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Pseudospin symmetry (PSS) plays critical roles in the formation of many physical phenomena, and has been studied extensively from spherical nuclei to deformed nuclei. However, there remains an open question about the PSS in resonant states in deformed systems. For the first time, we investigate the PSS in resonant states in deformed nuclei by solving the Dirac equation in the complex-momentum representation for a potential with quadrupole deformation at the first order obtained from relativistic mean-field (RMF) calculations. Taking 170Yb as an example, we explore the PSS in the single-particle resonant states by examining the energies, widths and the density distribution. Compared with the bound states, the pseudospin splittings between the resonant pseudospin doublets are found to be small, and the radial density distributions of pseudospin doublets look very similar, which indicates that the PSS of resonant states is well reserved in deformed nuclei. Moreover, we have comprehensively studied the dependencies of the PSS on nuclear deformations and the shape of potential, which are helpful to recognize the evolution of resonant pseudospin doublets in weakly-bound deformed nuclei and understand their exotic properties.

In this paper, the spectral statistics of prolatedeformed nuclei are investigated by using random matrix theory. To this aim, we used both available experimental data and also the energy levels of ground, beta, and gamma bands of 51 deformed even-even nuclei, which are determined via partial SU(3) dynamical symmetry limit of interacting boson model. The results verified the ability of the considered models in the restoration of experimental data and also the displacement of beta and gamma energy bands. Also, the dependence of the statistical situation of energy levels is considered to the mass of nuclei, spins, half-lives of the ground state, bands of energy, and different configurations of excited bands of energies. The results suggested obvious differences in the spectral situation of the levels in different rotational bands and also different mass regions. Also, the displacement of levels and the lower energy of state in comparison with level reduce the correlation of levels in spectral statistics.

The application of relativistic energy density functionals to the description of nuclei leads to the problem of solving self-consistently a coupled set of equations of motion to determine the nucleon wave functions and meson fields. In this work, the Lagrange-mesh method in spherical coordinates is proposed for numerical calculations. The essential field equations are derived from the relativistic energy density functional and the basic principles of the Lagrange-mesh method are delineated for this particular application. The numerical accuracy is studied for the case of a deformed relativistic harmonic oscillator potential with axial symmetry. Then the method is applied to determine the point matter distributions and deformation parameters of self-conjugate even-even nuclei from 4He to 40Ca.

Interaction energy between two nuclei considering to their deformations is studied. Coulomb and nuclear in-teraction energies, as well as the deformation energies of both nuclei, are taken into account at evaluation of the interaction energy. It is shown that the barrier related to the interaction energy of two nuclei depends on the de-formations and the height of the minimal barrier is evaluated. It is obtained that the heavier nucleus-nucleus sys-tems have large deformation values at the lowest barrier. The difference between the barrier between spherical nuclei and the lowest barrier between deformed nuclei increases with the mass and the charge of the interacting nuclei.