Some aspects of heavy-ion reactions close to the Coulomb barrier are reviewed in experiment and theory Fusion, complex reactions and quasi-elastic reactions are covered, both microscopic and macroscopic approaches to the theory are discussed A brief outlook is given

https://iopscience.iop.org/article/10.1088/0954-3899/20/9/004/pdf

Heavy-ion reactions close to the Coulomb barrier

Bound states of the Dirac equation with vector and scalar Scarf-type potentials

We study the problem of the relativistic motion of a 1/2-spin particle in an exactly solvable potential, which consists of the harmonic oscillator potential plus a novel angle-dependent potential, The analytic bound state solutions of the Dirac equation for this potential are obtained by using the Nikiforov–Uvarov method. The wave functions of the radial and angle-dependent parts of the Dirac equation are derived in the form of the Laguerre and Jacobi polynomials. The contribution of the angle-dependent potential to the relativistic energy spectra is discussed under the condition that the scalar potential is equal to or minus the vector potential.

http://iopscience.iop.org/article/10.1088/0031-8949/79/03/035003/pdf

On the exact solutions of the Dirac equation with a novel angle-dependent potential

The (1+3)- and (1+1)-dimensional Dirac equation with both scalar-like and vector-like potentials is discussed. The authors prove that if the scalar-like potential is just equal to the vector-like potential, the confinement is impossible, i.e. there must be scattering states. Two exact solutions with linear potential and harmonic oscillator potential in this condition are given.

https://iopscience.iop.org/article/10.1088/0305-4470/19/9/045/pdf

Confinement properties for the Dirac equation with scalar-like and vector-like potentials

The exact solutions of the Dirac equation with a linear scalar confining potential in a uniform electric field are given. It is found that, if the scalar potential is stronger than that of the electric field, confinement is permanent. On the contrary, if the electric field is strong enough, confinement is impossible due to the Klein paradox.

https://iopscience.iop.org/article/10.1088/0305-4470/17/4/026/pdf

Exact solutions of the Dirac equation with a linear scalar confining potential in a uniform electric field

Confining potentials in euqations involving the interaction of fermions lead to no Klein paradoxes if the strength of the vector potential is appropriately limited compared to the scalar potential For linear potentials the Regge trajectories are asymptotically like those of the harmonic oscillator, namely, ${E}^{2}\ensuremath{\sim}j$

David C. Johannsen

Papers

Vector and scalar confining potentials and the Klein paradox