https://doi.org/10.1140/epjp/s13360-025-06378-x
Regular Article
High-accuracy calculation on relativistic Compton profile of H-like ions
College of Physics and Electronic Engineering, Northwest Normal University, 730070, Lanzhou, China
Received:
12
February
2025
Accepted:
28
April
2025
Published online:
23
May
2025
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, 
and 
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).
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjp/s13360-025-06378-x.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
