The statistical theory of multi-step compound and direct reactions

Herman Feshbach, Arthur Kerman, Steven Koonin

Research output: Contribution to journalArticle

Abstract

The theory of nuclear reactions is extended so as to include a statistical treatment of multi-step processes. Two types are distinguished, the multi-step compound and the multi-step direct. The wave functions for the system are grouped according to their complexity. The multi-step direct process involves explicitly those states which are open, while the multi-step compound involves those which are bound. In addition to the random phase assumption which is applied differently to the multi-step direct and to the multi-step compound cross-sections, it is assumed that the residual interaction will have non-vanishing matrix elements between states whose complexities differ by at most one unit. This is referred to as the chaining hypothesis. Explicit expressions for the double differential cross-section giving the angular distribution and energy spectrum are obtained for both reaction types. The statistical multi-step compound cross-sections are symmetric about 90°. The classical statistical theory of nuclear reactions is a special limiting case. The cross-section for the statistical multi-step direct reaction consists of a set of convolutions of single-step direct cross-sections. For the many step case it is possible to derive a diffusion equation in momentum space. Application is made to the reaction 181Ta(p, n)181W using the statistical multi-step compound formalism.

Original languageEnglish (US)
Pages (from-to)429-476
Number of pages48
JournalAnnals of Physics
Volume125
Issue number2
DOIs
StatePublished - Apr 1 1980

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cross sections
nuclear reactions
convolution integrals
energy spectra
angular distribution
wave functions
formalism
momentum
matrices
interactions

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

The statistical theory of multi-step compound and direct reactions. / Feshbach, Herman; Kerman, Arthur; Koonin, Steven.

In: Annals of Physics, Vol. 125, No. 2, 01.04.1980, p. 429-476.

Research output: Contribution to journalArticle

Feshbach, Herman ; Kerman, Arthur ; Koonin, Steven. / The statistical theory of multi-step compound and direct reactions. In: Annals of Physics. 1980 ; Vol. 125, No. 2. pp. 429-476.
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