High-accuracy calculation on relativistic Compton profile of H-like ions

Abstract

The generalized pseudospectral (GPS) method has been used to solve the radial Dirac equation. It has been found that the energies of the bound states can be calculated with high accuracy, but there are inherent difficulties in obtaining globally accurate radial wavefunctions in position space, which are accurate only at intermediate r in position space. To improve the global performance of relativistic radial wavefunctions, a fitting procedure based on the structure of hydrogenic orbitals has been proposed, which can be called the pseudospectral fitting method. Then, the relativistic radial wavefunction in momentum space can be calculated analytically by the series method. Finally, a highly accurate relativistic Compton profile has also been calculated at an arbitrary momentum. In addition, the relativistic effect on the Compton profile of the 1s orbital in the H atom, \(\text {Xe}^{53+}\) and \(\text {U}^{91+}\) ions as well as the effect of the nuclear charge distribution on the Compton profile has been discussed in detail based on various extended models of the nucleus, including the uniform sphere model (USM), the Gaussian model (GM) and the Fermi model (FM).