Coupled-Channel Calculations for Nuclear Bound States

Abstract

The method of coupled channels is presented for situations where all channels are bound. A numerical relaxation technique is formulated for such problems and is found to be rapid and reliable. Calculations are performed for deformed nuclei (where angular momenta in a rotational band are coupled) and for the Lane isospin t\ifmmode\cdot\else\textperiodcentered\fi{}T potential (where proton-nucleus and neutron-analog compositions of a target nucleus are coupled). In either case the relevant radial functions may be used as form factors for the analysis of stripping or pickup experiments. The calculations are applied to (1) deformed components in spherical nuclei (${\mathrm{O}}^{18}$ and ${\mathrm{Ca}}^{40}$); (2) a deformed nucleus (${\mathrm{Mg}}^{25}$); (3) $j$-dependent effects in the $1{f}_{\frac{7}{2}}$ shell; and (4) the extraction of ($p, d$) spectroscopic factors in the $1{f}_{\frac{7}{2}}$ shell using the Lane potential. The effect of the channel coupling is found to be important in many instances.