Direct and compound processes in nuclear reactions

Sang, Mankun; Shiro, Yoshitsugu; Terasawa, T.

doi:10.1016/0029-5582(58)90073-7

Cited by 22 publications

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“…By taking this Ua as the optical potential describing the average elastic scattering, it is usually considered 9 ) that the third term on the right-hand side of Eq. (2 ·1) represents the contribution from the compound processes.…”

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Compound Levels and the Shell Model

Yazaki¹

1967

Prog. Theor. Phys.

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353A formalism of nuclear reactions is presented which clarifies the meaning of applying the usual shell model calculations to the resonance states as well as the bound states. The main point is the introduction of the internal region in the wave function space. An effective Hamiltonian is defined in this subspace, the diagonalization of which gives the energies and the wavefunctions for the resonance states as well as the bound states. As an application of the theory, calculations of the level widths are carried out for 5 He nucleus. § l. ln1troductionWhen we speak of the energy levels of nuclei, we usually consider them as including unstable levels as well as stable ones. In fact, if we look at the experimental data such as the energy spectra of particles inelastically scattered by a target nucleus, we are naturally led to the concept of "levels " irrespectively of whether they are stable or not. In the following, we call them compound levels. The compound levels in a more restrictive sense were first introduced by N. Bohr 1 l for the purpose of explaining many sharp peaks observed in neutron scattering and radiative capture cross sections. Though the concept of the compound levels was originally based on the strong coupling picture which is now found to be applicable only to the limited number of cases, it is not restricted to the picture, and has been found quite useful to understand low energy nuclear reactions. Now, experimental information on the compound levels has been obtained from the analysis of nuclear reactions, photoreactions, p-decays and so forth, while theoretical interpretations of them have been made in terms of the shell model, and the agreement between theory and experiment is such as to make us believe that we are not in the wrong direction. However, from the theoretical point of view, the applicability of the shell model to the unstable levels has not yet been clarified. Actually, the wave functions obtained by the model for the unstable cases have no such definite meaning as they have for the stable cases, because they satisfy none of the conditions required for the definition *l This work is based on a thesis submitted to Tokyo University in partial fulfillment of the requirements of the Ph. D degree.

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