Analytic advantages of spherically symmetric step-function potentials in the Dirac equation with scalar and fourth component of vector potential

摘要

The root mean square radii of the particle orbits are calculated (semi)analytically for every bound state, using the Dirac equation with a scalar potential U-S and fourth component of a vector potential U-V in the case of a spherically symmetric step-function shape with the same radius R for these potentials. In addition, a (semi)analytic expression of the expectation value of the corresponding potential energy operator is derived. For the above quantities, expressions of the energy eigenvalues in terms of the potential parameters are needed and approximate formulas may be used in certain cases. This study emphasizes the analytic advantages 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 R particle in hypernuclei. [References: 17]