Many-body theory of hyperfine interaction in the manganese atom including relativistic effects

Using the linked-cluster many-body perturbation procedure we have evaluated the magnetic hyperfine constant $A$ in the spin-Hamiltonian term $A\overrightarrow{\mathrm{I}}·\overrightarrow{\mathrm{J}}$ of manganese atom. The nonrelativistic value of $A$ is found to be -90.8 ± 3.0 MHz, composed of -152.6 MHz from the exchange core polarization (ECP) effect and 61.8 MHz from a combination of consistency and correlation effects. We have also made a relativistic calculation of the ECP effect and used this to make estimates of the relativistic effects on (1, 1) and (0, 2) diagrams. On combining these relativistic results with those from nonrelativistic theory and including the calculated Casimir contribution of -4.3 MHz discussed by Sandars and Beck, our net theoretical value for the hyperfine constant $A$ turns out to be -74.1 ± 3.0 MHz, which is in the good agreement with the experimental results of -72.422 ± 0.002 MHz. Physical explanations are discussed for the trends of the contributions from various effects and their variations from shell to shell.