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Description
This work reveals a remarkable similarity between the near-threshold energy dependence of the positronium (Ps) formation and photoionisation cross sections for several polyatomic molecules. The Ps-formation cross sections have been measured using a high resolution ($\sim$35 meV FWHM) trap-based positron beam for energies within a few eV of the Ps-formation threshold, $E_\text{thr} = E_I - |E_\text{Ps}|$, where $E_I$ is the target ionisation energy, and $E_\text{Ps}=-6.8$ eV is the Ps ground-state energy. Here we present the cross sections for aniline (C$_6$H$_5$NH$_2$), pyridine (C$_5$H$_5$N), and cyclopentane (C$_5$H$_{10}$). The cross section magnitude for pyridine are in agreement with earlier low-resolution data [1]. The Ps-formation cross sections are compared with measured photoionisation cross sections shifted to the Ps-formation threshold, with magnitudes scaled by a constant factor. This comparison shows that for each molecule, the two cross sections have a nearly identical dependence on the excess energy within a 1$-$2 eV of the threshold. This similarity is contrary to the significant difference between the two processes. In Ps formation, the interaction between the slow Ps and the residual cation is of short range, while in photoionisation, the electron moves in the attractive Coulomb field of the ion. As a result, at the basic level, the Ps-formation cross section is expected to obey the Wigner threshold law $\sigma \propto (E-E_\text{thr})^{1/2}$, while the photoionisation cross section must have a step-like onset with $\sigma =\text{const}$ at threshold. We discuss possible reasons for this similarity. In particular, it appears that the observed near-threshold behaviour is governed by vibrational excitations of the molecular cation and Franck-Condon factors, rather than the energy dependence of the underlying leptonic cross sections. For pyridine, this explanation is supported directly by comparisons with high-quality theoretical data for the vibronic excitation spectrum intensities [2]. We also discuss where the similarity breaks down and in what other targets it can be expected.
We are grateful to A. B. Trofimov for providing the results of their calculations in numerical form, and for numerous useful discussions.
References
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148, 144308 (2018). - A. B. Trofimov, A. D. Skitnevskaya, E. K. Grigoricheva, E. V.
Gromov, H. Köppel; Vibronic coupling in the ground and excited
states of the pyridine radical cation, J. Chem. Phys. 153,
164307 (2020).
