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

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

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

Description of the proton and neutron radiative capture reactions in the Gamow shell model

We formulate the Gamow shell model (GSM) in coupled-channel (CC) representation for the description of proton/neutron radiative capture reactions and present the first application of this new formalism for the calculation of cross-sections in mirror reactions 7Be(p,gamma)8B and 7Li(n,gamma)8Li. The GSM-CC formalism is applied to a translationally-invariant Hamiltonian with an effective finite-range two-body interaction. Reactions channels are built by GSM wave functions for the ground state 3/2- and the first excited state 1/2- of 7Be/7Li and the proton/neutron wave function expanded in different partial waves

Gamow shell model description of radiative capture reactions 6^6Li(p,γ)(p,\gamma)7^7Be and 6^6Li(n,γ)(n,\gamma)7^7Li

According to standard stellar evolution, lithium abundance is believed to be a useful indicator of the stellar age. However, many evolved stars like red giants show huge fluctuations around expected theoretical abundances that are not yet fully understood. The better knowledge of nuclear reactions that contribute to the creation and destruction of lithium can help to solve this puzzle. In this work we apply the Gamow shell model (GSM) formulated in the coupled-channel representation (GSM-CC) to investigate the mirror radiative capture reactions $^6$Li$(p,\gamma)$$^7$Be and $^6$Li$(n,\gamma)$$^7$Li. The cross-sections are calculated using a translationally invariant Hamiltonian with the finite-range interaction which is adjusted to reproduce spectra, binding energies and one-nucleon separation energies in $^{6-7}$Li, $^7$Be. All relevant $E1$, $M1$, and $E2$ transitions from the initial continuum states to the final bound states $J={3/2}_1^-$ and $J={1/2}^-$ of $^7$Li and $^7$Be are included. We demonstrate that the $s$-wave radiative capture of proton (neutron) to the first excited state $J^{\pi}=1/2_1^+$ of $^7$Be ($^7$Li) is crucial and increases the total astrophysical $S$-factor by about 40 \%.Comment: arXiv admin note: text overlap with arXiv:1502.0163