Atomic Bethe-Goldstone Calculations of the Hyperfine Structure ofB(P2)

A variational generalization of Brueckner's theory has been applied to the calculation of hyperfine parameters for the ${}_{}{}^2{}_{}{}^{}P$ ground state of atomic boron. The computational method makes use of a hierarchy of $n$th-order (or $n$-particle) variational Bethe-Goldstone equations defined in terms of configurational excitations of a Hartree-Fock reference state. Hyperfine parameters are computed as the sum of net increments defined at each level of the hierarchy. Orbital basis sets are extrapolated to practical completeness for each one- and two-particle net increment. Three-particle net increments are found to be small but not negligible. Computed magnetic hyperfine constants are within roughly 1% of experiment. The electric field gradient is computed, and its relative accuracy is estimated from that of the magnetic hyperfine constants. Combined with experimental quadrupole coupling constants, this implies values of the nuclear quadrupole moments $Q\left({\mathrm{B}}^{10}\right)=0.\mathrm{}08472\mathrm{}\left(56\right)\mathrm{}$ b and $Q\left({\mathrm{B}}^{11}\right)=0.\mathrm{}04065\mathrm{}\left(26\right)\mathrm{}$ b, with the indicated precision.