Dipole and nondipole photoionization of molecular hydrogen

We describe a theoretical approach to molecular photoionization that includes first-order corrections to the dipole approximation. The theoretical formalism is presented and applied to photoionization of ${\mathrm{H}}_2$ over the 20- to 180-eV photon energy range. The angle-integrated cross section $\sigma$, the electric dipole anisotropy parameter ${\beta }_e$, the molecular alignment anisotropy parameter ${\beta }_m$, and the first-order nondipole asymmetry parameters $\gamma$ and $\delta$ were calculated within the single-channel, static-exchange approximation. The calculated parameters are compared with previous measurements of $\sigma$ and ${\beta }_m$ and the present measurements of ${\beta }_e$ and $\gamma +3\delta$. The dipole and nondipole angular distribution parameters were determined simultaneously using an efficient, multiangle measurement technique. Good overall agreement is observed between the magnitudes and spectral variations of the calculated and measured parameters. The nondipole asymmetries of He $1s$ and Ne $2p$ photoelectrons were also measured in the course of this work.

Figure 1

The coordinate system for calculations and measurements of photoelectron angular distributions is defined by the photon propagation vector k along the $x$ axis and linear polarization vector $\mathbf{\epsilon }$ along the $z$ axis. The arrows labeled 1–4 represent the angular positions of the four electron analyzers used in the present work. The analyzers are positioned symmetrically around the $y$ axis and are rotatable about that axis. See text for details.

Figure 2

The positions of the four electron analyzers projected onto the $\mathbf{\epsilon }$-k plane. The top frame shows the positions used to measure nondipole asymmetries $\gamma +3\delta$. The bottom frame shows the positions used to measure dipole anisotropies ${\beta }_e$.

Figure 3

Nondipole asymmetry parameter $\gamma$ of He $1s$ photoelectrons. The present results (open circles) are compared with previous measurements (closed circles) and RPAE calculations from Ref. [27].

Figure 4

Nondipole asymmetry parameter $\gamma +3\delta$ of Ne $2p$ photoelectrons. The present measurements (open circles) are compared with RPAE calculations from Ref. [26].

Figure 5

Calculated and measured photoionization parameters of molecular ${\mathrm{H}}_2$. (a) Total cross section $\sigma$ compared with measurements from Ref. [4]. (b) Electric dipole anisotropy parameter ${\beta }_e$ compared with present measurements. (c) Nondipole asymmetry parameter $\gamma +3\delta$ compared with present measurements. (d) Molecular alignment anisotropy parameter ${\beta }_m$ compared with double photoionization measurements from Ref. [6].