Relativistic coupled-cluster calculation of the electron-nucleus scalar-pseudoscalar interaction constant Ws in YbF

Abstract

The scalar-pseudoscalar (S-PS) interaction, which has been predicted between the electrons and nuclei of atoms and molecules, violates parity (P) and time (T) reversal symmetries. The electric dipole moment of the electron (eEDM) and the S-PS interaction together give rise to an energy shift in paramagnetic polar molecules, which in principle can be measured. The determination of the S-PS interaction constant, k s,A , for an atom A could be a sensitive probe of physics beyond the standard model (SM). The upper limit for it can be obtained by combining the results of the measured energy shift mentioned above and the accurate quantum chemical calculation of the S-PS coefficient, W s,A. In this work, we use a method based on the four-component relativistic coupled-cluster singles and doubles (RCCSD) method to calculate this coefficient for YbF, one of the most promising candidates for the search of the eEDM and the S-PS interaction. We obtain W s,Yb = −40.5 [kHz] with an estimated error of less than 10% for YbF. We also calculate the effective electric field (E eff), the molecular dipole moment (DM), and the parallel component of the hyperfine coupling constant (A //) by the RCCSD method. The discrepancies in the results of these calculations with those of accurate measurements are used to estimate the accuracy of our calculation of W s,Yb.

Analysis of large effective electric fields of weakly polar molecules for electron electric-dipole-moment searches

“…This is because the contributions of the closed shell orbitals cancel out in the calculation of E eff [17]. Table IV shows the MPs only for the SOMO contributions.…”

“…E eff and PDM of the molecules were estimated by using the above equation. Table II shows our previous [17] and present results at the DF and CCSD levels using the Dyall-DZ and QZ basis sets for all the molecules that we have considered. The latest results for HgH based on the relativistic CCSD z-vector method with QZ basis sets has been reported by Sasmal et al [18] and they are also given in this table.…”

“…These functions were taken from the Dyall basis sets for Hg and Yb [22], and Sapporo basis sets [24] for H, F and Yb. The basis sets used for Yb and F were same as that used in the previous work [17]. In the calculation of HgF at the QZ level, some of the diffuse Sapporo basis functions, 1d1f, were removed for F atom to avoid a convergence problem.…”

“…The eEDM interaction in the molecule used by us is given by the following effective operator [16,17] .…”

“…The cluster amplitudes, and were evaluated using the RCCSD method, but the expectation values were calculated by using only the linear terms in the RCCSD wavefunction, written as [17,29,30] (8) The most important contributions are captured in this treatment with feasible computational costs. E eff and PDM of the molecules were estimated by using the above equation.…”