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Low energy neutron scattering for energy dependent cross sections. General considerations

Abstract

We consider in this paper some aspects related to neutron scattering at low energies by nuclei which are subject to thermal agitation. The scattering is determined by a temperature dependent joint scattering kernel, or the corresponding joint probability density, which is a function of two variables, the neutron energy after scattering, and the cosine of the angle of scattering, for a specified energy and direction of motion of the neutron, before the interaction takes place. This joint probability density is easy to calculate, when the nucleus which causes the scattering of the neutron is at rest. It can be expressed by a delta function, since there is a one to one correspondence between the neutron energy change, and the cosine of the scattering angle. If the thermal motion of the target nucleus is taken into account, the calculation is rather more complicated. The delta function relation between the cosine of the angle of scattering and the neutron energy change is now averaged over the spectrum of velocities of the target nucleus, and becomes a joint kernel depending on both these variables. This function has a simple form, if the target nucleus behaves as an ideal gas, which has a scattering  More>>
Authors:
Rothenstein, W; Dagan, R [1] 
  1. Technion-Israel Inst. of Tech., Haifa (Israel). Dept. of Mechanical Engineering
Publication Date:
Dec 01, 1996
Product Type:
Conference
Report Number:
INIS-mf-15507; CONF-961252-
Reference Number:
SCA: 663610; PA: AIX-28:024277; EDB-97:076478; SN: 97001789209
Resource Relation:
Conference: 19. conference of the Israel Nuclear Societies, Herzliya (Israel), 9-10 Dec 1996; Other Information: PBD: Dec 1996; Related Information: Is Part Of Program and book of abstracts; PB: 149 p.
Subject:
66 PHYSICS; NEUTRON TRANSPORT THEORY; SLOWING-DOWN KERNELS; CROSS SECTIONS; ENERGY DEPENDENCE; LEGENDRE POLYNOMIALS; NEUTRON FLUX; SCATTERING; SLOWING-DOWN
OSTI ID:
476013
Research Organizations:
Israel Nuclear Society, Yavne (Israel)
Country of Origin:
Israel
Language:
English
Other Identifying Numbers:
Other: ON: DE97616259; TRN: IL9606169024277
Availability:
INIS; OSTI as DE97616259
Submitting Site:
INIS
Size:
pp. 1
Announcement Date:

Citation Formats

Rothenstein, W, and Dagan, R. Low energy neutron scattering for energy dependent cross sections. General considerations. Israel: N. p., 1996. Web.
Rothenstein, W, & Dagan, R. Low energy neutron scattering for energy dependent cross sections. General considerations. Israel.
Rothenstein, W, and Dagan, R. 1996. "Low energy neutron scattering for energy dependent cross sections. General considerations." Israel.
@misc{etde_476013,
title = {Low energy neutron scattering for energy dependent cross sections. General considerations}
author = {Rothenstein, W, and Dagan, R}
abstractNote = {We consider in this paper some aspects related to neutron scattering at low energies by nuclei which are subject to thermal agitation. The scattering is determined by a temperature dependent joint scattering kernel, or the corresponding joint probability density, which is a function of two variables, the neutron energy after scattering, and the cosine of the angle of scattering, for a specified energy and direction of motion of the neutron, before the interaction takes place. This joint probability density is easy to calculate, when the nucleus which causes the scattering of the neutron is at rest. It can be expressed by a delta function, since there is a one to one correspondence between the neutron energy change, and the cosine of the scattering angle. If the thermal motion of the target nucleus is taken into account, the calculation is rather more complicated. The delta function relation between the cosine of the angle of scattering and the neutron energy change is now averaged over the spectrum of velocities of the target nucleus, and becomes a joint kernel depending on both these variables. This function has a simple form, if the target nucleus behaves as an ideal gas, which has a scattering cross section independent of energy. An energy dependent scattering cross section complicates the treatment further. An analytic expression is no longer obtained for the ideal gas temperature dependent joint scattering kernel as a function of the neutron energy after the interaction and the cosine of the scattering angle. Instead the kernel is expressed by an inverse Fourier Transform of a complex integrand, which is averaged over the velocity spectrum of the target nucleus. (Abstract Truncated)}
place = {Israel}
year = {1996}
month = {Dec}
}