Dipole and quadrupole transition strengths in Ba+ from measurements of K splittings in high-L barium Rydberg levels

Measurements of $K$ splittings in high-$L$ Rydberg states of barium are used to deduce electric-dipole and electric-quadrupole matrix elements in ${\text{Ba}}^{+}$. The model used to interpret these splittings is extended here to include the contributions of third- and fourth-order perturbation terms, altering the conclusions of a previous report that omitted those contributions. The analysis leads to improved experimental determinations of dipole $(6s\text{\ensuremath{-}}6p)$ and quadrupole $(6s\text{\ensuremath{-}}5d)$ transition strengths in ${\text{Ba}}^{+}$ that are in good agreement with recent a priori calculations.