Protonium formation in collinear collisions between antiprotons and hydrogen molecular ions: Quantum-classical hybrid method versus adiabatic approximation

Abstract

A quantum-classical hybrid (or semiclassical) method is applied to protonium formation p +H 2 + → p p +H and dissociation p +H 2 + → p + p + H at kinetic energies up to 200 eV. The electronic motion is accurately solved quantum mechanically, while the motion of the heavy particles p and p is described by classical mechanics. The p-p-p collinear configuration is assumed as a preliminary to three-dimensional calculations, and to assess the validity of the adiabatic approximation. Vibrational excitation to the dissociative continuum is crucial in p p formation in contrast to the importance of electron emission for the atomic-hydrogen target. For this reason, p p formation occurs efficiently even well beyond the ionization threshold if the target is a molecule.

Lagrange‐mesh method for quantum‐mechanical problems

“…Collisions involving electron exchange between an atom and a proton [35] or collisions between an atom and an antiproton leading to protonium formation [36] have been studied in a time-dependent framework involving Lagrange meshes.…”

Chemical reaction of protons with antiprotonic helium

“…The BO potential can support bound channels only forpHe + andpp, but not for HeH 2+ [28]. In the previousp + H 2 + study [4], the BO states were calculated by using spheroidal coordinates appropriate for two-center Coulomb nature of the homonuclear molecule H 2 + . In the present case, however the electron is always localized around He 2+ , and hence one can employ a onecenter treatment, in which the origin is located at He 2+ .…”

“…In the present case, however the electron is always localized around He 2+ , and hence one can employ a onecenter treatment, in which the origin is located at He 2+ . Equation (2) was solved by means of a grid-representation method [4], in which zero points of orthogonal polynomials were chosen as the grid points. The grid was constructed in polar coordinates with the z axis chosen along R p : 150 points of Laguerre polynomials for the radial distance s restricted to the range s 15 a.u., 14 points of Legendre polynomials for the polar angle, and 5 points of Chebyshev polynomials for the azimuthal angle.…”

“…As in Ref. [4], quadratic polynomial interpolation of E BO was made with respect to log R p , log Rp, and γ . For R p > 10 a.u., the PES was extrapolated from the value at R p = 10 a.u.…”

“…However, thep + He + collisions were found to be very rich in prominent Feshbach resonances which are associated with electronic excited states and can also decay promptly into electronic continuum states →pHe 2+ + e [3]: this fact indicates that the BO approach is not a good approximation. The applicability of the BO approximation to the collision problem was suggested in thep + H + 2 system [4]. Whether the target is an atomic or molecular ion is of fundamental difference.…”