Ren Zhong-Zhou

Exact Solutions to Three-Dimensional Schrödinger Equation with an Exponentially Position-Dependent Mass

For an exponentially position-dependent mass, we obtain the exact solutions of the three-dimensional Schrodinger equation by using coordinate transformation method for the reference problems with Coulomb potential, Kratzer potential, and spherically square potential well of infinite depth, respectively. The explicit expressions for the energy eigenvalues and the corresponding eigenfunctions of the three systems are presented.

Entanglement dynamics of a Heisenberg chain with Dzyaloshinskii–Moriya interaction

This paper investigates the entanglement dynamics of the system, composed of two qubits A and B with Heisenberg XX spin interactation. There is a third controller qubit C, which only has Dzyaloshinskii–Moriya (DM) spin-orbit interaction with the qubit B. It is found that depending on the initial state of the controller qubit C and DM interaction, the entanglement of the system displays amplification and sudden birth effects. These effects indicate that one can control the entanglement of the system, which may be helpful for quantum information processing.

Supersymmetry and Solution of Dirac Equation with Vector and Scalar Potentials

The Dirac equations with vector and scalar potentials of the Coulomb types in two and three dimensions are solved using the supersymmetric quantum mechanics method. For the system of such potentials, the analytical expressions of the matrix elements for both position and momentum operators are obtained.

Total nuclear reaction cross section induced by halo nuclei and stable nuclei

We develop a method for calculation of the total reaction cross sections induced by the halo nuclei and stable. nuclei. This approach is based on the Glauber theory, which is valid for nuclear reactions at high energies. It is extended for nuclear reactions at low energies and intermediate energies by including both the quantum correction and Coulomb correction under the assumption of the effective nuclear density distribution. The calculated results of the total reaction cross section induced by stable nuclei agree well with 30 experimental data within 10 percent accuracy. The comparison between the numerical results and 20 experimental data for the total nuclear reaction cross section induced by the neutron halo nuclei and the proton halo nuclei indicates a satisfactory agreement after considering the halo structure of these nuclei, which implies quite different mean fields for the nuclear reactions induced by halo nuclei and stable nuclei. The halo nucleon distributions and the root-mean-square radii of these nuclei can be extracted from the above comparison based on the improved Glauber model, which indicates clearly the halo structures of these nuclei. Especially, it is clear to see that the medium correction of the nucleon-nucleon collision has little effect on the total reaction cross sections induced by the halo nuclei due to the very, weak binding and the very extended density distribution.We develop the method for the calculation of the total reaction cross sections induced by the halo nuclei and stable nuclei. This approach is based on the Glauber theory, which is valid for nuclear reactions at high energy. It is extended for nuclear reactions at low energy and intermediate energy by including both the quantum correction and Coulomb correction under the assumption of the effective nuclear density distribution. The calculated results of the total reaction cross section induced by stable nuclei agree well with the 30 experimental data within 10 percent accuracy.The comparison between the numerical results and the 20 experimental data for the total nuclear reaction cross section induced by the neutron halo nuclei and the proton halo nuclei indicates a satisfactory agreement after considering the halo structure of these nuclei, which implies the quite different mean fields for the nuclear reactions induced by halo nuclei and stable nuclei. The halo nucleon distributions and the root mean square radii of these nuclei can be extracted from above comparison based on the improved Glauber model, which indicate clearly the halo structures of these nuclei. Especially, it is clear to see that the medium correction of the nucleon-nucleon collision has little effect on the total reaction cross sections induced by the halo nuclei due to the very weak binding and the very extended density distribution.

Ground-State Bands of Fm and No Isotopes in Cluster Model

We investigate the ground-state rotational bands of nuclei with Z≥100 using cluster model proposed by Buck et al. [Phys. Rev. Lett. 94 (2005) 202501]. The core-cluster decomposition of each nucleus is determined by the corresponding electric quadrupole transition strength B(E2:2+→0+). The theoretical spectra of fermium and nobelium isotopes are compared with available experimental data. Good agreement between model and data is obtained.

Theoretical Calculation for Half-Lives of Spherical Proton Emitters

Half-lives of the proton radioactivity for spherical proton emitters are investigated theoretically in the Wentzel-Kramers-Brillouin approximation. Microscopic proton-nucleus interaction potentials are obtained by folding the densities of the residual daughter nuclei with renormalized M3Y effective interactions. We also take the spectroscopic factor (Sp) into account in the calculation, which is evaluated in the relativistic mean field approach using the force NL3. The calculated results are found to be in good agreement with the experimental data.

Generalized Harmonic Oscillator and the Schrödinger Equation with Position-Dependent Mass

We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties for the system with PDM are also discussed. We give the corresponding effective potentials for several mass functions, the systems with such potentials are isospectral to the usual harmonic oscillator.

Benford's Law and β-Decay Half-Lives

The experimental values of 2059 β-decay half-lives are systematically analyzed and investigated. We have found that they are in satisfactory agreement with Benfords law, which states that the frequency of occurrence of each figure, 1–9, as the first significant digit in a surprisingly large number of different data sets follows a logarithmic distribution favoring the smaller ones. Benfords logarithmic distribution of β-decay half-lives can be explained in terms of Newcombs justification of Benfords law and empirical exponential law of β-decay half-lives. Moreover, we test the calculated values of 6721 β-decay half-lives with the aid of Benfords law. This indicates that Benfords law is useful for theoretical physicists to test their methods for calculating β-decay half-lives.

Proton Halo or Skin in the Excited States of Light Nuclei

Properties of nuclei N-13,N-15 and B-9 are investigated in the relativistic mean-field theory with NLZ and NL3 force parameters. The calculated binding energies are very close to the experimental ones. The calculations show that the first excited state (1p(1/2)) in B-9, the first excited state (2s(1/2)) in N-13 and the second excited state (2s(1/2)) in N-15 are weakly bound. In particular, for N-13 and N-15, the proton density distributions in the two above excited states have a long tail and the rms radii of the last proton are greatly larger compared with their respective matter radii. It is predicted that a proton halo exists in the first excited state of N-13 and in the second excited state of N-15, respectively. It also indicates that the first excited state in B-9 is a proton skin state.

Localization of s-Wave and Quantum Effective Potential of a Quasi-free Particle with Position-Dependent Mass

The properties of the s-wave for a quasi-free particle with position-dependent mass (PDM) have been discussed in details. Differed from the system with constant mass in which the localization of the s-wave for the free quantum particle around the origin only occurs in two dimensions, the quasi-free particle with PDM can experience attractive forces in D dimensions except D = 1 when its mass function satisfies some conditions. The effective mass of a particle varying with its position can induce effective interaction, which may be attractive in some cases. The analytical expressions of the eigenfunctions and the corresponding probability densities for the s-waves of the two- and three-dimensional systems with a special PDM are given, and the existences of localization around the origin for these systems are shown.