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We employ the non-perturbative time-dependent basis function (tBF) approach to study the scattering of the deuteron on $^{208}$Pb below the Coulomb barrier. We obtain the bound and discretized scattering states of the projectile, which form the basis representation of the tBF approach, by diagonalizing a realistic Hamiltonian in a large harmonic oscillator basis. We find that the higher-order inelastic scattering effects are noticeable for sub barrier scatterings with the tBF method. We have successfully reproduced experimental sub Coulomb barrier elastic cross section ratios with the tBF approach by considering only the electric dipole ($\mathit{E1}$) component of the Coulomb interaction between the projectile and the target during scatterings. We find that the correction of the polarization potential to the Rutherford trajectory is dominant in reproducing the data at very low bombarding energies, whereas the role of internal transitions of the deuteron projectile induced by the $\mathit{E1}$ interaction during the scattering becomes increasingly significant at higher bombarding energies., Comment: 12 pages, 6 figures, 1 table

In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, nuclear bubble configuration in the hypothetical $^{48}$Si nucleus is studied by proton induced central reaction at an incident beam energy of 0.8 GeV/nucleon. It is found that along the beam direction more energetic protons are emitted with bubble configuration in the target. In the forward angles, compared with the case without bubble configuration, less scattered energetic protons are emitted with bubble configuration in the target. We thus provide a new way to probe the bubble configuration in nuclei., Comment: 4 pages, 4 figures, accepted by PRC, Rapid Communication

Based on the Isospin-dependent transport model Boltzmann-Uehling-Uhlenbeck (IBUU), effects of the difference of the high momentum tails (HMTs) of nucleon momentum distribution in colliding nuclei on some isospin-sensitive observables are studied in the $^{197}\rm {Au}+^{197}\rm {Au}$ reactions at incident beam energy of 400 MeV/nucleon. It is found that the nucleon transverse and elliptic flows, the free neutron to proton ratio at low momenta are all less sensitive to the specific form of the HMT, while the free neutron to proton ratio at high momenta and the yields of $\pi^{-}$ and $\pi^{+}$ as well as the $\pi^{-}/\pi^{+}$ ratio around the Coulomb peak are sensitive to the specific form of the HMT. Combining the present studies with the experimental measurements at rare-isotope reaction facilities worldwide, one may get more insights into the nuclear short-range correlations in heavy nuclei or nuclear matter., Comment: 5 pages, 8 figures, accepted by PRC

In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, sensitive regions of some nucleon observables to the nuclear symmetry energy are studied. It is found that the symmetry energy sensitive observable n/p ratio in the $^{132}$Sn+$^{124}$Sn reaction at 0.3 GeV/nucleon in fact just probes the density-dependent symmetry energy below the density of $1.5\rho_0$ and effectively probes the density-dependent symmetry energy around or somewhat below the saturation density. Nucleon elliptic flow can probe the symmetry energy from the low-density region to the high-density region when changing the incident beam energies from 0.3 to 0.6 GeV/nucleon in the semi-central $^{132}$Sn+$^{124}$Sn reaction. And nucleon transverse and elliptic flows in the semi-central $^{197}$Au+$^{197}$Au reaction at 0.6 GeV/nucleon are more sensitive to the high-density behavior of the nuclear symmetry energy. One thus concludes that nucleon observables in the heavy reaction system and with higher incident beam energy are more suitable to be used to probe the high-density behavior of the symmetry energy. The present study may help one to get more specific information about the density-dependent symmetry energy from nucleon flow observable in heavy-ion collisions at intermediate energies., Comment: 5 pages, 6 figures

The studies, from several independent methods, consistently show that $\pi^-/\pi^+$ ratio in the $^{132}$Sn+$^{124}$Sn reaction at 300 MeV/nucleon, which is being carried out at Radioactive Isotope Beam Facility (RIBF) in Japan, just probes the symmetry energy around saturation density., Comment: 6 pages, 6 figures, accepted by Journal of Physics G: Nuclear and Particle Physics

Based on the isospin-dependent Boltzmann-Uehling-Uhlenbeck(IBUU) transport model, effects of $\Delta$ resonance potential on the free n/p and $\pi^-/\pi^+$ ratios in the central collision of $^{197}Au+^{197}Au$ at beam energies of 200 and 400 MeV/A are studied. It is found that the effect of $\Delta$ potential on the ratio of pre-equilibrium free $n/p$ is invisible. The effect of $\Delta$ isovector potential on the kinetic energy integrating ratio of $\pi^-/\pi^+$ may be observable only at lower incident beam energies and with stiffer symmetry energy. The strength of the $\Delta$ isoscalar potential affects the height of the $\pi^-/\pi^+$ ratio around the Coulomb peak but does not affect the kinetic energy integrating ratio of $\pi^-/\pi^+$. In heavy-ion collisions at intermediate energies, relating to the question of non-conservation of energy on $\Delta$ or $\pi$ productions, one can replace the $\Delta$ potential by nucleon isoscalar potential especially a soft symmetry energy is employed., Comment: 5 pages, 9 figures, revised version, accepted by PRC

Within the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck(IBUU) transport model, we studied the effects of the pion potential and the symmetry energy on the pion production in the central $^{197}Au+^{197}Au$ collisions around the pion production threshold. It is found that the pion potential has opposite effects on the value of $\pi^-/\pi^+$ ratio at low and high pion energies. The effect of the pion potential on the total $\pi^-/\pi^+$ ratio becomes larger in heavy-ion collisions at beam energies below the pion production threshold. And at beam energies below the pion production threshold, with the pion potential, the effect of the symmetry energy on the $\pi^-/\pi^+$ ratio becomes smaller compared with that above the pion production threshold., Comment: 13 pages, 10 figures, PRC in production

Within two different frameworks of isospin-dependent transport model, effect of nuclear symmetry energy at supradensities on the isospin-fractionation (IsoF) was investigated. With positive/negative symmetry potential at supradensities (i.e., values of symmetry energy increase/decrease with density above saturation density), for energetic nucleons, the value of neutron to proton ratio of free nucleons is larger/smaller than that of bound nucleon fragments. Compared with extensively studied quantitative observables of nuclear symmetry energy, the normal or abnormal isospin-fractionation of energetic nucleons can be a qualitative probe of nuclear symmetry energy at supradensities., Comment: 5 pages, 5 figures, accepted by Physics Letters B

We extract the mass-dependent symmetry energy coefficients $a_{\text{sym}}({A})$ with the nuclear mass differences reducing the uncertainties as far as possible. The estimated $a_{\text{sym}}({A})$ of $^{208}\text{Pb}$ is $22.4\pm 0.3 $ MeV, which is further used to analyze the density-dependent nuclear matter symmetry energy at subsaturation densities. The slope parameter of the symmetry energy at the saturation density $\rho_{0}$ is $L=50.0\pm15.5$ MeV. Furthermore, it is found that, at the density of $\rho=0.69\rho_{0}=0.11$fm$^{-3}$, the symmetry energy $S(\rho=0.11\text{fm}^{-3})=25.98\pm0.01$ MeV and the correspondingly slope parameter is $L=49.6\pm6.2$ MeV, which are consistent with other independent analysis., Comment: 4 pages, 1 figure

Within two different frameworks of isospin-dependent transport model, i.e., Boltzmann-Uehling-Uhlenbeck (IBUU04) and Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport models, sensitive probes of nuclear symmetry energy are simulated and compared. It is shown that neutron to proton ratio of free nucleons, pi-/pi+ ratio as well as isospin-sensitive transverse and elliptic flows given by the two transport models with their "best settings", all have obvious differences. Discrepancy of numerical value of isospin-sensitive n/p ratio of free nucleon from the two models mainly originates from different symmetry potentials used and discrepancies of numerical value of charged pi-/pi+ ratio and isospin-sensitive flows mainly originate from different isospin-dependent nucleon-nucleon cross sections. These demonstrations call for more detailed studies on the model inputs (i.e., the density- and momentum-dependent symmetry potential and the isospin-dependent nucleon-nucleon cross section in medium) of isospin-dependent transport model used. The studies of model dependence of isospin sensitive observables can help nuclear physicists to pin down the density dependence of nuclear symmetry energy through comparison between experiments and theoretical simulations scientifically., Comment: 9 pages, 7 figures, more discussions added, accepted by Phys. Lett. B

We have investigated the effect of tensor correlations on the depletion of nuclear Fermi sea in symmetric nuclear matter within the framework of the extended Brueckner-Hartree-Fock approach by adopting the AV18 two-body interaction and a microscopic three-body force. The contributions from various partial wave channels including the isospin-singlet T=0 channel, the isospin-triplet T=1 channel and the T=0 tensor 3SD1 channel have been calculated. The T=0 neutron-proton correlations play a dominated role in causing the depletion of nuclear Fermi sea. The T=0 correlation-induced depletion turns out to stem almost completely from the $^3SD_1$ tensor channel. The isospin-singlet T=0 3SD1 tensor correlations is shown to response for most of the depletion, which amounts to more than 70 percent out of the total depletion in the density region considered. The TBF turns out to leads to an enhancement of the depletion at high densities well above the empirical saturation density and its effect increases as a function of density., Comment: 5 pages, 3 figures. arXiv admin note: text overlap with arXiv:1301.3218

Within the framework of the Brueckner theory, the off-shell behaviors of the mass operator $M(k,\omega)=V(k,\omega)+iW(k,\omega)$, i.e., its dependence upon the momentum $k$ and upon the nucleon frequency $\omega$, are investigated by including nuclear three-body force (TBF). The first two terms of the hole-line expansion of the mass operator are taken into account. The TBF effects on their off-shell properties are discussed. A comparison is made between the on-shell and off-shell values of $M_{1}$. The nucleon spectral function and nucleon momentum distribution are also calculated, and the calculation shows that they are hardly affected by the TBF effect at the saturation density. At a high density two times greater than the saturation density, inclusion of the TBF may lead to a visible effect on the spectral function and may enhance the depletion of the hole states., Comment: 16 pages, 7 figures

We have investigated the three-body force (TBF) effect on the neutron and proton momentum distributions in asymmetric nuclear matter within the framework of the extended Brueckner-Hartree-Fock approach by adopting the $AV18$ two-body interaction plus a microscopic TBF. In asymmetric nuclear matter, it is shown that the neutron and proton momentum distributions become different from their common distribution in symmetric nuclear matter. The predicted depletion of the proton hole states increases while the neutron one decreases as a function of isospin-asymmetry. The TBF effect on the neutron and proton momentum distributions turns out to be negligibly weak at low densities around and below the normal nuclear density. The TBF effect is found to become sizable only at high densities well above the saturation density, and inclusion of the TBF leads to an overall enhancement of the depletion of the neutron and proton Fermi seas., Comment: 9 pages, 4 figures

Based on the Skyrme energy density functional, the spatial distribution of the symmetry energy of a finite nucleus is derived in order to examine whether the symmetry energy of a finite nucleus originates from its interior or from its surface. It is found that the surface part of a heavy nucleus contributes dominantly to its symmetry energy compared to its inner part. The symmetry energy coefficient $a_{\text{sym}}({A})$ is then directly extracted and the ratio of the surface symmetry coefficient to the volume symmetry coefficient $\kappa$ is estimated. Meanwhile, with the help of experimental alpha decay energies, a macroscopic method is developed to determine the symmetry energy coefficient of heavy nuclei. The resultant $a_{\text{sym}}({A})$ is used to analyze the density dependence of the symmetry energy coefficient of nuclear matter around the saturation density, and furthermore, the neutron skin thickness of $^{208}\text{Pb}$ is deduced which is consistent with the pygmy dipole resonance analysis. In addition, it is shown that the ratio $\kappa$ obtained from the macroscopic method is in agreement with that from the Skyrme energy density functional. Thus the two completely different approaches may validate each other to achieve more compelling results., Comment: 6 pages, 3 figures, to appear in Phys. Rev. C

We establish a correlation for the symmetry energy at saturation density $S_{0}$, slope parameter $L$ and curvature parameter $K_{\text{sym}}$ based on widely different mean field interactions. With the help of this correlation and available empirical and theoretical information, the density dependent behavior around the saturation density is determined. We compare the results obtained with the present approach with those by other analyses. With this obtained density dependent behavior of the symmetry energy, the neutron skin thickness of $^{208}$Pb and some properties of neutron stars are investigated. In addition, it is found that the expression $S(\rho)=S_{0}(\rho /\rho_{0})^{\gamma}$ or $S(\rho)=12.5(\rho /\rho_{0}) ^{2/3}+C_{p}(\rho /\rho_{0}) ^{\gamma}$ does not reproduce the density dependence of the symmetry energy as predicted by the mean-field approach around nuclear saturation density., Comment: 6 pages, 4 figures

We review our research work on the single-particle properties and the equation of state (EOS) of isospin asymmetric nuclear matter within the framework of the Brueckner-Hartree-Fock (BHF) approach extended by including a microscopic three-body force (TBF). The TBF is shown to affect significantly the nuclear matter EOS and the density dependence of nuclear symmetry energy at high densities above the normal nuclear matter density, and it is necessary for reproducing the empirical saturation property of symmetric nuclear matter in a nonrelativistic microscopic framework. The TBF-induced rearrangement effect and the ground state (g.s.) correlation effect on the s.p. properties in neutron-rich nuclear matter are investigated. Both effects turn out to be crucial for predicting reliably the s.p. properties within the Brueckner framework. The TBF effect on nucleon superfluidity in neutron star matter and neutron stars has also been discussed., Comment: Invited Talk given at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS)

Based on the Boltzmann-Uehling-Uhlenbeck (BUU) transport model coupled with a phase-space coalescence afterburner, spallation reaction of $p+^{197}Au$ at the incident beam energy of E$_{beam}$= 800 MeV/nucleon is studied. We find that the number of test particles per nucleon has minor effects on the neutron to proton ratio (n/p) of the produced heavier fragments while it affects much on their yields. The external strong magnetic field affects the production of heavier fragments much than the n/p of produced fragments. The n/p of free nucleons is greatly affected by the strong magnetic field, especially for the nucleons with lower energies., Comment: 5 pages, 6 figures, revised, accepted by EPL

A formula for the relationship between the $\alpha$-decay energies ($Q$ values) of superheavy nuclei (SHN) is presented, which is composed of the effects of Coulomb energy and symmetry energy. It can be employed not only to validate the experimental observations and measurements to a large extent, but also to predict the $Q$ values of heaviest SHN with a high accuracy generally which will be very useful for future experiments. Furthermore, the shell closures in superheavy region and the effect of the symmetry energy on the stability of SHN against $\alpha$-decay are discussed with the help of this formula., Comment: 2 figures

The alpha decay half-lives of recently synthesized superheavy nuclei (SHN) are calculated by applying a new approach which estimates them with the help of their neighbors based on some simple formulas. The estimated half-life values are in very good agreement with the experimental ones, indicating the reliability of the experimental observations and measurements to a large extent as well as the predictive power of our approach. The second part of this work is to test the applicability of the Wentzel-Kramers-Brillouin (WKB) approximation for the quantum mechanical tunneling probability. We calculated the accurate barrier penetrability for alpha decay along with proton and cluster radioactivity by numerically solving Schr\"odinger equation. The calculated results are compared with those of the WKB method to find that WKB approximation works well for the three physically analogical decay modes., Comment: 3 figures

Hard photon production from neutron-proton bremsstrahlung in intermediate energy heavy-ion reactions is examined as a probe of the in-medium pn scattering cross section within a transport model. Uncertainty of photon production probability pn-pngamma is cancelled out by using the ratio of hard photon spectra R_{12C+12C/p+n}(gamma) from two reactions. The in medium pn scattering cross section is constrained by using the ratio of hard photon production cross sections of proton-induced reactions p+12C and p+2H. A reduction factor sigma_pn^medium/sigma_pn^free of about 0.5 ~ 0.7 around saturation density is obtained by comparing with the existing experimental data., Comment: 9 pages, 3 figures, accepted by PLB

Based on a Relativistic Boltzmann-Uehling- Uhlenbeck transport model, proton and $^{3}$He induced reactions on $^{197}$Au target at beam energies of 2.8, 5, 10 and 16.587 GeV/nucleon are studied. It is found that compared with proton induced reactions, $^{3}$He induced reactions give larger cross sections of pion production, about 5 times those of the proton induced reactions. And more importantly, pion production from $^{3}$He induced reaction is more inclined to low-angle emission. Neutrino production via positively charged pion is also discussed accordingly., Comment: 5 pages, 11 figures, one figure(fig9) was added to show the scaling behavior of pion production, AMPT calculations were discussed, accepted by PRC

The alpha-decay half-lives of recently synthesized superheavy nuclei (SHN) are investigated based on a unified fission model (UFM) where a new method to calculate the assault frequency of alpha-emission is used. The excellent agreement with the experimental data indicates the UFM is a useful tool to investigate these alpha-decays. It is found that the half-lives become more and more insensitive to the Q_alpha values as the atomic number increases on the whole, which is favorable for us to predict the half-lives of SHN. In addition, a formula is suggested to compute the Q_alpha values for the nuclei with Z > 92 and N > 140 with a good accuracy, according to which the long-lived SHN should be neutron rich. With Q_alpha values from this formula as inputs, we predict the half-lives of isotopes of Z = 117, which may be useful for experimental identication in the future., Comment: 7 pages, 3 figures

The alpha decay half-lives of the recently produced isotopes of the 112, 114, 116 and 118 nuclei and decay products have been calculated in the quasi-molecular shape path using the experimental Qalpha value and a Generalized Liquid Drop Model including the proximity effects between nucleons in the neck or the gap between the nascent fragments. Reasonable estimates are obtained for the observed alpha decay half-lives. The results are compared with calculations using the Density-Dependent M3Y effective interaction and the Viola-Seaborg-Sobiczewski formulae. Generalized Liquid Drop Model predictions are provided for the alpha decay half-lives of other superheavy nuclei using the Finite Range Droplet Model Qalpha and compared with the values derived from the VSS formulae.

Based on an isospin- and momentum-dependent hadronic transport model IBUU04, effects of the nuclear symmetry energy on the single and double pi^{-}/pi^{+}ratios in central reactions of ^{132}Sn+^{124}Sn and ^{112}Sn+^{112}Sn at a beam energy of 400 MeV/nucleon are studied. It is found that around the Coulomb peak of the single pi^{-}/pi^{+} ratio the double pi^{-}/pi^{+} ratio taken from the two isotopic reactions retains about the same sensitivity to the density dependence of nuclear symmetry energy. Because the double pi^{-}/pi^{+}ratio can reduce significantly the systematic errors, it is thus a more effective probe for the high-density behavior of the nuclear symmetry energy., Comment: 11 pages, 3 figures, to appear in Physics Review C

The double neutron/proton ratio of nucleon emissions taken from two reaction systems using four isotopes of the same element, namely, the neutron/proton ratio in the neutron-rich system over that in the more symmetric system, has the advantage of reducing systematically the influence of the Coulomb force and the normally poor efficiencies of detecting low energy neutrons. The double ratio thus suffers less systematic errors. Within the IBUU04 transport model the double neutron/proton ratio is shown to have about the same sensitivity to the density dependence of nuclear symmetry energy as the single neutron/proton ratio in the neutron-rich system involved. The double neutron/proton ratio is therefore more useful for further constraining the symmetry energy of neutron-rich matter.

Major ingredients of an isospin and momentum dependent transport model for nuclear reactions induced by radioactive beams are outlined. Within the IBUU04 version of this model we study several experimental probes of the equation of state of neutron-rich matter, especially the density dependence of the nuclear symmetry energy. Comparing with the recent experimental data from NSCL/MSU on isospin diffusion, we found a nuclear symmetry energy of $% E_{sym}(\rho )\approx 31.6(\rho /\rho_{0})^{1.05}$ at subnormal densities. Predictions on several observables sensitive to the density dependence of the symmetry energy at supranormal densities accessible at GSI and the planned Rare Isotope Accelerator (RIA) are also made., Comment: 10 pages. Talk given at the 2nd Argonne/MSU/JINA/INT RIA Workshop at MSU, March 9-12, 2005 to be published in the Proceedings by the American Institute of Physics

The latest development in determining the density dependence of the nuclear symmetry energy using heavy-ion collisions is reviewed. Within the IBUU04 version of an isospin- and momentum-dependent transport model using a modified Gogny effective interaction, recent experimental data from NSCL/MSU on isospin diffusion are found to be consistent with a nuclear symmetry energy of $E_{sym}(\rho)\approx 31.6(\rho /\rho_{0})^{1.05}$ at subnormal densities. Predictions on several observables sensitive to the density dependence of the symmetry energy at supranormal densities accessible at GSI and the planned Rare Isotope Accelerator (RIA) are also made., Comment: 10 pages. Talk given at the 21st Winter Workshop on Nuclear Dynamics, Breckenridge, Colorado, USA, Feb. 5-12, 2005. To appear in Heavy-Ion Physics (2005)

Using an isospin- and momentum-dependent transport model we study the emission of free nucleons and the nuclear radial flow in central heavy-ion collisions induced by high energy radioactive beams. The midrapidity neutron/proton ratio and its transverse momentum dependence are found very sensitive to the high density behavior of nuclear symmetry energy. The nuclear radial flow, however, depends only weakly on the symmetry energy., Comment: 13 pages including 6 figures, submitted to Phys. Rev. C

Using an isospin- and momentum-dependent transport model we study near-threshold pion production in heavy-ion collisions induced by radioactive beams at the planned Rare Isotope Accelerator (RIA). We revisit the question of probing the high density behavior of nuclear symmetry energy $E_{sym}(\rho)$ using the $\pi^-/\pi^+$ ratio. It is found that both the total and differential $\pi^-/\pi^+$ ratios remain sensitive to the $E_{sym}(\rho)$ when the momentum-dependence of both the isoscalar and isovector potentials are consistently taken into account. Moreover, the multiplicity and spectrum of $\pi^-$ mesons are found more sensitive to the $E_{sym}(\rho)$ than those of $\pi^+$ mesons. Finally, effects of the Coulomb potential on the pion spectra and $\pi^-/\pi^+$ ratio are also discussed., Comment: 22 pages including 10 figures, submitted to Phys. Rev. C