Narrow Results

We investigate the charge-pickup cross section of 158A GeV ²⁰⁷Pb projectiles on Bi, Pb, Cu and Al targets using CR39 nuclear track detectors. The target-detector stacks were exposed at CERN SPS beam facility. Chemical etched detectors are scanned using optical microscope, and the data in the form of etched cone heights have been collected. We have identified the beam and fragment charge states in particular charge-pickup (Z = 83) by the Pb ions using the etched cone heights. Dependence of charge-pickup cross section of 158A GeV ²⁰⁷Pb projectiles on the target mass number is described and results are compared to similar measurements found in the literature.

The two-dimensional Dirac equation with spin and pseudo-spin symmetries is investigated in the presence of the maximally superintegrable potentials. The integrals of motion and the quadratic algebras of the superintegrable quantum $E{3}^{\prime }$, anisotropic oscillator and the Holt potentials are studied. The corresponding Casimir operators and the structure functions of the mentioned superintegrable systems are found. Also, we obtain the relativistic energy spectra of the corresponding superintegrable systems. Finally, the relativistic energy eigenvalues of the generalized Yang–Coulomb monopole (YCM) superintegrable system (a $SU(2)$ non-Abelian monopole) are calculated by the energy spectrum of the eight-dimensional oscillator which is dual to the former system by Hurwitz transformation.