Coupled-channel continuum eigenchannel basis

The goal of this paper is to calculate bound, resonant and scattering states in the coupled-channel formalism without relying on the boundary conditions at large distances. The coupled-channel solution is expanded in eigenchannel bases i.e. in eigenfunctions of diagonal Hamiltonians. Each eigenchannel basis may include discrete and discretized continuum (real or complex energy) single particle states. The coupled-channel solutions are computed through diagonalization in these bases. The method is applied to a few two-channels problems. The exact bound spectrum of the Poeschl-Teller potential is well described by using a basis of real energy continuum states. For deuteron described by Reid potential, the experimental energy and the S and D contents of the wave function are reproduced in the asymptotic limit of the cutoff energy. For the Noro-Taylor potential resonant state energy is well reproduced by using the complex energy Berggren basis. It is found that the expansion of the coupled-channel wave function in these eigenchannel bases require less computational efforts than the use of any other basis. The solutions are stable and converge as the cutoff energy increases.Comment: Accepted to be published in Physics Letters

Gamow Shell-Model Description of Weakly Bound and Unbound Nuclear States

Recently, the shell model in the complex k-plane (the so-called Gamow Shell Model) has been formulated using a complex Berggren ensemble representing bound single-particle states, single-particle resonances, and non-resonant continuum states. In this framework, we shall discuss binding energies and energy spectra of neutron-rich helium and lithium isotopes. The single-particle basis used is that of the Hartree-Fock potential generated self-consistently by the finite-range residual interaction.Comment: 13 pages, 2 figures, presented by N. Michel at the XXVII Symposium On Nuclear Physics, Taxco, Guerrero, Mexico, January 5-8 200

Perturbative method for generalized spectral decompositions

Imposing analytic properties to states and observables we construct a perturbative method to obtain a generalized biorthogonal system of eigenvalues and eigenvectors for quantum unstable systems. A decay process can be described using this generalized spectral decomposition, and the final generalized state is obtained.Comment: 21 Page

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.Comment: 11 pages, 4 figures, 59 reference

Two-Particle Resonant States in a Many-Body Mean Field

A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two particle states are calculated by using a single particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long lived two-body states (including bound states) are mostly determined by either bound single-particle states or by narrow Gamow resonances. However, they can be significantly affected by the continuum part of the spectrum.Comment: 11 pages, 4 figure