Calculation of the Magnetic Hyperfine Constant of the Nitrogen Atom

The magnetic hyperfine constant for the ⁴S3/2 state of the N¹⁴ atom has been calculated from a configuration interaction (CI) function built from the usual Hartree-Fock (HF) representation (where the orbitals are linear combinations of analytic functions) plus all singly-excited and some doubly-excited s→s configurations. We have found that the polarization of the s orbitals can be reasonably well represented by a basis set consisting of two series of Laguerre polynomials each of which is multiplied by an exponential function. If the energy is minimized with respect to the exponents of all s functions, then the calculated hyperfine constant appears to be in good agreement with experiment. For six s functions, the magnetic constant is found to be 13 Mc/sec (experimental 10.45 Mc/sec). Using seven s basis functions, the constant is 11 Mc/sec. We show in this paper that a configuration interaction function built from the usual HF representation plus all singly-excited s→s configurations is equivalent, to first order, to what L\"owdin has called the extended Hartree-Fock representation. In addition, we show that the magnetic constant calculated from the spin-polarized (or unrestricted Hartree-Fock) function should be relatively close to that calculated from the CI function of HF plus singly excited configurations.