TRANSMITTAL OF ATOMIC ENERGY PUBLICATIONS.

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• Publication Date: July 1, 1958
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STAT
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UNCLASSIFIED
On the Determination of
Nuclear Spins by the Study
of Neutron Capture Gamma Rays
by
GEORG TRUMPY
No 13
JENER PUBLICATIONS
JOINT ESTABLISHMENT FOR NUCLEAR ENERGY RESEARCH
Kjeller per Lillestrom, 1957
AKADEMISK TRYKNINGSSENTRAL ? BLINDERN, OSLO 1957
STAT
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's11
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On the Determination of
Nuclear Spins by the Study
of Neutron Capture Gamma Rays
by
GEORG TRUMPY
No. 13
JENER PUBLICATIONS
JOINT ESTABLISHMENT FOR NUCLEAR ENERGY RESEARCH
Kjeller per Lillestrom, 1957
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CONTENTS
ABSTRACT
CHAPTER I. INTRODUCTION
CHAPTER II. GENERAL THEORY
Page
5
7
11
1. Thermal neutron capture
11
2. Electromagnetic radiation
12
3. Nuclear energy levels
17
CHAPTER III. CIRCULAR POLARIZATION OF GAMMA-RAYS FOLLOWING
CAPTURE OF POLARIZED NEUTRONS
21
1. Main principles
21
2. Polarization of the radiation
24
3. Polarized thermal neutron beams ? . . ..... . . . ..........
31
4. Principles for the measurement of circular polarization
35
5. Experimental set-up
39
6. Treatment of experimental data
47
7. Measurements
49.
CHAPTER IV. COINCIDENCES AND ANGULAR CORRELATION OF GAMMA-
RAY CASCADES
51
1. Theory
51
2. Experimental set-up
54
3. Treatment of experimental data
60
4. Measurements
61
CHAPTER V. RESULTS
67
1. c 36
67
2. S33
68
3. ca41
69
4. Ti49
70
5, cr54
70
6. Fe57
72
7. Ni59 ?
73
8. cu64
73
9. Zn65
75
10. W183
?
76
11. Conclusion
76
ACKNOWLEDGEMENTS
77
REFERENCES
79
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ABSTRACT
Two types of experiments, studying angular momenta of y -rays and of energy levels connected
with radiative neutron capture, have been performed. Circular polarization of the y -rays
emitted from nuclei capturing polarized neutrons was studied by means of the dependence of
the Compton cross section upon the relative spin direction of the photon and the electron.
Thermal neutrons polarized by transmission through magnetized iron fell on the (n,)-target,
and the r -rays were detected by two Nal (TO-crystals after having passed through analyzers
of iron magnetized in the direction of transmission, The degree of circular polarization .was
found to be in accordance with theory. Measurements were performed for the most intense
neutron capture r -rays from S, Ca, Ti, Cr, Fe, Ni, Cu, Zn and W.
Coincidence and angular correlation experiments were carried out using neutron capturing
targets as sources. The existence of several r -ray cascades was established. An earlier
unobserved v-ray of 0.60 ? 0.05 MeV in Cu64 was found. The most prominent i-ray cascades
of Cl, Cr, Ni and Cu were studied by the angular correlation method.
Combined results of these experiments yielded several spin values for the nuclei studied. The
first part of the paper deals with theoretical aspects pertinent to methods of these kinds In
particular, the degree of circular polarization of -rays emitted from nuclei capturing polarized
neutrons has been calculated for various cases, including emission of mixed multipoles.
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CHAPTER I
INTRODUCTION
The existing theories on nuclear structure have led to various predictions about nuclear
properties. Particularly the nuclear shell model by Mayer (i950) and Haxel, Jensen and Suess
(1950) together with the theory on collective motions in nuclei by Bohr and Mottelson (1952,
1953) have successfully accounted for a greater ?art of the existing data on nuclear energy
level schemes. The spins x) and parities of stable nuclei are now very well understood, but
compared to the large number of energy levels that have been observed, rather little has been
experimentally determined about nuclear spins in excited states. From measurements on
energies, spins and parities of excited nuclear levels the reliability of theoretical predictions
can be checked. On the other hand, studies of cumulated experimental nuclear data may suggest
new theoretical methods.
No generally useful method has been developed for the study of the spins of the nuclear energy
levels. There are many different ways in which nuclear states can be observed, but any parti-
cular level is usually known from one or two types of reactions only.
Special conventional methods, primarily used for the study of the ground states of stable nuclei,-
are well developed. Among these are the measurement of the hyperfine structure of atomic
spectra, the atomic and molecular beam methods, the nuclear induction methods and microwave
spectroscopy. These techniques can also be applied to the measurement of the 'properties of
relatively long-lived radioactive and isomeric states, provided that the excited nuclei can be
obtained in sufficient quantity.
The spins of short-lived nuclear states must be studied by means of observation of their decay
products. In some cases this can be done for random orientation of the exited nuclei, for
example when one can measure the lifetime or internal conversion coefficient of 1-radiation,
the lifetime and form of the spectrum for -radiation, and the peak height and width of resonan-
ces for particle absorption and scattering. The theories for the lifetimes of y - and p -rays and
for the shape of g -spectra are, however, not complete and ambiguities may occur in the deter-
mination of nuclear spins with these methods.
The third group of experimental techniques consists of the measurement of angular distribution
or polarization of the reaction products. Clearly, these properties, being dependent upon a
preferred direction in space, require that the excited nuclei are polarized. Polarization here
includes any deviation from the usual random orientation of the nuclear spin directions, Spiers
(1948) first showed that the reaction products from aligned nuclei in general will be anisotropi-
cally distributed, The polarization and distribution of r -rays was calculated by Tolhoek and
Cox (1953).
x) According to current terminology, the total angular momentum of a nucleus in this paper
will be referred to as "nuclear spin" in cases where no confusion with intrinsic spin of
single particles should be possible.
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The most straightforward way of 'polarizing nuclei is the alignment bf nuclear magnetic moments
in magnetic fields, This method, however, requires very low temperatures,
A(L,M,r )
? ..M=-L
? f k" ?-??? s'.11L,1 ...t *?''.??"
. ,
?, ? '?? *. ? ;
( 2 9)
,
Here, the terms A(L,M,r) are pure multipole fields, being functions of vector spherical
harmonics. L is the angular momentum quantum number and M is the z-component, thereof.
Accordingly, also the electric field may be expanded into multipoles, and one gets:
I 1; 1: ;00 ? . . .? . '
, ?,.
0 j f.;B:4-.. 5 "1: ? o
. , r _ -
'
, L = ,M=-1
wherel-Vel are eletriclitectors,"of'the electric and magnetic rnultipole radiation
respectively and the amplitudes are of the form:
C =
+ 41
(2L 1 )
Here QLNI is the multipole matrix element of the transition. It is dependent upon the convection
currents and the varying rnagaspzation.denSity in the nucleus. An equation similar to (2.10)
. .
applies for the magnetic field H. ,
The parities for the two, types 9f multipoleza.diation are:
- It :Jo H r_. ?
1
(L + 1) -2-
kL+2
LLM
/?
?
' ? ? - ? '
? , ??? : , ?
(2.11)x)
and ,
TT (L,m)= (-1)
.?? ? k ?? ';';' "T.
IT
( 1 ( Lax)
mag ? ,
' * ,
?
:
?
?
' *?; ?'? : .
?
(2.l2).
Even and odd parities a.re denoted by 17= +1 and -1 respectively so that by the expansion of
the electromagnetic fields according to equation (2.10), the radiation is classified,in,terms of
the angular momentum and parity change it produces in the radiating system
.x) (2L + 1) fl = 3. 5
?
(2 L + 1 )
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PY Appr
??.?
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Transitions of multipole radiation between
Jb, are limited by the selection rule:
--+
or
= L
a
m rn M
a. b ,
where m is the z-component of the total angular momentum. The radiation at least carries
away angular momentum 1, so that L>1 Another selection rule follows from the parity of the
radiation:
nuclear levels with total angular momenta ja and
TT a =.rad
TT 7b
(2 16)
TABLE 1
The lowest multipole order allowed by the selection rules
Angular momentum carried away
by radiation = L
0
1
2
3
4
5
Parity of
the radiation
-1
None
El
M2
E3
M4
E5
Tr rad
+1
None
MI
E2
M3
E4
M5
The lowest possible order of multipole radiation is given in table las determined by the above-
mentioned selection rules. We shall see that this radiation generally has the highest transition
probability. Electric and magnetic 2L-poles are denoted by the symbols EL and ML respectively.
??'
The radiated energy is proportional to the square of the absolute value of the amplitude c, and
one gets for the transition probability of a
w(LM) 81T (L + 1)
, _
L [(2L + 1) :12
quantum per unit time:
k2L + 1 2
IQL1n1
(2.17)
The matrix element LM can only be derived when the nuclear properties are, completely known.
On the basis of the individual particle model, Weisskopf (1951) obtained a rough estimate for the
transition probability for the electric radiation of multipole order L:
w'l (L)N 4.4..1021(L+1) ( 3 )2
e
L? [(2L+1) !!)2 L+3
ck 2L+1 R2L s'ec-1
197 MeV /
where the nuclear radius R is given in 10-13 cm.
An estimate fbr the magnetic radiation is obtained by a comparison ,between the matrix elements
of the transitions, which are dependent upon the electric and magnetic moments of the nucleus.
The electric moment is of the order of eR, and the magnitude of the magnetic moment is a few
times e Ann c when the action of the orbital momentum and of. the spins of the nucleons are
added. Here mn is the nucleon Mass. The ratio of the transition probabilities is:
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RIM'IMIWZMO.r4MirrOPR MR,VaM
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This quantity is approlcimately 102 " for A = 100. The order of magnitude of the ratio between
successive multipole orders is (kR)2, which is as small as 10-5 for A = 100 and 'i-energy
=0.5 MeV. According to these estimates the transition probability is quickly reduced for succes-
sive radiations of the eries: El, Ml, E2 M2, ? ? ? ?
Figure 1.
Theoretical y-ray transition probability for various multipole orders, as calculated from
formulae (2.18) and (2.19). For the nuclear radius was used the value R = 6.73.10-13 cm,
corresponding to atomic weight A = 100.
Figure 1 is a graphical representation of the theoretical transition probability expressed by the
r
formulae (2.18) and (2.19). The magnitude of the resonance width for emission of r -radiation _ w. t, is also giveo in the figure. According to Weisskopf, formula (2.18) must be considered
r
as an upper limit for the transition probability. In fact, practically all measurements of
transition probabilities yield values which are several orders of magnitude smaller than w'
(Goldhaber. and Sunyar 1951). In spite of this, the theory accounts well for the ratio between
different multipoles, and for the dependence upon energy and nuclear radius.
As seen from the selection rules illustrated in table land in figure 1, the lowest allowed order
of magnetic radiation will be very improbable when the most intense radiation is of the electric
type. Mixing of two types of radiation is much more probable if the most intense y -ray according
to the above rules is a Magnetic multipole. Electric radiation of one multipole order higher,
?:n
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also being allowed, will in the region of 1
mixing observed are of the type M1 E2.
MeV be a. factor 1,00 less probable. Most cases
Mayer and Jertsen (1955) derived a separate selection rule for the case that the transition is due
to a single proton or a single neutron which changes its orbital angular momentum from .fdri t
In this case the additional condition is:
L "efl
Generally, this rule has not complete validity, but transitions violating the ,rule have a stronly
reduced transition probability as compared with the expressions (2.18) and (2.19).
When a neutron is captured, the nucleus is excited to approximately 8 MeV, and the following
'-ray emission leads, either directly, or by ,successive '-rays emitted in cascade, to the
,ground state of the compound nucleus. Blatt and Weisskopf (1952, chapter XII) have shown that
for emission from highly excited states a more correct form of the transition probability is
obtained when it is multiplied with a factor proportional to the average level spacing Dt in the
region of the initial state. Only levels from which radiative transitions of the same multipole
order can produce the same final state are concerned. The authors proposed the proportionality
constant Do k 0.5 MeV. -Transition probabilities forhigh energy dipole and quadrupole radia-
tion were determined by Kinsey and Bartholomew (1954), who found that the theoretical transition
probability w" = (DeDo)w' was too small by about a factor 10-2 for El radiation and somewhat
larger for M1 fadiation.
The -ray width, being proportional to the transition probability
for transitions to various lower levels:
From a careful study of various neutron resonances Levin and Hughes (1956) found that ri
was of the order of 0.1 eV for nearly all cases studied. As a general rule, ri is decreasing
slowly with increasing A,but seems to increase somewhat in the regions of closed nucleon
shells. Furthermore, Fir is not varying strongly, if at all, amongst resonances of the same
nucleus. A comparison of the measurements of Levin and Hughes with those of Kinsey and
Bartholomew indicates that most of the radiation emitted in neutron capture is of the electric
dipole type. This is a plausible result since generally the de-excitation may proceed by y -ray
emission to many lower levels, and there is a great chance that some of these levels can be
reached by electric dipole radiation, which because of its high transition probability then will
account for the greater part of the decay.
3. Nuclear energy levels.
The best general agreement with observed nuclear level data is obtained by the nuclear shell
theory combined with the theory on collective motion of the nucleons.
In the shell model (Mayer 1950; Haxel, Jensen and Suess 1950) the nucleons are supposed to be
moving in individual orbits. The eigenfunctions of the particle motion in the spherically, symme-
tric potential chosen, are, analogous to the electron states of an atom, given by the quantum
numbers n andl, where n is the number of radial nodes of the eigenfunction and2is the orbital
angular momentum quantum number. In order to explain the experimental data it is necessary
to add a spin-orbit-coupling potential which, implies a splitting of the.t-levels due to the nucleon
spin. The two total angular momentum states J =2.? ?i then have different energies, and contrary
to the case of atomic ,spectra, the state with parallel spin and angular momentum, J. ..,e + 1, has
the lower energy. Nucleon configurations are given by the quantum numbers ,(rieJ)V whe4.e
is the population of the level, and the value oais given by the usual letters s, p, d, f, . . . . . .
The level degeneracy is 2(2,10+ 1), and the parity-of the eigenflinction is 72. (-1)4 When the
parameters of the potentials are adjusted to give the best possible agreement between the theore-
tical and the existing experimental values of nuclear spins in ground sta.tes,one arrives a.ta.n energy
level scheme of which the lowest part is shown in figure 2, taken from Klinkenberg (1952).
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- 19
bands in molecular spectra. The lowest excited states in the regions 155 225
are very well explained by this theory. The quantum energies of collective motions are large
for small nuclei and for systems in the vicinity of closed shells. In these cases, the nuclear
shell levels account for the lowest excited states. -Above the two or three lowest states one
must expect contributions from combinations of single particle configurations which will be
hard to predict or explain unambiguously. As the excitation energy increases, the number of
combinations and the density of levels will increase rapidly. For odd-A nuclei, the single
particle model applies, and the lowest energy levels are simply give by figure 2. Even-even
nuclei can be excited when one nucleon pair obtains a change of the coupling in the same.
configuration as that of the ground state. The first excited state then becomes angular momen-
tum 2., and the second has the possibilities 0,2 and 4. A change of coupling only, involves no
change of parity. Also the first excited state of the collective motion in even-even nuclei has
angular momentum 2 and no change of parity. In fact this rule has been confirmed in almost
all cases studied (S charff-Goldhaber 1953). For the more complicated case of excited states
of odd-odd nuclei, no rules have been formed.
Generally the spacing of energy levels is decreasing as A increases, due to the action of collec-
tive motions in the nucleus. Because of this, most neutron capture y -ray spectra for heavy
nuclei have been resolved to a small extent only. Exceptions are encountered in the vicinity of
closed nucleon shells, where the spectra clearly resemble those of light nuclei. For capture of
thermal neutrons in even-even nuclei the spin of the compound nucleus has only one possible
I
= +! 1
Jc II _ = ? , and the spectrum may then be fairly simple. If
2 2
resulting nucleus is a p-state which has spin! or 3 and odd parity, the disintegration to the ground
2 2
state will be of electric dipole (E1)-type and of high intensity. For reasons of poor resolving power,
most of the -rays experimentally studied in the present work were of the type mentioned, and all
except one originated in light nuclei (Z 30).
value,
the ground level of the
Figure 2.
Energy level scheme of the nuclear shell model.
In the ground state of the nucleus the nucleons are filling the lowest possible energy states of
the level system. In order to excite the nucleus, one or more of them must be lifted to a higher
level. For the nuclei with filled shells, i.e. for proton and neutron numbers 2, 8, 20, 28, 50, 82
and 126, comparatively high energies are required for the excitation of the system. These
"closed shell" nuclei are therefore unusually stable.
The lowest energy states are obtained when pairs of protons and neutrons couple their angular
momenta to zero with even parity. Thus even-even nuclei always have zero spin and even parity
in the ground state. This rule has been verified in all cases experimentally studied. In nuclei
with odd mass number A, there will be a core consisting of even numbers of protons and neu-
trons, and one extra nucleon which alone determines the spin and parity of the nucleus. This
single particle model has given an extremely good explanation of the spins of stable odd-A nuclei.
A few exceptions to this rule and to the sequence of levels in figure 2 must be explained by
special coupling rules, (Mayer and Jensen 1955). In an odd-odd nucleus one proton and one neutron
couple their angular momenta to produce the total angular momentum of the nucleus. For :this
case complete coupling rules have not been deduced.
In general, the excited states of nuclei are due to the combined action of the shell structure and
the collective motion of the nucleons which has been treated by Bohr and Mottelson (1952, 1953).
For the larger nuclei far from closed shells the collective motion of the particles in the defor-
med nucleus contributes appreciably to the properties of the excited states. This is an additional
degree of freedom which gives rise to rotational and vibrational levels in analogy with rotational
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CIRCULAR POLARIZATION OF GAMMA-RAYS FOLLOWING CAPTURE
OF POLARIZED NEUTRONS
Consider the reaction in which; -rays are emitted from a target as a result of the absorption
of polarized thermal neutrons. We shall in the following discuss the effects that the polarization
may have upon the radiation, and the possibilities of detecting these effects. It shall also be
investigated to what extent these detecting methods may be used for the determination of nuclear
properties.
1. Main principles.
The polarization of a particle beam is generally defined as the net alignment of the particle spins:
I+ -;
=
I+ +I_
where P is the polarization and I+ and I are intensities of particles with spins parallel and
antiparallel to a certain axis of reference. This definition is also valid for photons as far as
circularly polarized radiation is concerned.
The experiment treated in the present chapter deals with polarized slow neutrons, which have
zero angular momentum, and with Circularly polarized 1-rays., Certain* rules, which imply a
limitation on the application of these effects to nuclear spectroscopy, may easily be deduced.
Consider a. nuclear reaction induced by particles with angular momentum zero, and the net spin
direction along the x-axis. The outgoing intensity must have symmetry about the x-axis, since
no other direction is defined for the compound system. Accordingly the intensity I emitted in
a certain direction (x, y, z) is independent of a, reversal of the ,y-co-ordinate:
1(x, y, z) = - y z).
If we perform the transformation
xl = x, y -y, z' = z,
(1.3
the polarization will reverse its direction since spin is an axial vector. The intensity will be
unaltered and equal to
I( y', z')
-y
z) y, z
which means that the direction of polarization has no influence upon the distribution of the
reaction products.
(1.4)
A similar restriction applies for the scattering of circularly polarized photons. If the radiation
_
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is incident along the z-axis, this is the direction of polarization, and accordingly it is the axis
of symmetry. Also in this case the transformation (1.3) will reverse the direction of polari-
zation, while the intensity is unaltered as in equation (1.4). Therefore one cannot distinguish
between left and right circular polarization of radiation purely by measurement of the scattered
photons.
These two conclusions on the application of polarization are also contained in the polarization
theorems number 2 and 3 formulated by Wolfenstein (1949 b)
Consider a material which mainly scatters particles having a definite spin direction. When
there are only two possible orientations of the spin due to quantum mechanical requirements,.
the total cross section may be expressed by
where do is the cross section for unpolarized particles, and o is the
or subtracted, depending upon whether the particle spins are parallel
axis of reference. The corresponding particle currents are It and I'
transmitted through polarizing material is given by
? e630 dp)
+ +
IT f= 1-
contribution that is added
or antiparallel to a certain
respectively. The intensity1.
(1.6)
where T1 is the transmission and 10.and II are the intensities of the incident and the transmitted
beams as indicated in the left part of figure 3. All the upper or all the lower signs should be
chosen, indicating the spin direction of the particles considered. is the number of atoms per
square centimetre of the beam.
An unpolarized incident beam is characterized by
of (1.1) and (1.6) gives:
e-fcip -
e9c/13
e 9 e 9n
cfp
0 2cri:,2
1+1
. In this case, the combination
1.7)
2
The condition for the validity of the approximate formula is dp < 1. The relative difference
between the transmission Tp and Tu,respectively, of the polarizer and of the same device with-
out polarizing properties is called the "single transmission effect":
V.
T -T
p .0
e (IP + e CC/13
for Cfp (
Polarization now becomes the
1.8
orm P Q/ (i , In many experiments the measurement
determination of 6p and the polarization P.
of rt can be used as a simple method for t
Equation (1.1) gives for unpolarized incident beam:
1 +
1 2? 1
(1.9
Generally, the properties of a polarizer are completely described by the transmission T and by
the polarization P of the emitted beam when the incident beam is unpolarized. The transmissions
for the two components of the beam with opposite polarization direc'tions are equal to T(1 +_ P).
Figure 3 shows the principle of a double transmission polarization experiment, which means
that the particle beam passes successively through, two polarizers with properties T1 ,Pi and
T2'P2 respectively. When the incident particles are unpolarized, the intensities emitted from
the second polarizer are:
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BEAM
23 -
TRANSMISSION Ti
POLARIZATION Pi
Figure 3.
Schematical double transmission experiment.
12
T2 (1 - P2)
T T P1) (1 - F2)
With a polarization-independent detector the intensity
DETECTOR
12 - 12+ + Ii = 10 T1 T2 (I + P1 P2)
1
is measured, If 12 is the observed counting rate for parallel polarizers (P 1P2 > 0
that obtained for antiparallel polarizers (P1P2 < 0) we get the relation
1.132
12 I 2
4+4
I
and 12 is
(Liz
Thus, the polarization P1 of a particle beam can be determined by means of an "analyzer"
whose polarization P2 is known.
In the production of polarized particles by passage through matter, a compromise must always
be made between the increase in polarization and the decrease in intensity as the thickness of
the polarizer is increased. When background counts are neglected, the standard deviation of a
counting experiment measuring polarization is
p oc 4 II .I1, = 1
I' I" P117,
9Cto
cc for 01/3(1
cf
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e cro
- 24 -
The minimum value of this quantity is obtained for S46
statistical accuracy of a measurement carried out in a certain time is obtained when the length
of the polarize I? is equal to twice the mean free path in the polarizing material.
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2. This means that the greatest
Po ariz
ion of the radiation.
In the discussion the radiation emitted after polarized neutron capture, one can make use of the
well known theory for the angular correlation of radiation. This procedure was used by Bieden-
,
ham) Rose and Arficen (1951 a), who treated the possibility of linearly polarized radiation. In
the following we shall give a short review of their theory, which then Will be used to calculate
the emission probability for circularly polarized photons.
NEUTRON
CAPTURED
INITIAL
STATE
COMPOUND
STATE
A+1
AMINO
1-RAY
EMITTED
FINAL
STATE
Figure 4.
Energy level scheme for (71,y )-reaction.
The angular momentum quantities involved are shown in the simple decay scheme of figure 4.
The target nucleus, having A nucleons, has total angular momentum Ji, with z-component mi.
The compound and final states of the nucleus have one nucleon more, and the total angular
momenta are Jc and Jf with z-components mc and mf respectively. Since the transition between
the compound and the final state is due to a single y-ray with multipole order L and angular
momentum in the z=direction M, we get the following relations between these quantities
1
13-f-Lf( - 1.1n figures 8 an 9 is shown the ratio /1; (d e (..pidsa)kdeIL) between
j,
the polarization dependent and the ordinary Compton cross section as function of the scattering
angle, for the two above Mentioned cases of electron polarization. The diagrams illustrate the
large effects resulting from circular polarization of low energy r-rays when the electrons are
polarized transverse to the incident beam. When the photon and the electron are polarized along
the same axis large effects can be obtained for all energies.
For the study of single y -rays resulting from neutron capture, discrimination between various
photon energies is required. When scattered quanta are studied, energy discrimination can
only be performed if narrow r-ray beams are available. In the present experiment rather
large y-ray sources must be used in order to obtain sufficient intensity. Therefore, a less
eclassified in Part - Sanitized Copy Approved for Release
0.51
?1.02
t
2:04MeV
4.09
8.18
- 37 -
0.51M0
102
2.04
4.09
8.18
0
cos n9
Figure 8.
The relative polarization dependent part of
the differential Compton cross section for
iron. The scattering electron is polarized
in the propagation direction of the y-ray.
-0.5
pm*
1-
-1
cos (19)
Figure 9.
The relative polarization dependent part of
the differential Compton cross section for
iron. The polarization vector of the scattering
electron is in the same plane as the incident
and the emitted y -ray, and it is perpendicular
to the incident beam.
polarization- sensitive method, which consists in measurmg tne transmission of r -radiation
through magnetized iron, was applied. In such an experiment one can, to some extent, distin-
guish between y -rays of different energies by selecting pulses from a scintillation crystal.
The transmission for iron is given by the total cross section which can be obtained by inte-
gration of the differential cross section over the sphere. As a result of the integration over
9, components of the electron spin perpendicular to the axis of incidence will cancel out. The
total, Compton cross section for a single electron then becomes
r 14 fr?
-e- dr).
e c
r-?
162 3 3
J d
where the ordinary Compton cross section is
17ff I + 2k -1 in(1+2k)]
e c = 2Tre
fr 2 {1 +k [ +i
and the polarization dependent part
fab
e P .2cre2 [1+k
(1+20 - 1+4k 4 5k2
2k4 k(1+2k)2
50-Yr 2013/10/24: CIA-RDP81-n1n4nn9Ann1 rirICI7
1 1 + 3k
? 1 n(1 +2k)
2k (1 +202
4.8)
(4.9)
(4.10)
Declassified in Part- Sanitized Copy Approved for Release @50-Yr 2013/10/24: CIA-RDP81-01043R002400120007-1
tf,
- 39 -
It is seen from figure 8 that the polarization effects of the forward and backward scattering
give opposite contributions to the integral (4.8).. The total polarization cross section et?p
becomes zero at abut 0,65 MeV. It is positive for lower energy, and negative for higher
energy photons, which are mainly scattered in the forward direction. This means that above
0.65 MeV the transmission is greatest when g3 and g3 have the same sign, i.e. when the
photon spin is parallel to the electron spin and antiparallel to the magnetic field.
Atomic cross sections are obtained by multiplication with the number of electrons:
GAMMA, RAY ENERGY IN MEV
Figure 10.
'-ray cross sections for iron. Note that the polarization cross section ri..p is on a hundred
times larger scale than the other quantities: The experimental value was obtained by Gun.st
.and Page (1953).
12
Z
a c
,v=v
a p eff
where Z = 26 is the atomic number for iron, and Veff is the effective number of polarized
electrons in magnetized iron. The cross sections a .11 and aTp are given in figure 10 as
functions of energy. For the number of polarized electrons, the value for saturated iron,
Vsat = 2.06 was used, as reported by Argyres and Kittel (1953). The photodisintegration and
pair formation cross sections for iron were taken from the tables of Davisson (1955). As seen
from the figure, the polarization cross section is only about 1.5 % of the total cross section in
the region of high energy neutron capture r-rays. This low value is mainly due to the fact that
only about two of the 26 electrons of the iron atom can be polarized. By performing a single
transmission experiment for r-radiation passing through magnetized iron Gunst and Page
(1953) have performed an experimental deterinination of the magnitude of al at 2.62 MeV.
Their result is indicated in figure 10.
5. Experimental set-up.
A schematica.l'top view of the main apparatus is shown in figure 11. A neutron flux of about
107 neutrons/cm?, sec is emitted from the collimator which "sees" a slug of graphite very near
the reactor centre in one of the isotope channels of JEEP. At the collimator opening the slightly
divergent beam has its narrowest cross section, which is 10 x 30 mm. After having passed
through the polarizer, it hits the (n, r)-target. The neutron polarizer is a 12 x 18 x 40 mm
block of iron, joined to the pole faces of a magnet by the 40 x 18 mm planes. The neutrons pass
through 18 mm of iron, which approximately satisfies the condition = 2A, for optimum
counting statistics. The block is cut from cold-rolled iron in such a way that the magnetic field
is applied in the direction of rolling. According to Hughes, Wallace and Holtzma.nn (1948), this
procedure gives the highest degree .of polarization. The field strength was measured by means
of a small search coil which could be inserted between the pole pieces near the surface of the
polarizing block. In pulling the coil quickly out of the field, the induced electrornotoric force
was measured on a ballistic galvanometer, giving the result of 14900 Oersted. During continuous
runs, water cooling was provided for the magnet coils.
Measurements of the single and double transmission effects were performed with a BF3 counting
tube placed in the beam in such a way that the neutrons would traverse at most the diameter of
the tube. Hence it is essentially a 1/v-detector. In order to use the Measured results to calcu-
late the polarization of the neutron beam, the integrals of the equations (3.5), (3.6) and (3.7)
were determined in the region of neutron velocities between 400 and 7000 m/sec. Contributions
to the thermal flux outside this region can safely be neglected. Multiplication, and integration
of the velocity dependent functions were performed graphically. In the double transmission
experiment the neutron beam once more passed through a polarizing block exactly like the first
.one. A duplicate of the polarizing magnet was not available, and a smaller magnet, producing a
field strength of 5200 Oersted, was applied for the second polarizer. In the formula (3.7) for
the double transmission experiment, the factor g2 should be replaced by gi:gz in the case of
different field,strengths. Measurements were performed, first with both fields at 5200 Oersted,
and then with the first magnet at 14900 Oersted. The results are quoted in table 4, where the
errors indicated are the statistical standard de.iritions.
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c;?
0
-40
proved
proved for Release @50-Yr 2013/10/24: CIA-RDP81-01043R002400120007-1
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TABLE 4.
Experimental results from measurements of neutron polarization.
Experiment
1
Oersted
H 2
,
Oersted
Observed
transmission
effect in %3,6)
Tmsct-tt-iiisrLi.olni
equation
or (3 7)
Ca
Calculated correction
factor
Single
transmission
effect
Im-Iu
14900
=7
5.25_+0.10
0.0676 f
0.775?0.015
0 67 0 02
.....
Iu
Double
transmission
effect
Iki) -I ( )
5200
5200
+
2.73_0.20
2
0 107 g2
0505-
0
. 02
14900
5200
3.49?0.20
0.107 g gz
0.65?0.04
(u2)
I
The integrals of equation (3.5) were calculated for both a 1/v-detector and a total absorption
detector. For the polarization of the neutrons detected we get, using the values of table 4:
Pn(l/v) = 0.325 g Ir. 20.4% ...0.8%
+ .17
Pn(total) = 0..283 g 18.0%
1 +
All the (n,r)-targets that were actually used had absorbing and scattering properties far from
these extremes. For the further calculations, the value Pn 19 % was considered as a satis-
factory approximation.
(5.2)
Between polarizer and target the neutrons travel 40 cm through an approximately homogeneous
magnetic field of aj)out 100 Oersted. This field, which insures that the neutrons keep their
direction of polarization is producedby two parallel iron plates that pick up part of the stray
field from the magnet.
The target is generally a thin walled aluminium cylinder of 35 mm diameter and 25 mm high,
,containing the element to be studied. For some materials such a thick target would result
too many scattered neutrons producing unpolarized r-rays in the target and the surroundings.
Then its extension in the direction of the neutron beam is reduced.
If the capturing material is ferromagnetic it.can depolarize the neutrons before absorption;
For iron- and nickel-targets the non-ferromagnetic compounds Fe203 and NiSO4 were chosen.
As small ferromagnetic impurities can reduce the polarization considerably, the targets were
studied for 'depolarizing action.by placing them at the position of the iron shim in the double
transmission experiment. It was found that, the neutron beam had 65%'of its original polarization
after having passed through 23 mm of the Fe203-target. When the target was placed in its
ordinary position, the average polarization of the neutrons 'captured was reduced by 78%. The
other materials, including the NiSO4 powder, gave no depolarizing effect.
The directions of greatest circular polarization of the r-rays'are given by an axis through the
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Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24 : CIA-RDP81-01043R002400120007-1
(n,r)-target,. parallel to the incident neutron spin, which is defined by the magnetic field direc-
tion of the polarizing magnet. Radiation emitted in both directions along this axis are detected
by NaI(T1)-crystals after ha.vingrpassed through analyzers consisting of 8 cm long pieces of
iron magnetized ih, the direction of transmission, The crystals, the cores of the analyzing
magnets and the Maximal size, of the target, constitute parts of a cylinder with diameter 35 mm.
As shown in figure 11, both ends of each iron core are formed as flat discs fitting into an outer
cylinder. The coil producing the magnetic field is placed within the cylinder and around the
core, which forms the narrowest part of the magnetic circuit. A few separate windings serve
for the measurement of the magnetic induction, which is found to be 18300 gauss, corresponding
to 86.,3 % of saturation. The polarization is then Pa 1.96 % at 7 MeV, and is slowly varying
with energy above 3 MeV, as indicated by figure 10.
An estimate for the sensitivity of the experiment can now be obtained by insertion of the derived
polarization quantities in equation (1.12) combined with (2.21) for cos 81:
R
0.0037,R
(5.3)
at 7 MeV. I is the 1-ray intensity a.s measured by the crystals. It is seen that in order to
determine the magnitude of R, which is between 0 and 1, extremely small relative variations
in the intensity should be measured. Furthermore, the sensitivity of the method is considerably
reduced by background and scattering.
Each detector consists of a cylindrical NaI(T1)-crystal, 35 mm in diameter and 25 mm high,
coupled to an EMI 6262 photomultiplier. Systematic errors may arise if the pulse height is
influenced by the inversion of the magnetic fields, because this effect can simulate polarization.
Therefore, long light pipers are used to bring the photomultipliers away from the magnets, and
the tubes are surrounded by /4 -metal and soft iron shields. The EMI venetian blind photo-
multipliers employed are reported by Wardley (1952) to be less influenced by magnetic fields
than other types. The influence is mainly due to magnetic deviation of the electron current
between the photocathode and the first dynode, since this is by far the largest interelectrode
distance in the tube. Ordinarily 180 volts, ,being the highest voltage allowed, is applied between
these electrodes. By lowering this voltage to 1/20 of the usual value, the sensitivity to magnetic
fields was increased accordingly. Using azadioactive source, the pulse discrimination was set
by trial to the position of highest magnetic sensitivity. Relative changes in the counting rates
due to inversion of the magnetic fields were less than 540'4, corresponding to less than 3.10-5
for the actual experiment in the worst case. In the next section is quoted the result of a
"symmetry Control" experiment, performed with a titanium target placed 12 cm from the ordinary
position, but still in the neutron beam, so that the y -rays passing from target to detector would
not pass through the analyzer core. The measurements showed the expected absence of asymme-
try, but the statistical accuracy is poor, so that no decisive conclusion can be drawn from this
experiment alone. As mentioned below, series of observations were carried out in such a way
that systematic errors due to reversal of magnetic fields would cancel Out.
Heavy shielding of lead and boron carbide .srve to reduce the intense background radiation,
which is largely due to r -rays resulting from neutron capture in and scattering from the
polarizing iron block. The effect of neutrons scattered from the target is reduced by boron
containing plastic plates, placed between target and analyzing magnets.
Figure 12 shows a block diagram of the electronic apparatus used.
The pulses from the two photomultipliers,are applied to two identical channels consisting of
cathode follower, linear amplifier, single channel discriminator and scaler, In channel No. 1
the scaling factor is 8, 16 or 32, and in channel:No. 2. it is twice this value. The output pulses
from the scalers can be led to the mechanical registers A og B. The switching between these
registers is performed by means of a relay circuit at every 100th pulse from scaler No. 2.
At the same moments the current in the analyzer magnets is reversed.
The analyzer magnets are oppositely coupled, meaning that the r -intensity P(1) in channel
No. 1. is registered at the same time as l" (2) in channel No. 2, and vice versa. As channel
No. 2, is used as a monitor, the number of counts per period in channel No. 1. is given by
CATHODE
FOLLOWER
CHANNEL NO 1
- 43 -
Nal (TO-CRYSTA-
LIGHT PIPER
PHOTO MULTIPLIER
CHANNEL NO 2
CATHODE
FOLLOWER
LINEAR
AMPLIFIER
SINGLE
CHANNEL
DISCRIMINATOR
SINGLE
CHANNEL
DISCRIMINATO
SCALE
OF N
SCALE
OF 100.
,0v
DC
INPUT
REGISTER
1A
0-
0?
REGISTER
1B
REGISTER I
2 B
Figure 12.
Block diagram of the electronic circuit for the po?farization experiment
E 1' (1.)
Na OC
I
N" OC "(1)
a (a)
and using equation (5.3), we get for the observed asymmetry:
Nia Niat 2'R Pn Pa
N' +N"
a
1 + (R PnPa )2
/-4(- 2 R Pn Pa
for Pn Pa c1
ALTERNATING
RELAY
CIRCUIT,
This condition is fulfilled as shown by equation (5.3).
By observation of opposite polarization in the two channels, fluctuations due to changes in
neutron flux or in background are compensated.
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(5.4)
(5.5)
(5.6)
???
(
- 44 -
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The numbers of counts NI and N! are observed alternatively, and the data are accumulated on
?, the registers .A And B. Each period with one definite polarizer current is of about 3 minutes'
duration, which is adjusted by means of the scaling factor in channel No. 2. When analyzer
magnet currents are inversed frequently, errors due to different drift in the electronics of the
two channels should be unimportant. If both polarizer and analyzer change field directions, the
values of the counting rate Na should remain the same, but the influence of the magnetic fields
upon the photornultipliers will be opposite in the two cases. An average of the two polarization
values thus obtained will compensate for the change in photomultiplier sensitivity. Measure..
ments are always done with a certain polarizing field direction for a longer period. The next
period is then performed with opposite polarizing field, in order to eliminate possible syste-
matic errors.
The resolving power of the experimental set -up was found by measurements of the spectra
from titanium, iron, sulphur and aluminium, which have quite prominent high energy r -rays.
In neither of these spectra was complete resolution of a single dr -ray performed, but by trial
it was found that curves calculated with a resolution of 14,5% give the best agreement with
the experimental results. By using the cross sections for NaI, as given by Bell (1955, fig. 17),
the total absorption of r -rays in a crystal of 25 mm length was calculated, together with the
contributions from the three different types of interaction. These properties are shown in
figure 13 as functions of energy.
0.8
0.
PHOTO
TOTAL
=PHOTO+COMPTON+PAIR FORMATION
EFFECTS
?
?
?
COMPTON/
?
?
?
'e
?
PAIR
4105 al 0.2 0.5 1 2
GAMMA RAY ENERGY I N MeV
5 10?
Figure 13.
Absorption of y-rays in 25 mm of Nal.
In the region of high energy neutron capture y -rays, i.e. from about 5 to 10 MeV, the Compton
and pair formation cross sections are of the same order of magnitude. Compton electrons are
widely distributed, as shown in figure 14 for r -rays of 7 MeV. In the small crystals used,
most of the annihilation quanta resulting from the positrons will escape. The pulses due to pair
formation will then correspond to a single peak at an energy 2mec2 lower 'than the r -ray energy.
This peak makes energy discrimination possible.
Declassified in Part - Sanitized Copy Approved for Release
INTENSITY IN ARBITRARY UNITS
- 45 -
?T
_ _x
CONTRIBUTION
DUE TO NON-IDEAL
GEOMETRY
\\
1
I I I I 1 !
0 2 4 6 8
ENERGY IN MeV
CALCULATED
EXPERIMENTAL
CURVE
PAIR PEAK
?COMPTON
DISTRIBUTION
Figure 14.
Pulse spectrum of a 7 MeV ''-ray in a 25 mm long crystal of NaI(T1). Pair and Compton
contributions are shown in the ideal case and for a resolution of 14.5 %. The full drawn
curve is the expected expe6rimental distribution.
The ideal theoretical spectrum of figure 14 was folded with a gaussian distribution with half
width equal to 14.5% of the total energy: The resulting distribution of the photomultiplier pulses
is shown. The r -ray spectra for the elements studied could then be constructed, by use of the
energy and intensity data given by Kinsey, Bartholomew and Walker (1951 c, 1952), Kinsey and
Bartholomew (1953 abe) and Groshev, Adyasevich and Demidov (1955 b).
Measurements of the spectra were performed with the analyzing magnets removed. Contri-
butions from slow neutrons scattered into the counters were determined by,comparison with a
graphite target, and cliht-rprtp.d. Four experimental pulse distributions are shown in figure 15.
Curves, as the one in figure 14, were used to construct these spectra, but in order to obtain
approximate agreement below the highest peaks, one must introduce an additional contribution
to the single r -ray spectrum. Such a contribution will result from electrons escaping from
the crystals and from 'r -rays scattered in the target and in the surroundings of the detectors.
The correction is shown as a broken line in figure 14.
The poor resolving power is mainly due to the fact that the crystals used were quite small for
the study of high energy r-rays. By use of a collimator, and without the light piper, the
resolution could be improved somewhat, but, these changes would imply a too large decrease in
intensity. Within experimental errors, the photomultiplier pulse height was found to be a linear
function of energy.
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I
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INTENSITY IN ARBITRARY UNITS
01 0
- 47 -
Treatment of experimenta.1 data.
During the polaiization measurements, several y -rays are simultaneously detected. ? Instead
of R Pn l'a of equation (5.6) one then measures the average ,quantity:
i \ 1
\ \
I \ \
\
i \ \
I ) '
z
R Pn Pa =
131.Pai
where G.j is the relative contribution of the i-th y -ray, and
var.ying with energy, a good approximation is
MEM
for. P constant
a
Pa. is slowly
Generally, Ri is unknown for all the y -rays in the spectrum. If the radiation X is predorninant,
i.e. if ax is large an approximate determination of Rx is obtained from a measurement of
1
II????
o-
ey
0
2 PnPa.
?
N.1
a a
where the sum is taken over all r -rays except X, and the values of R1 may be anything between
+1 and - 1/2. Using constructed spectra like the ones in figure 15, the best discrimination of
pulses could be chosen, and the intensities ati for the different y -rays entering the single
channel discriminator were easily evaluated.
For the experiment it must be appreciated that Na of equation (5.6) is the counting rate of
r -rays that are not scattered, produced by capture in the target of the incoming neutron beam
plus the non-depolarized part of the scattered neutrons. The asymmetry actually observed is
N - N"
1 t t
2 N' +'N
t t
(6.4)
where.Nt is the total counting rate which consists of direct and scattered 1-rays from the target
and r -rays due to capture of neutrons scattered from the target as well as background. The
difference in the numerator is dueto polarization only, thus NI = . Equation (6.3)
and (6.4) together with the abbreviation N = (N' + N")/2 give
Nt.
Na
If we define Nb '= counting rate of 'y'-rays that are not scattered, produced-by neutrons captured
in the target after depolarizing scattering, Na + Nb represents the direct -rays originating in
the target.
The correction factor = Na/(Na ' + Nb) due to depolarization of neutrons scattered in the
target, can be calculated. For the repeated scattering of an already scattered neutron we obtain
the probability (as/.1t)(1-en-dt '9 ) . where o's and dt are scattering and total cross sections
respectively, n is the atomic density of the target, and Tis the average distance that the neutron
must travel to escape from the target. Considering multiple scattering and depolarization, we
get the correction factor
p =1 - 2
as
eft
e ? )
The spin flip probability is given by Meyerhof and Nicodemus (1950):
2
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(6.6)-
( 6 . 7 )
.
7
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- 49 -
Here dinc is the incoherent scattering cross section due to spin effects only. A scattering
nucleus with angular m9mentum zero has 21= 0. For the targets employed rs was very near,
or equal to 1.
The relative contribution of the -rays originating in the target and detected without being
scattered, is is given by .0 = (Na. + Nb)/Nt. This quantity can be found indirectly by an experiment
in which the analyzing magnets and some of the shielding around the detecting crystals is
removed; Measurements were performed with the ordinary targets, and for correction purposes
with a graphite target, which does not produce r-rays. In. comparing observations with and
without thin boron shields in front of the counter, it was possible to determine the contribution
to the counting rate from neutrons scattered from the targets, followed by capture in the
crystals. By insertion of a cadmium foil in the neutron beam, it was found that the epithermal
neutrons did not contribute to the counting rate by a measurable amount.
The resulting r -ray intensity was multiplied by the calculated transmission through the
analyzer, yielding Na + Nb. From measurements with the analyzing magnets in the ordinary
positions Nt was determined. In this way the factor cS was found for all the targets and for all
the discriminator positions used to select r -rays. It had magnitudes from 9.5% for calcium
up to 91% for chromium. The complete correction factor needed for the determination of R
from Q as given by equation (5.6) is
/1\it = Pn 7)a '36 (6.8)
In the determination of the numerical values of the quantities given in (6.8), the relative errors
were estimated to be smaller than 8% for Pn, 2% for Pa , 3% for p , and 5% for 6 . When the
relative error of x is denoted by A (x)/x and considered as a standard deviation, the root mean
square error of (6.8) becomes
Even at the highest scaling factor applied usc = 32, the error due to scaling is negligible
compared with 6. j. (Q).
(Pn Pa 6 )
(Pn Pa p )
/1A(Poi
Pn
The measured quantity Q has the standard deviation
where
rzyp )1 2 r
+ i6(612,10v
I I:751 ?
(6:9)
(Q) = [Z11 (Q) 12 4- [A, (Q)] 2
(6.10)
La (Q?
) is the statistical error of counting, and LS,A) is due to the reduced accuracy
which results when the counts taken during each period are registered as an integral multiple
of the scaling factor. When the register counts the number n, the correct value may be anywhere
between n-1 and n+1. In a certain counting period, let uf be the number of pulses incident upon
the .scaler before the first register count, and u2 the number of pulses after the last count.
Then (v=u.i+u2+1-use) is the single error for this measurement. For a great number of measure-
ments K, ui and u2 are supposed to be uniformly distributed between zero and the scaling factor
use. The root mean square error for the arithmetic mean is then
Each complete determination of Q consisted of between 15 and 40 separate series of measure-.
ments. When Q,is Cletermined from each of these, the root mean square error is.
aop
usc-i usci
>
(ul
ill =0 U.2=0
u2sc (K - 1)
U +1-u )
Sc
...1=immimmormi.11?0?6
(6.11)
The corresponding errors in the total number of counts Ni is K t (p), when K is the number of
periods for one register. As the deviations in Nand N are equal and opposite, the error in
the measured quantity N't - in is equal to 2 K 6 (v). The number of register pulses per period
is about 200 in channel No. 1, where the measurement of Ni - NI' is performed. This gives
NtV200 K usc. In setting K-1"1 K, we get
,62 (Ne - Nb") K 6(v) 1 iI
usc
(Q) - 4Nt 2Nt 40
3Nt
The standard deviation due to counting is .61(Q) = 1/ frNt, and. the total error becomes
1
usc
1200/
(6.12)
(6.13)
A( =
Nti
(K - 1) N
s ti
where Ks is the number of measuring series., Generally, this error was of the same magnitude
as 1/Y4N, indicating that no fluctuations other than the statistical counting rate variation were
of any importance. For the quotation of the results in the next section, the largest of the two
errors has been chosen.
The experimental value of has has the relative standard deviation
[--4-9-11 2 Pn rai p 6 )
Pnra P
(6.15)'
In all the cases studied, the counting statistics were the largest contributor to the error in R.
7, Measurements.
A?????????
Measurements were taken with the JEEP running at -a. power level between 200 and 450 kW.
A few times 107 neutrons per second were emitted from the collimator. The r -ray counting
rates were from 300 to 3000 pulses per minute. In order to obtain standard deviations of Q as
low as 10-4 continuous counting must be carried on for weeks or months on each target.
In table 5 the results from measurements on 12 different 'y-rays are quoted. First the
emitting nuclei are listed, and the second and third columns give the r -ray terms and energies
taken from the papers of Kinsey, Bartholomew and Walker (1952), and Kinsey and Bartholomew
(1953 abe).'.Then the experimantal values obtained for Q are quoted, together with the standard
deviation. In the fifth column is listed the correction factor Pn Pa ps , which shows large
fluctuations, mainly due to the correction factor 6, being quite small for the measurement of
radiation with low intensity. The corresponding value of R= Q/(Pn ---Papb), is given in column
6, also with standard deviation. From constructed r -ray spectra the relative contributions to
R were found from the various energies of the spectrum, as shown by equation (6.3). They are
listed in the 7th column together with the maximum uncertainties which are due to the r -rays
not studied. Finally, the last column gives the derived value of R for the r -ray under,
investigation.
The table first gives the result of a "symmetry control" experiment, which has already been
mentioned in section 5.
For the 6.18 MeV neutron capture -ray from wolfram all the related spin properties are
known. Kinsey and Bartholomew (1953 e) showed that it is due to the ground state transition in
W183, as illustrated in the decay scheme of figure 36. W182 is an even-even nucleus, so that
the compound state has spin 1/2 and even parity. Walchli (1953) gives the ground state spin
If mg 1/2 for W183 and its nucleon configuration was put up by Mayer and Jensen (1955), who
place the extra nucleon in a pl-state, having odd parity. Then the radiation is of electric dipole
2
type, and according to table 2, RD = 1. The theoretical value for the measurement is Rth
= 0.80 +[+0.201
as compared to the obtained Rexp = 0.60 ? 0.16. This resultverifies the theoreti-
cal prediction for the direction and magnitude' of the circular polarization. However, the
-0 . 10
uncertainty in the numerical agreement with theory is still quite large.
For the determination of spin values by means of measuring the circular polarization of, r -rays,
we shall assume that the theory gives a quantitatively correct value for R. The most suitable
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Emitting
Nucleus
y-ray
term
X
r -ray
energy
in MeV
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- 50 -
TABLE 5.
Results of the polarization experiment.
Experimental
asymmetry
Units of 10"5
Correction
factor
?
PnPaPb.
Units of 10'
Ti
S33
Ca41
Ti49
Cr54
Cr54
F 57
Ni59
c 64
Cu.64
Zn65
w183
Symmetry
Control
,Experiment
5.44
6.42
6.75
6.41
9.72
8.88
7.64
9.00
7.91
7.63
7.88
6.18
13
-31 _1
-14 Ill
12 ?7.5
59 -16
-39 +_20
34 -13
42 '16.5
-45 ?39
41
_15
-10,5? 9
45 5 11
Experimental
value of
Rexp
Units of 10"*6
Theoretical alue of
EaiRi = Rth
Units of 10'2
+1
0.71 -44 ? 24 82RG ( 9 1
1 93
.0.35 -40 + 30 91R [
6 + 4
c
69RF + 22RG+ -4.5
4. 91 [+9
1.96 30 +. 9 50RF, + 4ORG+
2.55 -15 8 68RA + 31RB+
2.15 16?6
0.54 78 -2; 14
1.80 -25 '122
1.62 261 8 ?
1.66
0.50
0.76
-21?18
60?16
{+-2101,51
13RA + 66RB
[+13 1
82RA [?1f93.]
87RE
78RA + 18RB+
51R
77RE
8ORD
+41
-2
+ 3ORB + [419
- 9,5
[+23
-11.51
{+20
101
Derived
value of
X
+ .1
1
4
1
Ammo
2
?
+ 0.45
2
2
target materials for these experiments have relatively large capture cross sections, combined
with the emission of r -rays that are strong compared to the rest of the spectrum. Most of the
elements fulfilling these requirements are found in the region of atomic number 11 to 30. For
each r -ray studied, the derivation of Rx as given in table 5, and the spin properties obtained
from this value, will be discussed in chapter V.
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CHAPTER IV
COINCIDENCES AND ANGULAR CORRELATION OF GAMMA RAY CASCADES
When the coincidence method is applied to the study of the lowest excited levels in nuclei
resulting from capture of neutrons, it is necessary to observe the simiata.neous emission of
high energy y -rays of about 7 MeV and of lower energy -rays of 1 MeV or less. This
combination implies certain complications for the measurement of angular correlation between
the y-rays. An attempt to carry out these experiments is described in the following.
1. Theory.
The theory of angular correlations has been extensively treated by Biedenharn and Rose (1953)
and Frauenfelder (1955), and here we shall only review the main results of practical interest
for the experimentalist. A it -ray cascade where two photons, lel and 1/2 , are successively
emitted from the same nucleus, is schematically shown in figure 16.
The multipole orders are L1 and L2. Along a given axis of quantization, the successive nuclear
spins Ja, Ib and Jc will have the components ma, mb and mc respectively. Such a double cas-
cade shall be denoted by the '-ray terms as y,2/2 or by the spin values as Ja (141)4(1.02)Jc.
Each component of the disintegration, mec? my* mc, possesses a certain angular correlation,
and the -rays from the various components may interfere. The probability that rt2 is emitted
into the solid angle dn. at an angle fa with respect to yi is, similarly to the equation c2 2) of the
preceding chapter, given by
wheregE means summation over all unmeasured radiation properties, such as polarization. In
the matrix elements, Hi is the interaction Hamiltonian for the emission of the y-ray , and
a, b, c stands for the properties of the states A, B, C of figure 16 respectively. It is seen that
an experimental study of W ()can establish a connection betvfeen these properties..
In evaluating equation (1.1), one arrives at the result
1.4r(13) = 1+ av po (cosp)
Here the functions Pv (cos 0) are th
values from 2 upward
selectio
rule
egendre polynomials of order 1), and takes all even
? The highest term for which ap is different from zero is given by the
Vmax = Min(ZIb, 2L
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where Wi and W2 are the correlation functions for the pure cascades, as described above. For
the case that the transition between the levels A and B is a mixture of the multipole orders Li
and L'1 , the contribution due to interference is:
w12
(-1)Ib Ya-1
+1)(2L1+1)(2L1+1)
The sum is taken over all positive even numbers, and i) satisfies the rule (1.3) Also the
functions Gy have been tabulated by Biedenharn and Rose (1953). W12 has the same order
magnitude as the quantities W1 and W2. His seen that an intensity 'ratio as small as
(b1/b2)2 = 0.01) corresponding to the coefficient 21)0)2/(4+ bb= 0.2 for W12 can produce a
correlation function which is quite different from the case of b1 = 0.
In the case ofa '-ray cascade where one of the transitions is a pure dipole, formula (1.3)
shows that only the coefficient a2 of the expansion (1.2) is different from zero. We then have
=11 +a
2 3'+? a, cos
2 2
The only unknown,
coincidences:
, can be determined from a measurement of the anisotropy of the
Figure 16.
Energy level scheme for a double '-ray cascade.
For pure multipole transitions the coefficients ao can be separated into two factors, each of
them depending upon one single transition only:
-F (L1 aJO' Fp (L2 lc JO
where Fs) is expressed by the product of a Clebsch-Gordan and a Racah coefficient:
(1.4)
1
Ja Jb) (-1)Ja-jb-1 (2.Tb+ )7 (2L+1) (LL1(-1)I LL1)0) W(JbJb LL;PJa) (1.5)
Tables of the functions Fp (L JaJb) have been evaluated by Biedenharn and Rose (1953), so that
any angular correlatiOn function can immediately be written down.
As in the case of circularly polarized '-radiation, competing radiations of different multipole
orders ca?nterfere and produce a correlation distribution which is very different from either
of the distributions resulting from pure multipole transitions. When one of the transitions is
mixed, consisting of radiations with wave amplitudes b1 and b2 as defined in section 2 of
chapter III, the angular correlation function can be expressed as
b 2
1 W b2 W2 + 2b b W12.
2
w(p) (1.6)
2
+ b,
G
A
w(a) - w(ir/2)
=
3a;2
W(W/2) 2-a2
In a decay scheme like the one of figure 16, the level B may also be obtained by transitions
other than lei, or the state B may decay in different ways. The disintegration rate of the cas-
cade shall be called No. Then NO( i is the total disintegration rate of yi , where Wi is the
contribution of the cascade to this transition. Using the symbols wi and 8i for the solid
angle and efficiency, respectively, of the detector measuring the radiation yi we get for the
net counting rates of the two detectors:
N N (A) 6 At
o I 1
No 4)2 82//(2
N2
When angular correlation is neglected, the coincidence rate becomes
g 2
1
(1.9)
(1.10)
Random coincidences occur as a result of the accidental overlap of two pulses in the coincidence
circuit. The resolving time tr is equal to the maximum time separation for which two pulses
are registered as coincident. For two square pulses of equal duration this is equal to the pulse
length. If the counting rate is one pulse per channel per second, the chance of getting a false
coincidence is equal to 2 tr per second. With total counting rates WI and 1\112, the chance coin-
cidence rate is
Cch
2 N1 N2 tr
The ratio of true to chance coincidences is
c.
X X 2
Cch
2tr No
:1)
1.12)
which shows that the statistical accuracy of a coincidence experiment is not indefinitely
improved by increasing'the source strength, unless the electronic circuit or the detectors are
also improved.
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2. Experimental
For the presentlexperiment a narrow but intense beam of neutrons falling upon a small target
of the material to be studied is needed. A small target is advantageous because scattering of
the 1r-rays can produce false contributions to the angular correlation. The higher the intensity
of the beam the smaller the target can be made.
The neutron source is a graphi?te scatterer in one of the isotope channels of JEEP. For intensity
reasons the target should be placed as near to this source as possible. However, in the vicinity
of the reactor wall the neutron and %-ray background is very high, and the ratio of total to
background counts is considerably improved by moving the apparatus farther away from the
channel opening. The counting apparatus is actually placed 3 metres from the reactor wall, and
about 7 metres from the graphite scatterer. The main outline of the set-up is shown in figures
17 and 18. At the position of the (n, ptarget the neutron beam is cylindric3, with a diameter
of 7 mm. This is also the inner diameter of the aluminium tube containing the target material.
The target length, varying between 9 and 35 mm, is dependent upon the neutron absorption cross
section.
The two scintillation counters viewing the target consist of 38 mm diameter by 25 mm high
NagT1)-crystals mounted on RCA 6655 photomultipliers without light pipers. Crystal No. 2,
1.0
3.8 m
??????
01?..
GRAPHITE -
PLUG
REACTOR
CENTRE
2m---tame---?,-
? REACTOR
FACE
1.2m
DETECTOR 1
GRAPHITE
SI*7?7?WIV: ?
jimmammb'm/OGIONWAIWOre=4.4
-?
LEAD
DETECTOR 2
SHIELD OF IRON AND LEAD
Figure 17.
Main outline of the coincidence and angular correlation experimental set-up.
TARGET
- 55 -
DETECTOR NO. 2
(LOW ENERGY)
p-METAL SHIELD
\
/
\
/ \ \ ? 1 <
/ \ /
\\ v
?%(
? ?/
CORRECTION SHIELD
TARGET
Li2CO3
DETECTOR NO.1
(HIGH ENERGY)
A
/?
Nal(TI)-CRYSTAL
LEAD SHIELD
Figure 18.
Target and detectors seen in a plane perpendicular to the neutron beam.
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Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/24: CIA-RDP81-01043R002400120007-1
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which is used for measuring the lower energy '-rays, is placed a little farther from the target
than No. 1. During angular correlation measurements, detector No. 1. was stationary, and
detector No. 2 could be moved in a circle with the target as centre. As the measurements con-
sist in observing the asymmetry, only the positions p= Tr/ 2, and $=117 were used. These posi-
tions were chosen so that the change of distance between target and crystaLdue to the weight
of the detector, should be a minimum. Both boxes containing the detectors are made from soft
iron, tubes, and in addition the movable detector No. 2 has a 'A-metal shield around the upper
part of the photomultiplier. Thus the influence of the earth's magnetic field will not produce
changes in the counting rate as the detector is moved.
The detectors are surrounded by lead shielding, as shown in figure 18. Especially y -rays
emitted from one crystal into the other should be avoided. When a high energy y -ray is pro-
ducing an electron pair in one crystal, and the corresponding annihilation quant gives a pulse
in the other, a false coincidence can be recorded. Correction measurements are performed by
placing a shield in front of the low energy counter in such a way that only the direct low energy
v-rays are attenuated. Photons passing from one crystal to the other in the r/2-position are
unaffected by this shield, which is drawn with a broken line in figure 18. In order to reduce the
intensity of scattered neutrons reaching the crystals, shields of Li2CO3 are placed between
target and counter. Boron, which has a higher absorption cross section, could not be used for
this purpose, since it emits 'y-rays of 0.478 MeV following neutron capture, as reported by
Ajzenberg and Lauritsen (1955).
As a consequence of the large solid angles which are necessary, the absence of a y-ray
collimator, and scattering in the shielding surrounding the crystals, the resolving power of the
detectors is only about 15% at 1 MeV.
A coincidence circuit was built to receive pulses from NaI(T1)-crystals. The resolving time
ought to be at the most 50 millimicroseconds meu. sec ? to give an acceptable ratio between
true and chance coincidences. On the other hand, resolving times of the order of 10 mitt sec
would hardly be obtainable, as NaI(T1)-crystals give pulses with a rise time of about 250 mfrt sec
and distributed amplifiers were not at our disposal.
A block diagram of the electronic circuit employed is shown in figure 19.
From the photomultiplier, the pulse is fed via a cathode follower to the linear amplifier of the
type A.E.R.E. 1049B. Both differentation and integration time selectors were set to 320 m/U, sec.
From the amplifier, identical pulses are fed to the single channel discriminator and to the input
of the fast coincidence circuit. Some details of the latter instrument are shown in figure 19,
and figure 20 illustrates the form of the pulses that are counted, for various points of the circuit.
Very large amounts of scattered low-energy '-rays occur in the present experiment. Pulses
with approximately half the height of the ones that should be studied are removed by discrimi-
nation before entering the fast coincidence circuit, The rest is amplified to about 50 volts and
fed to a clipper circuit which gives an output corresponding to the rise of .a few volts only of
?the input pulse. This rise takes place within 10 to 20 mim. sec and as the clipper tube El80F
is a very fast broadband amplifier pentode, the output pulses should rise to maximum height
within the same time. A pulse forming delay line of a length corresponding to 20 metA. sec is
coupled to the output and shortcircuited at the end. In the ideal case it produces a square pulse
of 40M/44" sec duration, but the actual pulse has trapezoidal form. Coincidences between the
pulses from two identical clippers are recorded by a 6BN6-circuit, as described by Fischer and
Marshall (1952). As seen from figure 20, the time elapsing between the start of the original
pulse and the start of the clipper pulse, is strongly dependent upon pulse height and discrimi-
nator position. Therefore, only pulses of approximately uniform height can be studied by this
coincidence circuit. In fact, a height variation of 20 % can be allowed.
The real selection of pulses is performed by a single channel discriminator which has a fixed lower
discrimination of 20 volts, This height corresponds to the ideal input pulse for the fast coincidence
circuit. The width of the single channel can be up to 4 volts. It has been experimentally
verified that no coincidences are lost at this width. A slow triple coincidence circuit gives an
output pulse when the two discriminators admit pulses at the same time as a fast coincidence
occurs. To the first approximation the number of random coincidences can be calculated from
equation (c1.11) when the resolving time tr is given by the fast coincidence circuit, and N1 arid
N2 are counting rates obtained from the two single channel discriminators. At very high
CATHODE
FOLLOWER
4
LINEAR
AM P LI FJ ER
- 57 -
V
(a)
DISCRIMINATOR
AND
AMPLIFIER
PHOTOMFJET-IPLIER
Nal(TO-CRYSTAL
0 (n)-TARGET
V
CATHODE
FOLLOWER
DISCRIMINATOR
AND
AMPLIFIER
CLIPPER
r ?
300 V
I (b)
300Y
E 180 F /Th I
----3010vjiI 11106----?-0
I Z I I
6 B:
i I
FAST
COINCIDENCE
CIRCUIT
LINEAR
AMPLIFIER
-=-
E 180 F
L -J
CLIPPER
SINGLE
CHANNEL
DISCRIMINATOR
SCALER
AMPLIFIER
AND
PULSE
FORMER
SLOW
TRIPLE
CO IN C ID ENCE
CIRCUIT
AMPLIFIER
REGISTER
SINGLE
CHANN EL
DISCRIMINATOR
Figure 19.
Block diagram of the electronic circuit for the coincidence measurements.
SCALER
counting rates, when N1 or N2 is comparable to Os, where ts is the resolving time of the
triple coincidence circuit, the formula for Nch fails. In the present case, ts is of the order of
5 la sec.
The resolving time of the fast coincidence circuit is determined by the voltage at which the
6BN6-tube is triggered, and by the form of the input pulses. When they, are triangular, very
short resolving times can be obtained if only the upper part triggers the circuit. The available
cathode ray oscilloscopes were not fast enough to show the actual form of the pulses incident
upon the coincidence tube. The resolving time can be measured by other methods, however.
By placing different delay lines in the two channels, and measuring the coincidence rate as a
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.1
r%) 20V.
- 58 -
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DISCRIMINATOR
LEVEL When different sources are used for the two counters, only random coincidences occur, and by
means of formula (1.11) the resolving time is determined:
.,Cch (2,1)
2 N1 N2
- 59 -
function of the delay difference, curves like the ones in figure 21 are Obtained, When all the
pulses fed to the coincidence tube are equal, the measured curve should have a flat top with
vertical edges. Due to the fact that a spectrum of pulses is incident upon each channel, also
the shortened pulses,have somewhat different heights, and the 'edges of the experimental curves
are sloping. Pulse forming delay lines of 10 and 20 miu, sec were. used, giving the two curves
of figure 21. The narrowest curve indicates that the shorter pufses have triangular form, or
a very short flat top. The fact that the two curves have the same coincidence.rate at maximum,
indicates that all the true coincidences are counted.
PULSE FROM LINEAR AMPLIFIER (a)
fv150V
CUT OUT LEVEL
OF CLIPPER
PULSE BEFORE CLIPPING (b)
40 rnpsec
CURRENT IN CLIPPER TUBE
PULSE FROM CLIPPER (c)
0
1 1 1 1 _1 1 1 1 1
500 1000
TIME IN MILLIMICROSECONDS
Figure 20.
Pulse forms at certain points in the electronic circuit of figure 19.
150
,????
r."
?????????? ?????
'\1\f
-20 -15 -10 -5 0 5 10
TIME DIFFERENCE BETWEEN THE TWO PULSES, IN mp sec
Figure 21.
Coincidences obtained with different delay of the pulses in the two channels.
15 20
MINIMMIN Declassified in Part - Sanitized Copy Approved for Release
In this,,way the resolving times tr = 8 miu,sec and tr = 35 msec respectively were measured,
in rough agreement with the curves of figure 21.
The broader pulses, giving the 35 msec resolving time, were used in the actual experiment.
Although the random coincidences are more numerous in this case, the smaller probability of
losing any true coincidences justifies this choice.
As all the pulses fed to the fast coincidence circuit should be equal, or only varying very little
from a standard size, the selection of various /-ray energies is performed by keeping the
single channel discriminator in a fixed position while the photomultiplier voltage is altered by
means of a fine potentiometer. A calibration curve for the relative pulse height as a function
of the voltage is shown in figure 22. It is seen that the logaPithm of the pulse height is very
nearly a linear function of the high tension. ?
100
50
20
1 '
1200 1400 1600 1800
PHOTOMULTIPLIER VOLTAGE
2000
Figure 22.
Photomultiplier pulse height as a function of the voltage applied to the tube.
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-'60 -
3, Treatment of experimental data.
The data obtained are first Corrected for accidental coincidences Cch, which are .readily
calculated from formula (1.11). The influence of cosmic rays was measured and found to be
negligible compared to the effect to the targets. Scattered neutrons can be captured in the
Na,I(TI)-crystals, and resulting Ir-ray cascades can give rise to unwanted coincidences. In
order to measure this effect, the actual target was replaced by a paraffine scatterer, giving
no capture radiation. Coincidences due to scattering from the targets were estimated and
subtracted. This contribution was of the order of one percent of the total coincidence rate when
the lithium shields were applied in front of the crystals.
For the comparison of different coincidence rates it is advantageous to use the value
C
instead of the measured coincidence rate C. Here and N'2 arc single
obtained when background and perturbing activities have been subtracted.
mation this procedure corrects for small variations in the sensitivities of
the distance between the counters and the target.
(3.1)
counting rates,
To the first approxi-
the counters and in
False coincidences can be due to a high energy '-ray which produces a Compton recoil pulse
in one counter, and after scattering enters the other crystal, producing the second pulse.
Formula (4.2) of chapter III shows that the energy of a '-ray Compton scattered at 900 or more
is always less than mec2 = 0.51 MeV. In figure 18 it is clearly seen that all false coincidences
of this type must be due to scattering angles equal to or larger than 900, corresponding to energies
smaller than 0.51 MeV measured by the second detector.
As has already been mentioned, false coincidences can also be due to high energy '-rays pro-
ducing electron pairs in one counter, where the annihilation of the positrons gives rise to
quanta detected in the other counter. The energy of these quanta is me c2 = 0.51 MeV.
In the present experiment, detector No. 1 is set to count high energy ''-rays of several MeV.
The low energy 1-rays, causing false coincidences can, therefore, only be detected in counter
No. 2. The two aforementioned causes of false coincidences can be corrected for by means of
the lead shield mentioned in section 2. When accidental and background coincidences are sub-
tracted, let C (x, ) be the measured coincidence rate, where the correction shield is placed
between the target and counter x. When x = 0, no extra shielding is applied. Counter angle is
denoted by pi , as before. The measured coincidence rate can be separated into the true and
false parts:
C,4. (L.C.) + C124) (3.2)
2 2
Here, Cc (p) is due to the cascade only, and C12 (ft) results from y-rays originating in
counter 1, and being detected in counter 2. Using the shield, one can also measure the quantities
C' (2,1r7 T2 C ) + C (Tr )
T2 Cc (it ) + T12 C12(1r)
C'(i,TE) = T1 Cc + T12 Cucii".)
(3.3)
(3.4)
(3.5)
where T1 and T2 are the transmissions through the lead shield of the high and low energy cascade
'-rays respectively, and T12 is the transmission of the 'y-rays passing from one counter to the
other in the position pszTr. The quantity T1 can be determined from the single counting rates
of the high energy "-rays passing through the shield. T2 and T12 are not easily measured,
since scattering of the higher energy i-rays will strongly influence the observation. When T1
is known, we get from equations (3.1) to (3.4) the desired ratio
2
c(TC) tri )ci (1,7r. _ ci (2,Tt
Cc()
2 2 2
(3.6)
Declassified in Part - Sanitized Copy Approved for
- 61 -
W' is the measured correlation function. In the derivation of equation (3.5) we have neglected
the fact that for the y?-rays of the cascade can be slightly different from the average value
for the y -rays producing annihilation quanta that are counted as coincidences. However, the
''-ray cross section for lead varies very slowly with energy in the region between 4 and 10 MeV,
so this error can be considered as unimportant.
The symmetry axes of the two counters form a definite angle (3 . Since both the target and the
detectors have finite dimensions, i-ray pq.irs? with relative angles somewhat different from (3
can be detected as coincidences. Feingold and Frankel (1955) have developed the theory of
geometrical corrections in angular correlation experiments. They give methods for calculating
the coefficients hv of the experimental distribution
Wi((3) 1+
Pv (cosp) (3.7)
when the coefficients as) of the theoretical distribution (1.2) are given. In the application of
these corrections to the present experiment, the detectors axe considered as circular discs with
their axes going through the centre of the source. The source is considered part of a straight
line perpendicular to the axes of both counters, and it extends equally on either side of the centre.
When only the coefficient a2 is different from zero, the experimental angular correlation function
for a target of 30 mm length is
W13) = 1 + 0.814 a2 P2 (c
sp) + 0.042 a2
4 (cos)
+
(3.8)
A good approximation is obtained when this expansion is cut off after the third term. The ideal
anisotropy A as defined by (1.8) can be expressed in terms of the experimental anisotropy A':
1.201 A'
A -
1 - 0.087A'
(Target length = 30 mm)
(3.9)
The complete error in the anisotropy', due to the approximate validity of the corrections, is
estimated to be smaller than 2 %. This is of very little importance when compared to the
experimental errors due to the statistics, of counting.
By scattering in the target and in the surrounding material, the '-rays can change direction,
and produce coincidences with a false angular-correlation. When discrimination between
different '-ray energies is performed, this error is not serious, since scattering by more than
a few degrees will reduce the energy of the y-ray so much that it will not be counted by the
detector. The effect of this scattering is that the angular correlation is "smeared out", and the
numerical value of the anisotropy is reduced.
Absorption or reduction of the v-ray energy by interactions in the target itself is on the
average more important for the y-ray pairs which give coincidences in the 180? position, than
for those which give coincidences in the 900 position. Thus more coincidences are lost at
ii= 1800 than at jS= 900, The measured anisotropy will be somewhat more negative than the
true one. For the present experiment it was estimated that the largest contribution due to this
effect would not amount to more than half a percent in the anisotropy.
4. Measurements.
For the study of decay schemes, one of the counting circuits. is adjusted to count pulses from a
certain '-ray. In the other circuit, the coincidence spectrum is scanned by measurements
during a stepwise alteration of the photomultiplier voltage. The structure of this spectrum
reveals which '1-rays are coincident with the *1-ray.chosen by the first counter. Observation
of the coincidence spectrum can be used to choose the best position of the discriminators (i.e.
the best photomultiplier voltage) for special experiments like the angular correlation measure-
ment. The single counting rate spectrum which is obtained at the same time shows the positions and
relative intensities of the most intense y-rays emitted by the target.
50-Yr 2013/10/24: CIA-RDP81-01043R002400120007-1
Declassified in Part - Sanitized Copy Approved for Release @50-Yr 2013/10/24 : CIA-RDP81-01043R002400120007-1
- 62 -
TABLE 6.
Results of the coincidence and angular correlation experiments.
1
Decaying
Nucleus
Cascade
''-ray
energies
in
H her
MeV
Lower
Approximate
value of X1
(+ 0.1
Correction
shield
applied
Experimental
anisotropy
A'
Corrected
anisotropy
A
C136
(B,V)
7.79
0.77
2.8.
0.0881'0,015
0.107?0.018
(C,U)
7.40
1.16
1.2
0.076?0.021
0.092?0.025
(F+G,V)
166:471
1.39
0.97
(G W)
6.41
0.33
0.88
X
(G,U )
6.41
1..75
0.1
Cr54
(B U)
8.88
0.84
1.02
-0.27 ?0.05
-0.32 0.06
I
leil.....6
N i 5 9
(B,U)
8.53
0.45
1 i
0.45
X
0.36 1:0.10
0.46 +0.12
cu64
(B,V)
7.63
0.28
1.03
X
0.032?0.065
0.039'10.080
,
(C,U)
7.30
0.60
1.38
X
-0.22 '10.055
-0.26 ?0.06
n
(E,U)
7.88
0.052