Theoretical study of lifetimes and polarizabilities inBa+

Abstract

The $6s\text{\ensuremath{-}}n{p}_{j}$ $(n=6--9)$ electric-dipole matrix elements and $6s\text{\ensuremath{-}}n{d}_{j}$ $(n=5--7)$ electric-quadrupole matrix elements in ${\mathrm{Ba}}^{+}$ 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 $6{p}_{j}\text{\ensuremath{-}}5{d}_{{j}^{\ensuremath{'}}}$ matrix elements and magnetic-dipole $5{d}_{5∕2}\text{\ensuremath{-}}5{d}_{3∕2}$ matrix element are calculated using the same method in order to determine the lifetimes of the $6{p}_{1∕2}$, $6{p}_{3∕2}$, $5{d}_{3∕2}$, and $5{d}_{5∕2}$ levels. The accuracy of the $6s\text{\ensuremath{-}}5{d}_{j}$ matrix elements is investigated in detail in order to estimate the uncertainties in the quadrupole polarizability and $5{d}_{j}$ lifetime values. The lifetimes of the $5d$ states in ${\mathrm{Ba}}^{+}$ are extremely long, making precise experiments very difficult. Our final results for dipole and quadrupole ground-state polarizabilities are ${\ensuremath{\alpha}}_{E1}=124.15{a}_{0}^{3}$ and ${\ensuremath{\alpha}}_{E2}=4182(34){a}_{0}^{5}$, respectively. The resulting lifetime values are ${\ensuremath{\tau}}_{6{p}_{1∕2}}=7.83\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$, ${\ensuremath{\tau}}_{6{p}_{3∕2}}=6.27\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$, ${\ensuremath{\tau}}_{5{d}_{3∕2}}=81.5(1.2)\phantom{\rule{0.3em}{0ex}}\mathrm{s}$, and ${\ensuremath{\tau}}_{5{d}_{5∕2}}=30.3(4)\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. An extensive comparison with other theoretical and experimental values is carried out for both lifetimes and polarizabilities.