The statistical theory of multi-step compound and direct reactions: Herman Feshbach, Arthur Kerman, and Steven Koonin, Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; and California Institute of Technology, Pasadena, California 91109

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 87 KB
• Volume: 125
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(80)90127-x

✦ Synopsis

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 multistep 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 crosssections. For the many-step case it is possible to derive a diffusion equation in momentum space. Application is made to the reaction lslTa(p, n) lslW using the statistical multi-step compound formalism.