Relativistic calculations of differential ionization cross sections: Application to antiproton-hydrogen collisions

A relativistic method based on the Dirac equation for calculating fully differential cross sections for ionization in ion-atom collisions is developed. The method is applied to ionization of the atomic hydrogen by antiproton impact, as a nonrelativistic benchmark. The fully differential, as well as various doubly and singly differential, cross sections for ionization are presented. The role of the interaction between the projectile and the target nucleus is discussed. Several discrepancies in available theoretical predictions are resolved. The relativistic effects are studied for ionization of hydrogenlike xenon ion under the impact of carbon nuclei.

Figure 1

TDCS for antiproton-impact ionization of hydrogen at 200 keV in the scattering plane. The scattering angle of the projectile is 0.2 mrad and the ejected electron energy is 4 eV. The results of the QM-CCC and TDCC approaches are from Refs. [24] and [25], respectively.

Figure 2

Same as Fig. 1, but the results of calculation neglecting the NN interaction are also shown.

Figure 3

TDCS for antiproton-impact ionization of hydrogen at 200 keV in the scattering plane. The scattering angle of the projectile is 0.2 mrad and the ejected electron energy is 7 eV. The results of the QM-CCC and TDCC approaches are from Refs. [24] and [25], respectively.

Figure 4

TDCS for antiproton-impact ionization of hydrogen at 200 keV in the scattering plane. The scattering angle of the projectile is 0.2 mrad and the ejected electron energy is 10 eV. The results of the QM-CCC and TDCC approaches are from Refs. [24] and [25], respectively.

Figure 5

TDCS for antiproton-impact ionization of hydrogen at 200 keV in the scattering plane. The scattering angle of the projectile is 0.1 mrad and the ejected electron energy is 4 eV. The results of the QM-CCC and TDCC approaches are from Refs. [24] and [25], respectively.

Figure 6

TDCS for antiproton-impact ionization of hydrogen at 200 keV in the scattering plane. The scattering angle of the projectile is 0.3 mrad and the ejected electron energy is 4 eV. The results of the QM-CCC and TDCC approaches are from Refs. [24] and [25], respectively.

Figure 7

TDCS for antiproton-impact ionization of hydrogen at 500 keV in the scattering plane. The momentum transfer $q$ is 0.25 a.u. and the ejected electron energy is 5 eV. The results of the QM-CCC and TDCC approaches are from Refs. [24] and [25], respectively.

Figure 8

DDCS as a function of the transverse component of momentum transfer for an energy of the ejected electron of $1,10$, and 20 eV at an antiproton incident energy of 200 keV. The results of the TDCC approach are from Ref. [25].

Figure 9

DDCS as a function of the transverse component of momentum transfer for an ejected electron of 5 eV at an antiproton incident energy of 30 keV.

Figure 10

SDCS at an incident antiproton energy of 30 keV. The results of the CP, QM-CCC, and WP-CCC approaches are from Refs. [23], [24], and [26], respectively.

Figure 11

Impact-parameter dependence of the total ionization probability in the 100 MeV/u ${\mathrm{C}}^{6+}-{\mathrm{Xe}}^{53+}$ collision for various initial states. The results of the calculation in the nonrelativistic limit are also shown.

Figure 12

Impact-parameter dependence of the total ionization probability in the 100 MeV/u ${\mathrm{C}}^{6+}-{\mathrm{Xe}}^{53+}$ collision for various momentum projections of the initial $2p$ state. The results of the calculation in the nonrelativistic limit are also shown.