2024/03/30 by E. M. Tursunov, Tursunov, E. M., Sh. G. Norbutaev +2
Engineering · Physics and Astronomy · #Crystallography and Radiation Phenomena #FOS: Physical sciences #High Energy Physics - Experiment (hep-ex) #High Energy Physics - Phenomenology (hep-ph) #Muon and positron interactions and applications #Nuclear Theory (nucl-th) #Nuclear physics research studies #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2404.00444
openalex publication_date 2024/03/30 · openalex created_date 2024/04/04 · openalex updated_date 2026/07/28
A new theoretical method is developed to solve the two-body bound-state Dirac equation for positronium. Only Coulomb potential was included in the Dirac Hamiltonian. It is shown that the two-body Dirac Hamiltonian can be written in the Hermitian matrix form of the 4×4 size and diagonalized in the momentum-state representation. Numerical results for the energy spectrum of the para- and ortho-positronium ground states performed within the variational method using the harmonic oscillator basis functions are in good agreement with a high-precision finite-element method of T.C. Scott et al. After the Fourier transformation into the coordinate-state representation the bound state wave functions of the para-Ps and ortho-Ps do not contain any singularity at the origin in contrast to the method mentioned above. The weights of the large-small and small-large components of the ground state wave functions are estimated to be of order 10-6, while the weight of the small-small component is of order 10-12.