Stopping power of fast channeled protons in Hartree-Fock approximation

Abstract

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).

The Impact‐Parameter Dependence of Electron Stopping in Proton Collisions with Gas and Solid Atoms

“…As the proton velocity decreases, the role of ionization in stopping diminishes. The results obtained are interesting to compare with the data calculated in terms of Dettmann approximation [9] which describe the energy loss for the 1s state properly.…”

Effective Ion Charge

“…A similar treatment has been applied previously [14,16]. In the Bethe theory treating Sr for point charge projectiles [1][2][3][4]16] and for the approach to S r for nucleus-electrons composite staying in the ground state [7,8], the momentum ω/v is cancelled out after adding the sum rule and the dipole contributions. The physical meaning of the parameter ω (originally Ref.…”

“…The basic processes responsible for the slowing down of fast heavy ions in matter are qualitatively understood [1][2][3][4][5][6], but the interest in this problem remains alive for at least two reasons. Ions with velocity v proceed in the solid having, at least temporarily, bound electrons [7][8][9][10][11], even if v > Ζ m, and the distribution of charge is not completely predicted.…”

Channelling of H0and H+in Si Single Crystal

“…Rutherf ord ba ckscatteri ng (R BS) is used as a useful techni que f or i nvesti gati on of vari o us effects, for i nsta nce, di stri buti ons of i m pl anted i m puri ti es [6] or surf ace melti ng [7]. Al so the computer ana l ysi s of the channel li ng e˜ect wa s develop ed [8,9], showi ng tha t the results of sim ula ti on are, for i nsta nce, dependent on the pro j ecti le net charg e [10]. Howev er, the RBS m easurem ents [11], perf orm ed on Si crysta l i n r a n d om and channel l i ng di recti ons for He + and He ++ i nci dent i ons (i n the m axi m um stoppi ng p ower energy ra nge) showed tha t the spectra were sta ti sti cal l y i ndi sti ngui shabl e. It wa s due to the short pa th (4 nm ) on whi ch the heli um b eam rea ches i ts equi l i bri um charg e di stri buti on.…”