Determination of polarizabilities and lifetimes for the Mg, Zn, Cd and Hg isoelectronic sequences

Abstract

The dipole polarizability and adiabatic correlations of atomic ions are related to the energy levels and oscillator strengths of the levels through bracketing inequalities. For systems with a ground state ns 2 1 S 0 , the total oscillator strength is dominated by the unbranched intrashell ns 2 1 S 0-nsnp 1 P o 1 transition, and the remaining oscillator strength can be narrowly bracketed using the f-sum rule. Thus measurements of the lifetime of the lowest resonance transition can be used to specify the polarizabilities and, alternatively, measurements of the polarizabilities can be used to deduce lifetimes. Moreover, isoelectronic regularities in line strengths can be used to obtain a comprehensive database from a small number of precision lifetime determinations. These methods are applied homologously to produce values for polarizabilities and lifetimes for the Mg, Zn, Cd and Hg isoelectronic sequences. To confirm the reliability of these methods, fast ion beam lifetime measurements in P IV were performed using the arbitrarily normalized decay curve (ANDC) method, and a test of the f-sum was made for Ba II, for which precision measurements of both the polarizability and lifetimes exist.

Polarizabilities of Pb2+and Pb4+and ionization energies of PbHanni1, Keele2, Lundeen3 et al. 2010Phys. Rev. A214281View full textAdd to dashboardCite

“…The valence polarizability due to excitation of the 6s electrons can be estimated from the measured lifetime of the 6s6p 1 P 1 resonance state, using the oscillator strength sum rules to set limits on possible contributions from higher excited states. This is exactly what was done in 2008 by Reshetnikov et al [1], who inferred a polarizability of 7.8 (6) a.u. from the 0.380(21)-ns measured lifetime of the 6s6p 1 P 1 level [2].…”

“…The energy levels can then be expressed in terms of V eff by E(nL) = E 0 (n) + E rel (nL) + E [1] (nL) + E [2] (nL),…”

“…The third term, E [1] (nL), is the expectation value of V eff and is by far the most significant contribution to the fine-structure pattern. The fourth term, E [2] , comes from application of V eff in second order and has been calculated analytically by Drake and Swainson [9] in the approximation that only the term proportional to α 2 d is significant.…”

Relativistic general-order coupled-cluster method for high-precision calculations: Application to the Al+atomic clock

“…Although the size of the BBR shift in the Al + clock is smaller than those in most of the other ions considered for atomic clocks, the associated uncertainty in the estimated BBR shift is about 35% of the total uncertainty when calculated using static polarizabilities and oscillator strengths taken from different sources [11]. Other semiempirical configuration interaction (CI) calculations [12] and nonrelativistic results [13][14][15] agree with this estimate.The exact wave function in the single-reference (SR) CC theory involves an exponential parametrization of the formwhere |0 is the Dirac-Hartree-Fock (DHF) reference determinant, and the cluster operatorT can be decomposed aŝ T = n k=1T k , wherê …”

Static and dynamic polarizability for C2+ in Rydberg states

“…23 The link between dipole polarizabilities and oscillator strengths of resonance transitions has been pointed out quite recently by Reshetnikov et al 24 In our work, the Oxford code (GRASP Multi-Configuration Dirac-Fock (MCDF)) was used to obtain wave functions and energies of the highly excited Be-like C states included in Eq. (1).…”