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We have completed a measurement of the $(6s^26p^2)\, ^3\!P_0 \rightarrow \, ^3\!P_2$ 939 nm electric quadrupole ($E2$) transition amplitude in atomic lead. Using a Faraday rotation spectroscopy technique and a sensitive polarimeter, we have measured this very weak $E2$ transition for the first time, and determined its amplitude to be $\langle ^3\!P_2 || Q || ^3\!P_0 \rangle$ = 8.91(9) a.u.. We also present an ab initio theoretical calculation of this matrix element, which agrees with experiment at the 0.5\% level. We heat a quartz vapor cell containing $^{208}$Pb to between 800 and 940 $^{\circ}$C, apply a $\sim \! 10 \, {\rm G}$ longitudinal magnetic field, and use polarization modulation/lock-in detection to measure optical rotation amplitudes of order 1 mrad with noise near 1 $\mu$rad. We compare the Faraday rotation amplitude of the $E2$ transition to that of the $^3\!P_0 -\, ^3\!P_1$ 1279 nm magnetic dipole ($M1$) transition under identical sample conditions.

We report measurements of the $^{115}$In $7p_{1/2}$ and $7p_{3/2}$ scalar and tensor polarizabilities using two-step diode laser spectroscopy in an atomic beam. The scalar polarizabilities are one to two orders of magnitude larger than for lower lying indium states due to the close proximity of the $7p$ and $6d$ states. For the scalar polarizabilities, we find values (in atomic units) of $1.811(4) \times 10^5$ $a_0^3$ and $2.876(6) \times 10^5$ $a_0^3$ for the $7p_{1/2}$ and $7p_{3/2}$ states respectively. We estimate the smaller tensor polarizability component of the $7p_{3/2}$ state to be $-1.43(18) \times 10^4$ $a_0^3$. These measurements represent the first high-precision benchmarks of transition properties of such high excited states of trivalent atomic systems. We also present new ab initio calculations of these quantities and other In polarizabilities using two high-precision relativistic methods to make a global comparison of the accuracies of the two approaches. The precision of the experiment is sufficient to differentiate between the two theoretical methods as well as to allow precise determination of the indium $7p-6d$ matrix elements. The results obtained in this work are applicable to other heavier and more complicated systems, and provide much needed guidance for the development of even more precise theoretical approaches., Comment: 12 pages, 8 figures corrected two typos in version 2

A two-step, two-color laser spectroscopy technique has been used to measure the hyperfine splittings of the $8p$ excited states in $^{203}$Tl and $^{205}$Tl, as well as the $7s - 8p$ transition isotope shifts. For the case of the $8p_{3/2}$ state, our results show a hyperfine anomaly consistent with our recent measurements of other hyperfine splittings, and in disagreement with older results for this state. Our measurement of the $8p_{1/2}$ isotope shift is also in disagreement with earlier work. In this series of experiments, a UV laser was locked to the first-step transition and directed through a heated vapor cell, while a second spatially overlapping red laser was scanned across the two second-step transitions. To facilitate accurate frequency calibration, radio-frequency modulation of the second-step laser was used to create sidebands in the Doppler-free absorption spectrum., Comment: arXiv admin note: text overlap with arXiv:1310.7216