Ab initio calculations of the hyperfine structure of zinc and evaluation of the nuclear quadrupole moment Q(Zn67)

Abstract

The relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) and the non-relativistic multiconfiguration Hartree-Fock (MCHF) methods have been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants of zinc. The calculated electric field gradients for the 4s4p 3 P o 1 and 4s4p 3 P o 2 states, together with experimental values of the electric quadrupole hyperfine structure constants, made it possible to extract a nuclear electric quadrupole moment Q( 67 Zn) = 0.122(10) b. The error bar has been evaluated in a quasi-statistical approach -the calculations had been carried out with eleven different methods, and then the error bar has been estimated from the differences between the results obtained with those methods.

Ab initio electronic factors of the A and B hyperfine structure constants for the 5s25p6s<

“…On the other hand, when T substitutions are also considered, the values of the computed properties increase in relation to the respective calculations of the SD phase. This behavior has also been observed in many earlier calculations of hyperfine structures [35,[50][51][52][53][54][55]. When performing RCI calculations by allowing D substitutions from core orbitals, CSFs that account for CC correlation effects are included in the atomic-state expansions.…”

“…In a recent paper [35], the quadrupole moment Q( 67 Zn) was evaluated based on 11 independent multiconfiguration calculations of the EFG ∝ B el for the 4s4p 3 P o 1 and 4s4p 3 P o 2 states in Zn I. The final accuracy of the calculated EFGs was estimated using the scatter of the individual results of these 11 calculations, resulting in a relative error of about 8%.…”

“…Yet, if one wants to be in a position to discuss atomic, or nuclear, properties and their underlying physics, a rigorous assessment of the uncertainties of the computed values is required. In recent years, atomic physicists have been putting great efforts into providing reliable uncertainties on their theoretical results [6,35,[69][70][71]. In line with these efforts, the following subsections take into account a number of considerations to determine the accuracy of the final B el [ 1 P o 1 ] value.…”

“…The correlation between the M1 and E2 hyperfine structures was used as a tool to evaluate the theoretical uncertainty of the B/Q value for the 1 P o 1 state. Due to the sensitivity of the hyperfine electronic factors to different electron correlation effects, one must often perform more than one set of calculations, which follow different computational strategies and correlation models, to be in a position to evaluate the accuracy of the results [35]. That being the case, a detailed description of the employed computational strategies is deemed necessary to better understand the contributions from the different correlation effects in systems with similar electronic structure and to, eventually, advance the current computational methods and computer codes.…”

Natural orbitals in multiconfiguration calculations of hyperfine-structure parameters

“…Their optimization strategy consisted of the simultaneous variation of all correlation orbitals together with the spectroscopic 3s/3p orbital for the 3s 2 S/3p 2 P • state. The simultaneous optimization of all correlation orbitals together with the spectroscopic valence orbitals, which we refer to as the "full variational" (FV) approach, has been widely used in nonrelativistic calculations [3][4][5]. Because of numerical convergence issues, the relativistic counterpart of the MCHF method, the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, employs almost exclusively a layerby-layer (LBL) strategy [6,7] in which only the newly introduced orbitals for the layer considered are optimized while the remaining ones are kept frozen.…”