Theoretical study of lifetimes and polarizabilities in Ba+

TL;DR

This paper uses relativistic all-order calculations to determine lifetimes and polarizabilities of Ba+ ion states, providing highly accurate theoretical values and comparing them with existing data.

Contribution

It presents new high-precision calculations of matrix elements, polarizabilities, and lifetimes for Ba+ ion states using the relativistic all-order method, with detailed uncertainty analysis.

Findings

Ground state dipole polarizability: 124.15 a_0^3

Ground state quadrupole polarizability: 4182(34) a_0^5

Lifetimes of 5d states: 81.5(1.2) s and 30.3(4) s

Abstract

The 6s-np_j (n=6-9) electric-dipole matrix elements and 6s-nd_j (n=5-7) electric-quadrupole matrix elements in Ba+ are calculated using the relativistic all-order method. The resulting values are used to evaluate ground state dipole and quadrupole polarizabilities. In addition, the electric-dipole 6p_j-5d_j' matrix elements and magnetic-dipole 5d_{5/2}-5d_{3/2} matrix element are calculated using the same method in order to determine the lifetimes of the 6p_{1/2}, 6p_{3/2}, 5d_{3/2}, and 5d_{5/2} levels. The accuracy of the 6s-5d_j matrix elements is investigated in detail in order to estimate the uncertainties in the quadrupole polarizability and 5d_j lifetime values. The lifetimes of the 5d states in Ba+ are extremely long making precise experiments very difficult. Our final results for dipole and quadrupole ground state polarizabilities are alpha_{E1} = 124.15 a^3_0 and alpha_{E2} = 4182(34) a^5_0, respectively. The resulting lifetime values are tau(6p_{1/2})=7.83 ns, tau(6p_{3/2})=6.27 ns, tau(5d_{3/2})=81.5(1.2) s, and tau(5d_{5/2})=30.3(4) s. The extensive comparison with other theoretical and experimental values is carried out for both lifetimes and polarizabilities.