Quasi-particle states in the complex energy plane

R. ID BETAN; G. G. DUSSEL; ROBERTO LIOTTA,; TAMAS VERTSE,

Sankt Goar

Congreso; 2nd International Conference on Collective Motion in Nuclei under Extreme Conditions; 2006

The Shell Model in the complex energy plane (CXSM) was set up to describe the dinamics of unstable systems. For medium and heavy systems one need a very large basis to evaluate precisely many-body properties in the CXSM. The quasiparticle approximation is a way to circumvent this problem, in the sense that after one have define the single particle representation, by increasing the particle number in the system does not need increase the basis. The one-quasiparticle states are built on the Berggren basis form by bound states, resonances and a set of complex energy scattering states. One of the abvantages of this complex representation is that all the elements which form the basis are treated on the same footing, allowing one to study the relative importance of each component in building many particle observables. We are going to present an study of quasiparticles in the complex energy plane for one and two-quasiparticle exitations. For one-quasiparticle complex energy exitations we found that the imaginary part has not any direct relation to the widths, since the Bogoliubov transformation mixes normal particles and normal holes. But, as in the normal complex energy states, a meaningful quasi-particle resonance shoul correspond with a quasi-particle wave function which is localized and almost  eal outside the nuclear surface. The two-quasi-particle complex energy exitations are study in the framework of the QRPA. We found that the behaviour of a two-quasitparticle exitations could  e a physically meaningfull two-quasiparticle resonance at the beginning of the shell, to become unphysical in the middle and physical again at the end of the shell. This behaviour is rather diferent compared with the one-quasiparticle exitation, because in that case if a normal state is a physically meaningful resonance, then it will remain as such throughout the shell and if it is unphysical it will also remain as such throughout the shell.