Forbidden Decays of Hydrogenlike and Heliumlike Argon

Four forbidden decay modes of hydrogenlike argon (${\mathrm{Ar}}^{+17\mathrm{}}$) and heliumlike argon (${\mathrm{Ar}}^{+}$16) have been observed and the lifetimes of the states decaying via these modes have been measured by a beam-foil time-of-flight technique. The decays are the two-photon decay $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\to 1{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ of ${\mathrm{Ar}}^{+17\mathrm{}}$, the two-photon decay $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\to 1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ of ${\mathrm{Ar}}^{+16\mathrm{}}$, the relativistically induced magnetic dipole decay $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\to 1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ of ${\mathrm{Ar}}^{+16\mathrm{}}$, and the magnetic quadrupole decay $2{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\to 1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ of ${\mathrm{Ar}}^{+16\mathrm{}}$. The measured lifetimes of the levels are $\tau \left(2\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)=3.54\mathrm{}\pm 0.25$ nsec, $\tau \left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)=2.3\mathrm{}\pm 0.3$ nsec, $\tau (2\mathrm{}{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}=1.7\mathrm{}\pm 0.3$ nsec, and $\tau \left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\right)=172\mathrm{}\pm 30$ nsec. From the agreement between the measured and calculated lifetimes it is possible to place an upper limit on the amount of parity impurity in the $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$-state wave function of hydrogenlike ${\mathrm{Ar}}^{+17\mathrm{}}$. Writing $\psi \left(2\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)=\Phi \left(2\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)+\epsilon \Phi \left(2\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)$, where the $\Phi \text{'}\mathrm{s}$ are the Schrödinger solutions to the hydrogen atom, we obtain $\left|\epsilon \right|\le 6\times {10}^{-4\mathrm{}}$.