Figure 1

Geometry of the two-photon decay. The $z$ axis is collinear with the first photon momentum vector ${\mathit{k}}_{\mathbf{1}}$. The plane $zx$ contains the second photon momentum vector ${\mathit{k}}_{\mathbf{2}}$ The angle $\theta$ is the opening angle between the direction of the two photons.Reuse & Permissions

Figure 2

Values of the parameters $a_i$ defined in Eq. (9), for the $2s_{1/2}\to 1s_{1/2}$ transition as a function of $Z$. The values obtained in this work, which correspond to different energy shares $y=0.1$, 0.25, and 0.5, are represented by a black-solid, red-dashed, and green-dot-dashed curve, respectively. With exception of $a_0$ (given in s${}^{-1}$), all parameters are dimensionless. The same energy shares values given by Au [17] are represented by a blue dotted line ($y=0.5$), a cyan dot-dot-dashed line ($y=0.25$), and by the purple short dashed line ($y=0.1$). The parameters $a_2$ of Ref. [17] are always equal to one, as represented by the purple dotted line. On the bottom right plot, the blue dotted line refers to values of the total decay rate obtained from the parametrization of Ref. [17]. The black line represents the total decay values obtained from our current parametrization. The dark green dashed line contains the values provided by Refs. [18, 19]. The level of precision of the plot does not allow one to distinguish differences between these references. Values of parameters $b_i$ can be obtained from this figure using the relations $b_0\approx -a_0$, $b_1\approx a_3$, and $b_4\approx -a_4$.Reuse & Permissions

Figure 3

Values of the parameters $a_i$ defined in Eq. (9), for the $2d_{3/2}\to 1s_{1/2}$ transition as function of $Z$. The different energy shares $y=0.1$, 0.25, 0.5 are represented by a black-solid, red-dashed, and green-dot-dashed curve, respectively. With exception of $a_0$ (given in s${}^{-1}$), all parameters are dimensionless. Values for parameters $b_i$ can be obtained from this figure (within its resolution) using the relations $b_0\approx -a_0/13$ and $b_1\approx 13a_3$.Reuse & Permissions

Figure 4

Values of the parameters $a_i$ defined in Eq. (9), for the $2d_{5/2}\to 1s_{1/2}$ transition as a function of $Z$. The different energy shares $y=0.1$, 0.25, 0.5 are represented by a black-solid, red-dashed, and green-dot-dashed curve, respectively. With exception of $a_0$ (given in s${}^{-1}$), all parameters are dimensionless.Reuse & Permissions