M. Baranger
(Plenum Press, Inc., New York, 1971), V01. 4.

7oEmilio Segre, Nuclei and Particles, (W. A. Benjamin, Inc.), New York

1965).

APPENDICES

9.
lCL
11"
£12.
213.

Zl4~

JMS.

96

APPENDIX A

Separation of Nickel from Irradiated Iron Shimstock

Dissolve sample in HCl.

Add Mn and Ni hold—back carriers.

Adjust acidity to 1M with HCl.

Precipitate CuS by adding thioacetamide sparingly.

Remove precipitate by centrifugation and discard precipitate.
Boil supernatant with concentrated nitric acid and bromine water
to destroy hydrogen sulfide and colloidal metal sulfides. (This
step is extremely important.)

Precipitate iron hydroxides with 15M aqueous ammonia.

Remove precipitate by centrifugation and discard precipitate.
Precipitate N1 in supernatant with dimethylglyoxime (DMG).
Remove precipitate by centrifugation and discard supernatant.
Dissolve precipitate in HCl and add Co carrier.

Reprecipitate Ni DMG by the addition of NH OH.

4

Remove precipitate by centrifugation and discard supernatant.

Rinse precipitate twice with distilled H
and discarding supernatant each time.

20 using centrifugation

Finally, dissolve precipitate in HCl and transfer to a small
plastic vial for counting.

97

APPENDIX B

Integral Coincidence and Gated Spectra from the

55Fe(p,ry-y)56Co Reaction at Eg=7.38 and 8.36 MeV.
v

Figure 15.

Integral coincidence and gated spectra from the
56Fe(p,ny)56Co Reaction at Ep - 7.38 and 8.36 MeV.

The x-axis is from the 2.52 detector while the y-axis
is from the 7.42 detector. Background subtraction
using the adjacent continuum has been included. Peaks
labeled in parenthesis are believed to be from chance
coincidences or insufficient background subtraction.

More details are given in the text.

COUNTS PER CHANNEL

98

 

' ‘ v #—

 
 
   
   
   

 

 

 
       
 

 

 

 

 

 

  
 
 

 

 

 
 

 

 

 

 

 

 

 

104. 158A V ‘ ‘
8468561: X - INTEGRAL GATE
'03 8 . ' ° 6,, = 7.38 MeV
1037956133 '23 -3 56"" ‘
102 A 1771.4 551-1. ,
3‘? + 'F ‘--—o- - 2.
'0 158.4 - keV GATE ‘
IO2 , "58"” 259.5 480.5 811.9
85.0 671. 55 ‘
7500 (846.8 Fe)
10' » .
'03 ' 1 . | l 1 '1
269.5 _ keV GATE
2
l0 1
4805 811.9
1 . '
, e
285.0 " keV GATE
10' .
l
31? T5
'0 '58-“ 4805- keV GATE
'02 ' 2695 811.9 1
I0l ’ w 1 1
3‘ 1 '1‘ l i I Ti
10 V -
'58,, 67!.3 keV GATE
1
750.0- keV GATE
10' 1 ’
31? 1 11 1 111 i 1 1 £
5'
'0 '58‘4 8119- keV GATE
'02’ 2695 4805
10' 1 II" 1 1
I00 '1“ 1. 1 .- .
0 |000 2000 3000 4000

CHANNEL NUMBER
Figure 15.

COUNTS PER CHAN NEL

99

       

 

 

 

         

 

 

 

 

 

   

   

 

 

 

 

'04 [MM .1....---___-.-_-._--_..-.- .. .- . 56-.-”- . _ .. .--__ -_ ,_ .
158.4 480.5 511.0)“ 8'8368 Fe y- INTEGRA17368AII/IEV
103 , 269.:2285'0 123 .3 56Fe 0 ‘ ' e
'02 " '7“ ‘ 1771.453
3 1; g _ __- -_¢—--———- o- ._____. . o - 4:
IO 811.9
2 (158.4) 269.5 480.5 67"3 7500 158.4 — keV GATE
IO 1 -2850 ' 1846.8 569.») 1
1 1561.9
IO 1 1
g r 1 ‘ 1
102 158A
8||.9 269.5 ' keV GATE
10'
1
102
285.0 .. keV GATE
1 '58'4 67"3 829.8
IO 1 I
1 l
10 T
480.5 _ keV GATE
I02 ? “38.4 8II.9
10'
102‘? . I ‘ T
15.4 67L3 - keV GATE
10' . 285.0
1 1 l
217 i ' ‘
'0 1584 750.0 - keV GATE 7
| ‘ 811.9
l0
3., 1' "? . 111111. .11 11
1
O l584 811.9 - keV GATE 1
2 .
l0 '
1 750.0
10
100 i ‘ ' ‘ L”
O 2000 3000 4000

 

CHANNEL NUMBER

Figure 15 — continued.

COUNTS PER CHANNEL

100

 

 

6 " 12 01 LL
'0 v. m. 1n.>~ °°- 1°: .86; “‘3 x- INTEGRAL GATE
105 8 $8 898 '3 9393 39996.19” 1 o 3.4: ED: 8.36 MeV
“N w?" c 86‘” 19 NE w _-No - 1.0
'04 \I \ In ‘0 9 Em_ 70” [Eye P28 ”‘12 . w
I l ’l‘ \ /: 2’2 2:9 - $883“
103 n d ‘ ‘ ' \I N 88
2 —.
'0 38 $2 9.
4 We A
'0 7 3% 89' g «1 09-035 158.4 _ keV GATE 7
a “('3 <7 1: o'w‘g
/ (D u’) a)
1x .3

104‘? g,
«.1

I58.4

104T

|58.4

 

 

 

480.5

285.0

8|l.9

8|L9

IOOO

 

2000
CHANNEL NUMBER

Figure 15 - continued.

269.5 - keV GATE

285.0 — keV GATE

480.5 - keV GATE

576.6 - keV GATE

671.3— keV GATE

750.0 - keV GATE

 

3000 4000

COUNTS PER CHANNEL

  
 

101

 

 

 

l.’72.l

[

X - INTEGRAL GATE_‘
Ep: 8.36 MeV

 

   
  
   

 

 

 

811.9

 

IOOO

CHANNEL NUMBER
Figure 15 - continued.

8||.9 - keV GATE

 

829.8 - keV GATE

945.5 — keV GATE

956.1- 81 960J - keV
GATE

|090.l — keV GATE

III0.0 - 81 l|l4.6 - keV
GATE

 

 

“84.9 — keV GATE

 

3000 4000

COUNTS PER CHANNEL

102

 

Io2

 

x - INTEGRAL GATE
Ep= 8.36 MeV

 
 

 

3‘7

103"

3‘7
102
I0

103‘

102

10‘

 

10°
0

| 58.4

l58.4

V.
as
'2

|58.4

I 58.4

—8|l.9

8||.9

8|L9

IOOO

 

11111111 11 1 1] 11

 

 

1 238.3
56Fe

lhiflimm 1111 111 111 1 1

2000
CHANNEL NUMBER
Figure 15 - continued

|254.4 - keV GATE.

.—

dllnlm 11 111 111 1
I3I9.8 - keV GATE

I334] — keV GATE

1387.3 - keV GATE

1561.9 - keV GATE

1760.1 - keV GATE

1
l77|.4- 81 |772.|- keV
GATE

 

3000 4000

COUNTS PE R CHANNEL

103

 

6 - s 4 -
'05 5‘5- 88 82:3 ,0 Q.» m x- INTEGRAL GATEJ
IO 9 (Om (”ZN .2 2. 1n-: 8 .02 (gm. _‘ E = 8.36 MeV
.64 “<1 “119%” “,3 85-615 82.1; s v

3 \I 7- '2""2 t ‘

. I
in A
V W l W

 

 

 

 

ISBA

 

IOOO

 

1

 

2000
CHANNEL NUMBER

Figure 15 - continued.

1111| 1,1 1

I782.4 - keV GATE

H

g
r

 

|90|.5- keV GATE

 

1]

H

111

2066.1— keV GATE

111: 1:

11

v

lllflillfl l ; I

2|3l.l - keV GATE

1 1J1,11 1 , 1 1
2l46.4 - keV GATE

 

l-l J [[1 - l

 

3000 4000

 

 

104

 

    

   

        

 

 

 

 

< ‘1 S: < ><
E F. E
E W W T T - W T
A A A A A 1 A A
G G G G G G G
$89 v v v 1 v
V . I V e e e V e
m fig- 111. k 1.“ k m k
_ . . . _ _
D 5 6 D
M % 5 0 a B O
Show; 6 8 8 7 7 5
|¢.®V_Nl 2 2 4 5 6 7
SENT
flooON
m._om_ Nmm?
immt
EEO
_owt
m._wm_
“~me
Nemmr
was.
vdmfl
mvm:- va:
fiomoT
_. 1 Ema
Enham 0an
Qwvmv 1mjm mwmm . sz
00m~ mzm m:m
Vim nib
mdmv
mdmv
0.89 m.
m8 3%
6mm: v.3. can. can. 11 $9
7» 7r ‘7» 1" 1" ‘7»
4 3 2 l. 3 2 I 3 2 | 3 2 I 2 3 2 I 0
mmmmmmmoommmmm mmmm

JMZZ<IU mum meDOU

3000 4000

2000

CHANNEL NUMBER
Figure 15 - continued.

IOOO

COUNTS PER CHANNEL

105

 

fw'w. NM _
03v (Der' m. (\3
m_m mmm — ~
01— —m w
»I - w»—” m t
1 1 _\{7— T

|||0.0

Y- INTEGRAL GATE
Ep= 8.36 MeV

 

4?

 

v.
co
‘9.

 

2635

285.0

285.0

480 5
750.0

 

‘9.
E

   
 
      

0'!
as

 

945.5
l||0.0
”MG

468

56
|238.3

5(S'Fe

1000 2000
CHANNEL NUMBER
Figure 15 - continued.

8H9 — keV GATE

8238- keV GATE

945.5 - keV GATE

956.|- 81960.| - keV
GATE

|090.| - keV GATE

IJ111111111LLL11_1J_

1>

1110.0- 8 ||14.6- keV
GATE

‘
l77L4- 8 I772J— keV

 

11.

3000 4000

106

APPENDIX C

y:ra1 Angular Distributions from the 56FerLnI)56Co

Reaction at E. = 5.77, 6.65; 7.03, 7.05. 7.30, and 7.40 MeV.
1’—

Figure 16.

y-ray Angular Distributions from the 56Fe(p,nty)56Co
Reaction at Ep = 5.77, 6.65, 7.03, 7.05, 7.30, and 7.40
MeV. The solid lines through the data represent least
squares fits using the equation for W(6) given in the
text. W(8) has been normalized to l at 90°. Except

for the Ep = 7.40 MeV case, two experimental points were
taken at each angle; only their weighted average is
presented. The assignment of errors is outlined in

the text.

L1

107

 

B -158.4 keV
E;-5.77 MeV

lllLLllLl

E -158.4 keV
E;-6.6S MeV

 

_ rag-6. 65 MeV

 

E -285.0 keV

 

W1—
0’ 10 ’ 20’ 3’ ‘90. 50‘ so- 70’ ea- 00’

E =576.6 keV
E;=6.65 MeV

o- no- eoO 30- w' 50- co- 7o- an- no"

RNBLE

Figure 16.

 

 

108

 

E -671.3 keV
Ez-6.65 MeV

I l L l l l I J L i

E -811.9 keV
Eg-6.65 MeV

 

E -1009.2 keV
Eg-6.65 uev

 

B -1114.6 keV
Eg-6.65 uav

 

_1__.t_;_|_1._1_l_—I—L—I- .

 

W
00190[unpac-uuulsoo{:uhpoo'luvgol

o- 19' 20' w w so- w 70' oo- oo-

RNBLE

Figure 16 - continued.

INTENSITY

109

 

E 8158.4 keV
Eg-7.03 mev

E =-285.0 keV
Eg-7.03'Mev

 

 

E -S76.6 keV
Ez-7.03 MeV

 

"1iFflTF1EiF5571fii7§571§i77%71§i7357

 

 

'- E =671.3 keV
E;-7.03 MeV

on llflfllfig. 11530 l|7blilfllfio

RNBLE

Figure 16 - continued.

 

110

 

E -811.9 keV E -1009.2 keV
lag-7.03 uev E;-7.03 MeV

 

 

 

 

 

 

 

 

ray-1114. 6 keV Ey-158. 4 keV
1.2 _ Ep-7.03 MeV . _ lip-7.05 MeV
u .- —
1.. § § § J a .1.
i i i 11 11
. .9 _ _
a - -
.7 - -
1 1 1 1 l I l 1 1 I 14 !—al——J——‘k——L——l——Jh——L——l1v
o- 10' 20' aa- wo- 50- cm 700 9'00 90- o-w' ea- 30- . so! so! 70' 00' no
mate

Figure 16 — continued.

111

 

E -285. 0 keV
Eg-7.05 MeV

I I I I I I l J I

E -480.5 keV
BIZ-7 . 05 MeV

1-
L
P
1.

 

INTENSITY

L2 h-

Ll -

 

E -576.6 keV
Eg-7.05 MeV

[WWW—4'44
o- 10 0 eat no! no. 50- ar 70' an! 00' o- m - en- 300 ‘10- so- en- 700 oo- oo-

 

E -671.3 keV
- Eg=7 . 05 MeV

 

 

BNBLE

Figure 16 - continued.

INTENSITY

112

 

E =811.9 keV
Eg-7.0S MeV

E -1009.2 keV
Elli-7 . 05 MeV

 

 

 

 

 

 

E -1114.6 keV
1.. EY-7. 05 MeV
p

4W

 

E 3158.4 keV
- Eg-7.30 MeV

 

‘ .1_|._.I__I__L__I_L_1_L_l__L—L——LJ,
W 1 to aa- wso- em 70¢ 00' oo- o-w-eo-ao-wso-co-ro-eo-oo-

RNBLE

Figure 16 - continued.

 

113

 

B -269.5 keV E -285.0 keV
ELY-7.30 MeV Ely-7.30 MeV
L-
- p
D
I L L I I I I I I I I L I I I l I I I L

 

E =576.6 keV

__ Ely-7 . 30 MeV _
P
1— 1n-
— b i

E -67l.3 keV
r — Egg-7. 30 MeV

0 eat an- w- so- u» 70' oo- oo- o- - en- 200 '10- so- an- 700 90' on"

 

 

 

Figure 16 - continued.

 

114

 

E -750.o keV
FIE-7. 30 MeV

E -811.9 keV
E;-7.30 uev

 

E '100942 keV
u I— E;-7.30 MeV

14%-

 

 

  

’iflfl'ifl"flfl'Sfl'tIfl'7D'Ilfl'90'
HNBLE

E -lll4.6 keV
._ E;-7 . 30 MeV

 

 

"W‘A—WW

Figure 16 - continued.

INTENSITY

115

 

 

    
 

 

 

 

 

 

 

 

E -158.4 Rev E =269.5 keV
EY-7.4O MeV EY-7.4O MeV
.Lt - P P
14 r- ..
.. - - i
.9'- _.
.0 1- __
J7.. ._
l I I I I J I I I I L I I I I I I I I I
qr 1 Ey-480.5 keV
l1
.1 *1
u _
1.
u 1'
1» —-~ W
A h I 1
“I 11 '-
3 .11 '-
‘7 "' E -285.o keV "
Eli-7.40 MeV

 

 

HNELE

Figure 16 - continued.

116

 

E I576.6 keV

_ lag-7. 40 MeV

I I L I

I

 

lag-7.40 MeV

LIIILIILII

 

 

E -750.0 keV

_ E;-7. 40 MeV

* 1

E -811.9 keV
BIZ-7 . 40 MeV

'11
‘1

 

.e... . GWWW

HNBLE

Figure 16 - continued.

 

INTENSITY

117

 

 

 

 

B -1009.2 keV E -lll4.6 keV
EY-7.4O MeV EY-7.4O MeV
:— P P
.. +- }
1 1 1 1 17 1 1, 1 1 L7 1 1 1 1 1 1 14
Stainless Steel Stainless Steel
E -158.4 keV E -269.5 keV
- EY-7.52 MeV " EY-7.52 MeV
P P
*
- -' A2 - -0.30:|:0.10
g *
A4 = 0.01:0.13
m
— * '-
A2 - -0.01i0.01
*
‘- "ll
_I__J___L__1__J___L__J___L__J___L_

 

cow-eo-ao-wso-eono-ao-oo- 0010-20-20! oso-oo- oven-00'

HNELE

Figure 16 - continued.

118

 

INTENSITY
h

Stainless Steel

E -480.5 keV
E;-7.52 MeV

I—

 

A -0.0li0.02

I
I'M!-

A '0.00i0.03

&

 

 

finkfiahfidhfidmfifii

 

INTENSITY
II'

Stainless Steel

E -811.9 keV
Ez-7.52 Mev

_
*
— *
A4 - 0.02:0.01
F

 

 

INTENSITY

TY

b b E E

\1

SEBRBQGQQQ

I l l l I IE‘I l T

L!

 

 

Stainless Steel

E -67l.3 keV
Eg-7.52 uev

 

A -0.0Zi0.07

A

-0.0310.10

AFN-Na-

 

 

 

l I Al I l l

 

_.:::ssn;§

E -829.8 keV
E;-6.65 nev

80 In! 30 3H! .0
flNILI

Figure 16 - continued.

 

 

INTENSITY

119

 

} E =829.8 keV
E;-7.03 MeV

bSESSSES‘SSSEB

E -829.8 keV
E;-7.05 MeV

 

 

E
1

E I829.8 keV
E;-7.3O nev

.91—

RNBLE

 

Figure 16 - continued.

 

 

E -829.8 keV
Eg-7.40 MeV

 

1

"I13 10' i anl "Ll‘Jao w'i'so' T'so"LT'LT7o so'LT‘soL"

 

 

120

APPENDIX D

* *
The Experimental and Theoretical Values of the A“ and A,

55Cogxrray Angular Distribution Coefficients as_§_

Figure 17.

Function of the y—ray Mixing:Ratio 6.

 

Plots of the Experimental and Theoretical Values of

the A: and A: 56Co y-ray Angular Distribution Coefficients
as a Function of y-ray Mixing Ratio 6. (Definitions and
descriptions for the calculations are presented in the
text.) Only those cases are shown where y-ray feeding
from above was judged to be insignificant. In each case
the spin used for the final state was that determined
from this experiment; the possible initial state spins
and parities label their appropriate 6-ellipses. Ap-
proximate locations for the values of 6 can be found by
comparison with Fig. 12. In each case the 1+ "ellipse"
is a short straight vertical line passing through the

3 = 0.0, A: = 0.0. The experimental A: and A:

coefficients including uncertainties are shown on each

point A

plot as a rectangle.

0.8

0.4

0.0

0.4

0.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p E -158.4 keV
EY-6.65 MeV
p
L
6+

b
A .. +

1L 5

E I576.6 de E I671.3 keV
1 lay-6.65 MeV 4 EYJ-6.65 MeV
p p
r 1»
F «11-
5+

L 1P
L ..
F
-O.8 -0.4 0.0 o 4 -o.4 0.0 0.4

A*

4

Figure 17.

 

 

 

 

’\

 

‘V T W V V j

E a811.9 keV

 

 

 

 

 

E 3829.8 keV
BIZ-6. 65 MeV

A

‘ L J
V V V

a A
TV v f v f 1

 

L l J l
V

    

 

 

 

 

 

 

 

 

E '1009.2 keV E '1114.6 keV /
0.8 _ E;-6.65 MeV .. Eli-6.65 MeV / J
/ ..
0.4 ~ «~ ’ .
0 6+ ’ J
0.0 b ‘L d
. ‘ 1
.0.4 _ 1’ 4+ ‘
. 1. 2+ .
-008 P «b ‘ 3+ 1
1
b + 1b 4
5+
-1.2 ‘ L A A4 A A A Li I 4* A A
-008 -004 000 004 -004 000 004
*
A4

Figure 17 - continued.

 

0.8

0.4

0.0

0.8

0.4

0.0

 

' V V V i V I V U v I V

E -285.0 keV E -S76.6 keV
' Eli-7.03 MeV '- Eli-7.03 MeV

 

 

 

 

 

—L I A A A

 

 

0
4b
1

E 5611.} keTI
Ext-7.03 MeV

E :671.‘3 kg}
1 Fig-6.65 MeV

 

 

 

 

 

 

 

 

 

Figure 17 - continued.

 

' V

E -lOO9.2 keV
Eg-7.03 uev

' I V V 1 v f

E -1114.6 keV
‘1 Eg-7.03 MeV

     

 

 

 

 

 

0.8

0.4

0.0

 

 

 

 

 

 

 

 

   

 

 

 

 

 

b q»
E I“2851.0 keV E -480.5 keV
. EY-7.05 uev 1- EY-7.os MeV
P P
L
6+
2+
L +
5 3
-008 -004 000 004 -004 0.0 004
*
A4

Figure 17 - continued.

0.8

0.4

0.0

0.8

0.4

0.0

 

V V V V V

E -576.6 keV
E;-7.05 uev

 

1

 

 

A A

V V V V V T'

E =67l.3 keV
Eg-7.05 MeV

 

 

 

A L L

4L
0
db

 

L
V

‘P

E I811.9 keV
E;-7.05 MeV

 

 

 

 

 

 

E -829.8 keV
E;-7.05 MeV

 

 

 

 

 

Figure 17 - continued.

 

 

f *7 v v v v v V V V

E -lOO9.2 keV E -lll4.6 keV

  

 

 

 

0'8 ’ EY-7.os nev ’ EY-7.os uev
p p
0.4 . ..
0.0 . 1' 6+
L 4L
-o.4 ' *-
D 1%
-008 L Eb

 

    

 

 

A A A A
V V V' V

E -285.0 keV
0.8 - Eg-7.3O MeV

_A A A A
V V V

E I576.6 keV
Eg-7.30 MeV

1P
4!

 

b

0.4 ’

 

 

 

 

 

 

 

 

 

Figure 17 - continued.

 

 

 

0.8 .

0.4 L

0.0 '

V V V

E -671.3 keV
E;-7.30 MeV

.A

 

' V r V' V

E -750.o keV
-1 E;-7.3o MeV

 

 

n-

         
    

 

 

 

o.8 -

0.0 '

 

A I
V r r

E -829.8 keV
E;-7.30 uev

d»

 

A
V V V V

_ E =1009.2 keV
Eg-7.30 MeV

A

 

 

 

 

 

 

Figure 17 - continued.

 

 

 

0.8 -

0.4

0.0

0.8

0.4

0.0

 

V V V V V V

E -1114.6 keV
E;=7.30 MeV

 

 

 

V V V

_ E =285.0 keV

E;=7.40 MeV

 

 

 

 

 

 

A A A L AL
V V V V

E =480.5 keV
E;=7.40 MeV

 

 

 

 

 

L A A
V V V

_ E =576.6 keV

E;=7.40 MeV

 

1b

 

 

 

 

 

-0.4 0.0 0.4

Figure 17 - continued.

 

 

 

 

 

 

   
 
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o 8 L E =671.3 keV E =750.1 keV
’ EY=7.40 MeV EY-7.4O MeV
p p
0.4 ’
0.0 ~ 5
3
-004 E +
2 2+
-008 E 4+
3+
‘ E =1ll4.6 keV
0.8 ’ E;=7.40 MeV
b ‘P
0.4 ' "
000 P «D
p 41-
+
. 2+
+ +
.. 2 3+ «~ 3
-O.8 - "
_ 5+ 1. 5+
-1.2 ‘* ‘ ‘ ‘ ‘ ‘ *“ ‘ ‘ ‘ ‘ ‘
-O.8 -o.4 0.0 0.4 -o.4 0.0 o 4
*
A4

Figure 17 - continued.

 

130

APPENDIX E

Relative x2 as a Function of Arctan 6 for the

56Co y-ray Angular Distributions

Figure 18. Plots of Relative x2 Versus Arctan 6 for 56Co y-ray
Angular Distributions. Only those cases are shown
where y-ray feeding from above was judged to be in-
significant. Assignment of errors necessary for the
determination of x2 is outlined in the text. In each
case the spin used for the final state was that deter-
mined from this experiment; the possible initial state
spins and parities label their appropriate curves. It
is instructive to compare these plots with the corres-

ponding plot of Fig. 17.

131

 

E '158.4 keV EY-158.4 keV
Efi-5.77 MeV Ep-6.65 MeV

 

 

3 5 2 4 3+ 5+ 2
1
X2
_ I I I I L I I I I I
V E 285 o k
- . eV EY=576.6 keV
EY-6.65 MeV E -6.65 MeV
P p
1000

 

I
’1
I v I
1 3 5+ 2 5 + 2
- 1 1 L 1 1 g 1 1 1 1 1
-90 -80 -30 0 30 80 -80 -30 O 30 80 90

 

 

orc+on 8 [deg]

Figure 18.

 

132

 

E -671.3 keV E -81l.9 keV
E;-6.65 MeV ’ E;-6.65 MeV

 

 

1 2 3 4 2 4 1+
X2
__ 1 1 1 1 1 1 1 1 1 1
'l/ E -829.8 keV E -1009.2 keV
EY-6.65 MeV EY-6.65 MeV
p p
1000
100

 

V1 1 1 11 ‘11 114
-90 -80 -30 0 30 BO -60 -30 0 30 80 90

orc+on 8 [deg]

Figure 18 - continued.

133

 

' E -lll4.6 keV
FIE-6. 65 MeV

‘::1I‘T'(.

E I“285.0 keV
Eg-7.03 MeV

 

 

 

 

 

4+ ‘»
1 3+ 5+ + 4+ 3+ 5+ 2+
2
gig, I I I I I I, I I I I
“V E -576.6 keV E -671.3 keV.
EY-7.03 MeV EY-7.03 MeV
p P .
1000
6+
1‘") I’l‘lllllll‘“iii""l--\\\\‘ /, ‘\\\‘~
- 10 __| F‘ /" '
‘7 ‘3 h ’1
a + I V
1 " 5+3+ 2’r 2+ 3+ 4+
- 1 1 1 1 1 g 1 1 1 1 1
-90 -80 -30 0 30 80 -80 -30 0 30 80 90

orc+on 8 [deg]

Figure 18 - continued.

134

 

E I1114.6 keV

E -1009.2 keV
E;-7.03 MeV

E;-7.o3 MeV

1000

 

 

 

 

 

 

.1.
4+ 3+5 2+ 4+ 3+ 5+ 2
2
_>_<_ IIJIL 11111
1” E -285.0 keV E -480.5 keV
Ez-7.05 MeV E;-7.05 nev
1000 .
1C")
' 1C) 9
1
_11111 11111
~90 ~80 ~30 0 30 80 ~80 ~30 0 30 80 90

orc+on 8 [deg]

Figure 18 - continued.

 

135

 

1311-7. 05 MeV Eli-7 . 05 MeV

 

 

 

 

 

- 1 1 L 1 L a 1 1 1 L L
~90 ~80 ~30 0 30 80 ~80 ~30 0 30 80 90

orc+0n 8 [deg]

Figure 18 - continued.

 

136

 

E -1ll4.6 keV E -285.o keV
Ep-7.05 MeV lag-7.30 MeV

 

 

+ 2
1 4 3+ 5+ 4"" 3+5.» 2+
2
_>_<_ 1 1 1 1 1 1 1 1 1 1
V E -576.6 keV E -671.3 keV
Eli-7.30 MeV Elf-7.30 MeV

 

 

 

'1 1 .I v
1 4+ 5+ 3-1- 2+ 1 3+ 2+ 4
- L I L I I V I I I l I
-so -so -3o 0 so so -so ~30 0 so so so

orc+on 8 [deg]

Figure 18 — continued.

 

137

 

EY-7so.o keV E -829.8 keV
Ep-7.30 MeV BIZ-7.30 MeV

 

 

 

3+ ‘
4.
6+ 4
2
_>_<_ 1 1 1 1 1 1 1 1 1 1
V E -1009.2 keV E -1114.6 keV

Eli-7. 30 MeV Eli-7 . 30 MeV

 

 

 

_ 1 1 11 1 1 1 1 1 1
-90 -60 -30 0 30 80 -60 ~30 0 30 80 90

orc+on 8 [deg]

 

Figure 18 - continued.

 

1000

100

10 .5, V 'J /‘ v V
i \I V‘ 1
I + 1+ '7

1 4 5+3+ 2+ 3+2+ 4+
- I I I I I I I I | I

-90 ~60 -30 0 30 80 -80 -30 0 30 80 90

     

138

 

E lI285.0 keV E a480.5 keV
BE-7.40 MeV Eg-7.40 MeV

 

 

B -576.6 keV

Y E =671.3 keV
Ep-7.40 MeV

Ez-7.40 MeV

  
    

 

3
§

 

 

orc+on 8 [deg]

Figure 18 - continued.

 

139

 

 

E -750.o keV
E;-7.40 uev

E -1009.2 keV
Fig-7.40 MeV

 

+ 3+ 4+

- 1 1 1 1 1 e 1 1 1
-90 -80 -30 0 30 80 -60 -30 0

orc+on 8 [deg].

 

 

 

 

E =1114.6 keV
E;-7.40 MeV
1000 ~
+
100 [6
2
25. 1‘ A"
v 10 V‘
II
_ 1 1 1 1 1
‘90 '80 "30 0 30 80 90

orc+on 8 [deg]

Figure 18 - continued.

+
3+ 5+ 2

6+

 

“’.

 

1 1
30 80 90

   

 

fi—T

 

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