Mixed-mode shell-model theory for nuclear structure studies

Abstract

We introduce a shell-model theory that combines traditional spherical states, which yield a diagonal representation of the usual single-particle interaction, with collective configurations that track deformations, and test the validity of this mixed-mode, oblique basis shell-model scheme on 24 Mg. The correct binding energy (within 2% of the full-space result) as well as lowenergy configurations that have greater than 90% overlap with full-space results are obtained in a space that spans less than 10% of the full space.The results suggest that a mixed-mode shell-model theory may be useful in situations where competing degrees of freedom dominate the dynamics and full-space calculations are not feasible.

Confined one-dimensional harmonic oscillator as a two-mode system

“…͑24͔͒. 4 Our oblique basis consists of modified harmonic oscillator ͑MHO͒ basis states that satisfy the boundary conditions along with the basis states of a free particle in a box. To obtain the wave functions and eigenenergies we solve the generalized eigenvalue problem within this oblique basis.…”

“…This set of states will form an oblique ͑mixed-mode͒ basis for the calculation. 4,5 In general, such a basis is nonorthogonal and may even be over complete. Nevertheless, as recent studies 4,5 demonstrate, such oblique bases have merit.…”

“…4,5 In general, such a basis is nonorthogonal and may even be over complete. Nevertheless, as recent studies 4,5 demonstrate, such oblique bases have merit. In this paper we consider a pedagogically simple problem to illustrate the oblique basis approach.…”

Benchmark calculation of inclusive electromagnetic responses in the four-body nuclear system

“…[61]. Thus, one could use basis states with a frequency that ensures fast convergence for the ground state, adding also basis states of smaller frequencies, which would allow a better discretization of the complex-energy continuum at low energies, and basis states corresponding to larger frequencies for a better description of the response at higher energies.…”

SU(3) versus deformed Hartree-Fock state

“…This understanding provided motivation for a recent proposal for a "mixed-mode" approach to the selection of shellmodel basis states, combining a few irreps of SU(3) to account for deformation with spherical configurations favored by pairing-like modes and single-particle degrees of freedom, keeping the combined total number of basis states well-below that of the full space [7].…”