Configuration Mixing and the Effects of Distributed Nuclear Magnetization on Hyperfine Structure in Odd-$A$ Nuclei

The theory of Blin-Stoyle and of Arima and Horie, in which the deviations of the nuclear magnetic moments from the single-particle model Schmidt limits are ascribed to configuration mixing, is used as a model to account quantitatively for the effects of the distribution of nuclear magnetization on hyperfine structure (Bohr-Weisskopf effect). A diffuse nuclear charge distribution, as approximated by the trapezoidal Hofstadter model, is used to calculate the required radial electron wave functions. A table of single-particle matrix elements of $R^2$ and $R^4$ in a Saxon-Woods type of potential well is included. Explicit formulas are derived to permit comparison with experiment. For all of the available data satisfactory agreement is found. The possibility of using hyperfine structure measurements sensitive to the distribution of nuclear magnetization in a semiphenomenological treatment in order to obtain information on nuclear configurations is indicated.