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.