Compound Levels and the Shell Model

Abstract

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.

Constituent quark model study of the meson spectra

“…This may be the reason why the OPE generates contributions that are not obtained from the OGE, while the ρ and ω meson exchanges give rise to contributions already generated by the OGE [28]. Explicit studies on the literature about the double counting problem concluded that while the pion can be safely exchanged together with the gluon, the vector and axial mesons cannot [29]. Finally, any model imitating QCD should incorporate another nonperturbative effect, confinement, that takes into account that the only observed hadrons are color singlets.…”

Two-body correlations in nuclear systems

“…As an example we mention the non-relativistic constituent quark models, which are very successful in describing the properties of baryons [146]. Based on such constituent quark models, so-called quark cluster models have been developed for the NN interaction [1,147,148]. These models include the effects of one-gluon-exchange terms and account for the exchange of mesons between the quarks.…”

Quark-meson coupling model with constituent quarks: Exchange and pionic effects

“…[22] to derive an effective NN interaction from pion-quark exchange. The resulting NN interaction is non-local and gives scattering phase-shifts numerically similar to the ones obtained with the resonating group method [21]. After a long calculation, with the extensive use of the substitution rules of Ref.…”