Nuclear hexadecapole shielding factor for the holmium atom

The nuclear hexadecapole shielding factor $R_H$ for the $4f$ electrons of the holmium atom ($Z=67\mathrm{}$) has been obtained. This calculation was carried out in connection with a recent atomic-beam experiment of Dankwort, Ferch, and Penselin, which indicates the presence of a nuclear hexadecapole interaction with the $4f$ electron, leading to a value of the nuclear hexadecapole moment $H\left({\mathrm{Ho}}^{165}\right)=0.8\mathrm{}\times {10}^{-48\mathrm{}}$ ${\mathrm{cm}}^4$. This result has to be corrected for shielding or antishielding effects of the holmium atomic core electrons on the $4f$ electron, which experiences the interaction with the nucleus. The present paper gives the procedure and the results of the calculation of $R_H$, which was found to be + 0.24 (shielding). Thus the value of the moment $H\left({\mathrm{Ho}}^{165}\right)$ obtained by Dankwort et al. should be multiplied by the factor $\frac{1}{(1-R_H)}=\frac{1}{0.76}$, giving a corrected value $H{\left({\mathrm{Ho}}^{165}\right)}_{\mathrm{corr}}=1.06\mathrm{}\times {10}^{-48\mathrm{}}$ ${\mathrm{cm}}^4$.