Nonvanishing $J=1\leftrightarrow 0$ equal-frequency two-photon decay: $E1M2$ decay of the He-like $2{}^{3}S_1$ state

The selection rule which forbids $J=1\leftrightarrow 0$ two-photon decay when the energies of the two photons are equal is shown to apply only when the multipolarities of the two photons are the same (i.e., $2E1$, $2M1$, etc.) and does not generally apply to mixed multipolarity amplitudes such as $E1M2$. A calculation of the two-photon decay rate for He-like ions in the $2{}^{3}S_1$ state including both $2E1$ and $E1M2$ two-photon decay amplitudes is presented. It shows a significant contribution for the case of equal-energy photons. The ratio of the $E1M2$ contribution to the $2E1$ contribution is found to be surprisingly large. For example, it is 0.27 for two-photon decay of the $2{}^{3}S_1$state in He-like uranium.

Figure 1

Lower half of the continuum distribution for the $E1M2$ part of the total decay rate as a function of the fractional energy $y=\omega ∕{\omega }_0$. The curves are normalized to area 2 over the full interval $y=0$ to $y=1$.

Figure 2

Low-energy part of the He-like $2{}^{3}S_1$ two-photon continuum distribution as a function of the fractional energy $y=\omega ∕{\omega }_0$ normalized to area ($=2$ photons) over $y=0$ to $y=1$. (Present calculation in length gauge.)

Figure 3

Lower energy part of the spectral distributions of the $2E1$ and $E1M2$ contributions to the He-like $2{}^{3}S_1$ two-photon decay rate as a function of the fractional energy $y=\omega ∕{\omega }_0$. (Present calculation in length gauge.) The sum of the two contributions (total) is also given. The upper plot is for $Z=40$ and lower plot is for $Z=92$. All curves are normalized to area ($=2$ for the “total” curves over $y=0\to 1$).