Proton-neutron coupling in the Gamow shell model: The lithium chain

Abstract

The shell model in the complex k-plane (the so-called Gamow Shell Model) has recently been formulated and applied to structure of weakly bound, neutron-rich nuclei. The completeness relations of Newton and Berggren, which apply to the neutron case, are strictly valid for finite-range potentials. However, for long-range potentials, such as the Coulomb potential for protons, for which the arguments based on the Mittag-Leffler theory do not hold, the completeness still needs to be demonstrated. This has been done in this paper, both analytically and numerically. The generalized Berggren relations are then used in the first Gamow Shell Model study of nuclei having both valence neutrons and protons, namely the lithium chain. The single-particle basis used is that of the Hartree-Fock-inspired potential generated by a finite-range residual interaction. The effect of isospin mixing in excited unbound states is discussed

Asymptotic normalization coefficients and continuum coupling in mirror nuclei

“…Other nuclei with η > η crit are 29 P, 32 Cl, and 36,37 K whereas 17 F, 30 S, 33 Cl, and 37 Ca are situated at the critical line η crit (Z a ). A pronounced odd-even staggering of η and β ℓ,j is seen for both protonrich and neutron-rich systems.…”

“…The T = 0 constants V N J,T =0 are listed in Table II In the pole approximation, in which only resonant states are considered, amplitudes of 2p-2h and 4p-4h 0p 1/2 → sd excitations are of the order of 10 −3 and 10 −6 , respectively. Consequently, as configuration mixing effects in the states considered are weak, only two particletwo hole excitations have been allowed from the proton and neutron 0p 1/2 states, and only one particle has been allowed to occupy s [37] corresponding to a parent nucleus. Sphericity of the GHF potential is guaranteed by the use of the uniform filling approximation.…”

“…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.…”

Bound states of dipolar molecules studied with the Berggren expansion method

“…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]).…”

Density matrix renormalization group approach to two-fluid open many-fermion systems

“…[35], s.p. bases for protons and neutrons are generated by their respective spherical Hartree-Fock (HF) potentials corresponding to the GSM Hamiltonian [Eq.…”