Anisotropy of the static dipole polarizability induced by the spin–orbit interaction: the S-state atoms N–Bi, Cr, Mo and Re

Abstract

A systematic ab initio study is performed on the ground state static dipole polarizabilities of the 2S +1 S, S > 1/2, atoms from N to Bi, Cr, Mo, Mn, Tc and Re. The benchmark scalarrelativistic values of the scalar polarizability components are obtained using the coupled cluster method. The spin-orbit configuration interaction calculations are carried out for the anisotropic (tensor) polarizability components of these atoms (except Mn and Tc) that arise from the second-order spin-orbit interaction. The tensor polarizabilities are calculated for the first time and found to increase from 10 −5 (N) to 3.8 atomic units (Bi) approximately as the fourth power of the nuclear charge. The simple correlations and implication to magnetic trapping of cold atoms are discussed.

Zeeman relaxation induced by spin-orbit coupling in cold antimony-helium collisions

“…The rates of Zeeman relaxation of Bi, Sb, and N in collisions with He are consistent with a Z 4 scaling for temperatures near 1 K and magnetic fields near 1 T [9,18], following the same trend shown in the static dipole polarizability anisotropy [17]. A natural extension of this work is to look further up the pnictogen column to arsenic (As) and phosphorus (P), for which our theoretical model predicts significantly reduced relaxation in collisions with He.…”

“…In particular, the 2 and 2 + states of Sb-He correlating to the 2 P • atomic term have D e = 7.5 cm −1 , R e = 4.83Å and D e = 11.0 cm −1 , R e = 4.53Å, respectively (D e = 6.9 cm −1 , R e = 4.96Å and D e = 11.5 cm −1 , R e = 4.44Å for Bi-He [9]). This indicates that the anisotropy of the 2 P • state is slightly larger for the Bi atom, in accord with the behavior of static dipole polarizabilities [17]. Similarity of the potential energy curves of all the molecular states arising from the ns 2 np 3 configuration of Sb or Bi likely reflects the similarity in the scalar dipole polarizabilities of the corresponding atomic states.…”

“…As shown in Ref. [17], this is the source of anisotropy in the static dipole polarizability of 4 S • states of the pnictogens. To the second order of perturbation theory, only the coupling to the excited 2 ( 2 P • ) and 2 + ( 2 P • ) states given by the B SP parameter contributes to the splitting.…”

“…Zeeman relaxation driven by this anisotropy is too fast for straightforward magnetic trapping of Sb atoms using buffer-gas cooling. Our results suggest, however, that such trapping could be achieved for the lighter and more isotropic [17] pnictogens arsenic (As) and phosphorus (P).…”

“…[13][14][15][16]). A recent theoretical study [17] demonstrated that the anisotropic static dipole polarizability increases from N to Bi by 6 orders of magnitude, roughly in accord with the hydrogenlike Z 4 scaling of spin-orbit coupling with the nuclear charge Z. While the collision dynamics with a buffer gas have been explored for the extreme cases of N [18] and Bi [9], the transition between N-like elastic collisions and Bi-like inelasticity thus far has not.…”