Scaling of analytical cross sections for K-shell ionization by nonrelativistic protons to cross sections by protons at relativistic velocities

A procedure is given by which nonrelativistic cross sections are scaled to the K-shell ionization cross sections by protons of any velocity up to the speed of light. To perform this scaling in an analytical manner, the ECPSSR theory of Brandt and Lapicki (1981 Phys. Rev. A 23 1717) and its recent modifications that go beyond the plane wave Born approximation with exact (e) limits on the energy and momentum transfers (ePWBA) are formulated analytically. They are expressed in terms of a formula that fits numerically evaluated ePWBA to within 3% for carbon and all heavier elements. With an extension to GeV protons, the ECPSSR and its relativistic modifications are reviewed to untangle consequences of various relativistic treatments of protons and different methods to account for the relativistic nature of the K-shell electron. The adequacy of the scaling to obtain the relativistic K-shell ionization cross sections is scrutinized through departures of the developed theories from a comprehensive compilation of the data. Excellent agreement with 1 GeV data of Vodopyanov et al (1996 J. Phys. B: At. Mol. Opt. Phys 29 2543) is demonstrated, and an apparent discrepancy with 4.88 GeV data of Anholt et al (1976 Phys. Rev. A 14 2103) is examined in light of other theories.

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