The Physical Properties of Muon Cation: The Ab Initio Results
J.M. Truszkowskia, M.W. Jarosikb, A.P. Durajskib, R. Szczęśniaka, b
aDivision of Theoretical Physics, Jan Długosz University in Częstochowa, al. Armii Krajowej 13/15, 42-200 Częstochowa, Poland
bDivision of Physics, Częstochowa University of Technology, al. Armii Krajowej 19, 42-200 Częstochowa, Poland
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We determined the physical properties of the muon cation (M+2). The energy parameters of the Hamiltonian (the molecular orbital energy ε and the hopping integral t) were calculated by the variational method taking into account the Wannier's functions consisting of 1s Slater-type orbitals. We calculated the equilibrium distance R0 between the cores, the ground state energy E0, and the dissociation energy ED. Then we estimated the harmonic oscillation energy ωH0 and the anharmonic Morse energy ωM0. We also determined the rotational constant B0 and the values of the muon-phonon coupling functions, gε and gt. In the paper, we have demonstrated the influence of the environment on the properties of the muon cation in a balanced gain and loss energy scheme, where γ as energy, associated with the cation-environment interaction. We have shown that the cation may be in a metastable state. In the system, there is no the PT-symmetry breaking of the Hamiltonian, because t>γ.

DOI:10.12693/APhysPolA.142.39
topics: muon cation, physical properties, stable and metastable state, \mathcal{PT}-symmetry