Electron transfer, excitation, and ionization in p-H (1s) collisions studied with Sturmian bases

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 80, Issue 3, 2009, Pages

  Winter, Thomas G ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COLLISIONAL SYSTEM; CROSS SECTION; DIRECT EXCITATION; ELECTRON TRANSFER; ENERGY RANGES; EXCITATION CROSS SECTION; IONIZATION CROSS SECTION; NUMERICAL RESULTS; PROTON ENERGY; PSEUDO STATE; STURMIAN;

ELECTRON TRANSITIONS; PROTON TRANSFER; PROTONS;

IONIZATION;

EID: 69749105155     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.80.032701     Document Type: Article

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38. The first parameters are zmin =-200 ao, zmax =2000 ao, Rmax =50 ao, Nλ =32, Nμ =40, and ρ=0 (0.15) 3.6 (0.3) 20.4 ao; the second (more stringent) parameters are e1, e2 = 10-8,-6, zmin =-2000 ao, zmax =3000 ao, Rmax =100 ao, Nλ >40, Nμ >80, and ρ=0 (0.1) 3.6 (0.2) 25.6 ao.
39. The 92-Sturmian parameters are zmin =-200 ao, zmax =2000 ao, Rmax =120 ao, Nλ >40, Nμ >80, and ρ=0 (0.3) 3.6 (0.6) 20.4 ao. The error in the summed cross section is | ΣQ-π ρ max 2 | ≤0.00004× 10-17 cm2 for E>70keV and ≤0.0009× 10-17 cm2 at lower energies.
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59. The effect of g states on the ionization cross section is difficult to establish directly in the present Sturmian calculations: for example, whereas the change in the 1 MeV ionization cross section on increasing a purely one-center basis from ≤12 (s,p,d,f) to ≤12 (s,p,d,f,g) is only 0.04%, the change from ≤15 (s,p,d,f) to ≤15 (s,p,d,f,g) is 0.13%. It would take an impractically large Sturmian basis in the present form to establish the converged ionization limit including g states, owing to the long-range behavior of g waves.
60. To test the convergence with respect to nmax, cross sections were also calculated at 1, 2, 4, 8, and 16 MeV with the single-center bases ≤35 (s,p,d,f) (330 states) and ≤40 (s,p,d,f) (380 states); except for ionization, the changes are in at most the fourth digit and are smaller on going from the 330- to the 380-state basis than from the 280- to the 330-state basis.
61. These Born results were obtained here in the impact-parameter version using the same impact parameters as in the coupled-Sturmian approach, with ρmax increasing with energy to 202.8 ao by 16 MeV due to the increasingly long-range behavior of p excitation and p -wave ionization as well as, to some extent, d -wave ionization. The 280-Sturmian cross sections were obtained using the same ρ 's (now extended at high energy) and z range as with the 281-Sturmian basis (with a slightly coarser ρ mesh at 0.6 and 9.6 MeV). For excitation, halving the ρ mesh at 1, 4, and 16 MeV changes the Born results (and presumably the coupled-state results) in at most the fourth digit, except for 4d at 1 MeV and 3d at 16 MeV, for which, however, the changes are only 0.2%. As a further test, the z range in the 280-Sturmian calculation was increased by a factor of 5 to - zmin = zmax =5000 ao at each energy from 1 to 16 MeV, with the maximum change in any cross section being 1 unit in the last reported digit.