Manipulating state-selective charge exchange in laser-assisted collisions of He$^{2+}$ with atomic H

We solve the time-dependent Schr\"odinger equation within a finite-differences approach and the propagation Crank-Nicolson method to calculate the n = 2, 3, and total electron capture cross section of He$^{2+}$ colliding with atomic H in the energy collision range 0.25-35 keV/amu. We use a laser pulse of 3, 2, and 1 fs at FHWM, wavelength of 800 nm and intensity 3.15 $\times 10^{12}$ W/cm$^{2}$. We demonstrate that the laser assistance in the collision increases an order of magnitude the electron charge capture in the 0.25-2 keV/amu energy collision range. We compare our numerical results with those obtained experimentally for the laser-free case to asses the validity of our method. Also, we study the effect of the laser pulse in the excitation cross-section for n =2 states of the hydrogen atom and the dependence of the charge exchange as function of the FWHM of the laser pulse.