10-14 July 2016
Africa/Johannesburg timezone
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Bound states and decays in Relativistic Quantum Mechanics.

12 Jul 2016, 12:00
Oral Presentation High Energy, Nuclear and Particle physics Parallel Track B


Riccardo Giachetti (Physics Department, University of Florence, Italy)

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The numerical aspects of the solution of a bound state problem
in relativistic quantum mechanics are considered and the completely
covariant formulation of the problem is first presented. The systems
with a general central potential are quantized and the wave equation
for the eigenstates given by 16-components spinor, is deduced in a
spherical basis. Because of the symmetries the spectral problem reduces
to the solution of a singular boundary value problem of the fourth order.
It is shown how Padé approximants can help or directly substitute the
integration of the system. It is also shown how to deal with the addition
of a perturbation term representing the spin-spin interaction.
The calculation of the hyperfine levels and decays of hydrogenic atoms,
the determination of the meson masses and the widths of radiative decays
of bottomonium states are finally described showing the excellent
agreement with experimental data. (Refs: J. Phys. A 38 (2005)
1345–1370; J. Phys. A 39 (2006) 15207–15223; Phys. Rev. D 87,
034021 (2013); J. Phys. B 48 (2015) 085002 (9pp);
arXiv:1604.08043 (2016)).

Primary author

Riccardo Giachetti (Physics Department, University of Florence, Italy)

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