Abstract
The relativistic quantum dynamics of scalar bosons in the background of a full vector coupling (minimal plus nonminimal vector couplings) is explored in the context of the Duffin–Kemmer–Petiau formalism. The Coulomb phase shift is determined for a general mixing of couplings and it is shown that the space component of the nonminimal coupling is a sine qua non condition for the exact closed-form scattering amplitude. It follows that the Rutherford cross section vanishes in the absence of the time component of the minimal coupling. Bound-state solutions obtained from the poles of the partial scattering amplitude show that the time component of the minimal coupling plays an essential role. The bound-state solutions depend on the nonminimal coupling and the spectrum consists of particles or antiparticles depending on the sign of the time component of the minimal coupling without chance for pair production even in the presence of strong couplings. It is also shown that an accidental degeneracy appears for a particular mixing of couplings.
Highlights
(η → γ γ )/ (π 0 → γ γ ), and level shifts and widths in pionic atoms [5,6,7]
We show the correct use of the nonminimal vector interaction in view of misconceptions propagated in the literature and we address the problem of scalar bosons embedded in a full vector Coulomb potential
We have addressed the relativistic quantum dynamics of scalar bosons embedded in a full vector Coulomb interaction in the context of the Duffin–Kemmer– Petiau (DKP) formalism
Summary
The formalisms are equivalent in the case of minimally coupled vector interactions [25,26,27] , the DKP formalism enjoys a richness of couplings not capable of being expressed in the KG and Proca theories [28,29]. Elsewhere [36], using the proper form of the nonminimal vector coupling and considering spherically symmetric potential functions, it has been shown that the solution for the problem can be found in a clear and transparent way in terms of a Schrödinger-like equation for just one component of the DKP spinor and the remaining components are expressed in terms of that one in a simple way. We show the correct use of the nonminimal vector interaction in view of misconceptions propagated in the literature and we address the problem of scalar bosons embedded in a full vector Coulomb potential. The Coulomb interaction is a long-range like, but allows us to obtain analytical solutions that can give us a heuristic look of strong interactions in the tail, so that the new results reported in the present work are very important for a better understanding in the phenomenological description of elastic meson-nucleus scattering.
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