Introduction to the Theory and Analysis of Resolved (and Unresolved) Neutron Resonances via SAMMY Page: 2 of 43
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(for those nuclides for which no experimental data exist) can be made much more readily from
systematics than from raw data. (Additional discussions on this topic are given in papers by
At relatively low energies, individual peaks (resonances) can be seen in the energy-dependent
cross sections; this energy region is labeled the "resolved-resonance region." At higher energies,
the natural widths of the resonances are comparable to their spacing, so it is not possible to separate
one peak from another; this is the "unresolved-resonance region." At even higher energies, the very
concept of resonance is inappropriate; this region is referred to as the "high-energy region." Our
primary concern in this paper is the resolved-resonance region, in which the experimental data (cross
sections vs energy) may be parameterized in terms of resonance energies, widths, and other
quantities. The important features of data analysis in the resolved-resonance region are discussed,
with particular emphasis on techniques used in the author's analysis code SAMMY.3 (Another
approach to the same topic is given in Ref. 4.) Here we begin with a description, in general terms,
of the kinds of experimental data that are available for analysis.
2 Experimental Data
2.1 Neutron Time-of-Flight Experiments
Neutron time-of-flight experiments are used to measure energy-dependent neutron cross sections at
facilities such as the Oak Ridge Electron Linear Accelerator (ORELA) in Tennessee, the Geel
LINAC (GELINA) in Belgium, or the Gaerttner LINAC at Rensselaer Polytechnic Institute in New
York. These accelerators produce beams of electrons, which are then directed onto a target (tantalum
at ORELA, uranium at GELINA); the resulting interaction produces neutrons, which exit outward
in all directions. Shielding is used to collimate the beam by stopping neutrons traveling in an
unwanted direction. For purposes of this report, the entire operation described above can be viewed
as a "black box"; only the resulting neutron beam is of interest here.
Neutrons produced as described above are used as probes to (e"n
study nuclei. Samples of the material to be studied are placed in
the beam line, where neutrons interact with nuclei in the sample.
Detectors, placed in or near the beam line (depending upon the neuron-
type of data to be collected), are used to count the particles that r
reach them. The schematic shown in Fig. I depicts a typical setup Nem
for a transmission experiment, in which the quantity to be
determined is the ratio of the number of neutrons impinging on the
sample to the number of neutrons leaving the sample; this quantity L
is directly related to the total cross section. Other types of
differential (i.e., energy- and/or angle-dependent) measurements
can also be performed with time-of-flight techniques, with
appropriate modifications in the experimental setup.
The electron beam (and hence the neutron beam) is pulsed,
with the beam "on" for, typically, a few nanoseconds, and "off' for Figure 1: Schematic of
a neutron time-of-flight
several milliseconds. The detector (with associated electronics) transmission experiment.
records not merely the total number of arriving neutrons but also
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Larson, N. Introduction to the Theory and Analysis of Resolved (and Unresolved) Neutron Resonances via SAMMY, article, March 13, 2000; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc717748/m1/2/: accessed March 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.