Calculation of the Hyperfine Constants forB11andO17

Abstract

The hyperfine constants for ${\mathrm{B}}^{11}$ and ${\mathrm{O}}^{17}$ have been calculated using a configuration interaction (CI) function based on the usual Hartree-Fock (HF) representation (where the orbitals are expressed as linear combinations of analytic functions) plus singly excited $s\to s^{\prime }$ functions and, for oxygen, singly excited $p\to p^{\prime }$ functions. The $s$ functions are made up two second-degree polynomials, each multiplied by a different exponential function. The $p$ functions are linear combinations of several $2p$ analytic orbitals. The energies were minimized with respect to the exponents of $s$ functions. The values obtained are (experimental results are given in parentheses): for the ${}_{}{}^2{}_{}{}^{}P$ state of ${\mathrm{B}}^{11}$, $a_{\frac{3}{2}}=67\mathrm{}$ Mc/sec (73.3 Mc/sec); $a_{\frac{1}{2}}=360.5\mathrm{}$ Mc/sec (366.5 Mc/sec); $Q=0.039\mathrm{}$ b (deduced from $b_{\frac{3}{2}}=2.695\mathrm{}$ Mc/sec); for the ${}_{}{}^3{}_{}{}^{}P$ state of ${\mathrm{O}}^{17}$: $a_2=-216\mathrm{}$ Mc/sec (-218.57 Mc/sec) ${a_2}^{\prime }=-132\mathrm{}$ Mc/sec (-126.6 Mc/sec), $a_1=-3.8\mathrm{}$ Mc/sec (4.74 Mc/sec), ${a_1}^{\prime }=-113\mathrm{}$ Mc/sec (-91.8 Mc/sec), $Q=-0.024\mathrm{}$ (deduced from $b_2=-10.4\mathrm{}$ Mc/sec). For oxygen, the CI calculation where each excited $p\to p^{\prime }$ configuration is represented by three independent functions is shown to be an approximation to the most general formulation of what Löwdin has called the extended Hartree-Fock (EHF) functions. The unrestricted Hartree-Fock (UHF) functions have also been calculated. As the UHF functions are not eigenfunctions of $J^2$, there is no unambiguous way to define functions for states corresponding to definite values of $J$. For both boron and oxygen the values of the Fermi contact term obtained from projection of the UHF functions are in better agreement with experiment than the values calculated from the UHF functions.