High-precision measurement and ab initio calculation of the $(6s^{2}6p^2){}^3{P}_0\to {}^3{P}_2$ electric quadrupole transition amplitude in ${}^{208}$Pb

Abstract

We have completed a measurement of the $(6s^{2}6p^2){}^3{P}_0\to {}^3{P}_2$ 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 ${⟨}^3{P}_2||Q|{|}^3{P}_0⟩$ = 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 $\sim 10\mathrm{G}$ 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.

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