Configuration mixing calculation for complete low-lying spectra with the mean-field Hamiltonian

Abstract

We propose a new theoretical approach to ground and low-energy excited states of nuclei extending the nuclear mean-field theory. It consists of three steps: stochastic preparation of many Slater determinants, the parity and angular momentum projection, and diagonalization of the generalized eigenvalue problems. The Slater determinants are constructed in the three-dimensional Cartesian coordinate representation capable of describing arbitrary shape of nuclei. We examine feasibility and usefulness of the method by applying the method with the BKN interaction to light 4N-nuclei, 12C, 16O, and 20Ne. We discuss difficulties of keeping linear independence for basis states projected on good parity and angular momentum and present a possible prescription.

12 pages, revtex4

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• Deformation and cluster structures in ${}^{12}$C studied with configuration mixing using Skyrme interactions
• Correlated-basis description of $\alpha$-cluster and delocalized $0^{+}$ states in ${}^{16}$O
• Application of efficient generator-coordinate subspace-selection algorithm to neutrinoless double-$\beta$ decay
• Optimization of generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double-beta decay: ridge regression for nuclei with axial deformation
• Properties of $K^{\pi }=0_1^{+}$, $K^{\pi }=2^{-}$, and $K^{\pi }=0_1^{-}$ bands of ${}^{20}$Ne probed via proton and alpha inelastic scattering
• Generator coordinate method with a conjugate momentum: application to the particle number projection
• An extension of the generator coordinate method with basis optimization
• Cluster model of 12C in density functional theory framework
• Eulerian Rotations of Deformed Nuclei for TDDFT Calculations
• Applications of the dynamical generator coordinate method to quadrupole excitations
• Five-dimensional collective Hamiltonian with improved inertial functions
• Nuclear structure and reaction with quantum shape fluctuation