Nuclear quadrupole moment of Au197 from high-accuracy atomic calculations

Abstract

The electric field gradient (EFG) at the gold nucleus is calculated using a finite field approach, to make the extraction of the nuclear quadrupole moment Q from experimental nuclear quadrupole coupling constants possible. The four-component Dirac-Coulomb Hamiltonian serves as the framework, 51 of the 79 electrons are correlated by the relativistic Fock-space coupled cluster method with single and double excitations, and the contribution of the Gaunt term, the main part of the Breit interaction, is evaluated. Large basis sets (up to 26s22p18d12f8g5h uncontracted Gaussians) are employed. Energy splittings of the 2D5/2 and 2D3/2 levels, rather than level shifts, are used to extract the EFG constants, as the former remain linear with Q up to 10(-5) a.u., whereas the latter display significant nonlinearity even at Q=10(-8) a.u. Larger Q values lead to larger energy changes and better precision. Excellent agreement (0.1%) is obtained between Q values derived from 2D5/2 and 2D3/2 data. Systematic errors connected with neglecting triple and higher excitations, truncating the basis and orbital active space, and approximating the Gaunt contribution are evaluated. The final value of Q(197Au) is 521(7) mb. It is lower than the muonic 547(16) mb and agrees within error bounds with the recent value of 510(15) mb obtained from molecular calculations.

Year-2008 nuclear quadrupole moments

“…Both atomic and molecular data suggest that the true value may be slightly lower. Yakobi et al [96] obtain 521(7) mb using atomic data for the 5d 9 6s 2 2 D 3=2, 5=2 states. Four-component CCSD(T) calculations were performed.…”

Complete-active-space multiconfiguration Dirac-Hartree-Fock calculations of hyperfine-structure constants of the gold atom

“…In the formula above, r ij = | r i − r j | is the inter-electronic distance, ω ij is the energy of the photon exchanged between two electrons, α i are Dirac matrices, and c = 1/α is the speed of light. The Breit corrections are highly state-dependent (see also [19], where the Gaunt part was evaluated) and yield 2.3 mb and 0.6 mb for the two states, 2 D 3/2 and 2 D 5/2 , respectively. The quantum electrodynamics (QED) corrections to the Q values are expected to be very small.…”

“…Yakobi et al [19] performed calculations for the 5d 9 6s 2 2 D 3/2 and 5d 9 6s 2 2 D 5/2 states of atomic gold within the four-component Dirac-Coulomb framework [41,42]. They correlated 51 out of the 79 electrons in the large basis sets (up to 26s22p18d12f8g5h uncontracted Gaussian functions) with the relativistic Fockspace coupled cluster method, including single and double excitations (CCSD).…”

Development of a configuration-interaction plus all-order method for atomic calculations

“…It is rather difficult to apply this method for calculation of other atomic properties, such as transition matrix elements. However, using the finite field technique one can use this method, for example, to calculate quadrupole hyperfine constants in such a heavy atoms as Au [36].…”