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ABSTRACT

MEASUREMENTS OF NUCLEAR RESONANCE FLUORESCENCE

ON THE 1.27 Mev LEVEL OF Sn116

by John M. Gonser

The 1.27 Mev level of Sn116

was investigated by nuclear resonance
fluorescence techniques. Moments from previous emissions were used to
restore the resonance condition to a gaseous source. weakness of the

source prevented accurate determination of the mean life of the 1.27 Mev

state which was found to be less than 0.84.iD.7 x 10"12 seconds.

MEASUREMENTS OF NUCLEAR RESONANCE FLUORESCENCE

ON THE 1.27 Mev LEVEL OF Sn116

by

John M. Gonser

A THESIS

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

MASTER OF SCIENCE
Department of Physics

1964

é ZNBE‘i

%{.’.§iw+

To Mar 1 lyn

ii

ACKNOWLEDGMENT

The author wishes to express his gratitude to Dr. W. H. Kelly
for his guidance throughout this endeavor, and to Dr. G. B. Beard for
his added guidance during the experimental phase, and to the Michigan
State University Department of Physics and the U.S. Air Force Office
of Scientific Research for their financial support. The author wishes
also to thank Mr. William Dunbar of the university of Michigan Phoenix
Reactor staff, and to Mr. D. G. Parker and Mr. M. Mallory for their

assistance.

111

TABLE OF CONTENTS

Page

I. INTRODUCTION .......... ..... ........... . .............. .......... 1
Definition 1
Historical Background 1

II. EXPERIMENTALCONSIDERATIONS............................. ..... . 6
Sample Preparation , 6
Apparatus 10

III. CALCULATIONS ......... .. l6
Cross-Section for Resonance Fluorescence l6

Doppler Line Shape 18

IV. RESULTS ....................................................... 26
Data Analysis 26
Conclusions ... 30

BIBLIOGRAPHY .... ....... .... ..... . ..... . ....................... 31

Figure

10

INDEX OF FIGURES

Decay Scheme for 54 min. In116 ............................

Gamma-Ray Spectrum of Sn116 ...............................
Block Diagram of Experimental Apparatus ...................
Scattering Apparatud ......... ... ....... .. ..... . .......... .
Oven for Source ...........................................

Plot of Counts Detected due to Test Source on Ring ........

Emission of First Gamma ..... ... ...... .............. .......

Composite Plot Of one Day's Data ......................O...

iv

Page

13
14
15
20
22
25

27

I. INTRODUCTION

Definition

 

Nuclear resonance fluorescence is the name given to a particular
class of gamma-ray scattering phenomena. This class is distinguished
by resonance in its interactions, as opposed to those classes in whose
interactions the quality of resonance is absent. Resonance can occur
in a target nucleus which has an excited state whose preferred mode of

de-excitation to the ground state is a single gamma-ray transition.

The primary body of information obtainable from nuclear resonance
fluorescence is contained in the relative intensity of the resonance
line in a scattering or an absorption experiment. From this intensity
the average cross-section for resonance fluorescence may be found. This
average cross-section is related to transition probability of the de-
excitation gamma-ray, which, in turn, is related to the level width
of the excited state of the nucleus. Once the level width is known, the
lifetime of the excited state is found through use of the uncertainty

relationship.

Historical Background

The existance of resonance fluorescence phenomena in atomic transitions
was known and verified experimentally before a single successful nuclear
resonance fluorescence experiment was carried out. In 1929 Kuhn [11*
suggested the possibility of the nuclear analogue to atomic resonance

fluorescence and performed an unsuccessful eXperiment in an attempt to

The numbers in square brackets refer to references listed in the Bibliography.

detect this effect. The next few years brought forth other similarly
unsuccessful attempts [2], [3] in which the researchers were relying on
the natural width of the emission and absorption lines to produce the
conditions for resonance fluorescence. Actually, the occurrence of
resonance fluorescence depends strongly on the Doppler shifts in the
emitted gamma-rays due to previous emissions as well as the emission

and absorption in question.

This is due to the fact that a photon emitted by a nucleus gives
up some of its energy to the nucleus in the form of recoil energy. This
Doppler energy loss is large compared to the natural width of the emission
and absorption lines in the nuclear case. Thus, the possibility of observing
nuclear resonance fluorescence through overlap of the absorption and
emission lines is slight. In the atomic case this is not so; the natural
line widths are large compared to the recoil energy losses, and atomic
resonance will occur by natural overlap of the absorption and emission
lines. Therefore, success in observing nuclear resonance lies in
restoration of the Doppler energy losses to the gamma-ray so that the

emission and absorption lines will overlap.

The effect of the DOppler shifts due to nuclear recoil may be studied
by conservation considerations. Such a study is given below. Non-

relativistic velocities are assumed throughout.

Momentum conservation requires that when a nucleus emits a particle
the nucleus recoil with a momentum equal and opposite to the momentum of

the particle. The gamma-ray, then, yields some energy to the nucleus in

-3-

the form of recoil energy. The amount of energy lost in this manner may
be found through the conservation laws. If the assumption of a freelyu
recoiling nucleus is made and if the emitted particle is a gamma-ray,
then conservation of momentum states:
My - EY/c,
where E.= energy of the gamma-ray, r

M - mass of the nucleus,

and v - velocity of the nucleus due to recoil.
The energy conservation statement for this reaction is:
%Mv2 + EY- E0,
where E0 is the transition energy.
The gamma-ray energy differs from the transition energy by an amount
My2/2, or ‘2

/ EV
Ev‘Eo'an—cz

116

As an example, the 1.27 Mev gamma-ray transition in Sn results

116 nucleus

in a Doppler shift in the energy of 16 ev, assuming the Sn
recoils freely. Thus, the energy left to the gamma-ray is 1.27 Mev

minus 16 ev. On the basis of results of Coulomb excitation experiments [14],
the natural line width is of the order of 10'3 ev. This means that the
Dappler shift is several orders of magnitude larger than the expected

line width, and so, overlap of the emission and absorption lines is

prevented.

If the gamma-ray is now allowed to impinge on a nucleus of mass M

that can recoil freely, then another amount of energy

is lost to this nucleus in recoil. Now, since

 

I2 ‘2
Evy/iv
2Mc2 2Mlc2

the total amount of energy lost by the gamma-ray is approximately

E 2
LIAE

Mo2

3

 

’4--.

Thus, in order for resonance of this gamma-ray with the level E0 to
exist, energy of the magnitude AE must be restored to the gamma-ray

by some outside source.

The first successful observation of the resonance fluorescence
phenomenon was made by Moon [4] in 1951. Moon concentrated on the
restoration of the resonance condition by external means. For this
purpose, an air-driven ultra-centrifuge was utilized, and speeds up
to 7 x 104 cm/sec at the periphery were obtained, which were sufficient

to restore the resonance condition to Hg198.

A later effort by Malmfors [5] used thermal agitation to restore
the resonance condition in the same isotOpe. In this case a source of

198

Au was heated in an oven in much the same arrangement as in the present

consideration.

More recent investigations, [6], [7], as well as the present one,
have utilized the Doppler shifts due to previous radiation in a gaseous

source to bring about correct conditions for resonance fluorescence.

DECAY SCHEME FOR 54 MIN. In116 [8]

116

 

 

 

 

 

 

 

 

 

 

 

In 54 min.
5+
‘\~ 4+
0.60, 21% 2 0.137
+ Ff
4
t
0.87 28%
’ 0.406
1.00, 51% 0.80
1.49
1.08
2+
2.09
1.27
o+

 

 

Stable Sn116

FIGURE 1

II. EXPERIMENTAL CONSIDERATIONS

Sample Preparation

116 is given in Figure 1. From this decay

The decay scheme for Sn
scheme it is seen that the 1.27 Mev level decays directly to the ground
state by a gamma-ray transition, and that it has but one mode of de-
excitation. The necessity of using a level which decays directly to
the ground state is due to the use of a ground state nucleus as a target.

The fact that there is only one mode of de-excitation, a gamma-ray, lends

to ease in analysis, as will be seen in a later section (see Section III).

The decay scheme in Figure 1 shows a 1.49 Mev transition following
an 0.60 Mev beta. At this point, it would appear that the Doppler shift
in the energy of the 1.27 Mev gamma-ray due to this beta-gamma cascade
could restore the resonance condition to the 1.27 Mev gamma-ray.
Consideration of the other decay modes leading to the 1.27 Mev level
suggest that they may aid in the restoration of the resonance condition.
This is investigated further in a later section (see Section III). Therefore,
it was decided to utilize this Doppler broadening of the 1.27 Mev level
due to these previous emissions to restore the momentum lost to the 1.27

Mev gamma-ray through recoil.

Promotion of the Doppler broadening is attained by lengthening the
mean free path; i.e., making the source gaseous. This also serves to
approximate more nearly the case of freely-recoiling nuclei. The source

was made gaseous by combining it before irradiation (In116) with chlorine

to form InCl3. A small amount of this was dissolved in concentrated HCL
and placed in one section of a two-section quartz ampoule. The sample

was then frozen and evacuated, driving off excess water.

After this operation, the sample, while still in the vacuum system,
was heated slightly to drive off any remaining water. Then the sample was
evacuated further and distilled over into the second section of the ampoule, i
3 1

whose volume was approximately 5 cm . This.section was then sealed off and

removed from the rest of the system.

The sample was irradiated in the Ford Reactor of the Phoenix Laboratory,
University of Michigan in Ann Arbor, Michigan. Irradiation times upwards
of two hours were used at a flux of 5 x 1012 cm'2 sec-1. From two to three,
hours elapsed between the removal of the sample from the reactor and the

beginning of the first experimental run. At this time, the strength of the

source was about one millicurie, for a 5 x 104 gm. sample.

The gamma-ray spectrum for a typical sample is shown in Figure 2.
This Spectrum was taken from the data acquired by the monitor side of
the apparatus shown in Figure 3. In order to obtain these data, a 1.5
inch diameter x 1 inch high NaI(Tl) scintillation crystal with photo-
multiplier apparatus was placed 190 cm from the source. Because a spectrum
which would be free from scattering or attenuation effects was desired,
the scintillation crystal was placed so it had a relatively unimpeded view
of the source. These data were used to monitor the strength of the source
throughout the course of the experiment, and such data were taken concurrently

with nearly every run.

-3-

r'.\flt.u £11.." .'

 

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A

70

10

 

 

 

100

 

mugs: hamuuann< aw muflsoo

Channel Number

GAMMA-RAY SPECTRUM

0F Sn116

FIGURE 2

 

 

DETECTOR
(MONITOR)

 

 

 

 

 

PREAMP

 

 

 

 

 

LINEAR
AMPLIFIER

 

 

 

 

 

 

M DETECTOR

 

 

 

 

 

 

 

 

 

PREAMP

 

 

 

 

 

LINEAR
AMPLIFIER

 

 

 

 

 

SOURCE SCATTERING
APPARATUS
256 CHANNEL
PULSE HEIGHT
ANALYZER

 

 

 

 

 

PRINTER

 

 

BLOCK DIAGRAM OF
EXPERIMENTAL APPARATUS

FIGURE 3

-10-

Apparatus

A method of measuring the average cross-section for resonant
scattering is desired. For this measurement a source, scatterer, and
detector are needed, along with suitable shielding to prevent detection
of unscattered radiation. The scattering apparatus used in the present

consideration is shown in Figure 4.

The scattering ring for resonance fluorescence was made of tin, and
was arranged so it could be replaced quickly by a non-resonant scattering
ring of like dimensions. This was to allow a comparison between the
resonant and non-resonant components. The material chosen for the non-
resonant scattering ring was cadmium, while the resonant scattering ring
was tin. The choice of cadmium was made because of the nearness of the
atomic number of cadmium to that of tin. This allowed approximately equal
attenuation due to electronic absorption effects in the two scattering
rings [18]. The oven arrangement shown in Figure 5 allowed wide variations
in the source temperature so it could be made gaseous or solid at will.
The oven temperature was commonly held at 750°C, to assure a gaseous
source [8]. The tin-lead graded absorber at the crystal was used to
attenuate the large number of Compton scattered photons detected by the

crystal.

Some of the 1.27 Mev gamma-rays originating at the source will
impinge on the scattering ring. Some of these, depending on the cross-
116

section for nuclear resonance fluorescence, can excite Sn nuclei in the

scatterer to their 1.27 Mev state and be remradiated. Some of these re-radiated

-11-

gamma-rays can be detected by the-crystal and stored as counts by the
associated electronic apparatus. The crystal was prevented from detecting
sunscattered radiation by the tungsten-lead shield shown in Figure 4. .A

block diagram of the electronic system used is shown in Figure 3.

In order to relate correctly the number of events detected by the
crystal to the number occurring at the source (hence, to the cross-section
(52v), the effects of the geometry of the system must be considered. This
means that the solid angles between the source and scattering rings, and

between the scattering ring and the crystal must be used in the calculations

of 62v.

The solid angle subtended by the crystal at the scattering ring is
not easily calculated and an empirical method was employed. The approach
used here was measuring the relative source strength of a known source as
detected by the crystal. The source used was the 1.33 MCv gamma level in
Co60 because of the nearness of this level to that level under investigation,
1.27 Mev. The source was moved in l/4" intervals vertically on the inside
of the scattering ring, and data were taken at each point. A graph of

these data is shown in Figure 6.

The mean value of these data, when compared to the source strength,
provides a measure of the probability that an event in the 1.3 Mev range
occurring on the scattering ring will be detected by the crystal. This
probability may be regarded as a composite factor consisting of the solid
angle in question, the attenuation due to the Pb-Sn graded absorber, the

crystal efficiency, and the photofraction. Thus,

-12-

(2 A??? , Number of counts detected
D Number of disintegrations occurring at the ring

where QD = fractional solid angle subtended by the detector at the
scatterer,
A = attenuation due to the Pb-Sn absorber,

TI 8 crystal efficiency,

p photofraction.

xii]

This composite factor is used in later calculations.

’1;:

-13-

 

M

U
/

Oven Holding Sn116

sten
}> Shield
a

d
g
m m
T.

//\\\\\\\\\\ V

 

7/////////

 

 

 

 

 

 

 

 

//// /

 

 

 

m/V///.///A

 

Scattering Ring-—w\\\\\/

\\\\—-Sn-Pb Absorber

Nal(T1) Crystal

  

Photomultiplier

SCATTERING APPARATUS

FIGURE 4

 

 

 

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/
A].
4,

 

 

Brass Cap UEJLJ

 

-14-=

Electrical Leads

 

 

 

 

 

 

,/

 

 

 

"0" Ring Seal

 

 

Mica Spacer _____//

Alundum Cement _____J/

Heater Wire _—__/

 

 

   
 

 

 

 

I
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0' ‘
Q
l ‘
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I "
’ t
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for Thermocouple
Leads

  

\\\e_-Ampoule Containing
Source

\.

 

 

-1r

 

 

Mica Plug

 

FIGURE 5

 

 

 

Counts (Arbitrary Units)

Mean Value

 

 

l l

-156

 

l 2

Distance from Top of Scatterer, Inches

PLOT OF COUNTS DETECTED DUE TO
TEST SOURCE ON RING

FIGURE 6

_. f -‘-—-—-—_v—1

-16-
III. CALCULATIONS

Cross Section for Resonance Fluorescence
The cross section for resonance fluorescence is given by an expression

of the Lorentz shape [9], [10]

 

2
0/(E) 2J1 + l A [-3 1—1' (1) M
2 2 ' '
2Jo + 1 8n[(E - EY) + (F/2)] !
where 6i==cross section for resonance fluorescence, :

1, J = spins of the excited and ground levels, respectively,

}{== wavelength of the resonance photon,
[3, [i 3 partial level widths for direct transition to ground, and
for transition through the mode in question, reSpectively,

E = energy of the incident photon,

['11
I

Y E at resonance,

and r“ = total natural width of the excited level.

In the present case the internal conversion may be neglected [11],
so the major mode of decay from the 1.27 Mev level will be through photons
which will be available for resonance fluorescence. Therefore, expression
(1) becomes

2 2
N0 + 1 8n[<E ~ Ey)2 + (F/2)2]

In practice, the cross-section is determined by the number of gamma-
rays resonantly scattered from a scatterer of finite dimensions. Analysis

of such a situation is made easier for the case where the natural width [fl

-17-

is much smaller than the thernal Doppler width A» where

 

1/2
A.= E 2k T
Mc2
Here k = Boltzmann's constant,
and T = absolute temperature.

This limitation of [1 however, is good for most gamma lines. As an

116

example, for the 1.27 Mev level of Sn the thermal Doppler width is

.5 '* ‘ ""_“"!

of the order of 1 ev, while the natural width is of the order of 10'3 ev.

In these cases, the cross-section has the Doppler form [6]

2
6D(E) _ 2J1 + 1 F A e {_(E _ EY)2/A2}

2.10 + 1 4\[;13
This form for 65(E) is normally used to compute results in a self-

absorption experiment. However, in the present case the sources were

too weak to permit such an experiment to be performed.

Equation (2) represents a sharply-peaked function of energy. The
average value of the cross-section, 6;v, is the measurable quantity.

To obtain this

Ida) N(E) dE

[N(E) dE

where the integrals are taken over the incident Spectrum. As mentioned

 

6m.

above, 62E) is a sharply-peaked function, and so N(E), being slowly
varying in the region of resonance, may be regarded as constant at E = Eres,
the resonant energy. This energy, Eras: is the energy at which O/(E)

reaches its maximum value. Hence,

-13-

av = N '

If the de-excitation mode is restricted as previously stated, the integral
in equation (3) is

[K(E)dE= 2J__1__+1 _1’/‘[( LF2

2.10 ‘1’ 1 81‘! E _ EreS)2 + (r/2)2]dE,

where the integration is to be carried out over the incident Spectrum.

 

This has been done [17] with the result

[as .E 3..._J1“(’§°) 1“

2J + 1

Substitution into equation (3) gives

 

6;v_= N(Eres) 2J1 +'1 ()Lo _)2 [q (4)

N 2Jo+1

Heisenberg's principle states
TIerUfi, where T'is the mean lifetime of the state so that substitution

into equation (4) for [wwill give

6 g N(Eres) 2.11 + 1 A0 2 ,5 (5}
av N 2Jo + 1

 

Once ({av is obtained from the experiment, the calculation of
N(Eres)/N must be made in order to use equation (4) to relate 6;v to

I: The value of N(E )/N is estimated through knowledge of the line

res

Shape of the incoming radiation and is explored in the next section.

DOppler Line Shape

The value of N(E )/N can be estimated from information about the

res

nature of the recoil process. This ratio represents the Shape of the

emission line and depends on Doppler shifts due to previous radiations

 

-19-

and thermal broadening. In order to obtain a numerical value for this
ratio the various modes of decay to the 1.27 Mev level must be investigated
as to their effect on the line shape of that level. The assumption is made
that the nuclei recoil freely. Also, for simplicity, it is assumed the

molecules remain intact upon emission of a particle.

Figure 1 shows there are a total of four cascades which lead to the
1.27 Mev level: two of these involve one beta and one gamma transition
preceeding the 1.27 Mev level, and two involve one beta and two gamma
transitions preceeding the 1.27 Mev level. These are the 1.00 Mev beta -
1.08 Mev gamma, 0.60 Mev beta - 1.49 Mev gamma, 0.87 Mev beta - 0.137 Mev
gamma - 1.08 Mev gamma, and the 0.37 Mev beta - 0.406 Mev gamma - 0.80 Mev
gamma cascades, each of which is followed by the 1.27 Mev gamma transition.
The remaining cascades are ignored because they do not lead to the 1.27

Mev level.

The effect of these cascades on the gamma line shape may be found
(see Section I) by energy and momentum considerations. Such an analysis
is carried out below, for the case where the preceeding radiation is'a
beta-gamma-gamma cascade. Similar procedures may be used for analysis

of other cascades.

If a nucleus of mass M.emits a beta particle of momentum PB’ the
nucleus will recoil with a velocity v1. The kinetic energy of the nucleus,
assumed initially to be at rest, is then

T '- lMVlz
2

 

-20-

Conservation of momentum requires that

PB = mwl.

If the nucleus now emits a gamma-ray, the energy requirement is for this

emission

2

2
Mvz ,

1 a

NIH

Y2

where E2 = transition energy of the gamma emission,

EYZ = energy of the gamma-ray,

 

v2 = velocity of the nucleus after emission of the gamma-ray.
From Figure 7, the momenta are resolved into components along the direction
of the gamma and perpendicular to it. For the components parallel to Y2,

EYz/C - le cos 9 = Mvz cos 0

 

Figure 7

-21-

For the components perpendicular to Y2,
le sin 9 = Mvz sin 0.
Elimination of 0 between the expressions for the components of momentum

leads to the equation
2

2
E E 2
ZMCZ 2 MC 2

This expression, in conjunction with the energy equation for this gamma
emission, may be used to eliminate v2. The resulting expression will

give E as a function of EYZ’ v1, and 0. This expression is

2

E 2 E 2
‘ ZMCZ MC

Since the end result of this analysis is to show the effect of these two
emissions on the second gamma-ray, it will be well to introduce this
emission. Calling this second gamma-ray Y3, to identify it as the third

emission, a similar procedure to that above leads to the expression

3 Y3 2Mc2 Mc
where E3 = transition energy of the Y3 level,
E - energy of Y3
and V]- angle between v2 and Y3. (See Figure 8)

As before, it is desirable to eliminate v2, sinqe it is not a determined
quantity. This may be done through the momentum components for the emission

of Y2, which suggest

. 2 2 _ 1/2
sz (P Y2 + P B 2PY2 PB cos 0)
where P -.EI§ - momentum of Y ,
Y2 c 2

and Pa = le a momentum of B.

+ -22-

Y3

V! "i
V2 I
Y3
Figure 8
Substitution for Mvz in the expression for E3 yields
E2Y3 EY3 2 2 1/2
E3-EY3+-2-};-3--—ME[PY2+PB-ZPBPYZCOSQ] COSW.

This is the desired result which shows the Doppler shift in Y3 due to

previous emissions whose momenta are PB and PYZ'

The preceeding development may be utilized to yield the Doppler

broadening of Y3 with the approximation suggested in Section I; that is,

2
£212.95;
Me2 Me2

With this, then, the energy of the Y3 photon may be written:

 

E2 E
= - 3 - 3 2 2 _ 1/2
EY3 E3 2 ii; [P Y2 + P B 2PY2 PB cos 0] cos yV.
2Mc
E23

 

The Doppler line shape of Y3 is centered about E3 - and depends for
ZMC

its form on the third term of the right member above.

 

-23-

The line shape may now be estimated by graphical methods. The
procedure is to calculate the energy Spread due to the previous emissions
leading to the energy level in question, and add these graphically to
produce a plot of N(Eres)/N per electron volt interval; In the present
investigation the Doppler Spectra due to beta emissions were regarded as

triangular, as an approximation due to the Shape of the beta spectrum.

 

This approximation results in a triangular shape for the neutrino Spectrum

as well. The beta and neutrino emissions were considered to be isotropic.

The contributions to the line shape due to each cascade may now be
calculated. For the 1.0 Mev beta - 1.08 Mev gamma cascade, the maximum
momentum which may be imparted to the nucleus by the beta and neutrino
emission is 2.78 moc. This means that the maximum Doppler energy shift
of the 1.27 Mev photon due to this emission is.i6.95 ev. The gamma in
this cascade, having an energy of 1.08 Mev, can add to cause a maximum

Doppler Shift of.i12.25 ev.

Assuming isotropic emissions, the line shape due to one cascade
consists of elemental trapezoidal segments. The major base of a segment
is given by the maximum Doppler energy shift due to the particular emissions.
The minor base of a segment is given by the smallest combination of these
same Doppler energies. The area of the trapezoidal segment is proportional
to that fraction of the total emissions leading to the 1.27 Mev level which
occur in the manner being considered. Hence, the height of each segment

is well defined.

-24-

The line shape of the l. - Mev beta - 1.08 Mev gamma cascade results
in a bell-shaped curve whose base is 24.5 ev wide and whose height is at
0.0472 ev-l. Similar curves are found for the remaining three cascades.
For the 0.60 Mev beta - 1.49 Mev gamma cascade, the width is 24.24 ev,
and the height is 0.0179 ev'l; for the 0.87 Mev beta - 0.137 Mev and
1.08 Mev gammas, the width is 15 ev and the height is 0.0046 ev'lg for
the 0.87 Mev beta - 0.41 Mev and 0.80 Mev gammas, the width is 24.26 ev,

and the height is 0.0081 ev'l.

The composite line shape is shown in Figure 9. The center of this
line Shape is located a distance from the energy at which resonance will

occur. This energy, E is equal to the level energy plus the total

res’
energy lost to that photon through recoil in the emission and absorption
processes of nuclear resonance fluorescence. Hence, the expression for

the line shape center-to-Eres distance, E', is

2 2

...—2,
Mlc Mzc
where E' is the distance mentioned above,
Ey4 is the gamma-ray energy in question,
and M1 and M2 are the masses of the emitting and absorbing nuclei.

For the proposed case, E' is found to be 11.4 ev.~ From Figure 9, the

value for N(E)/N at E a Ere is found to be 0.004 per ev.

8

"1

N(E)/N in Percent per ev

4.

 

 

 

 

 

-25-

 

 

-12 -s -4

 

Energy in ev About Line Shape Center

LINE SHAPE OF 1.27 Mev GAMMA IN Sn116

FIGURE 9

 

-25-
IV. RESULTS

Data Analysis

A composite set of data is shown in Figure 10. These data are the
sums of the data taken over one entire day. Figure 10 consists of three
separate plots: one for resonant scattering, one for non-resonant
scattering, and a plot showing the difference between the first two.
A total of four days of data were accumulated with approximately ten
runs being taken each day. Three distinct sources were used on different
days, one source being used twice. The remaining three days' data were
divided so there were about two runs with the resonant scatterer to each
run with the non-resonant scatterer. The average result of all of these

runs is the result which is reported here.

In order to obtain a correct idea of the differences between the data
for the resonant case and the non-resonant Case, One must somehow correct
these data for the decrease in source activity in time and the dead time
of the electronics. The first of these adjustments was done through the
expression

A:

which describes the exponential decay of the quantity N whose initial

N -Nbe'

value was No, with )1 being the decay constant and t being time. Integration
of this expression over a time inverval At beginning at t1 shows that the
average value of N in the interval Am, N, may be used to find the initial

value, N provided )1 and t1 are also known. For this purpose

0)

-27..

 

Counts in Arbitrary Units

 

 

 

 

40 50 60
Channel Number

COMPOSITE PLOT OF ONE DAY'S DATA

 

<:) Resonant Scatterer -—-——--—. <:) Nonresonant Scatterer
6) Difference -- .‘ -—

FIGURE 10

-23-

N .‘E AN: eAt1 (1)
9 l 4- e'AAt

116, which gives

For the present case of the 54-minute-activity of Sn
rise to the 1.27 Mev level, the decay constant is found to be
A - 0.0128 min'l.

This value for )i was used in equation (1) to correct the data for sOurce‘

decay.

The second adjustment of the data, that for the dead time of the
electronics, is an integral part of the design of the R.I.D.L. 256 channel
pulse height analyzer used in the measurements. This correction caused the
counting periods to be somewhat longer than the time during which the .
measurements were actually being taken. For example, if a dead time of
25% were maintained throughout a counting period of length T, the actual
length of time during which counting was being done would be 0.75T. This
corrected length of counting period must be used in place of AI in equation

(1) to account for dead time. Such corrections were made in all cases.

Further calibrations are required, as mentioned in Section II, to
allow for the various parameters of the experiment other than the cross-
section for resonant scattering. Thus, equation (4) of Section 111 must

be mmdified to take into account these parameters.

The number of gamma-rays impinging on the scattering ring, N'(EY), is

given by
way) - 119,,

-29-

where ()8 - fractional solid angle subtended by the scattering ring
' at the source.
Also, the number of resonantly-scattered gamma-rays detected by the crystal,
S, is related to the total number of resonantly-scattered gamma-rays, 8',
through the expression
3 - 3' QB ATlpd,
where D - fractional solid angle subtended by the crystal at the

l

scattering ring, ‘
A - absorption by the graded Sanb absorber,
7? I efficiency [16] of the crystal,

photofraction,

'U
I

and d - non-selective electronic absorption in the ring obtained

from the average value of e"4i¥ over the depth of the
scatterer, where./V1 - 0.0484 cm2/gm, and x~- scatterer
depth in gm/cmz. In this Case, deg 0.81.

The factors Q, A, 7?, and p are determined as a single factor f taken

from the mean value of the plot in Figure 6.

Hence, the expression which may be used to calculate the average
cross-section for resonance fluorescence from the scattering data is
S - NQS QD (av Aanq (3)
where q I term representing the selective-absorption by the scatterer.

For this case qrgl since the scatterfr is essentially thin

. [10].

n I number of Sn116

2

nuclei per cm. in the scatterer.

-30-

This expression may now be used in conjunction with equation (4) of

Section III to find the lifetime of the 1.27 Mev state.

In all cases the source strength was of the order of one millicurie
(with the exception of the first day's set of runs which were not used due
to the very weak source) under the 1.27 Mev peak. The number of counts
registered which could be attributed to resonantly-scattered radiation was.
extremely low; in fact, it was of the order of magnitude of the statistical
error. The result obtained for the lower limit average cross-section was
1.3111 x 10'2 barns. With this value for 6;v the value for the upper
limit of Tfrom equation (5), Section. III, becomes 0.84 i.7 x 10"12

seconds.

Conclusions
The result that T'is less than 0.84 x 10"12 seconds differs by a
factor of two from those results quoted in [14] and [15]. Coulomb

12

' excitation in [14] yielded a lifetime of 0.5 x 10- seconds, while

12 seconds for 7:

resonance fluorescence [15] gave a value Of 0.33 x 10-
The very low counting rate, of the order of one count per second, which
could be attributed to the resonant peak, contributed to the large

statistical errors in the present result.

It has been suggested [16] that the weakness of the source, coupled
with the small cross-section and a high background of non-resonant Scattered
counts, helped to obscure the resonance peak. Because of this it was not
possible to accumulate the large number of counts necessary to measurethe
effect accurately. Reference [15] has shown that experiments with more active

sources give better results.

10.

11.
12.
13.
14.
15.
16.

17.

-31-
BIBLIOGRAPHY

W. Kuhn, Phil. Mag. 8, 625 (1929)

F. R. Metzger, Phys. Rev. 83, 842 (1951)

F. R. Metzger and W. B. Todd, Phys. Rev. 21, 1286 (1953)

P. B. Moon, Proc. Phys. Soc. Lond.‘A§4, 76 (1951)

K. G. Mmlmfors, Arkiv Fysik‘g, 49 (1952)

F. R. Metzger, Phys. Rev. 123, 983 (1956)

N. Delyagin, Sov. Phys. JETP‘QZLIQ), 837 (1960)

Handbook of Physics and Chemistry, 37th edition, C. D. Hodgman, ed.
(Chemical Rubber Publishing Co., Cleveland, Ohio)

F. R. Metzger, "Resonance Fluorescence in Nuclei" in.§£ggress in Nuclear
Ph sics, 0. R. Frisch, ed., (Pergammon Press), pp. 59-60

M. E. Rose, Internal Conversion Coefficients, (Interscience Publishers,
Inc., New York)

C. P. Swann and F. R. Metzger, Phys. Rev.'IQ§, 982 (1957)

S. Ofer and A. Schwartzchild, Phys. Rev.‘ll§, 725 (1959)

N. R. C. Data Sheets

G. B. Beard and W. H. Kelly, Nuc. Phys.'43, 523 (1963)

W. H. Kelly, Private Communication (1963)

F. R. Metzger, Phys. Rev. .131, 286 (1956)

Evans, R. D., The Atomic Nucleus (MeGraw-Hill Book Co., New York)

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