Linear and circular dichroism in photoelectron angular distributions caused by electron correlation

Electron correlation can break the symmetry of photoelectron angular distribution upon two-step ionization to a doubly degenerate ionic state via a doubly degenerate intermediate state. The interference between the two components of the intermediate state prepared using linearly and circularly polarized light is discussed for cyclopropane as an example.

Figure 1

(a) Two-step ionization scheme from the ground state ${\mathrm{\Gamma }}_0$ to a cation state ${\mathrm{\Gamma }}_{+}$ via an intermediate state $\mathrm{\Gamma }$. The polarization of light for the excitation is linear or circular, whereas linearly polarized light is assumed for the ionization. (b) A cyclopropane molecule with molecular frame axes. The $z$ axis is parallel to the threefold symmetry axis ($C_3$). Typical polarizations of light for the first and second steps, respectively, are shown by arrows $E_1$ and $E_2$. LDAD and CDAD represent linear and circular dichroisms in the photoelectron angular distributions, respectively.

Figure 2

Linear dichroism in photoelectron angular distributions. (a) A cyclopropane molecule and two linearly polarized laser lights. The arrows indicate the propagation direction of the laser lights. The electric-field vector for the excitation (ionization) light is perpendicular (parallel) to the threefold symmetry axis. Molecular frame photoelectron angular distributions are calculated with (b) single-configuration (SC) and (c) multiple-configuration (MC) wave functions of the $3p$ Rydberg state at a photoelectron kinetic energy (PKE) of 0.1 eV. (d)–(f) are the same as (a)–(c), respectively, but with the different propagation direction of laser light. The photon energies are assumed to be 8.5 and 3.0 eV for $h{\nu }_1$ and $h{\nu }_2$, respectively.

Figure 3

Photoelectron angular distributions for different photoelectron kinetic energies. The molecular and laser configurations are the same as Fig. 2, and the wave function is the multiple-configuration wave function of the $3p$ Rydberg state.

Figure 4

Circular dichroism in photoelectron angular distributions. (a) Excitation scheme for the randomly oriented molecular ensemble. Calculated difference of anisotropy parameter $\mathrm{\Delta }\mathrm{Im}\left(B_{22}\right)/B_{00}=\mathrm{Im}\left(B_{22}^{\mathrm{left}}\right)/B_{00}^{\mathrm{left}}-\mathrm{Im}\left(B_{22}^{\mathrm{right}}\right)/B_{00}^{\mathrm{right}}$ for the (b) $3s$ and (c) $3p$ Rydberg states as a function of the photoelectron kinetic energy. The solid and dashed lines indicate the results for single- and multiple-configuration wave functions, respectively. The inset of (b) defines the axes. The excitation laser light is circularly polarized and propagates along the laboratory $Z$ axis, whereas the ionization laser light is linearly polarized parallel to the $X$ axis and propagates in the same direction of excitation laser light. The photon energies of $h{\nu }_2$ are assumed to be $h{\nu }_2=\mathrm{PKE}+\mathrm{IE}-h{\nu }_1\mathrm{eV}$, where IE is the ionization potential of cyclopropane 11.4 eV [23] and $h{\nu }_2$ are the excitation energies for the Rydberg states (7.9 and 8.5 eV for $3s$ and $3p$, respectively).