Geodesic
Asymptotic behavior of charge-exchange amplitude at relativistic velocities and binding energies
Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 3, pp. 451-477

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The leading asymptotic term (for large impact parameters) of the charge-exchange amplitude for $1s_{1/2}\to 1s_{1/2}$ transitions is calculated in a modified relativistic eikonal approximation. Relativistic effects are taken into account in the kinematics of electron capture and in the description of the bound states. A study is made of the effects of the long-range interaction due to the Coulomb interaction between the particles in the entrance and exit reaction channels. The analytic results obtained in the nonrelativistic limit ($c\to \infty$) for the charge-exchange amplitude in the asymptotic region of large impact parameters are valid for all velocities, going over in the adiabatic limit into the well-known expressions of Firsov and in the limit of high velocities into the expressions of the Born approximation. 
@article{TMF_1993_95_3_a4,
     author = {P. P. Gorvat and V. Yu. Lazur},
     title = {Asymptotic behavior of charge-exchange amplitude at relativistic velocities and binding energies},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {451--477},
     publisher = {mathdoc},
     volume = {95},
     number = {3},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_95_3_a4/}
}
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P. P. Gorvat; V. Yu. Lazur. Asymptotic behavior of charge-exchange amplitude at relativistic velocities and binding energies. Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 3, pp. 451-477. http://geodesic.mathdoc.fr/item/TMF_1993_95_3_a4/