Resonance in Electron Capture by a Proton from a Hydrogen Atom

The probability of electron capture by a proton from a hydrogen atom has been calculated for a fixed scattering angle and for low incident proton energies using a variational method with a trial wave function in which only the $1s$ and $2s$ electron states around the two nuclei are retained. The resulting coupled differential equations with appropriate initial conditions have been solved numerically; the results of our theoretical calculations for the capture probability at an angle of scattering of 3° (laboratory system) for various incident proton energies have been compared with the experimental findings of Lockwood and Everhart.