Analytical Calculation of the Scattering Length in Antihydrogen-Atom Collisions

We have extended the method of [1] to cold antihydrogen-atom collisions. The scattering length is determined by the mean scattering length $\bar a = 0.478 (2mC_6)^{1/4}$, where $m$ is the reduced mass and $C_6$ the van der Waals constant (in atomic units), and the semiclassical phase at zero energy. In addition, the antiproton-nucleus interaction is included through the strong-force scattering length $a_{\rm sf}$, whose imaginary part accounts for the antiproton annihilation. Our final result is \begin{displaymath} a=\bar{a}\left[1-\frac{1-a_0/\bar a-2\pi a_{\rm sf}/a_c} {1+(1-a_0/\bar a)(2\pi a_{\rm sf}/a_c)}\right], \end{displaymath} where $a_0$ is the scattering length found neglecting the strong interaction, and $a_c=(mZ)^{-1}$ is the antiproton-atom Coulomb radius. Our value for for hydrogen agrees with [2]. Estimates are made for the noble gas atoms. \begin{enumerate}\setlength{\itemsep}{-3pt}\setlength{\itemindent}{-12pt} \item G. F. Gribakin and V. V. Flambaum, Phys. Rev. A {\bf 48}, 546 (1993). \item S. Jonsell et al., J. Phys. B {\bf 37}, 1195 (2004); E. A. G. Armour, Y. Liu and A. Vigier, {\em ibid.} {\bf 38}, L47 (2005). \end{enumerate}