Effect of a Diffuse Nuclear Charge Distribution on the Hyperfine-Structure Interaction

A diffuse nuclear charge distribution, with approximately the trapezoidal Hofstadter shape, is used to calculate the effect of the distributed nuclear charge on the magnetic-dipole hyperfine-structure (hfs) interaction between the nucleus and the atomic electron. For a surface or a uniform charge distribution model this effect is known as the Breit-Rosenthal-Crawford-Schawlow correction to the point-charge interaction. The hfs interactions calculated with the diffuse and with the uniform charge distributions differ by over 4% for medium to heavy nuclei. The results, combined with our previously calculated values for the Bohr-Weisskopf correction (the effect on the hfs due to the nonpunctual distribution of nuclear magnetization), allow a more realistic determination of the total hfs anomalies, caused by the extended nuclear electric and magnetic structures, and therefore also of ${\left|\psi \mathrm{}\right(0\left)\right|}^2$, the probability of the electron wave function at the origin.