High-precision measurement and ab initio calculation of the $(6s^26p^2)\,^3\!P_0 \rightarrow \, ^3\!P_2$ electric quadrupole transition amplitude in $^{208}$Pb

TL;DR

This paper reports the first precise measurement of a weak electric quadrupole transition in atomic lead and confirms it with ab initio calculations, advancing atomic physics and precision measurement techniques.

Contribution

The study provides the first experimental measurement of the $(6s^26p^2)\, ^3 ext!P_0 ightarrow \, ^3 ext!P_2$ E2 transition amplitude in $^{208}$Pb and validates it with high-accuracy theoretical calculations.

Findings

Measured the E2 transition amplitude as 8.91(9) a.u.

Achieved sensitive detection of very weak optical rotation signals.

Confirmed theoretical calculations with 0.5% agreement.

Abstract

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.