Continuum wave functions for the two-center, one-electron system

Total, Partial, and Differential Ionization Cross Sections in Proton–Hydrogen Atom Collisions in the Energy Region of 0.1–10 keV/u

“…Therefore, we need to revert to a discrete sampling scheme as described further. Our study and also previous works in the literature 15,34 find the couplings with continuum states to be generally weak, and the full close-coupled Eqs. ͑2͒ can be partitioned into separate groups.…”

“…Single differential cross sections ͑in 10 Ϫ16 cm 2 ) at E ϭ2 34. keV/amu ⑀ ͑Ry͒ 0.010 0.012 0.013 0.016 0.018 0.021 0.024 0.028 s 2.81 Ϫ4 2.79 Ϫ4 2.77 Ϫ4 2.74 Ϫ4 2.72 Ϫ4 2.68 Ϫ4 2.64 Ϫ4 2.60 Ϫ4 p 6.28 Ϫ2 6.22 Ϫ2 6.15 Ϫ2 6.07 Ϫ2 5.98 Ϫ2 5.87 Ϫ2 5.76 Ϫ2 5.62 Ϫ2 d 2.92 Ϫ4 2.89 Ϫ4 2.86 Ϫ4 2.82 Ϫ4 2.78 Ϫ4 2.73 Ϫ4 2.68 Ϫ4 2.62 Ϫ4 f 3.95 Ϫ3 3.90 Ϫ3 3.85 Ϫ3 3.79 Ϫ3 3.72 Ϫ3 3.64 Ϫ3 3.56 Ϫ3 3.45 Ϫ3 g 7.99 Ϫ5 7.88 Ϫ5 7.75 Ϫ5 7.59 Ϫ5 7.40 Ϫ5 7.18 Ϫ5 6.92 Ϫ5 6.62 Ϫ5 h 1.36 Ϫ3 1.32 Ϫ3 1.27 Ϫ3 1.22 Ϫ3 1.16 Ϫ3 1.10 Ϫ3 1.04 Ϫ3 9.65 Ϫ4 p 1.90 Ϫ2 1.88 Ϫ2 1.86 Ϫ2 1.84 Ϫ2 1.81 Ϫ2 1.78 Ϫ2 1.75 Ϫ2 1.72 Ϫ2 d 9.89 Ϫ5 9.71 Ϫ5 9.51 Ϫ5 9.28 Ϫ5 9.02 Ϫ5 8.73 Ϫ5 8.41 Ϫ5 8.05 Ϫ5 f 6.29 Ϫ3 6.27 Ϫ3 6.24 Ϫ3 6.21 Ϫ3 6.17 Ϫ3 6.13 Ϫ3 6.08 Ϫ3 6.01 Ϫ3 g 3.03 Ϫ4 2.99 Ϫ4 2.94 Ϫ4 2.88 Ϫ4 2.82 Ϫ4 2.75 Ϫ4 2.67 Ϫ4 2.58 Ϫ4 h 4.64 Ϫ3 4.58 Ϫ3 4.50 Ϫ3 4.41 Ϫ3 4.31 Ϫ3 4.21 Ϫ3 4.09 Ϫ3 3.96 Ϫ3 Ϫ4 2.48 Ϫ4 2.41 Ϫ4 2.33 Ϫ4 2.25 Ϫ4 2.15 Ϫ4 2.05 Ϫ4 1.94 Ϫ4 p 5.47 Ϫ2 5.30 Ϫ2 5.11 Ϫ2 4.89 Ϫ2 4.66 Ϫ2 4.41 Ϫ2 4.13 Ϫ2 3.84 Ϫ2 d 2.56 Ϫ4 2.50 Ϫ4 2.43 Ϫ4 2.36 Ϫ4 2.28 Ϫ4 2.21 Ϫ4 2.14 Ϫ4 2.08 Ϫ4 f 3.34 Ϫ3 3.21 Ϫ3 3.07 Ϫ3 2.92 Ϫ3 2.76 Ϫ3 2.60 Ϫ3 2.44 Ϫ3 2.29 Ϫ3 g 6.26 Ϫ5 5.85 Ϫ5 5.37 Ϫ5 4.82 Ϫ5 4.21 Ϫ5 3.56 Ϫ5 2.89 Ϫ5 2.23 Ϫ5 h 8.92 Ϫ4 8.16 Ϫ4 7.40 Ϫ4 6.66 Ϫ4 5.95 Ϫ4 5.30 Ϫ4 4.71 Ϫ4 4.22 Ϫ4 p 1.69 Ϫ2 1.66 Ϫ2 1.62 Ϫ2 1.59 Ϫ2 1.56 Ϫ2 1.54 Ϫ2 1.53 Ϫ2 1.52 Ϫ2 d 7.65 Ϫ5 7.22 Ϫ5 6.75 Ϫ5 6.25 Ϫ5 5.72 Ϫ5 5.17 Ϫ5 4.61 Ϫ5 4.05 Ϫ5 f 5.94 Ϫ3 5.84 Ϫ3 5.73 Ϫ3 5.58 Ϫ3 5.40 Ϫ3 5.17 Ϫ3 4.88 Ϫ3 4.51 Ϫ3 g 2.47 Ϫ4 2.36 Ϫ4 2.24 Ϫ4 2.10 Ϫ4 1.96 Ϫ4 1.81 Ϫ4 1.66 Ϫ4 1.50 Ϫ4 h 3.82 Ϫ3 3.67 Ϫ3 3.51 Ϫ3 3.34 Ϫ3 3.17 Ϫ3 2.98 Ϫ3 2.78 Ϫ3 2.56 Ϫ3 ⑀ ͑Ry͒ 0.108 0.125 0.145 0.168 0.195 0.226 0.263 0.305 s 1.84 Ϫ4 1.74 Ϫ4 1.65 Ϫ4 1.57 Ϫ4 1.50 Ϫ4 1.45 Ϫ4 1.39 Ϫ4 1.32 Ϫ4 p 3.53 Ϫ2 3.20 Ϫ2 2.87 Ϫ2 2.52 Ϫ2 2.18 Ϫ2 1.83 Ϫ2 1.50 Ϫ2 1.19 Ϫ2 d 2.02 Ϫ4 1.98 Ϫ4 1.94 Ϫ4 1.91 Ϫ4 1.87 Ϫ4 1.78 Ϫ4 1.62 Ϫ4 1.37 Ϫ4 f 2.17 Ϫ3 2.08 Ϫ3 2.04 Ϫ3 2.05 Ϫ3 2.10 Ϫ3 2.16 Ϫ3 2.18 Ϫ3 2.00 Ϫ3 g 1.64 Ϫ5 1.17 Ϫ5 8.53 Ϫ6 6.86 Ϫ6 5.98 Ϫ6 4.95 Ϫ6 3.35 Ϫ6 1.77 Ϫ6 h 3.83 Ϫ4 3.60 Ϫ4 3.62 Ϫ4 4.03 Ϫ4 4.87 Ϫ4 5.90 Ϫ4 6.44 Ϫ4 5.74 Ϫ4 p 1.53 Ϫ2 1.54 Ϫ2 1.55 Ϫ2 1.55 Ϫ2 1.53 Ϫ2 1.47 Ϫ2 1.37 Ϫ2 1.24 Ϫ2 d 3.50 Ϫ5 2.96 Ϫ5 2.46 Ϫ5 2.00 Ϫ5 1.56 Ϫ5 1.17 Ϫ5 8.31 Ϫ6 5.47 Ϫ6 f 4.07 Ϫ3 3.53 Ϫ3 2.92 Ϫ3 2.26 Ϫ3 1.59 Ϫ3 9.84 Ϫ4 5.15 Ϫ4 2.32 Ϫ4 g 1.35 Ϫ4 1.22 Ϫ4 1.09 Ϫ4 9.90 Ϫ5 9.00 Ϫ5 8.17 Ϫ5 7.24 Ϫ5 6.06 Ϫ5 h 2.33 Ϫ3 2.08 Ϫ3 1.79 Ϫ3 1.48 Ϫ3 1.15 Ϫ3 8.17 Ϫ4 5.02 Ϫ4 2.43 Ϫ4 ⑀ ͑Ry͒ 0.353 0.410 0.476 0.552 0.640 0.743 0.862 1.000 s 1.21 Ϫ4 1.07 Ϫ4 9.21 Ϫ5 7.88 Ϫ5 6.78 Ϫ5 5.71 Ϫ5 4.60 Ϫ5 3.65 Ϫ5 p 9.23 Ϫ3 6.91 Ϫ3 4.95 Ϫ3 3.28 Ϫ3 1.96 Ϫ3 1.09 Ϫ3 5.82 Ϫ4 2.57 Ϫ4 d 1.05 Ϫ4 7.29 Ϫ5 4.98 Ϫ5 3.60 Ϫ5 2.53 Ϫ5 1.38 Ϫ5 5.52 Ϫ6 2.46 Ϫ6 f 1.55 Ϫ3 9.40 Ϫ4 4.97 Ϫ4 3.19 Ϫ4 2.41 Ϫ4 1.66 Ϫ4 7.18 Ϫ5 2.72 Ϫ5 g 1.03 Ϫ6 8.46 Ϫ7 5.47 Ϫ7 3.67 Ϫ7 3.69 Ϫ7 2.85 Ϫ7 1.46 Ϫ7 6.42 Ϫ8 h 3.90 Ϫ4 2.20 Ϫ4 1.73 Ϫ4 1.93 Ϫ4 1.80 Ϫ4 1.55 Ϫ4 9.65 Ϫ5 7.81 Ϫ5 p 1.11 Ϫ2 9.88 Ϫ3 8.95 Ϫ3 8.07 Ϫ3 6.94 Ϫ3 5.64 Ϫ3 4.47 Ϫ3 3.43 Ϫ3 d 3.39 Ϫ6 2.08 Ϫ6 1.37 Ϫ6 9.66 Ϫ7 6.78 Ϫ7 5.17 Ϫ7 4.44 Ϫ7 3.86 Ϫ7 f 1.31 Ϫ4 1.34 Ϫ4 1.37 Ϫ4 8.86 Ϫ5 3.32 Ϫ5 2.07 Ϫ5 2.13 Ϫ5 1.41 Ϫ5 g 4.59 Ϫ5 2.97 Ϫ5 1.57 Ϫ5 6.77 Ϫ6 3.04 Ϫ6 1.60 Ϫ6 6.23 Ϫ7 1.26 Ϫ7 h 7.50 Ϫ5 1.14 Ϫ5 2.50 Ϫ5 5.51 Ϫ5 5.48 Ϫ5 2.67 Ϫ5 6.78 Ϫ6 6.19 Ϫ6…”

Grid-based methods for diatomic quantum scattering problems: A finite-element discrete-variable representation in prolate spheroidal coordinates

“…We note that our approach differs from earlier work on H + 2 continuum states using prolate spheroidal coordinates where the asymptotic behavior was expressed in terms of two-center phaseshifts [15,[21][22][23].…”

Grid-based methods for diatomic quantum scattering problems. III. Double photoionization of molecular hydrogen in prolate spheroidal coordinates

“…With this choice, we can solve the driven equations obtained from Eq. (41) for each partial wave and then construct Φ (+) k (ξ, η, φ) any direction of k. Our approach differs from earlier work on H + 2 continuum states using prolate spheroidal coordinates, as well as the recent work of Serov and Joulakian on H 2 DPI, where the asymptotic behavior of the one-electron continuum states was expressed in terms of two-center phaseshifts [16,19,[23][24][25].…”