Ionization cross-sections for ion–atom collisions in high-energy ion beams

Comparison of quantum-mechanical and classical trajectory calculations of cross sections for ion-atom impact ionization of negative and positive ions for heavy-ion fusion applications

“…Moreover, in some cases the CTMC calculations yield results close to the quantum mechanical calculations [11,14,15]. The reason for similar results lies in the fact that the Rutherford scattering cross section is identical in both classical and quantum mechanical derivations [16].…”

“…In both classical mechanics and in the Born approximation, the ionization cross section can be recast in the form [10,15,19,20],…”

“…Accounting for the electron atomic velocity gives an additional factor of 5/3 [15]. The Bethe formula [19] derived by means of the Born approximation of quantum mechanics gives The results of cross sections calculations using Eq.…”

US Heavy Ion Beam Research for High Energy Density Physics Applications and Fusion

“…A hybrid method has been developed for calculation of the charge-changing cross sections of ions or atoms by fast ions by combining the quasi-classical approach and the Born approximation of quantum mechanics in the regions of impact parameters in which they are valid, and summing the results to obtain the total cross section [16,17]. This approach has been tested by comparison with available experimental data and full quantum mechanical calculations.…”

Comparison Of Quantum Mechanical And Classical Trajectory Calculations Of Cross Sections For Ion-Atom Impact Ionization of Negative - And Positive -Ions For Heavy Ion Fusion Applications

“…Accounting for the electron atomic velocity gives an additional factor of 5/3 [15]. The Bethe formula [19] derived by means of the Born approximation of quantum mechanics gives…”