Quantum Monte Carlo calculations of excited states in $A=6–8$ nuclei

A variational Monte Carlo method is used to generate sets of orthogonal trial functions, ${\Psi }_T(J^{\pi };T)$, for given quantum numbers in various light $p$-shell nuclei. These ${\Psi }_T$ are then used as input to Green’s function Monte Carlo (GFMC) calculations of first, second, and higher excited $(J^{\pi };T)$ states. Realistic two- and three-nucleon interactions are used. We find that if the physical excited state is reasonably narrow, the GFMC energy converges to a stable result. With the combined Argonne ${\mathrm{v}}_{18}$ two-nucleon and Illinois-2 three-nucleon interactions, the results for many second and higher states in $A=6–8$ nuclei are close to the experimental values.

Figure 1

(Color online) GFMC energies of four ${\frac{5}{2}}^{-}$ states in ${}^7\mathrm{Li}$ vs imaginary time, $\tau$. The solid symbols show the computed energies at each $\tau$; open symbols show the results of the rediagonalization discussed in the text.

Figure 2

(Color online) Overlaps of the GFMC wave functions for the first ${\frac{5}{2}}^{-}$ state in ${}^7\mathrm{Li}$ with the other three ${\frac{5}{2}}^{-}$ states vs imaginary time.

Figure 3

(Color online) GFMC excitation energies computed for the $\mathrm{AV}18$, $\mathrm{AV}18∕\mathrm{UIX}$, and $\mathrm{AV}18∕\mathrm{IL}2$ Hamiltonians compared with experimental values. The shaded bands show the Monte Carlo statistical (or experimental) errors. The narrow shaded bars on the experimental values show the experimental widths.