ECAMP 15

We calculate the cross section and the rate constant for the process of dissociative positronium attachment to the F$_2$ molecule at thermal energies. The process results in an anomalously large positronium annihilation rate, which can possibly explain the observed rapid positronium annihilation in halogen gases.

When fast positrons (e.g., those produced in $\beta ^+$ decay) thermalise and ultimately annihilate in matter, a sizeable fraction of them forms positronium (Ps) [1,2]. Its formation is typically statistical, with 25% of it being para-Ps ($p$-Ps, total spin $S=0$), and 75% being ortho-Ps ($o$-Ps, $S=1$). In vacuum, they annihilate predominantly by $2\gamma $ ($p$-Ps) and $3\gamma$ ($o$-Ps) annihilation, with the lifetimes of 0.125 and 142 ns, respectively. In gases and condensed-matter systems, the lifetime of $o$-Ps is usually reduced by its interaction with surrounding molecules or surfaces.

The $o$-Ps annihilation rate due to collisions with gas molecules is written as $\lambda =4\pi r_0^2cn\,{^1Z_{\rm eff}}$, where $n$ is the gas density and $4\pi r_0^2cn$ is the Dirac rate for singlet positron annihilation in a gas of electrons. The measured values of the parameter $^1Z_{\rm eff}$ are quite small for most molecular gases, $^1Z_{\rm eff}\sim 1$. By contrast, $o$-Ps annihilation in several molecular gases yileds much larger $^1Z_{\rm eff}$ values. In particular, $^1Z_{\rm eff}=1.15\times 10^4$ and $1.26\times 10^4$ for Br$_2$ and I$_2$, respectively [3]. We suggest that these high $^1Z_{\rm eff}$ values of are due to the process of dissociative Ps attachment, ${\rm Ps} + X_2 \to {\rm Ps}X + X$, where $X$ stands for a halogen atom. This process is similar to the dissociative electron attachment which leads to the formation of negative ions.

We calculate the cross section and rate of this process for the F$_2$ molecule for which the process is exothermic, and therefore can occur at room temperature. We start with the Ps-F$_2$ scattering calculations which take into account electron exchange and correlations within the framework of the free-electron-gas model [4]. The calculations reveal several resonances. Similar to the process of dissociative electron attachment, a $\Sigma_u$ resonance contributes to the dissociative Ps attachment at thermal energies. We determine the resonance position and width as functions of the internuclear separation, and use them as inputs for the local version of the quasiclassical theory of dissociative attachment [5]. Our calculations yeild the rate constant $\alpha=0.19\times 10^{-10}$ cm$^3$/s, which corresponds to $Z_{\rm eff}\sim 10^3$. This value is anomalously large and is only one order of magnitude lower than those for Br$_2$ and I$_2$.
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[1] M. Charlton, Rep. Prog. Phys. 48, 737 (1985).
[2] P. J. Schultz and K. G. Lynn, Rev. Mod. Phys. 60, 701 (1988).
[3] K. Wada et al., Eur. Phys. J. D 66, 108 (2012).
[4] I. I. Fabrikant and R. S. Wilde, Phys. Rev. A 97, 052707 (2018).
[5] A. K. Kazansky and I. S. Yelets, J. Phys. B: At. Mol. Phys. 17, 4767 (1984).