Covariant description of shape evolution and shape coexistence in neutron-rich nuclei at N\approx60

The shape evolution and shape coexistence phenomena in neutron-rich nuclei at $N\approx60$, including Kr, Sr, Zr, and Mo isotopes, are studied in the covariant density functional theory (DFT) with the new parameter set PC-PK1. Pairing correlations are treated using the BCS approximation with a separable pairing force. Sharp rising in the charge radii of Sr and Zr isotopes at N=60 is observed and shown to be related to the rapid changing in nuclear shapes. The shape evolution is moderate in neighboring Kr and Mo isotopes. Similar as the results of previous Hartree-Fock-Bogogliubov (HFB) calculations with the Gogny force, triaxiality is observed in Mo isotopes and shown to be essential to reproduce quantitatively the corresponding charge radii. In addition, the coexistence of prolate and oblate shapes is found in both $^{98}$Sr and $^{100}$Zr. The observed oblate and prolate minima are related to the low single-particle energy level density around the Fermi surfaces of neutron and proton respectively. Furthermore, the 5-dimensional (5D) collective Hamiltonian determined by the calculations of the PC-PK1 energy functional is solved for $^{98}$Sr and $^{100}$Zr. The resultant excitation energy of $0^+_2$ state and E0 transition strength $\rho^2(E0;0^+_2\rightarrow0^+_1)$ are in rather good agreement with the data. It is found that the lower barrier height separating the two competing minima along the $\gamma$ deformation in $^{100}$Zr gives rise to the larger $\rho^2(E0;0^+_2\rightarrow0^+_1)$ than that in $^{98}$Sr.Comment: 1 table, 11 figures, 23 page

Channel Parameters Estimation Algorithm Based on The Characteristic Function under Impulse Noise Environment

Under communication environments, such as wireless sensor networks, the noise observed usually exhibits impulsive as well as Gaussian characteristics. In the initialization of channel iterative decoder, such as low density parity check codes, it is required in advance to estimate the channel parameters to obtain the prior information from the received signals. In this paper, a blind channel parameters estimator under impulsive noise environment is proposed, which is based on the empirical characteristic function in MPSK/MQAM higher-order modulation system. Simulation results show that for various MPSK/MQAM modulations, the estimator can obtain a more accurate unbiased estimation even though we do not know which kind of higher-order modulation is used

Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods

A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in momentum space with the help of the discrete Fourier transform, i.e., the spectral method. This method is demonstrated in solving the Dirac equation for a given spherical potential in 3D lattice space. In comparison with the results obtained by the shooting method, the differences in single particle energy are smaller than $10^{-4}$~MeV, and the densities are almost identical, which demonstrates the high accuracy of the present method. The results obtained by applying this method without any modification to solve the Dirac equations for an axial deformed, non-axial deformed, and octupole deformed potential are provided and discussed.Comment: 18 pages, 6 figure

Energy-dependent Lorentz covariant parameterization of the NN interaction between 50 and 200 MeV

For laboratory kinetic energies between 50 and 200 MeV, we focus on generating an energy-dependent Lorentz covariant parameterization of the on-shell nucleon-nucleon (NN) scattering amplitudes in terms of a number of Yukawa-type meson exchanges in first-order Born approximation. This parameterization provides a good description of NN scattering observables in the energy range of interest, and can also be extrapolated to energies between 40 and 300 MeV.Comment: 18 pages, 7 figures, Final version accepted by Physics Review

Nuclear quantum shape-phase transitions in odd-mass systems

Microscopic signatures of nuclear ground-state shape phase transitions in odd-mass Eu isotopes are explored starting from excitation spectra and collective wave functions obtained by diagonalization of a core-quasiparticle coupling Hamiltonian based on energy density functionals. As functions of the physical control parameter -- the number of nucleons -- theoretical low-energy spectra, two-neutron separation energies, charge isotope shifts, spectroscopic quadrupole moments, and $E2$ reduced transition matrix elements accurately reproduce available data, and exhibit more pronounced discontinuities at neutron number $N=90$, compared to the adjacent even-even Sm and Gd isotopes. The enhancement of the first-order quantum phase transition in odd-mass systems can be attributed to a shape polarization effect of the unpaired proton which, at the critical neutron number, starts predominantly coupling to Gd core nuclei that are characterized by larger quadrupole deformation and weaker proton pairing correlations compared to the corresponding Sm isotopes.Comment: 6 pages, 4 figure

Microscopic Analysis of Order Parameters in Nuclear Quantum Phase Transitions

Microscopic signatures of nuclear ground-state shape phase transitions in Nd isotopes are studied using excitation spectra and collective wave functions obtained by diagonalization of a five-dimensional Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. As a function of the physical control parameter -- the number of nucleons, energy gaps between the ground state and the excited vibrational states with zero angular momentum, isomer shifts, and monopole transition strengths, exhibit sharp discontinuities at neutron number N=90, characteristic of a first-order quantum phase transition.Comment: 5 pages, 4 figures, accepted for publication as a Rapid Communication in Physical Review

Low-lying states in 30^{30}Mg: a beyond relativistic mean-field investigation

The recently developed model of three-dimensional angular momentum projection plus generator coordinate method on top of triaxial relativistic mean-field states has been applied to study the low-lying states of $^{30}$Mg. The effects of triaxiality on the low-energy spectra and E0 and E2 transitions are examined.Comment: 6 pages, 3 figures, 1 table, talk presented at the 17th nuclear physics conference "Marie and Pierre Curie" Kazimierz Dolny, 22-26th September 2010, Polan

New parametrization for the nuclear covariant energy density functional with point-coupling interaction

A new parametrization PC-PK1 for the nuclear covariant energy density functional with nonlinear point-coupling interaction is proposed by fitting to observables for 60 selected spherical nuclei, including the binding energies, charge radii and empirical pairing gaps. The success of PC-PK1 is illustrated in its description for infinite nuclear matter and finite nuclei including the ground-state and low-lying excited states. Particularly, PC-PK1 improves the description for isospin dependence of binding energy along either the isotopic or the isotonic chains, which makes it more reliable for application in exotic nuclei. The predictive power of PC-PK1 is also illustrated for the nuclear low-lying excitation states in a five-dimensional collective Hamiltonian in which the parameters are determined by constrained calculations for triaxial shapes.Comment: 32 pages, 12 figures, 4 tables, accepted by Phys. Rev.

Rapid structural change in low-lying states of neutron-rich Sr and Zr isotopes

The rapid structural change in low-lying collective excitation states of neutron-rich Sr and Zr isotopes is tudied by solving a five-dimensional collective Hamiltonian with parameters determined by both relativistic mean-field and non-relativistic Skyrme-Hartree-Fock calculations using the PC-PK1 and SLy4 forces respectively. Pair correlations are treated in BCS method with either a separable pairing force or a density-dependent zero-range force. The isotope shifts, excitation energies, electric monopole and quadrupole transition strengths are calculated and compared with corresponding experimental data. The calculated results with both the PC-PK1 and SLy4 forces exhibit a picture of spherical-oblate-prolate shape transition in neutron-rich Sr and Zr isotopes. Compared with the experimental data, the PC-PK1 (or SLy4) force predicts a more moderate (or dramatic) change in most of the collective properties around N=60. The underlying microscopic mechanism responsible for the rapid transition is discussed.Comment: 10 pages (twocolumn), 10 figure