The cross section for radiative electron transfer from H atoms to bound states of an incident ion is calculated for velocities much greater than the orbital velocity of the captured electron. It is shown to dominate over the Coulomb-charge-exchange cross section for E > 9 MeV per incident nucleon.The process of charge transfer from a target atom to an incident ion by the Coulomb interaction has been the subject of considerable theoretical effort, particularly with regard to the asymptotic behavior of the cross section at high velocity. 1 It has been recognized from the outset 2 that the transfer of charge by a radiative process will provide a competing channel although its contribution was estimated to be small at high velocity. Since that time attention has been mostly directed towards the evaluation of cross sections for this process at very low velocity, in the region of thermal encounters. 3 For relativistic projectile energies the radiative capture of free electrons has been discussed with the theory of the relativistic photoeffect. 4 It has been pointed out that charge exchange in metal foils for sufficiently high incident energies is due predominantly to radiative electron capture. Recent observations 5,6 of the radiation emitted in collisions of fast charged ions with gases have indicated a broad x-ray band which has been attributed to the process of radiative charge transfer of bound electrons. It is our purpose in this Letter to examine the nonrelativistic limiting behavior of the cross section for this process under conditions where the velocity of the incident ion is much greater than the initial and final orbital velocity of the electron which is captured.Throughout we will work in atomic units.The probability for transferring an electron from a hydrogen atom 2 to an incident ion 1 in a collision at impact parameter b and velocity v (see Fig. 1), with concomitant emission of a photon of frequency co, iswhere k is the photon propagation vector and d 3 k = k 2 dk dQ, with k =tx)/c. As we will subsequently restrict discussion to high velocities, we will adopt the impact-parameter formalism 1 to describe the ion-atom collision. In addition we will consider only the first-order interaction with the radiation field and assume the dipole approximation of replacing the factor exp(zk* r) occurring in this interaction by unity. So long as the impact FIG.

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Abstract. The electronic energy loss of MeV-protons in crystals is investigated in the Hartree-Fock approximation for the core electrons of the target. It turns out that each core electron can be regarded as stopping the proton independent of all other electrons without restriction by the Pauli principle. For the channeling stopping power the impact parameter dependent energy loss of a proton moving rectilinearly past a crystal ion is calculated in first Born approximation. Low excitations of the core electrons lead to a long range impact parameter dependence, whereas high excitations contribute to the energy loss proportional to the electron density sampled along the proton trajectory. The results are applied to 4 MeV proton channeling along the main channels of Si using Clementi wave functions for the core electrons and a free electron approximation for the valence electrons. The comparison with the experimental results of Clark et al. yields good agreement. In the high velocity limit a reduction of the channeling stopping power to 0.64(0.83) of the random value is predicted for Si(C).

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