Angular correlation in the two-electron continuum

Following absorption of a single photon, angles of simultaneous emission of two electrons from a $\mathrm{He}\left(n{}^{1}S\right)$ atom become more correlated with increasing $n$. We find that the strength of this correlation is due to the two-electron continuum of the electron-impact ionization of the ${\mathrm{He}}^{+}\left(ns\right)$ ion. The strength is determined by the width of the momentum profile of the ionic $ns$ state but not the strength of the electron correlation in the He initial state. This can explain the increasing (over He) angular correlation strength found in double photoionization of targets such as Be, Ne, and ${\mathrm{H}}_2$.

Figure 1

(Color online) Gaussian width parameters for DPI of $\mathrm{He}\left(n{}^{1}S\right)$ and $(e,2e)$ of ${\mathrm{He}}^{+}\left(ns\right)$ for $n⩽3$ plotted versus excess energy over the corresponding double ionization threshold. Circles, diamonds, and triangles correspond to widths for the $n=1$, 2, and 3 initial states, respectively. Filled symbols are for DPI on He and open symbols are for $(e,2e)$ on ${\mathrm{He}}^{+}$.

Figure 2

(Color online) Top panel: Gaussian width parameters for the $(e,2e)$ on ${\mathrm{He}}^{+}$ ion in various $ns$ states as functions of excess energy over the corresponding ionization threshold. Solid lines indicate the fitting with Eq. (9). Bottom panel: Energy-independent width constants $C_n$ in Eq. (9) plotted versus the width of the corresponding momentum profile extracted from Fig. 3.

Figure 3

(Color online) Momentum profiles (squared momentum space wave functions) ${\mid R_{ns}\left(q\right)\mid }^2$ of the lowest $ns$ states of the ${\mathrm{He}}^{+}$ ion, the mixed $2s$ plus $2p$ state of ${\mathrm{Ne}}^{+}$, the $2s$ state of the ${\mathrm{Li}}^{+}$ ion, and the $1s\sigma$ state of the ${\mathrm{H}}_2^{+}$ ion. The momentum profiles are normalized to ${\mid R_{1s}\mid }^2$ of ${\mathrm{He}}^{+}$ at its maximum.