Nuclear binding energies from moment methods: Realistic effective no-core Hamiltonian

Total binding energies for nuclei with $14\le A\le 18$ are obtained from a realistic effective no-core Hamiltonian, $H_{\mathrm{eff}}$, using moment methods. The lowest few moments of $H_{\mathrm{eff}}$ are evaluated in an oscillator model space of four major shells. These moments are then used to determine a number of continuous and discrete density of states functions, each of which yields an estimate for the $H_{\mathrm{eff}}$ ground state energy. The adjustable discrete density of states functions which we introduce are based upon realistic single-particle Hamiltonians. With a reasonable selection of moment method ingredients we obtain good agreement between theory and experiment for relative binding energies within each $A$ chain. The most stable isobar is correctly predicted in all cases and Coulomb energy differences are in close agreement with experiment. Thus, the valley of $\beta$ stability is well reproduced in this approach with a simple overall shift in absolute binding energies for each $A$ chain.