Interaction between antiprotonic helium ion and He atom: Potential Energy Surface

Potential Energy Surface for the ($\mathrm{\bar{p}} - \mathrm{He}^{2+} - \mathrm{He}$) system is calculated in the framework of the restricted (singlet spin state) Hartree-Fock method with subsequent account of the electronic correlations within the second order perturbation method (MP2). The geometry of heavy particles is described in variables of distance $r$ from nucleus $a$ to antiproton, distance $R$ from the center of mass of the $(\bar{p} - a)$ pair to $\mathrm{He}$ atom containing nucleus $b$, and an angle $\theta$ between $\mathbf{r}$ and $\mathbf{R}$. The potential $V(R,r,\cos\theta)$ of the interaction between $\mathrm{He}$ atom and a $\bar{p} - a$ subsystem involves a total energy of two electrons in the field of three heavy particles and Coulomb interactions of the $b$ nucleus with antiproton and the $a$ nucleus. The expansion of this potential in terms of Legendre polynomials $\mathrm{P}_k(\cos\theta)$ is obtained. Matrices of the multipole terms $V^k(r,R)$ ($k=0,1,2$) are obtained in the basis of antiprotonic helium ion states. The results are compared with the model potential that was used earlier in the calculations of collisional Stark transitions of $(\mathrm{\bar{p}He}^{2+})$ ion.Total cross sections of collisional Stark transitions obtained with the PES potentials exceed the model results by 15 - 20\% at $E \leq 12$ K.