Semiclassical Calculation of Elastic H^{+}He Differential Scattering Cross Sections
Abstract
Elastic differential cross sections for protonhelium scattering are calculated in the semiclassical approximation for two assumed interaction potentials. Both potentials are of the form V(r;A,B,C)=(2r)e^{rA}[1+rA+12r^{2}(1A^{2}UB)] U[1+rB+(rC)^{2}+2Ur^{4}α]^{1}, where U is the difference between the groundstate energies of He and Li^{+} (4.373 11 hartree) and α is the polarizability of He (1.3835 bohr^{3}). The first potential V_{M}≡V(r0.423,0.483,0.441) fits the HeH^{+} groundstate energies which Michels has calculated. The second, V_{W}≡V(r0.442,0.505,0.451), is similar to V_{M} except that its minimum is decreased by 10% to agree with the value obtained by Wolniewicz. The cross sections for these two potentials are shown for protons incident at energies T of 7, 19, 58, and 116 eV in the laboratory frame and for scattering angles, at each energy, out to the rainbow angle θ_{R}. θ_{R} is given in centerofmass coordinates by the expression θ_{R}T≅0.1 rad hartree. As the collision energy decreases, the cross sections develop oscillatory structure not present in the classical cross sections. This structure and the rainbow angle are sensitive to the choice of potential, which suggests that measurements of H^{+}He cross sections may be used to test the suitability of, e.g., the BornOppenheimer potential for scattering phenomena. It is also suggested that manybody calculations of these cross sections would allow, by comparison with the present results, an evaluation of the potential scattering model.
 Publication:

Physical Review A
 Pub Date:
 September 1970
 DOI:
 10.1103/PhysRevA.2.771
 Bibcode:
 1970PhRvA...2..771H