Blackbody radiation shift, multipole polarizabilities, oscillator strengths, lifetimes, hyperfine constants, and excitation energies in Ca+

Abstract

A systematic study of Ca + atomic properties is carried out using high-precision relativistic allorder method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the levels up to n = 7. Recommended values and estimates of their uncertainties are provided for a large number of electric-dipole transitions. Electric-dipole scalar polarizabilities for the 5s, 6s, 7s, 8s, 4pj , 5pj, 3dj , and 4dj states and tensor polarizabilities for the 4p 3/2 , 5p 3/2 , 3dj , and 4dj states in Ca + are calculated. Methods are developed to accurately treat the contributions from highly-excited states, resulting in significant (factor of 3) improvement in accuracy of the 3d 5/2 static polarizability value, 31.8(3) a + is calculated to be 0.381(4) Hz at room temperature, T = 300 K. Electric-quadrupole 4s−nd and electric-octupole 4s−nf matrix elements are calculated to obtain the ground state multipole E2 and E3 static polarizabilities. Excitation energies of the ns, np, nd, nf , and ng states with n ≤ 7 in are evaluated and compared with experiment. Recommended values are provided for the 7p 1/2 , 7p 3/2 , 8p 1/2 , and 8p 3/2 removal energies for which experimental measurements are not available. The hyperfine constants A are determined for the low-lying levels up to n = 7. The quadratic Stark effect on hyperfine structure levels of 43 Ca + ground state is investigated. These calculations provide recommended values critically evaluated for their accuracy for a number of Ca + atomic properties for use in planning and analysis of various experiments as well as theoretical modeling.

Experimental and theoretical study of the6d3/2polarizability of cesium

“…Our calculation of the polarizabilities and their uncertainties follows recent work on Ca + polarizabilities [13].…”

“…We also estimate omitted correlation correction terms in both of these approximations using the semiempirical scaling procedure described in detail in Ref. [13]. The resulting values are referred to as SD sc and SDpT sc data in text and tables below.…”

“…Strategies to determine uncertainties of the all-order values were discussed in detail in Ref. [13]. The relative uncertainties in percent are listed in the last column of Table III.…”

“…In both of these cases, nd 5/2 states are used as upper clock levels, so their polarizabilities must be precisely known for evaluating the BBR shift [13,14].…”

Blackbody radiation shift, multipole polarizabilities, oscillator strengths, lifetimes, hyperfine constants, and excitation energies in Hg+

“…Recently, we have developed some general criteria to establish the final values for all transitions and evaluate uncertainties due to the need to analyze a very large number of transitions [48]. To evaluate the uncertainties of our matrix elements and to provide recommended values, we carried out semiempirical evaluation of the missing correlation corrections using the scaling procedure.…”