The statistical theory of multi-step compound and direct reactions

Herman Feshbach; Arthur Kerman; Steven Koonin

doi:10.1016/0003-4916(80)90140-2

The statistical theory of multi-step compound and direct reactions

Herman Feshbach, Arthur Kerman, Steven Koonin

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	429-476
Number of pages	48
Journal	Annals of Physics
Volume	125
Issue number	2
DOIs	https://doi.org/10.1016/0003-4916(80)90140-2
State	Published - Apr 1 1980

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1016/0003-4916(80)90140-2

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title = "The statistical theory of multi-step compound and direct reactions",

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.",

author = "Herman Feshbach and Arthur Kerman and Steven Koonin",

note = "Funding Information: In this paper, we continue our study of the fundamental mechanisms underlying nuclear reactions. The phenomena upon which we will focus our attention can be seen by reference to Fig. 1, which is a schematic representation of the energy spectrum of particles emitted as a consequence of a nuclear reaction, at a given angle and for a specific residual nucleus. At the high energy end of the spectrum the particles will have discrete energies corresponding to the excitation of specific energy levels in the residual nucleus. As the excitation energy of the residual nucleus increases, and the particle energy correspondingly decreases,t he density of levels in the residual nucleus will eventually become so large that the measured spectrum will be continuous. For the reactions to be discussedb elow, the high-energy end of the particle spectrum is dominated by direct reactions. These involve a short interaction time with the excita- * This work is supported in part through funds provided by the United States Department Energy (DOE) under contract EY-76-C-02-3069.",

year = "1980",

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doi = "10.1016/0003-4916(80)90140-2",

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T1 - The statistical theory of multi-step compound and direct reactions

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AU - Koonin, Steven

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PY - 1980/4/1

Y1 - 1980/4/1

N2 - 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.

AB - 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.

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The statistical theory of multi-step compound and direct reactions

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