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NATIONAL QUREAU OF STANDARDS - 1963
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ORNL 8-3299
Conf- 67/102 ..hy CASTRES
MASTER 20 $2.00; max b5

Calculation of Neutron-Capture Ganina-Ray Spectrex
K. J. Yost
It is well known that certain classes of nuclei exhibit marked changes
in the shapes of their neutron-capture gamma-ray spectra with incident neu-
tron energy.
This fact may have an important effect on reactor shield
thicknesses in cases where secondary capture gamma rays are the primary
consideration in shield design.
Capture spectrum variation associated with incident neutron energy
occurs generally in light (A < 70) and "magic" and "near-magic" nuclei. It
is a consequence of (a) nearest neighbor mean level spacings of magnitudes
such that neutron capture is effected into energetically well defined com-
pound nuclear states, and (b) an increase in the relative probability of
p-wave capture with neutron energy.
The shape of the neutron-capture gamma-ray spectrum is largely detern. i ned
by (primary) transition probabilities obtaining between the compound capture
state and its ground state and first few excited level.s. These probabilities
are in turn functions of the nuclear selection rules as they relate to
radiative transitions. They are also sensitive to variations in transition
"matrix element" magnitude given by
iww.
Sve O NE AT
where (Veelle) denote initial and final states of a transition, respectjvely,
and O is an operator characteristic of a radiative mechanism.
A nuclear gamma-ray cascade model has been developed which defines the
cascade process described above in terms of electric and magnetic dipole
*Research sponsored by the U. S. Atomic Energy Commission under contract with
the Union Carbide Corporation.
DISTRIBUTION OF THIS DOCUMENT, IS UNLIMITED
-2-
and quadrupole transition probabilities and corresponding conditional spin
branching probabilities. It represents in part an extension of the work of
Troubetzkɔy and Lund and Starfelt. Allowance is made for predictable
variations of reduced intensities among states of like spin and parity. A
level spectrun is constructed in the compound nucleus' unresolved energy
region by statistically sampling nearest neighbor level spacings from a
Porter-Thomas or chi-squared distribution with "four degrees of freedom."
The mean value of the distribution is a nearest neighbor mean level spacing
that is dependent on the cascade transition number and is calculated by
weighting the Newton spin-zero spacing with the product of the probability
that a spin-J state is excited by the transition and a factor relating the
magnitudes of the spin-zero and spin-J mean level spacings.
The figure represents a comparison between the experimental data of
Gibbons et al.4 for the 39-kev resonarce of %7 Al and a spectrum calculated by
DUCAL,a computer code based upon the method outlined above. In order to
effect a meaningful comparison, a histogram spectrum was calculated whose
energy bins corresponded to the channel configuration used in the experiment
to differentiate gamma-ray pulse heights.
The data thus calculated were then
"smeared" with the appropriate response matrix.
It is of practical interest to determine the extent to which the method
is successful when insufficient information is available for the estimation
of preferred spin branching probabilities. To this end a calculation was.
made with equal spin branching probabilities. The results are shown as a
comparison of primary intensities for the two cases.
LEGAL NOTICE
This report mo prepared as an account of Goverament sponsored work. Noither the United
Statos, aor the Commission, nor any person acting on behalf of the Commission:
A. Makes any warranty or representation, expressed or implied, with respect to the accu.
racy, complotonces, or usefulness of the information contained in this report, or that the wo
of any information, apparatus, mothod, or process dlaclonad lo this report may not infringo
privately owned righto; or
B. Assumos any liabillues with respect to the use of, or for damages resulting from the
use of any information, apparctus, motbod, or process disclosed in this report.
As used in the above, "person acting on bobull of the Commission" includes way om-
ployee or contractor of the Commission, or employme of such contractor, to tho extent that
such employee or contractor of the Commission, or employee of much contractor properts,
disseminates, or provides access to, any Information pursuant to his employment or contract
with the Commission, or his employment with such contractor.
.
Comparison of Primary Radiative Transition Intensities
(per 100 captures) Calculated with Preferred and Equal
Spin Branching Probabilities
Spin Branching Probabilities
Boat
(MeV)
Preferred
Equal
3.56
8.7
8.2
3.90
4.6
4.8
4.26
10.4
9.0
4.70
11.6
21.0
5.13
13.3
14.1
5.55
15.0
17.8
6.14
8.5
6.78
11.4
10.7
16.3
7.8
17.3
References
1. E. S. Troubetzkoy, "Statistical Theory of Gamma-Pay Spectra Following
Nuclear Reactione," Phys. Rev. 222, 212 (1961).
2.
B. Lundberg and N. Starfelt, "Gamma Rays from the Capture in Ta and Au
of Neutrons from 1 to 4 MeV," Nucl. Phys. 67, 321 (1965).
3. T. D. Newton, "Shell Effects on the spacing of Nuclear Levels," Canadian
J. Phys. 34, 804 (1956).
4. I. Bergqvist, J. A. Biggerstaff, J. H. Gibbons, and W. M. Good, "Neutron
Resonance Capture in 20-10 Shell Nuclei," Phys. Rev. 18, 323 (1965).
5. K. J. Yost, DUCAL: A Code for the Calculation of Gamma-Ray Production
Cross Sections, ORNL-)165 (to be publiehed).
..
ORNL-DWG 67-7239

EXPERIMENTAL POINTS
EXPERIMENTAL FIT
CALCULATED
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GAMMA INTENSITY (arbitrary units)
R
8
1
2
3
4 5 6
GAMMA ENERGY (MeV).
7
Fig. 1. Comparison of Calculated and Experimental Capture Gamma-Ray
Spectra for 39-keV Resonance 37 A2.
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DATE FILMED
10 / 12 / 67








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