Many-Body Approach to Hyperfine Interaction in Atomic Nitrogen

Abstract

The Brueckner-Goldstone many-body perturbation theory has been applied to calculate the hyperfine constant $a$ of atomic nitrogen in its ground state ${}_{}{}^4{}_{}{}^{}S_{\frac{3}{2}}^{}{}_{}{}^{}$. The exchange core-polarization diagrams lead to contributions of -49.710 72 and 55.418 82 Mc/sec from the $1s$ and $2s$ states, respectively, adding to a total of 5.708 10 Mc/sec. Higher-order diagrams characterizing mainly correlation effects produce an additional contribution of 4.780 22 Mc/sec. The total theoretical result 10.49 ± 0.15 Mc/sec is in excellent agreement with the experimental value of 10.45 ± 0.000 07 Mc/sec. The major correlation effect arises from the interaction between the valence electrons and core $s$ electrons, the effect of the $2s$ being the dominant one. It is found that a knowledge of the wave function up to second order is adequate for a sufficiently accurate evaluation of the hfs constant. The trends in the contribution from various physical effects observed by an analysis of pertinent diagrams are expected to be helpful in simplifying the analysis of more complex atoms.