Gamow shell model description of weakly bound nuclei and unbound nuclear states

Abstract

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.

Bound states of dipolar molecules studied with the Berggren expansion method

“…In the above formula, θ is an angle of rotation chosen so that Φ k,c (R + xe iθ ) → 0 for x → +∞, which is always possible provided θ is larger than a critical value depending on k [84]. Note that no modulus enters Eq.…”

“…The Berggren completeness relation is a resonant-state expansion; it treats the resonant and scattering states on the same footing as bound states. We have successfully applied this tool to a variety of nuclear structure problems pertaining to weakly-bound and unbound nuclear states [48][49][50][51] (for a recent review see Ref. [52]).…”

Asymptotic normalization coefficients and continuum coupling in mirror nuclei

“…SMEC is particularly suited for studies of the qualitative effects of the continuum coupling because the strength of this coupling can be changed continuously from a SM limit (V 0 = 0) to physically relevant values. One should stress here that increasing V 0 lowers all the eigenvalues E α (E, V 0 ) in (36). The lowest eigenvalue describes the ground state (g.s.)…”

“…The many-body GSM states have been determined by a diagonalization of the GSM matrix using the Davidson method extended to complex-valued Hamiltonians. The identification of the outgoing GSM states has been carried out by applying the overlap method [36]. The parameter optimization was carried out using the multidimensional Newton method.…”

“…Recently, a different strategy based on the rigged Hilbert space formulation of quantum mechanics [34] has resulted in the complex-energy CSM (the GSM) [35][36][37], which is a natural generalization of the standard SM for unbound systems. In this formulation, the maximum number of particles in the scattering continuum is not a priori prescribed, but follows from the Schrödinger variational principle for the many-body Hamiltonian.…”