Proton-helium collisions at intermediate energies: Singly differential ionization cross sections

This study is on the theory of single electron capture by fast nuclei from a variety of molecular targets of biological significance with high relevance to ion therapy of deep-seated tumors. The adopted theoretical framework is that of the first principles of quantum physics. As such, no free, adjustable parameters are used. This is in sharp contrast to the associated existing cross section input data to Monte Carlo simulations that all abound with empirical/phenomenological formulae. The present theory has the well-established track of its predictive power. This means that the computed cross sections can confidently be used in the cases for which no experimental data exist. These cross sections are from the full continuum distorted wave method (CDW). We first compute atomic cross sections in the independent electron model and then generate the corresponding molecular cross sections. The latter follow from the former within the independent atom model accompanied by the Bragg additivity rule. The investigated atomic targets are from the backbone of DNA and/or RNA molecules. These are atomic hydrogen, carbon, nitrogen and oxygen (H, C, N, O). Neon is also added to this sequence of targets as an isoelectronic atomic counterpart of water vapor, methane and ammonia molecules. The studied molecular targets are H 2 O (water vapor), CO (carbon-monoxide), CO 2 (carbon-dioxide), CH 4 (methane), C 2 H 4 (ethylene), C 2 H 6 (ethane), C 4 H 10 (butane) as well as the DNA/RNA nucleobases C 4 H 4 N 2 O 2 (uracil), C 5 H 5 N 5 (adenine), C 5 H 5 N 5 O (guanine), C 5 H 6 N 2 O 2 (thymine) and C 4 H 5 N 3 O (cytosine). The obtained total cross sections for any electronic target shell are compared with the available experimental data and overall favorable agreement is recorded at intermediate and high impact energies, which is the validity domain of the CDW method.

Single charge exchange in collisions of energetic nuclei with biomolecules of interest to ion therapy.

Integrated total and state-selective cross sections for bare beryllium ion collisions with atomic hydrogen

In ion-atom collisions involving multielectron targets the role of inner-shell electrons becomes important with increasing collision energy. Usually, processes involving the outer-shell and inner-shell electrons are treated using an independent-event model. However, the independent-event model becomes impractical when the number of shells is more than two. We develop an effective single-electron approach to ion collisions with multielectron atomic targets that overcomes this difficulty by treating all the atomic electrons on an equal footing. The approach allows the calculation of single-ionization and single-electron transfer cross sections by including the excitation of any one of the inner- or outer-shell target electrons. Accordingly, the approach does not differentiate which one of the many target electrons is captured or ionized. This is a unique feature of the proposed approach. The ground-state wave function for the target atom obtained in the multiconfiguration Hartree-Fock approach is used to calculate the probability density for the whole atom. The latter is then averaged over the spatial coordinates and spin variables of all of the target electrons except for the position of one electron from the nucleus. The obtained single-electron probability density is then used to derive a pseudopotential describing the interaction of one electron with an effective field produced by the target nucleus and the other electrons. The procedure reduces the many-body Schr\"odinger equation governing the collision system effectively into a three-body one. The reduced Schr\"odinger equation is solved using the two-center wave-packet convergent close-coupling approach. As an illustrative example we calculate integrated cross sections for single-electron transfer and ionization in proton collisions with lithium, sodium, and potassium. The results obtained agree very well with available experimental data for electron transfer. However, we find significant discrepancies with experiment for single ionization of Na and K, which warrant further experimental and theoretical investigations.

Effective single-electron treatment of ion collisions with multielectron targets without using the independent-event model

Abstract The two-centre wave-packet convergent close-coupling approach to ion–atom collisions is extended to study proton collisions with molecular hydrogen including electron-capture channels. We use a model potential to represent the molecular target as an effective one-electron spherically symmetric system. This greatly simplifies the target structure, allowing us to use already existing code developed for ion collisions with single-electron targets. Calculated total cross sections for electron capture, single ionisation, and excitation processes generally agree well with experimental data and other theoretical calculations where available. However, the total electron capture cross section is found to overestimate the experimental data at low energies, while the total ionisation cross section is slightly underestimated. Additionally, we present state-resolved cross sections for capture into the 1s, 2 $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> , and 3 $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> states of the projectile where deviation between various previous calculations is substantial. Our results lead to overall improvement over previous theoretical studies although discrepancies with experiment are observed for 3p and 3d capture. We conclude that treating molecular hydrogen as an effective one-electron system within the two-centre coupled-channel approach to one-electron targets can give reasonably accurate total cross sections at intermediate and high energies, without the need for a complex and computationally demanding two-electron target representation. 

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Effective one-electron approach to proton collisions with molecular hydrogen

Calculations of ionization and electron-capture cross sections in ion-atom collisions usually require solving the Schro dinger equation governing the collision system by expanding the total scattering wave function in a basis of target- and projectile-centered pseudostates. This approach leads to the two-center close-coupling equations which in some cases may become ill-conditioned due to the non-orthogonality of the underlying combined basis. Here we develop a technique which allows to accurately extract the necessary collision information, including that for the rearrangement channels, from the computationally more convenient one-center close-coupling equations which are built from only target-centered pseudostates. The robustness of the method is demonstrated by considering the proton-hydrogen scattering problem across a wide incident energy range. The developed method is then applied to study proton scattering on multielectron target of lithium. The obtained results for the 2s → 2p excitation and the total electron-capture cross sections are in good agreement with corresponding experimental data. It is concluded that the presented technique could be a simpler alternative when integrated cross sections are required.

Corey Plowman

Papers

One-center close-coupling approach to two-center rearrangement collisions