Analytic Advantages of Spherically Symmetric Step-Function Potentials in the Dirac Equation with Scalar and Fourth Component of Vector Potential

The root mean square radii of the particle orbits are calculated (semi)analyticallyfor every bound state, using the Dirac equation with a scalar potentialU_s andfourth component of a vector potentialU_v in the case of a spherically symmetricstep-function shape with the same radiusR for these potentials. In addition, a(semi)analytic expression of the expectation value of the corresponding potentialenergy operator is derived. For the above quantities, expressions of the energyeigenvalues in terms of the potential parameters are needed and approximateformulas may be used in certain cases. This study emphasizes the analyticadvantages of the relativistic, spherically symmetric step-function potential model.Its applicability is discussed in connection with a problem of physical interest,namely that of the motion of a particle in hypernuclei.