Internal Conversion Coefficients with Relativistic Hartree-Fock Model for the Deformed Region

Internal conversion coefficients for $E2\mathrm{}$ transitions in six cases of the deformed nuclear region are presented. New calculations are based upon the relativistic Hartree-Fock potential in the Slater-exchange approximation with the inclusion of only the static finite-nuclear-size effects. For the $2^{+}$→$0^{+}$ transitions in ${\mathrm{Gd}}^{156}$, ${\mathrm{Dy}}^{160}$, ${\mathrm{Er}}^{166}$, ${\mathrm{Yb}}^{170}$, ${\mathrm{Os}}^{186}$, and ${\mathrm{Os}}^{188}$, a comparison of present calculations with the weighted mean of all experimental values for $\frac{L_1}{L_2}$ indicates that the latter are larger by (6.2±3)%, (5.9±4.3)%, (8.4±4.4)%, (7.3±3.9)%, (7.5±6.4)%, and (2.8±5.6)%, respectively. Corresponding results for $\frac{L_1}{L_3}$ are (5.5±1.8)%, (5.5±2.5)%, (6.3±2.3)%, (5.5±2.4)%, (6.6±4.6)%, and (4.3±4.1)%. The uncertainties assigned to the percentage deviations correspond to an estimate of error at approximately 90% confidence level. Deviations of about the same magnitudes were pointed out by several experimentalists in a comparison with the calculations of Sliv and Band and of Rose. Numerical results are also given for the $K$ subshell and $M$ subshells in the above cases. It is suggested that $M$-subshell ratios be measured. A comparison of the experimental $M$-subshell ratios and $K$-conversion coefficient (within an accuracy of 2% or so) would provide additional information so that the origin of deviations in $L$-subshell ratios could be pinpointed. A possible explanation may be the effects of nuclear deformation on the $L_1$ internal conversion coefficient.