Fraunhofer and refractive scattering of heavy ions in strong laser fields

Abstract.

Until recently the potential scattering of a charged particle in a laser field received attention exclusively in atomic physics. The differential cross-section of laser-assisted electron-atom collisions for n emitted or absorbed photons is provided by a simple law which casts the result as a product between the field-free value and the square of the Bessel function of order n with its argument containing the effect of the laser in a non-perturbative way. From the experimental standpoint, laser-assisted electron-atom collisions are important because they allow the observation of multiphoton effects even at moderate laser intensities. The aim of this study is to calculate the nucleus-nucleus differential cross section in the field of a strong laser with wavelengths in the optical domain such that the low-frequency approximation is fulfilled. We investigate the dependence of the n-photon differential cross-section on the intensity, photon energy and shape of the pulse for a projectile/target combination at a fixed collision energy which exhibits a superposition of Fraunhofer and refractive behavior. We also discuss the role of the laser perturbation on the near and farside decomposition in the angular distribution, an issue never discussed before in the literature. We apply a standard optical model approach to explain the experimental differential cross-section of the elastic scattering of ⁴He on ⁵⁸Ni at a laboratory energy E = 139 MeV and resolve the corresponding farside/nearside (F/N) decomposition in the field-free case. We give an example of reaction in which Fraunhofer diffraction and refractive rainbow hump effects are easily recognized in the elastic angular distribution. Next, we apply the Kroll-Watson theorem, in order to determine the n -photon contributions to the cross-section for continuous-wave (cw) and modulated pulses. In the elastic scattering of heavy ions in a radiation field of low intensity, the amplitude drops by orders of magnitude with respect to the unperturbed case once the exchange of photons is initiated. For intensities approaching $I=10^{17}$ W/cm² multiphoton effects become important. In the case of short laser pulses we conclude that the strength of n-photon contribution increases with the pulse duration.