Scalar bosons with Coulomb potentials in a cosmic string background: scattering and bound states

Abstract

The relativistic quantum motion of scalar bosons under the influence of a full vector (minimal A µ and nonminimal X µ ) and scalar (V s ) interactions embedded in the background of a cosmic string is explored in the context of the Klein-Gordon equation. Considering Coulomb interactions, the effects of this topological defect in equation of motion, phase shift and S-matrix are analyzed and discussed. Bound-state solutions are obtained from poles of the S-matrix and it is shown that bound-state solutions are possible only for a restrict range of coupling constants. PACS. 0 4.62.+v -0 4.20.Jb -0 3.65.Ge -0 3.65.Pm

Non-inertial effects on a non-relativistic quantum harmonic oscillator in the presence of a screw dislocation

“…where F (x) is a function to be determined. Substituting equation (11) into equation (10) we obtain an equation of the form…”

“…Like cracks that form when water freezes out into ice, topological defects as cosmic strings [1,2] have an analogue interpretation which is related to phase transitions occurred in the early universe [3]. It is believed that these defects can modify the trajectory of test particles such that the energy spectrum of quantum systems can carry a dependence on the defect parameters, which characterize the spacetimes associated to them [4][5][6][7][8][9][10]. In this context, particles under the influence of potentials that have been studied in relativistic and nonrelativistic quantum mechanics in the flat spacetime with a trivial topology, can be analysed in a scenario which corresponds to spacetimes with different geometries as well as topologies, as for example, the geometries associated to disclinations and dislocations [11][12][13].…”

“…In this context, particles under the influence of potentials that have been studied in relativistic and nonrelativistic quantum mechanics in the flat spacetime with a trivial topology, can be analysed in a scenario which corresponds to spacetimes with different geometries as well as topologies, as for example, the geometries associated to disclinations and dislocations [11][12][13]. Indeed, this is a fruitful field of research and applications have been found in several works in the background spacetime generated to a cosmic string [6][7][8][9][10]14]. In which concerns similar research in the geometry associated to dislocations, several works have been performed.…”

Scattering cross-section in gravitating cosmic string spacetimes

“…Clearly, if one includes the z-direction, the total cross-section diverges. By substituting equation ( 14) into equation ( 22) and then integrating (22) in ϕ, we obtain…”

“…Motivated by this approach, [20] showed that the evolution of a wave packet in the conical spacetime of an ideal cosmic string is highly dependent on the many possible boundary conditions of the scalar field at the vertex of the cone. In [21], the authors generalized the procedure proposed in [19] to the relativistic scattering of a charged scalar field by an ideal cosmic string considering non-minimal coupling to gravity, and in [22] they analyzed the scattering of scalar particles in the same spacetime but considering minimal and non-minimal coupling to vector and scalar fields. In the present work, we propose a new formalism dealing with the scattering problem of bosonic and fermionic fields in the general spacetime of a gravitating cosmic string, which possesses a conical structure far from the core.…”