Channel-coupling effects in the resonating-group study of the seven-nucleon system

A three-channel resonating-group calculation is performed to study the effects of channel coupling on the properties of the ${}_{}{}^3{}_{}{}^{}\mathrm{H}$+$\alpha$ system. The channels included are ${}_{}{}^3{}_{}{}^{}\mathrm{H}$+$\alpha$, n+${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, and n+${}_{}{}^6{}_{}{}^{}\mathrm{Li}$* channels, with ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$* described by ${\mathrm{}\left(1s\right)\mathrm{}}^4{\mathrm{}\left(1p\right)\mathrm{}}^2$ harmonic-oscillator functions representing d+$\alpha$ cluster configurations with relative orbital angular momenta equal to 0 and 2, respectively. By comparing with the ${}_{}{}^3{}_{}{}^{}\mathrm{H}$+$\alpha$ single-channel result, it is found that the three-channel calculation improves the $L=1\mathrm{}$ ground state energy by 0.68 MeV and yields additional features such as cusps in the $L=0\mathrm{} \mathrm{and} 2$ phase shifts and a dispersionlike resonance structure in the $L=1\mathrm{}$ phase shift. In addition, it is noted that, in states with larger $L$ values, the n+${}_{}{}^6{}_{}{}^{}\mathrm{Li}$* aligned configurations make particularly important contributions. Characteristics of nucleon-exchange terms have also been briefly investigated; here one finds that, as far as the ${}_{}{}^3{}_{}{}^{}\mathrm{H}$+$\alpha$ system is concerned, the important one-exchange and core-exchange contributions are only weakly affected by the presence of other channels.