Extraction of hyperfine anomalies without precise values of the nuclear magnetic dipole moment

Abstract

A new method for extracting the hyperfine anomaly from experimental hyperfine structure constants is suggested. Instead of independent high-precision measurements of the nuclear magnetic dipole moment, precise measurements of magnetic dipole hyperfine interaction constants for two atomic states and a theoretical analysis can be used. This can lead to determination of hyperfine anomaly for radioactive isotopes where the nuclear magnetic dipole moment is not known with high accuracy. PACS. 31.30.Gs Hyperfine interactions and isotope effects -21.10.Ky Electromagnetic momentsThe influence on the hyperfine structure (hfs) of the finite size of the nucleus was considered by Bohr and Weisskopf [1]. They calculated the hyperfine interaction (hfi) of s 1/2 and p 1/2 electrons in the field of an extended nucleus, and showed that the magnetic dipole hfi constant a for an extended nucleus is generally smaller than that expected for a point nucleus. Isotopic variations of magnetic moments become larger than those in the point dipole interaction when there are different contributions to the hfs from the orbital and spin parts of the magnetisation in the case of extended nuclei. The fractional difference between the point nucleus magnetic dipole hfi constant and the constant obtained for the extended nuclear magnetisation is commonly referred to as the Bohr-Weisskopf (BW) effect [2]. The magnetic dipole hfi constant a can therefore be written aswhere BW is the BW-effect, and a point the a constant for a point nucleus. Because electronic wavefunctions cannot be calculated with high accuracy in complex atoms it is not possible to determine BW directly; only the difference of the BW-effect in two isotopes, the so-called hyperfine anomaly (hfa), can be determined experimentally. Therefore one compares the ratio of the measured hfs constants for two isotopes (or isomers) of the same element with the independently measured ratio of the nuclear magnetic dipole moments to extract the hfa, 1 ∆ 2 , for the isotopes 1 and 2, and a given atomic state:

Hyperfine structure and hyperfine anomaly in Pb

“…The optimum would be to make measurements in all possible states in the 6p 2 configuration, thus giving in total three atomic states that enable a cross-check of the results. The 3 P 1 state offer another complication, as the contact contribution to the hyperfine structure in this state ( 0.452 A A c = ) is close to the contribution of the 6p7s 3 P 1 state ( 0.422 A A c = ), which is not suitable for an analysis of the hyperfine anomaly [23]. The contact contribution to the hyperfine structure for the 6p 2 3 P 2 state ( 0.247…”

“…The hyperfine structure of 207 Pb has been analysed and the analysis has been used as the basis for determining the hyperfine anomaly in four unstable isotopes, 191 Pb, 193 Pb, 195 Pb and 197m Pb, using the method of Persson [23]. The derived hyperfine anomaly has then been used to obtain better values of the nuclear magnetic moment for these isotopes.…”

Hyperfine Anomaly in Eu Isotopes and the Universiability of the Moskowitz–Lombardi Formula

“…They addressed the question of the universality of the empirical Moskowitz-Lombardi formula [24]. In this article, the method of Persson [13] is applied to the measurements of Ahmad et al [25] and Hühnermann et al [26] in order to give an estimate on the validity of the Moskowitz-Lombardi formula in Eu. In addition, a calculation of the hyperfine anomaly using the particle-rotor model is presented.…”

“…Measurements have also been performed by Enders et al [28][29][30] using a Paul-trap, to obtain the hyperfine structure constants in the ground and first metastable states of Eu + . The high precision values from the ion trap measurements cannot, for the time being, be used to extract the hyperfine anomaly, as the s-electron contribution is almost the same at these levels [13].…”

“…The ratio can be determined in two different ways; either by making an analysis of the hyperfine interaction or by using a known hfa as a calibration. It should be pointed out that the atomic states used must differ significantly in the ratio A s A , as a small difference will lead to an increased sensitivity to errors, as can be deduced from Equation (5) [13].…”