Proton scattering from excited states of atomic hydrogen

Abstract

Wavepacket continuum-discretisation approach is used to calculate excitation, ionization and electron-capture (ec) cross sections for proton collisions with n=2 states of atomic hydrogen, where n is the principal quantum number. The approach assumes a classical motion for the projectile and is based on the solution of the three-body Schrödinger equation using the two-center expansion of the total scattering wave function. The scattering wave function is expanded in an orthonormal basis set built from negative-energy eigenstates and wavepacket pseudostates representing the continuum of both the target atom and the atom formed by the projectile after capturing the electron. With a sufficiently large basis, due to the strong coupling between channels, the method produces converged cross sections for direct-scattering, ionization and ec processes simultaneously. For the quasi-elastic transitions, where both orbital and magnetic quantum numbers change, the integrated cross section is infinite. Nevertheless, the corresponding transitions probabilities are finite at any given impact parameter, indicating that the angular differential cross sections can be measured. Calculated cross sections for scattering on the metastable 2s state are compared with other theoretical results obtained using atomic-orbital close-coupling and classicaltrajectory Monte Carlo approaches. Considerable disagreement with previous calculations has been found for some transitions at various incident energies.

Proton impact on ground and excited states of atomic hydrogen

“…However, the excitation cross sections for H(2s) collisions are larger in magnitude than those of H(1s) collisions. From the comparisons with previous results, it can be seen that the present TC-BGM calculations from 1 to 10 keV are mostly consistent with the AOCC-GTO [10], AOCC-PS and TDL results [8] and follow the WP-CCC [9] trends at higher energies while the discrepancies with AOCC-PS are more pronounced in this regime. Although the cross section curves from the CTMC calculations [8] have similar structures as the other results, quantitative differences in the intermediate [14].…”

“…Although the cross section curves from the CTMC calculations [8] have similar structures as the other results, quantitative differences in the intermediate [14]. Theory: AOCC-PS, CTMC and TDL [8]; Sturmian-CC [4]; SC-CCC [5]; WP-CCC [9]; AOCC-GTO [10]; and present TC-BGM.…”

“…Experiment: Shah1981 [18]; Shah1987 [19]; and Shah1998 [20]. Theory: QM-CCC [17]; WP-CCC [9]; AOCC-GTO [10]; and present TC-BGM.…”

“…In figure 4, several sets of ionization cross sections for H(n = 1) and H(n = 2) collisions are compared with the present TC-BGM results. The sets include experimental measurements by Shah and co-workers [18][19][20] along with theoretical data from QM-CCC [17], WP-CCC [9], and AOCC-GTO [10] approaches. Additional results based on a scaling model are also presented for comparison in order to help understand some of the discrepancies shown in the present results.…”

“…Moreover, the analysis showed that using the O-shell (i.e., n = 5) model yields probabilities for higher n-shells that are modest in magnitude (i.e., neither too small nor too large) compared to the other models, and thus, the O-shell is chosen as the reference point for (11). With probabilities of the electronic transitions to higher n-shells computed in this way, new ionization probabilities are obtained from the unitarity criterion (9). By denoting n ′ = n + k, several choices of n ′ were made to obtain additional sets of ionization cross sections.…”