The BCIS-4B method for state-selective and state-summed total cross sections: Proton–helium​ charge exchange at 10–4000 keV

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This work is on single electron capture by protons from helium targets at intermediate and high impact energies (10–4000 keV). Assessed is the overall performance of the second-order four-body boundary-corrected continuum intermediate state (BCIS-4B) method by detailed comparisons with all the available measurements. The state-selective Qnl,Qn and state-summed QΣ total cross sections are computed for n≤4, including all the sub-levels. Cross sections Qn are the sum of Qnl for 0≤l≤n−1. The state-summed cross sections QΣ are obtained by using Qn exactly for 1≤n≤3 and approximately for n≥4 through the Oppenheimer n−3 scaling rule. Overall, the measured cross sections are extremely favorably represented by the BCIS-4B method for Qnl,Qn and QΣ, even toward the lowest part of the considered intermediate energy region. Most notably, at all the energies above 10 or 20 keV, e.g. cross sections Q2p,Q3p and Q3d from the BCIS-4B method are in excellent agreement with the corresponding experimental data. This is very important since it is precisely for the non-spherically symmetric states (l≠0) of the captured electron that the existing discrepancies between measurements and other theories are the largest or even enormous.