Lifetime of the metastableP23andP03states of rare-gas atoms

The lifetimes of the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ states of Ne, Ar, Kr, and Xe are calculated by considering the spin-dependent magnetic-quadrupole ($\mathrm{SM}2\mathrm{}$) radiative transition to the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state as the decay mechanism. By expressing the $\mathrm{SM}2\mathrm{}$ operator as a contraction of the spin magnetic dipole and the electric dipole, the lifetime of the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ state can be expressed very simply in terms of that of the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ state. With the known lifetimes of the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ state, the calculated lifetimes of the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ states are 24.4, 55.9, 85.1, and 149.5 sec, respectively, for Ne, Ar, Kr, and Xe. The lifetime of the ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ state is calculated by considering both the magnetic-dipole ($M1\mathrm{}$) transition to ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ and the electric-quadrupole ($E2\mathrm{}$) transition to ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ as the decay mechanism. The calculated lifetimes are 430, 44.9, 0.488, and 0.078 sec, respectively, for Ne, Ar, Kr, and Xe. These calculated lifetimes are above the lower limits of the experimental lifetimes measured by Van Dyck, Johnson, and Shugart.