Resonances in Complex-Scaled Orthogonality Condition Model of Nuclear Cluster System

Abstract

The complex scaling of the Hamiltonian of the orthogonality condition model of two-cluster systems is introduced. It is shown that the energy and width of various kinds of resonance states in the 160+a system can be calculated accurately. 2 ) Actu­ ally, many cluster states have been observed as resonance states. Therefore, from a theoretical point of view, it is very important to describe correctly resonance states. Usually the energy and width of a resonance state are calculated by solving the scattering problem. However it is not necessarily easy to solve the scattering problem especially for multi-cluster systems, though a useful method for cluster systems has been developed. 3 ) Alternative ways to obtain the parameters of a resonance state are so-called direct methods. These procedures supply the poles of the S-matrix and/ or the wave function of the Gamow-state. The complex scaling method is proved to be a very powerful procedure to determine the parameters of resonances in atomic and molecu­ lar physics. 4 ) In this method, the energy and the width of resonance states can be obtained by means of bound-state techniques to calculate the energy spectrum. It is not necessary to set asymptotic boundary conditions prescribing outgoing wave functions associated to open channels. Therefore this method seems much promising to calculate resonance states unambiguously in multi-cluster systems where various open channels have to be considered. The application of the complex scaling method to the cluster model has been discussed by one (Kruppa) of the present authors, Lovas and Gyarmati. 5 ) They introduced the complex scaling of the relative coordinate between clusters and solved the resonating group equation for the a+ a cluster system. The results well repro­ duce the resonance states of 0+,2+ and 4+ in the system, and are interesting enough to drive us to apply this method to other complex systems. The multi-cluster model is very interesting in study of highly excited nuclear structures. However, a microscopic calculation such as the resonating group method (RGM) isnot still easy for the multi-cluster model, though the technique has greatly been developed in recent years.