Solving the Dirac equation has played an important role in many areas of fundamental physics. In this work, we present the Dirac equation solver DiracSVT, which solves the Dirac equation with scalar, vector, and tensor nuclear potentials in spherical coordinate space. The shooting method was used with a Runge–Kutta 4 integration scheme. The potentials are parameterized in a Woods–Saxon form, which reproduce well the known single-particle states around all doubly magic nuclei and can be applied to study the shell evolution of exotic nuclei. The code can be easily extended to the study of other systems, including atomic, hadron, and molecular physics.

It is shown that the proton formation probabilities, extracted from experimental decay half-lives, can be well reproduced by a simple multilinear formula with only three parameters. The parameters obtained by considering the standard root mean square deviation and the mini-max criteria are very similar to each other. In addition, we applied Bayesian analysis to study the uncertainties of the parameters and the model predictions. In this way we explain the systematics of proton decay half-lives. The multilinearity of the model also provides a way to classify the relative hindrance of different proton decays. All the recent experimental data agree very well with the model prediction. Our Bayesian analysis suggests that those new data do help constrain the uncertainty of the model parameters.

The anomalous low-energy E2-related behavior of a triaxially deformed nuclei is examined within the framework of the interacting boson model. The results show striking features that include a B(E2; 4(1)(+) -> 2(1)(+))/B(E2; 2(1)(+) -> 0(1)(+)) < 1.0 transition rate and a E(4(1)(+))/E(2(1)(+)) > 2.0 excitation energy ratio that can be tracked back to a finite-Neffect, which in a large-Nlimit of the theory yields normal results for a stable gamma-deformation. This description is shown to explain experimentally observed results in Pt-172 and Os-168, and in doing so yields a deeper understanding of the physical features of a soft triaxially-deformed nucleus.