Quasi-bound state wavefunctions

For studying the rates of radioactive nuclei in various decay chains we propose an approach unifying the advantages of the superfluid model for nucleon clustering and of the classical model for resonance tunneling in many-particle systems. We discuss the theoretical bases and numerical approach for decay rate predictions for some highly unstable proton rich trans-tin nuclei. Information on structure and nuclear mass of some exotic nuclei not yet experimentally accessible have also been obtained from a detailed analysis of the $\text{p}$, $\text{α}$ and cluster decay rates. It is shown that the Casten-type rate systematics works very well in various schemes of valence nucleon numbers revealing similar decay properties for the nuclei with the same numbers of valence protons and neutrons above the ¹⁰⁰₅₀Sn₅₀ and ²⁰⁸₈₂Pb₁₂₆ magic cores.

A global method to identify all the S-matrix poles k = k_l(g) in the k-plane for a central potential gV(r) (g ϵ $\text{C}$) is presented. The method involves construction of the Riemann surface R_g^(l) over the g-plane, on which the function k = k_l(g) is single valued and analytic. It implies the division of the Riemann surface R_g^(l) into Σ_n^(l) sheets and the construction of the sheet images Σ′_n^(l) in the k-plane. The method is first applied to potentials having Jost entire functions in both variables g and k. In this case the general properties of the function k = k_l(g) and of its Riemann surface R_g^(l) are obtained. The method is then extended to other classes of potentials. The construction of the Riemann surface R_g^(l) as well as the construction of the images of its sheets in the k-plane for some particular potentials is given in detail. The method is allowed to identify new classes of resonant state poles. These poles remain in a neighborhood of some special points called “stable-points” as the strength of the potential increases to infinity; i.e., these resonant state poles do not become bound or virtual state poles. Moreover, the wave functions of the resonant states corresponding to the new-class poles situated in the neighborhood of the stable-points are almost completely localized outside the potential well. The method provides a quantum number n, characterizing the bound and resonant state S-matrix poles. This quantum number has a topological significance: it is the label of the sheets of the Riemann surface R_g^(l). The existence of new classes of resonant state poles seems to be a general property of the potentials with barriers used in nuclear scattering theory.

The ¹⁶O(⁶Li, d)²⁰Ne reaction has been studied at bombarding energies of 20, 32 and 38 MeV. The α-particle spectroscopic strengths have been extracted for levels up to 12.15 MeV in excitation. Nondirect processes appear to contribute significantly to all levels at 20 MeV and to high spin levels (6⁺ and 8⁺) at 32 MeV. Strengths extracted for members of the ground state band assuming (sd)⁴ transfer are unequal at both 32 and 38 MeV, in marked contrast to theoretical predictions. To explain this, particle-hole correlations in ¹⁶O(g.s.), inelastic channel coupling in the reaction and perhaps other effects as well, have to be considered. Strengths extracted for members of excited bands and α-decay reduced widths compare poorly with each other and with simple SU(3) predictions.

The systematic behavior of the (⁶Li, d) reaction on doubly even fp shell targets, as it has been observed in experiments at Rochester during the past years, is reviewed and an attempt is made to relate the results to the structure of the nuclei involved.