Quantum Monte Carlo calculations of $A=9,10$ nuclei

Abstract

We report on quantum Monte Carlo calculations of the ground and low-lying excited states of $A=9,10$ nuclei using realistic Hamiltonians containing the Argonne $v_{18}$ two-nucleon potential alone or with one of several three-nucleon potentials, including Urbana IX and three of the new Illinois models. The calculations begin with correlated many-body wave functions that have an $\alpha$-like core and multiple p-shell nucleons, $LS$-coupled to the appropriate $(J^{\pi };T)$ quantum numbers for the state of interest. After optimization, these variational trial functions are used as input to a Green's function Monte Carlo calculation of the energy, using a constrained path algorithm. We find that the Hamiltonians that include Illinois three-nucleon potentials reproduce ten states in ${}^9$Li, ${}^9$Be, ${}^{10}$Be, and ${}^{10}$B with an rms deviation as little as 900 keV. In particular, we obtain the correct 3${}^{+}$ ground state for ${}^{10}$B, whereas the Argonne $v_{18}$ alone or with Urbana IX predicts a 1${}^{+}$ ground state. In addition, we calculate isovector and isotensor energy differences, electromagnetic moments, and one- and two-body density distributions.

Comments: 28 pages, 12 tables, 7 figures