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) 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(Ho¹⁶⁵)=0.8×10⁻⁴⁸ cm⁴. 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(Ho¹⁶⁵) obtained by Dankwort et al. should be multiplied by the factor 1/(1-R_H)=1/0.76, giving a corrected value H(Ho¹⁶⁵)cₒᵣᵣ=1.06×10⁻⁴⁸ cm⁴.