Supersymmetric structure in the Dirac equation with cylindrically-deformed potentials

The Dirac equation plays a key role in microscopic descriptions of many-fermion systems, employing covariant density functional theory and the relativistic mean-field approach. In application to nuclei and hadrons, the required Dirac mean-field Hamiltonian involves a mixture of Lorentz vector and scalar potentials. Recently, symmetries of Dirac Hamiltonians with such Lorentz structure were shown to be relevant for explaining observed degeneracies in the spectra of nuclei (pseudospin doublets [1]) and mesons (spin doublets [2]). Corresponding supersymmetric patterns were identified for spherically-symmetric potentials [3]. In the present contribution, we extend these studies to Dirac Hamiltonians with axially-deformed scalar and vector potentials [4]. The essential ingredients of supersymmetric quantum mechanics [5] are the su-