Asymptotic solution of a Coulomb multichannel scattering problem with
Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 2, pp. 269-279 Cet article a éte moissonné depuis la source Math-Net.Ru

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We develop a well-posed multiparticle Coulomb scattering problem based on asymptotic solutions of a Coulomb multichannel scattering problem constructed in the adiabatic representation. A key feature of the studied problem is that the nonadiabatic channel coupling matrix is nontrivial at large internuclear distances. We consider the scattering problem in the case with an arbitrary momentum value and study solutions for small channel coupling matrix values in detail, constructing explicit representations for the asymptotic solution of the scattering problem.
Keywords: multichannel Coulomb scattering, asymptotic solution of scattering problem, nonadiabatic channel coupling.
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S. L. Yakovlev. Asymptotic solution of a Coulomb multichannel scattering problem with. Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 2, pp. 269-279. http://geodesic.mathdoc.fr/item/TMF_2020_203_2_a7/

[1] N. F. Mott, H. S. W. Massey, The Theory of Atomic Collisions, Clarendon Press, Oxford, 1949

[2] C. A. Mead, D. G. Truhlar, “Conditions for the definition of a strictly diabatic electronic basis for molecular systems”, J. Chem. Phys., 77:12 (1982), 6090–6098 | DOI

[3] B. D. Esry, H. R. Sadeghpour, “Split diabatic representation”, Phys. Rev. A, 68:4 (2003), 042706, 8 pp. | DOI

[4] J. B. Delos, W. R. Thorson, “Diabatic and adiabatic representations for atomic collision processes”, J. Chem. Phys., 70:4 (1979), 1774–1790 | DOI

[5] J. B. Delos, “Theory of electronic transitions in slow atomic collisions”, Rev. Modern Phys., 53:2 (1981), 287–357 | DOI

[6] M. Gargaud, J. Hanssen, R. McCarroll, P. Valiron, “Charge exchange with multiply charged ions at low energies: application to the N$^{3+}$/H and C$^{4+}$/H systems”, J. Phys. B, 14:13 (1981), 2259–2276 | DOI

[7] A. Macias, A. Riera, “Ab initio quantum chemistry in the molecular model of atomic collisions”, Phys. Rep., 90:5 (1982), 299–376 | DOI

[8] J. Grosser, T. Menzel, A. K. Belyaev, “Approach to electron translation in low-energy atomic collisions”, Phys. Rev. A, 59:2 (1999), 1309–1316 | DOI

[9] A. K. Belyaev, D. Egorova, J. Grosser, T. Menzel, “Electron translation and asymptotic couplings in low-energy atomic collisions”, Phys. Rev. A, 64:5 (2001), 052701, 9 pp. | DOI

[10] V. I. Korobov, “Multichannel scattering with velocity-dependent asymptotic potentials”, J. Phys. B, 27:4 (1994), 733–745 | DOI

[11] S. L. Yakovlev, E. A. Yarevskii, N. O. Elander, A. K. Belyaev, “Ob asimptoticheskom reshenii mnogokanalnoi zadachi rasseyaniya s neadiabaticheskoi svyazyu kanalov”, TMF, 195:3 (2018), 437–450 | DOI | DOI

[12] W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Pure and Applied Mathematics, 14, Wiley and Sons, New York, 1965 | MR | Zbl

[13] A. K. Belyaev, A. Dalgarno, R. McCarroll, “The dependence of nonadiabatic couplings on the origin of electron coordinates”, J. Chem. Phys., 116:13 (2002), 5395–5400 | DOI

[14] A. K. Belyaev, “Revised Born–Oppenheimer approach and a reprojection method for inelastic collisions”, Phys. Rev. A, 82:6 (2010), 060701, 4 pp., arXiv: 1011.1583 | DOI

[15] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, Nauka, M., 1979 | MR | MR | Zbl

[16] M. V. Volkov, S. L. Yakovlev, E. A. Yarevsky, N. Elander, “Potential splitting approach to multichannel Coulomb scattering: the driven Schrödinger equation formulation”, Phys. Rev. A, 83:3 (2011), 032722, 12 pp., arXiv: 1102.0549 | DOI

[17] M. V. Volkov, S. L. Yakovlev, E. A. Yarevsky, N. Elander, “Adiabatic versus diabatic approach to multichannel Coulomb scattering for mutual neutralisation reaction $\text{H}^++\text{H}^-\to \text{H}_2^*\to \text{H}(1)+\text{H}(n)$”, Chem. Phys., 462 (2015), 57–64 | DOI