Energy levels of Bi 210 and Po 210 and the shell-model residual force

The low-lying energy-level spectra of Bi ²¹⁰ and Po ²¹⁰ are calculated by using the j- j coupling shell-model and a residual nucleon-nucleon Gaussian potential without a hard core deduced from the free two-nucleon potentials of Blatt-Jackson and Brueckner-Gammel-Thaler. The spin-orbit force is neglected, but all direct and exchange components of the central and tensor forces are considered. Tensor-force effects are examined as a function of the range. A tensor force with reasonable range and strength accounts for the 1 ^- state of the h_{9}/{2}g_{9}/{2} multiplet being the ground state of Bi ²¹⁰, instead of the 0 ^- predicted by central forces. Eigenvalues and eigenfunctions are presented and compared with the experimental spectra. Finally it is shown that the ground-state wave functions for Bi ²¹⁰ and Po ²¹⁰ are consistent with the RaE β-decay parameter i< r>/< σ × r> and the measured magnetic dipole moment of Bi ²¹⁰.