Spontaneous Ionization of a Hydrogen Atom in an Electric Field. I

The time‐independent Schrödinger equation expressed in parabolic coordinates for a hydrogen atom in an electric field was numerically integrated for the state ${\text{n\hspace{0.17em}=\hspace{0.17em}5, n}}_1{\text{\hspace{0.17em}=\hspace{0.17em}3, n}}_2\text{\hspace{0.17em}=\hspace{0.17em}0}$ , and $\text{m\hspace{0.17em}=\hspace{0.17em}1}$ to obtain the resonance energy $E_r$ and the rate of ionization ${\tau }^{\text{−1}}$ for field intensities ranging from 8 × 10⁵ to 11 × 10⁵ V/cm. It is found that near the resonance energy, ${\tau }^{\text{−1}}$ varies quadratically with ${\mathrm{(E\hspace{0.17em}-\hspace{0.17em}E}}_r{)}^2$ in accordance with the well known Weisskopf–Wigner treatment of metastable states. When $E$ is nearly equal to $E_r$ , the wavefunction has a node at the outer turning point—no explanation is offered. At the very high field intensities considered, there was considerable difference between $E_r$