Quantum Monte Carlo calculations of $A=9,10\mathrm{}$ nuclei

We report on quantum Monte Carlo calculations of the ground and low-lying excited states of $A=9,10\mathrm{}$ 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, $\mathrm{LS}$-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 ${}^9\mathrm{Li},$ ${}^9\mathrm{Be},$ ${}^{10}\mathrm{Be},$ and ${}^{10}\mathrm{B}$ with an rms deviation as little as 900 keV. In particular, we obtain the correct $3^{+}$ ground state for ${}^{10}\mathrm{B},$ 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.