Analysis of atomic electric dipole moment in thallium by all-order calculations in many-body perturbation theory

Abstract

A procedure is presented for calculations of double-perturbation problems in the coupled-cluster formalism. With use of this method to include to all orders the correlation effects of single and pair excitations, the enhancement factor R--585 is obtained for the electric dipole moment (EDM) in atomic thallium.Equations for EDM perturbed single-excitation amplitudes are solved by diagonalization to take into account mixing between excited core states, and perturbed pair functions are introduced to incorporate correlation effects. Considering contributions from higher-order perturbation terms, we estimate the accuracy of the obtained enhancement factor is approximately at the 5-10% level.PACS number(s): 31.20.Tz, 31.90.+s, 35.10.Wb, 35.10.Di The neutral thallium atom, due to its high Z and high polarizability ao, has been extensively studied to search for a possible electric dipole moment (EDM), which can exist only if parity (P) and time-reversed invariance (T) are violated [1]. According to Sandars [2], the ratio of the atomic to the electron EDM is of order Z3a tto, which indicates that the enhancement factor for Tl is expected to be greater than 100. The first experimental limit for the EDM of the 6p~lq state in Tl was obtained bythen, continuous efforts have been made to lower the upper limit by 3 orders of magnitude. In a recent atomic-beam experiment, Abdullah etal. [4] obtained a limit dT1=(1.6 + 5.0) &10 ecm, which, when converted to the electron EDM, is close to the range capable of testing some theoretical models of charge-parity (CP) violation. In fact, the value of d"() 10 ecm) produced by a Higgs-Boson model [5] is already at this level. Motivated by progress in experiments, several atomic calculations have provided the enhancement factor R for Tl. Johnson etal. [6] obtained R -1041 by calculating first-order corrections in many-body perturbation theory (MBPT). Further calculations to consider correlation effects, however, gave dramatically reduced results, namely, R -301 by Kraftmakher [7] and R = -179 by Hartley, Lindroth, and Martensson-Pendrill [8]. All these abinitio calculation results were quite different from the semiempirical estimates, e. g., R -716 given by Sandars and Sternheimer[9], R -500 by Flambaum [10], R -502--607 by Johnson eral. [6]. Therefore it is clearly of great interest to obtain a reliable value of the atomic EDM enhancement factor for Tl, which not only provides an important parameter to set the upper limit of the electron EDM, but also can clarify the discrepancies of different calculations.The ground state of Tl has one unpaired electron 6pig outside closed shells, so that it can be treated as an alkalimetal atom. However, the last filled shel16s is relatively loosely bound, and can mix strongly with the valence 6p]g2 state and virtual 6py2, 6d3i2, 6dy2 states. The correlation effects between configurations consisting of these states play significant roles. Thus the behavior of Tl in MBPT differs from that in alkali-metal atoms, as discussed by several authors [7,8,11]....

Calculation of the(T,P)-odd electric dipole moment of thallium and cesium

“…However, there are small contributions like higher-order correlations, correction toΣ Ref. [11], coupled cluster -1041…”

“…The results show strong dependence on electron correlations and change significantly depending on how many correlation terms are included. The most complete calculations were performed by Liu and Kelly [11] using the coupled cluster approach. The result is in relatively good agreement with the semiempirical estimations of Ref.…”

New Limit on the Electron Electric Dipole Moment

“…In heavy paramagnetic atoms an electron EDM results in an atomic EDM enhanced by a factor R ≡ d atom /d e . Thus we search for a permanent EDM of atomic thallium in the 6 2 P 1/2 F = 1 ground state, where R −585 [4]. …”

Probing the Electron EDM with Cold Molecules

“…Heavy atoms such as Cs and Tl alleviate this problem by their large enhancement factors. In particular, α(E) = −585 for the thallium atom [6], which relaxes the necessary field control to the challenging, but achievable fT level. Two magnetic effects are most troublesome.…”