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Register a new userScattering and bound states of a spin--1/2 neutral particle in the cosmic string spacetime
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In this paper the relativistic quantum dynamics of a spin-1/2 neutral particle with a magnetic moment $mu$ in the cosmic string spacetime is reexamined by applying the von Neumann theory of self--adjoint extensions. Contrary to previous studies where the interaction between the spin and the line of charge is neglected, here we consider its effects. This interaction gives rise to a point interaction: $boldsymbol{ abla} cdot mathbf{E}= (2lambda/alpha)delta(r)/r$. Due to the presence of the Dirac delta function, by applying an appropriated boundary condition provided by the theory of self--adjoint extensions, irregular solutions for the Hamiltonian are allowed. We address the scattering problem obtaining the phase shift, S-matrix and the scattering amplitude. The scattering amplitude obtained shows a dependency with energy which stems from the fact that the helicity is not conserved in this system. Examining the poles of the S-matrix we obtain an expression for the bound states. The presence of bound states for this system has not been discussed before in the literature.
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In this work we study the Dirac equation with vector and scalar potentials in the spacetime generated by a cosmic string. Using an approximation for the centrifugal term, a solution for the radial differential equation is obtained. We consider the scattering states under the Hulth{e}n potential and obtain the phase shifts. From the poles of the scattering $S$-matrix the states energies are determined as well.
The Dirac equation with both scalar and vector couplings describing the dynamics of a two-dimensional Dirac oscillator in the cosmic string spacetime is considered. We derive the Dirac-Pauli equation and solve it in the limit of the spin and the pseudo-spin symmetries. We analyze the presence of cylindrical symmetric scalar potentials which allows us to provide analytic solutions for the resultant field equation. By using an appropriate ansatz, we find that the radial equation is a biconfluent Heun-like differential equation. The solution of this equation provides us with more than one expression for the energy eigenvalues of the oscillator. We investigate these energies and find that there is a quantum condition between them. We study this condition in detail and find that it requires the fixation of one of the physical parameters involved in the problem. Expressions for the energy of the oscillator are obtained for some values of the quantum number $n$. Some particular cases which lead to known physical systems are also addressed.
The relativistic quantum motion of scalar bosons under the influence of a full vector (minimal $A^{mu}$ and nonminimal $X^{mu}$) 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.
We point out a misleading treatment in the literature regarding to bound-state solutions for the $s$-wave Klein-Gordon equation with exponential scalar and vector potentials. Following the appropriate procedure for an arbitrary mixing of scalar and vector couplings, we generalize earlier works and present the correct solution to bound states and additionally we address the issue of scattering states. Moreover, we present a new effect related to the polarization of the charge density in the presence of weak short-range exponential scalar and vector potentials.
A simple model of the dynamics of lightly bound skyrmions is developed in which skyrmions are replaced by point particles, each carrying an internal orientation. The model accounts well for the static energy minimizers of baryon number $1leq Bleq 8$ obtained by numerical simulation of the full field theory. For $9leq Bleq 23$, a large number of static solutions of the point particle model are found, all closely resembling size $B$ subsets of a face centred cubic lattice, with the particle orientations dictated by a simple colouring rule. Rigid body quantization of these solutions is performed, and the spin and isospin of the corresponding ground states extracted. As part of the quantization scheme, an algorithm to compute the symmetry group of an oriented point cloud, and to determine its corresponding Finkelstein-Rubinstein constraints, is devised.
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