On Laser-Modified Rutherford Scattering

Sergey A Zaytsev,Konstantin A Kouzakov,Alexander S Zaytsev,Lorenzo U Ancarani

doi:10.3390/atoms8030040

Sergey A Zaytsev, Konstantin A Kouzakov + Show 2 more

Open Access

https://doi.org/10.3390/atoms8030040

Copy DOI

Abstract

We present a theoretical analysis of a charged-particle scattering by a Coulomb potential in the presence of laser radiation. The effect of a laser field is studied using our recently developed nonperturbative parabolic quasi-Sturmian approach for solving the system of coupled Lippmann–Schwinger–Floquet equations in the Kramers–Henneberger frame. We calculate the ratio of multiphoton differential cross sections to the Rutherford cross section in the case of a laser-assisted electron-proton scattering process. Our results are compared with predictions of the Bunkin–Fedorov, Kroll–Watson, and Coulomb–Volkov analytical approximations: marked discrepancies are found for different net numbers of exchanged photons and different orientations of the laser-field polarization vector. Our findings clearly demonstrate deficiencies of those well-known approximations for describing laser-modified Rutherford scattering processes.

Highlights

The Rutherford scattering, i.e., scattering of a charged particle in a Coulomb potential, is a fundamental phenomenon in atomic physics that played a historical role in establishing the planetary and, eventually, the Bohr model of the atom. This process is well understood in quantum mechanics: a closed-form solution of the corresponding Schrödinger equation—the Coulomb scattering state—is known exactly, and the angular differential cross section is given by the famous Rutherford formula
We have presented a theoretical investigation of laser-modified Coulomb scattering
We have compared the ratio of these cross sections to the field-free Rutherford cross section with the results obtained within the Bunkin–Fedorov/Kroll–Watson and Coulomb–Volkov approximations

Summary

Introduction

The Rutherford scattering, i.e., scattering of a charged particle in a Coulomb potential, is a fundamental phenomenon in atomic physics that played a historical role in establishing the planetary and, eventually, the Bohr model of the atom. This process is well understood in quantum mechanics:. Atoms 2020, 8, 40 in an experiment, the indicated approximations yield results which markedly differ from advanced numerical calculations For this purpose, we use our recently developed nonperturbative approach for computing laser-modified Coulomb scattering states [8], which we already have successfully utilized in the theoretical treatment of the laser-assisted (e, 2e) process of atomic hydrogen [9].

Theoretical Formulation

The Parabolic QS Approach

The Customary Analytical Approximations

Results and Discussion

Summary and Conclusions