Polarizabilities of the beryllium clock transition

Abstract

The polarizabilities of the three lowest states of the beryllium atom are determined from a large basis configuration interaction calculation. The polarizabilities of the 2s 2 1 S e ground state (37.73a 3 0 ) and the 2s2p 3 P o 0 metastable state (39.04a 3 0 ) are found to be very similar in size and magnitude. This leads to an anomalously small blackbody radiation shift at 300 K of −0.018(4) Hz for the 2s 2 1 S e -2s2p 3 P o 0 clock transition. Magic wavelengths for simultaneous trapping of the ground and metastable states are also computed.

Tune-out wavelengths for the alkaline-earth-metal atoms

“…(6) was taken as an average of the s, p, d and f cutoff parameters. The specific values are detailed elsewhere [9][10][11][12][13]. There appears to be no experimental or theoretical data available for the strontium 5s 2 1 S e → 5s6p 3 P o 1 transition [35].…”

“…The use of such large basis sets means that the error due to incompleteness of the basis is typically very small. Details of the calculations used to represent Be, Mg, Ca and Sr have been previously described [9][10][11][12][13]. We refer to these semi-empirical models of atomic structure as the configuration interaction plus core polarization (CICP) model in the subsequent text.…”

“…The transition arrays for the alkaline earth atoms are essentially those used in previous calculations of the polarizabilities and dispersion coefficients for these atoms [9][10][11][12][13]. These were computed with a frozen core configuration interaction (CI) method.…”

“…[9]. However, the energies of the low-lying 2s2p 1,3 P o states were set to the experimental binding energies.…”

“…The atomic parameters that determine the values of the longest tune-out wavelengths are identified. The calculations utilize tables of matrix elements from earlier calculations of polarizabilities and dispersion coefficients [9][10][11][12][13]. These were computed using a non-relativistic semi-empirical fixed core approach that has been applied to the description of many one and two electron atoms [14][15][16][17].…”