Recent Results on K-Shell Ionization by Ion Collisions
The experimental K-shell ionization cross sections of 48Cd, 50Sn, 52Te, 53I and 56Ba for alpha particles, between 2.2 MeV and 2.8 MeV, and of 52Te for protons, between 1.6 and 3 MeV, are presented. The justification for making these measurements comes, on the one hand, in filling a region where, at present, data are sparse: for example, 52Te ionization cross sections by alpha particles have never been reported before, and, on the other hand, checking between previously reported and diverging sets of experimental results: for example, for alpha particles on tin. In addition, the K-shell ionization cross sections of 52Te for protons can be considered as an extension of Khelill's measurements.
Universal cross sections for K-shell ionization by heavy charged particles. II. Intermediate particle velocities
Experimental K-shell ionization cross sections of /sub 13/Al and /sub 28/Ni are reported for ions of /sup 1//sub 1/H, /sup 2//sub 1/H, /sup 4//sub 2/He, /sup 6//sub 3/Li, and /sup 7//sub 3/Li with kinetic energies in the range from 2 to 36 MeV, and of /sub 28/Ni for ions of /sup 12//sub 6/C, /sup 16//sub 8/O, and /sup 19//sub 9/F in the range from 4 to 90 MeV. The theory of direct Coulomb K-shell ionization, as developed in an earlier paper (Phys. Rev. A 7, 983 (1973)) for projectiles of atomic number Z/sub 1/, small compared to the target atomic number Z/sub 2/, and of velocities v/sub 1/ small compared to the target K-shell electron velocity v/sub 2K/, i.e., v/sub 1/ very-much-less-than v/sub 2K/, is extended to intermediate velocities v/sub 1/ approx. = v/sub 2K/. New effects appear. They add to the Z/sup 2//sub 1/-proportional cross sections one derives from linear-response theories for direct ionizations. They are attributed to the polarization of the target K shell in the field of the projectile, and to electron capture by the projectile. Guided by the perturbed stationary-state theory of atomic collisions, the polarization effects are incorporated so that the theory retains the unifyingmore » aspects of the cross sections derived in the plane-wave Born approximation, but the variables now contain the nonlinear effects as scaling factors. Electron-capture cross sections are added. When v/sub 1/ >> v/sub 2K/, such contributions subside, and one retrieves the cross sections of the linear-response approximation. The theory predicts K-shell ionization cross sections for projectiles with Z/sub 1//Z/sub 2/ < 0.5 at all velocities in a comprehensive manner. It agrees with experimental data covering six orders of magnitude for collisions partners with Z/sub 1//Z/sub 2/ ranging from 0.03 to 0.3 and v/sub 1//v/sub 2K/ from 0.07 to 2.« less
Two-dimensional gravitational anomalies, Schwinger terms and dispersion relations
Abstract We are dealing with two-dimensional gravitational anomalies, specifically with the Einstein anomaly and the Weyl anomaly, and we show that they are fully determined by dispersion relations independent of any renormalization procedure (or ultraviolet regularization). The origin of the anomalies is the existence of a superconvergence sum rule for the imaginary part of the relevant formfactor. In the zero mass limit the imaginary part of the formfactor approaches a δ-function singularity at zero momentum squared, exhibiting in this way the infrared feature of the gravitational anomalies. We find an equivalence between the dispersive approach and the dimensional regularization procedure. The Schwinger terms appearing in the equal time commutators of the energy momentum tensors can be calculated by the same dispersive method. Although all computations are performed in two dimensions the method is expected to work in higher dimensions too.