Hyperspherical effective interaction for nonlocal potentials

The effective interaction hyperspherical-harmonics method, formulated for local forces, is generalized to accommodate nonlocal interactions. As for local potentials this formulation retains the separation of the hyper-radial part leading solely to a hyperspherical effective interaction. By applying the method to study ground-state properties of ${}^4\mathrm{He}$ with a modern effective-field-theory nucleon-nucleon potential model (Idaho-N3LO), one finds a substantial acceleration in the convergence rate of the hyperspherical-harmonics series. Also studied are the binding energies of the six-body nuclei ${}^6\mathrm{He}$ and ${}^6\mathrm{Li}$ with the JISP16 nuclear force. Again an excellent convergence is observed.

Figure 1

The ground-state energy of the ${}^4\mathrm{He}$ nucleus with the Idaho N3LO $\mathit{NN}$ force [12]. A comparison between different nonlocal HH effective interactions that correspond to different choices of the operator $\mathcal{O}$ (see text).

Figure 2

The ground-state energies of ${}^6\mathrm{He}$ and ${}^6\mathrm{Li}$ with the bare JISP16 nuclear force [18] and with the corresponding nonlocal effective interaction taking $\stackrel{\wedge }{\mathcal{O}}=1/{\rho }^2$; dashed lines: extrapolated final results for the bare JISP16 force.