T. Vertse

A representation to describe nuclear processes in the continuum

Bound single-particle states, outgoing resonances and a limited number of scattering states along a path in the complex k-plane (Berggren space) are used as a representation to describe the eigenstates of a realistic nuclear Hamiltonian. It is found that these eigenvectors are contained in the Berggren space, i.e. that the diagonalization of the Hamiltonian provides all the bound states and resonances while the rest of the eigenvalues still remain on the same complex path.

Complex energy approaches for calculating isobaric analogue states

Parameters of isobaric analog resonance (IAR) are calculated in the framework of the Lane model using different methods. In the standard method, the direct numerical solution of the coupled channel (CC) Lane equations served as a reference for checking two complex energy methods, namely the complex energy shell model (CXSM) and the complex scaling (CS) approaches. The IAR parameters calculated by the CXSM and the CS methods agree with that of the CC results within 1 keV for all partial waves considered. Although the CXSM and the CS methods have similarities, an important difference is that only the CXSM method offers a direct way for studying the configurations of the IAR wave function.

Shadow poles in a coupled-channel problem calculated with Berggren basis

In coupled-channel models the poles of the scattering S-matrix are located on different Riemann sheets. Physical observables are affected mainly by poles closest to the physical region but sometimes shadow poles have considerable effect, too. The purpose of this paper is to show that in coupled-channel problem all poles of the S-matrix can be calculated with properly constructed complex-energy basis. The Berggren basis is used for expanding the coupled-channel solutions. The location of the poles of the S-matrix were calculated and compared with an exactly solvable coupled-channel problem: the one with the Cox potential. We show that with appropriately chosen Berggren basis poles of the S-matrix including the shadow ones can be determined.

Complex shell model with antibound states

An unified shell model scheme to evaluate simultaneously the contributions of bound single-particle states, Gamow resonances, antibound (virtual) states and continuum complex scattering states is presented. The formalism could be very suitable to study processes occurring in the continuum part of the nuclear spectra.

Shell model representation with antibound states

The generalized Berggren representation treats antibound states on an equal footing with bound states and resonances. The advantage of this approach is that the effects of the antibound poles and the complex continuum can be studied separately. In order to show the power of the method we applied it for shell model problem with two valence neutrons for drip line nuclei.In the example of 11Li nucleus we generated the bound ground state from the unbound basis elements and observed that the antibound state is very important in the building up the halo. However the huge contribution of the antibound pole is partly canceled by that of the complex continuum. We predicted a two‐particle resonance in 11Li but for making more reliable predictions probably a more sophisticated model has to be used.

Description of the Continuum in Calculating Partial Decay Widths of Giant Resonances

Since giant resonances are collective excitations, lying in general, above the threshold of the particle emission one has to take into account the possibility of the nucleon escape in the theoretical description. The usual treatment is in the frame of the continuum random phase approximation 1 (CRPA), in which the effect of the continuum is taken into account exactly. For heavy nuclei CRPA calculations are time consuming since a large number of p-h configurations form the giant multipole resonance. Dealing with a realistic single particle potential one has to integrate the Schrodinger equation numerically in order to get the solutions which determine the Green’s function. Therefore the major part of the computation time in the CRPA is spent on calculating the Green’s function at different energies.