Quantum Monte Carlo calculations ofA=8nuclei

Abstract

We report quantum Monte Carlo calculations of ground and low-lying excited states for $A=8\mathrm{}$ nuclei using a realistic Hamiltonian containing the Argonne $v_{18}$ two-nucleon and Urbana IX three-nucleon potentials. The calculations begin with correlated eight-body wave functions that have a filled $\alpha$-like core and four p-shell nucleons $\mathrm{LS}$ coupled to the appropriate ${(J}^{\pi };T)$ quantum numbers for the state of interest. After optimization, these variational wave functions are used as input to a Green’s function Monte Carlo calculation made with a new constrained path algorithm. We find that the Hamiltonian produces a ${}^8\mathrm{Be}$ ground state that is within 2 MeV of the experimental resonance, but the other eight-body energies are progressively worse as the neutron-proton asymmetry increases. The ${}^8\mathrm{Li}$ ground state is stable against breakup into subclusters, but the ${}^8\mathrm{He}$ ground state is not. The excited state spectra are in fair agreement with experiment, with both the single-particle behavior of ${}^8\mathrm{He}$ and ${}^8\mathrm{Li}$ and the collective rotational behavior of ${}^8\mathrm{Be}$ being reproduced. We also examine energy differences in the $T=1,2\mathrm{}$ isomultiplets and isospin-mixing matrix elements in the excited states of ${}^8\mathrm{Be}.$ Finally, we present densities, momentum distributions, and studies of the intrinsic shapes of these nuclei, with ${}^8\mathrm{Be}$ exhibiting a definite $2\alpha$ cluster structure.