B L Moiseiwitsch

The K-shell ionisation of atoms by relativistic protons

The K-shell ionisation is investigated using an extension of the first-order time-dependent perturbation-theory treatment of Moller (1932) taking Dirac plane waves for the description of the incident and scattered protons and the Darwin approximation for the relativistic wavefunctions of the K-shell atomic electrons and the ejected electron. The differential cross sections delta 2 sigma / delta k delta q and d sigma /dk, where k is the wavenumber of the ejected electron and hq is the momentum change of the proton, are calculated. The double differential cross section for collisions in which a change of spin of the atomic electron occurs is less sharply peaked for small q, and has a broader overall distribution with respect to q, than the double differential cross section for collisions without spin change, although being much less in magnitude than the latter for small q. This leads to total K-shell ionisation cross sections sigma with significant contributions coming from collisions with spin change of the atomic electron for large atomic numbers at high energies of impact.

The excitation of the 6 1P1 and 6 3P0,1,2 states of mercury by electron impact

The mercury atom is treated as a two-electron system with the orbitals determined using the Coulomb approximation, and intermediate-coupling wave functions are employed which allow for the spin-orbit interaction of the 6p electron of the 6 1P1 and 6 3P1 states of mercury. The oscillator strengths of the 6 1P1 -> 6 1S0 1850 Angstrom line and the 6 3P1 -> 6 1S0 2537 Angstrom line are calculated to be 1.17 and 0.037, respectively, which are in very good agreement with the experimentally determined values. The Ochkur approximation is then used to calculate the cross sections for the excitation of the 6 1P1 and 6 3P0,1,2 states of mercury by electron impact. Finally these excitation cross sections are employed to evaluate the percentage polarizations of the 2537 Angstrom and 1850 Angstrom lines of mercury excited by incident electrons.

Relativistic second Born approximation for electron capture

In previous papers we have investigated the Is state to Is state capture of an electron from a hydrogenic ion by an incident fully stripped positive ion using relativistic generalisations of the Oppenheimer-Brinkman-Kramers (OBK) approximation (Moiseiwitsch and Stockman 1980) and the second Born approximation (Humphries and Moiseiwitsch 1984). In the present paper we analyse the same problem to a greater level of accuracy by using a relativistic form of the third Born approximation, expanding in powers of αƵA, αƵB and retaining leading terms, where ƵA, ƵB are the target and projectile charges respectively and α is the fine structure constant. In the limit of non-relativistic but high impact energies our formulae for the scattering amplitude and the total capture cross section without spin flip are in agreement with the results obtained by Shakeshaft (1978) and, as far as the total cross section is concerned, also with the work of Drisco (1955) and Dettman (1971) using the non- relativistic third Born approximation.

Electron capture by charged particles at relativistic energies

The Oppenheimer-Brinkman-Kramers approximation is used to derive scattering amplitude for electron capture by a nucleus of charge ZBe from a hydrogenic ion having nuclear charge ZAe. Allowance is made for relativistic effects arising from the high velocity of relation motion of the charged particles involved in the collision and from the use of Dirac atomic wavefunctions. Simple analytical expressions fot the OBK cross sections for capture without and with spin flip are derived by expanding in powers of alpha ZA and alpha ZB where alpha is the fine-structure constant. These formulae are found to be in very good agreement with our numerical integrations of the full analytical expressions for the scattering amplitudes when alpha ZA and alpha ZB are small. The authors results are also in excellent accordance with the relativistic calculations of Shakeshaft (1979) for the case of electron capture without spin flip.

NEGATIVE IONS AND SHAPE RESONANCES.

A simple model potential having one adjustable radius parameter r0 is employed to obtain electron affinities and the positions and widths of shape resonances by performing an extrapolation along an isoelectronic sequence of positive ions and the associated neutral atom. The values of the parameter r0 are determined by requiring the potential to yield the experimentally observed energies of a given state of the members of the isoelectronic sequence. A quadratic extrapolation of r0-1 then provides a model potential representing the field of the atomic core on the additional electron in the negative-ion system, stable or unstable, belonging to the isoelectronic sequence. This potential is then used to determine the energy of binding of the extra electron in the negative ion, if it exists, thus giving the electron affinity of the neutral atom concerned with an accuracy to within about 0.1 eV in most cases. Metastable states of certain negative ions are considered in the same manner. The model potential is also used to investigate the elastic scattering of electrons by neutral atoms. When the potential field produced by the atomic core is insufficiently strong to bind the additional electron, p-wave shape resonances are found and the positions and widths of these have been determined. Atoms in the periodic table from hydrogen through to chlorine have been investigated.

The K-shell ionization of atoms by relativistic electrons

The theoretical investigation carried out by Arthurs and Moiseiwitsch (1958) has been extended to higher energies and to atoms with greater nuclear charge Z. Allowance for the difference between the theoretical and experimental ionization energies arising from the potential field of the electrons in the outer shells is made using a similar procedure to that due to Perlman (1960). The authors have calculated K-shell ionization cross sections as functions of the electron impact energy for C, Al, Ni, Cu, Ag, Sn, Au and compared their theoretical curves with the available experimental data, the accordance being somewhat variable.

Relativistic second-order OBK approximation for electron capture

The capture of an electron from a target hydrogenic ion T by a fully stripped projectile ion P, having atomic numbers ZT and ZP respectively, is investigated using the relativistic second-order Oppenheimer-Brinkman-Kramers (ROBK2) approximation. By expanding in powers of alpha ZT and alpha ZP and retaining the leading terms, alpha being the fine-structure constant, approximate formulae are derived for the scattering amplitude which are used to obtain approximate closed analytical expressions for the differential and total cross sections for electron capture between ground states. These differ from the authors previous formulae in that second-order terms in alpha are retained in the denominator leading to considerable improvement in the capture cross sections. Total cross sections for 1s-1s electron capture by incident protons from target hydrogen atoms calculated using the ROBK2 approximation are in good agreement with the relativistic continuum distorted-wave calculations of Deco and Rivarola (1987) over a wide range of projectile energies. Also the ROBK2 total cross sections for 1s-1s electron capture by incident bare neon ions from target atoms with ZT=13, 30, 47, 73, 92 are in satisfactory accordance with the relativistic eikonal and first Born approximation calculations of Eichler. Moreover reasonably satisfactory agreement is obtained between the ROBK2 total cross sections and the experimental data for incident bare C, Ne and Ar ions on various atomic targets.

Total cross sections for electron capture at relativistic energies

Total cross sections for the capture of electrons from the K shell of target atoms with atomic numbers ZA=13, 29, 47 to the K shell of incident fully stripped ions with atomic numbers ZB=6, 10, 18 having impact energies E=140, 250, 400, 1050 MeV amu-1 are calculated by numerical integration using a relativistic form of the second Born approximation together with exact Dirac relativistic atomic wavefunction.

Relativistic symmetric eikonal approximation for electron capture

Formulae are derived using the eikonal approximation for the probability amplitude for electron capture from a target hydrogenic ion with nucleus A by an incident fully stripped positive ion B moving with relativistic velocity referred to A. It is shown that the post and prior relativistic formulae are equivalent for exact Dirac atomic wavefunctions and also that the corresponding formulae for the capture cross section are symmetric with respect to A and B.

Application of a simplified second Born approximation to the scattering of electrons and protons by hydrogen atoms

A simplification of the second Born approximation, in which the terms arising from coupling to the lowest N levels are evaluated exactly and those arising from coupling to all the higher levels with principal quantum numbers n >or= N + 1 and to the continuum states are determined approximately by using the closure relation, is employed to investigate the elastic scattering of electrons by hydrogen atoms and the 1s -> 2s and 1s -> 2p excitations of atomic hydrogen by electron and proton impact. For the case of elastic scattering the inclusion of coupling to higher states increases the total cross section above the first Born approximation at all electron impact energies. However, for the 1s -> 2s and 1s -> 2p excitations the effect of coupling to states with principal quantum numbers n >or= 3 is opposite to that of coupling to the n = 2 level, and brings the total cross sections closer to the first Born approximation at the highest impact energies (greater,similar 100 ev for incident electrons).