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NATIONAL BUREAU OF STANDARDS - 1963

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LEGAL NOTICE
This report was prepared as an account of
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B. Assumes any liabilities with respect
to the use of, or for damages resulting from
the use of any information, apparatus,
method, or process disclosed in this report.
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employee of such contractor, to the extent
that such employee or contractor of the
Commission, or employee of such contractor
prepares, disseminates, or provides access
to, any information pursuant to his employ-
ment or contract with the Commission, or
his employment with such contractor.
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ORNL-D 1226
(Paper to be presented at International Conference on the Study of
Nuclear Structure with Neutrons, Antwerp, Belgium, July 19-23, 1965)
1969 ;
11 196
CONF-650706-7
MASTER
outobelloa, expcoon behall of the work. Neither
..or while
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Session V B
(N. Starfelt)
Neutron Capture Cross Sections from 5 to 100 keV
R. L. Macklin and J. H. Gibbons
Oak Ridge National Laboratory
Oak Ridge, Terınessee, USA
Introduction
We have recently reviewed the available experimental data on
neutron capture applicable to calculations of slow stellar
nucleosynthesis [1]. The techniques involved point up useful systematic
regularities in the capture data as well as regions of inadequacy of
both available data and techniques.
Nuclides with Resolved Resonances
Among the lighter nuclides and a few close to closed nuclear
shells capture in resolved compound nucleus resonances has been observed
.
by activation, scintillator tank and other techniques [2-6). The
.
contribution of each resonance to capture in a broad neutron spectrum
S...
"
(slowing down spectrum, thermal spectrum at stellar temperatures, etc.)
can be written approximately as
Research sponsored by the U. S. Atomic Energy Commission under
contract with the Union Carbide Corporation.
PATENT. CLEARANOE OBTAINED, RELEASH TO
THE PUBLIC IS APPROVED. PROCEDURES
rr
'ng
(barn - eV)
where k? = 0.004818 (
.00895) Eres barns-?,
A is the "atomic weight" of the target nucleus
Eme is the resonant neutron energy (lab kev)
2J + 1
by = 2(21 +1)
J is the spin of the compound state formed
I is the spin of the target nucleus
n
I, is the radiative width of the resonance (ev)
In is the laboratory neutron width of the resonance (ev)
I is the total width of the resonance (ev)
(usually I = In + Ty in our range of interest)
n
'
For very thin samples An is directly measured as the area under the
resonance in a plot of observed cross section versus energy. In most
experiments (and applications) important self-shielding effects must
be taken into account. While ela!orate Monte Carlo computer techniques
are coming into use for this purpose, simpler methods are available for
not too thick circular discs [7]. The self-shielding effects depend
on knowledge of other parameters (than A, and Eres, such as the
neutron width which are generally available from transmission
measurements of total cross section. For many of the p-wave resonances
that make their appearance in keV range neutron capture the necessary
parameters are not so generally available; in fact a careful search
with the highest resolution is often required even to observe resonances
in transmission for which capture is prominent at low resolution. Table
III of reference I summarizes individual capture area measurements in
the 5-200 keV range.
The combination of capture, transmission, and more recently, resonance
capture gamina ray studies provide enough information to point up the
incompleteness of theories of the average properties of resonances.
In particular, empirical evidence is accumulating that average radiative
widths and level densities may have an additional strong dependence (of
the order of a factor of two) on parity. This shows up in comparisons
of S-wave and p-wave resonance statistics
Elements and Isotopes with Unresolved Resonances
Most of the heavier elements have neutron resonance spacings
less than a few kilovolts. Data are now available for most heavy
elements, but unfortunately only in a few cases are they available for
individual isotopes. The majority of these data were derived from
liquid scintillator [9], lead slowing down time spectrometer [6], or
Moxon-Rae detector measurements (10,11]. The average behavior of
resonances has been intensively studied over the past decade and is
well formulated in terms of strength functions, Porter-Thouas distri-
butions, and particularly important for the case of average capture
cross sections, the ratio of radiative width to level spacing. We have
largely followed the formulation given in an earlier paper [9], which
LL
..
A
.
.
need not be repeated here. Briefly this treatment assumes only s-wave
I
and p-wave contributions are important in our energy range, or alternatively
that d-wave and higher contributions tend to be offset by inelastic
scattering competition. Otier assumptions for which experimental confirme-
tion is weak are the parity independence of the radiative width, I've
and level spacing. The effect of relaxing these assumptions would be
to give more fitting parameters and it is to be emphasized that even
with the four main parameters used (Tv, Dobs, sº and st, the capture
cross section fits are not unique. For instance, the tin isotope capture
curves have been fitted with very small p-wave strength functions.
Obs
Equally good fits can be obtained with moderately large p-wave strength
functions (which incidentally, agree better with optical model calcu-
lations) by adjusting the other parameters T, and DohaAverage resonance
parameters are summarized in Table II of reference 1.
Actually, one can empirically fit most of these cases with even
fewer parameters. First, the cases fitted with strength function
parameters were used to test empirical fitting functions such as one
suggested in reference 9. This was modified to include an asymptotic
1/v behavior at low energy. A good fit (well within the errors) was
found in the 10-100 keV range with essentially one free parameter for
most heavy elements. The fitting function was
with E in lab kev
and B = (0.508 - 0.0044 2)
Z being the atomic number.
S
EV
N
-
'.-
'
,
'
'.
.." 1'7.'
"
With this fitting function nearly all the gaps in the periodic
table from iron to bismuth could be filled in. Exceptions are the
radioactive elements (TC and Pm), the rare gases (Kr and Xe), and four
cases (Te, Ce, Nd and Ti), in which there have not been adequate measure-
ments,
Values of the constant c derived for various elements are
included in Table I of reference l.
A few of the cross section curves show an excess near 100 keV,
probably attributable to a high d-wave strength function. These cases
occur near tungsten in the periodic table and tungsten shows the most
definite effect (see curve in reference 9).
Problem Areas and Techniques
A great deal of progress has been made in our ability to measure
kilovolt neutron capture in the past eight years or so. Earlier measure-
ments were mostly limited to the activation technique. The large liquia
scintillator permitted measurements of nearly all the natural elements,
and those isotopes available in nearly gram-mole quantities. The
Moxon-Rae detector (11), chiefly through better time resolution (about
2 ns vs. 18 ns for a large liquid scintillator), has enabled smaller
samples of isotopes to be used, in favorable cases as little as a gram.
Recent developments stemming from the suggestions of H. Maier-Leibnitz
(12,13) promise factors of 5 to 10 higher capture gamma ray detector
efficiency.
By applying a weighting function depending on pulse height
alone, any gamma detector can be given the special properties of the
5
Moxon-Rae detector. Further development of pulsed Van de Graaff and
Linear Electron accelerators promises still higher neutron fluxes.
Thus at this time further attention is being given to improving
the accuracy of capture cross section standards in anticipation of being
able to make measurements on nearly all stable isotopes. Further
developments of technique will probably be required before we can hope
to extend the measurements to short lived radioisotopes, though some
results are already becoming available for 23°U and 232Th.
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u
References
1. R. L. Macklin and J. H. Gibbons, Rev. Moz. Phys. 31, 166 (1965).
2. R. L. Henkel and H. H. Barschall, Phys. Rev. 80, 145 (1950).
3. F. Cabbard, R. H. Davis, and T. W. Bonner, Phys. Rev. 114, 201
(1959).
4. R. L. Macklin, P. J. Pasma, and J. H. Gibbons, Phys. Rev. 135,
B695 (1964).
5. R. C. Block anå M. C. Moxon, Bull. Am. Phys. Soc. II, 8, 513 (1963).
6. S. P. Kapchigashev and Yu. P. Popov, Atomaya Energia 15, 120 (1963).
7. R. L. Macklin, Nucl. Instr. and Methods 26, 213 (1964).
H. E. Jackson, Phys. Rev. Letters 11, 378 (1963).
9. J. H. Gibbons, R. L. Macklin, P. D. Miller, and J. H. Neiler,
Phys. Rev. 122, 182 (1961).
10. M. C. Moxon and E. R. Rae, Neutron Time-of-Flight Methods, ed. by
J. Spaepen (EURA L'OM, Brussels, 1961).
11. R. L. Macklin, J. H. Gibbons, and T. Inada, Nuclear Physics
43, 353 (1963).
12. H. Maier-Leibnitz, "Proposed method for Obtaining a Weighted
Average over a Spectrum" (11-22-63).
13. F. Rau, Nucleonik 5, 191 (1963).
24
9/ 9 / 65
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