Relativistic Stark energies of hydrogenlike ions

The relativistic energies and widths of hydrogenlike ions exposed to the uniform electric field are calculated. The calculations are performed for the ground and lowest excited states using the complex-scaling technique in combination with a finite-basis method. The obtained results are compared with the nonrelativistic values. The role of relativistic effects is investigated.

Figure 1

Real part of the complex Stark energy $E$ as a function of the complex-scaling angle $\mathrm{\Theta }$ for a hydrogen atom exposed to an electric field of strength $F=0.05$ a.u. Here $\mathrm{\Delta }E=E-E_0$, where $\mathrm{Re}{E}_0=-0.5061117144$ a.u. The solid line corresponds to the results obtained using the basis set with $N_{\theta }=21$ and the dashed line corresponds to the values obtained with $N_{\theta }=17$.

Figure 2

Imaginary part of the complex Stark energy $E$ as a function of the complex-scaling angle $\mathrm{\Theta }$ for a hydrogen atom exposed to an electric field of strength $F=0.05$ a.u. Here $\mathrm{\Delta }E=E-E_0$, where $\mathrm{Im}{E}_0=-3.85812927\times {10}^{-5}$ a.u. The solid line corresponds to the results obtained using the basis set with $N_{\theta }=21$ and the dashed line corresponds to the values obtained with $N_{\theta }=17$.

Figure 3

Relativistic Stark width $\mathrm{\Gamma }$ of the ground state of the hydrogenlike ion with nuclear charge $Z$ in the presence of a uniform electric field $F$. In the nonrelativistic limit, the values for all $Z$ should be the same. The difference is caused by the relativistic effects.

Figure 4

Relativistic Stark width $\mathrm{\Gamma }$ for the ground state of the hydrogenlike ion with nuclear charge $Z$ in the presence of a uniform electric field $F$. Solid lines show the results obtained with the complex-scaling methods and dashed lines the values calculated using the semiclassical theory. The upper curves correspond to $Z=1$ and the lower ones correspond to $Z=82$.

Figure 5

Stark shift $\mathrm{\Delta }E$ for the $2s$ state of the hydrogenlike ion with the nuclear charge $Z$ in the presence of a uniform electric field $F$.