Entrance channel effects on the role of isospin-dependent momentum interaction in isospin fractionation in heavy ion collisions

An isospin degree of freedom is inserted into the momentum dependent interaction in the quantum molecular dynamics model to obtain an isospin dependent momentum interaction given in a form practically usable in isospin dependent quantum molecular dynamics model. We investigate the entrance channel effects for the role of isospin momentum dependent interaction on the isospin fractionation ratio and its dynamical mechanism in the intermediate energy heavy ion collisions. It is found that the isospin dependent momentum interaction induces a significant reduction of isospin fractionation ratio under all entrance channel conditions. However the strong dependence of isospin fractionation ratio on the symmetry potential is preserved after considering the isospin degree of freedom in the momentum dependent interaction.

Circumstantial Evidence for a Soft Nuclear Symmetry Energy at Suprasaturation Densities

Within an isospin- and momentum-dependent hadronic transport model, it is shown that the recent FOPI data on the pi(-)/pi(+) ratio in central heavy-ion collisions at SIS/GSI energies [Willy Reisdorf , Nucl. Phys. A 781, 459 (2007)] provide circumstantial evidence suggesting a rather soft nuclear symmetry energy E-sym(rho) at rho >= 2 rho(0) compared to the Akmal-Pandharipande-Ravenhall prediction. Some astrophysical implications and the need for further experimental confirmations are discussed.

Effect of entrance-channel asymmetry on the isospin dependence of nucleon emission in heavy ion collisions

Using the isospin- and momentum-dependent hadronic transport model 1BUU04, we have investigated the influence of the entrance-channel isospin asymmetry on the sensitivity of the pre-equilibrium neutron/proton ratio to symmetry energy in central heavy-ion collisions induced by high-energy radioactive beams. Our analysis and discussion are based on the dynamical simulations of the three isotopic reaction Systems Sn-132+Sn-124, Sn-124+Sn-112 and Sn-112+(112)Su which are of the same total proton number but, different isospin asymmetry. We find that, the kinetic-energy distributions of the pre-equilibrium neutron/proton ratio are quite sensitive to the density-dependence of symmetry energy at incident beam energy E/A = 400 MeV, and the sensitivity increases as the isospin asymmetry of the reaction system increases.

Probing the medium effect and isospin dependence of the in-medium nucleon-nucleon cross section in heavy ion collisions

Probing in-medium nucleon-nucleon (NN) cross section sigma(1)(NN)(alpha) in heavy ion collisions has been investigated by means of the isospin-dependent quantum molecular dynamics (IQMD) with the isospin- and momentum- dependent interaction (IMDI(tau)). It is found that there are the very obvious medium effect and the sensitive isospin- dependence of nuclear stopping R on the in-medium NN cross section sigma(1)(NN)(alpha) in the nuclear reactions induced by halo-neutron projectile and the same-mass stable projectile. However, R induced by the neutron-halo projectile is obviously lower than that induced by the corresponding stable projectile. In particular, there is a very obvious dependence of R on the medium effect of sigma(1)(NN)(alpha) in the whole beam energy region for the above two kinds of projectiles. Therefore, the comparison between the results of R's in the reactions induced by the neutron-halo projectile and the corresponding same-mass stable projectile is a more favourable probe for extracting the information of sigma(1)(NN)(alpha) because of adding a new judgement.

Probing the high density behavior of the symmetry energy by using the free neutron-proton ratio

Based on the isospin- and momentum-dependent transport model IBUU04, the transverse momentum distributions of the free neutron-proton ratio in the Sn-132+(124) Sn reaction system at mid-central collisions with beam energies of 400/A MeV, 600/A MeV and 800/A MeV are studied by using two different symmetry energies. It is found that the free neutron-proton ratio as a function of the transverse momentum at the mid-rapidity is very sensitive to the density dependency of the symmetry energy especially at incident energies around 400/AMeV.

Probing the high density behavior of the symmetry energy by using proton elliptic flow

Based on the isospin- and momentum-dependent transport model IBUU04, we calculated the reaction of the Sn-132+Sn-124 systems in semi-central collisions at beam energies of 400/A MeV, 600/A MeV and 800/A MeV by adopting two different density dependent symmetry energies. It was found that the proton differential elliptic flow as a function of transverse momentum is quite sensitive to the density dependence of symmetry energy, especially for the considered beam energy range. Therefore the proton differential elliptic flow may be considered as a robust probe for investigating the high density behavior of symmetry energy in intermediate energy heavy ion collisions.

Double neutron-proton differential transverse flow as a probe for the high density behavior of the nuclear symmetry energy

The double neutron-proton differential transverse flow taken from two reaction systems using different isotopes of the same element is studied at incident beam energies of 400 and 800 MeV/nucleon within the framework of an isospin- and momentum-dependent hadronic transport model IBUU04. The double differential flow is found to retain about the same sensitivity to the density dependence of the nuclear symmetry energy as the single differential flow in the more neutron-rich reaction. Because the double differential flow reduces significantly both the systematic errors and the influence of the Coulomb force, it is thus more effective probe for the high-density behavior of the nuclear symmetry energy.

Probing the high density behavior of the symmetry energy by using the neutron-proton differential flow

Based on the isospin- and momentum-dependent transport model IBUU04, we investigated the neutron-proton differential flow in the (132) Sn + (124) Sn mid-central collisions at beam energies of 400MeV/A, 600MeV/A and 800MeV/A by adopting two different symmetry energies. It was found that the neutron-proton differential flow as a function of rapidity is very sensitive to the density dependence of symmetry energy, especially at incident energies around 400MeV/A

Three-body force rearrangement contribution to single nucleon potential in nuclear matter

Within the framework of microscopic Brueckner-Hatree-Fock, the contribution of the three-body force (TBF) rearrangement to the. single nucleon potential is calculated. The TBF rearrangement effects on the momentum and the density dependence of the single nucleon potential are investigated. The influence of the TBF rearrangement on the effective mass of nucleon is also discussed. It is shown that the rearrangement contribution of TBF is repulsive and momentum-dependent. The TBF rearrangement effect and its momentum dependence increase rapidly as increasing density and momentum. At high densities and high momenta, the repulsive rearrangement contribution reduces strongly the attraction of the single nucleon potential and enhances considerably the momentum dependence of the single nucleon potential.

Three-body force rearrangement effect on single particle properties in neutron-rich nuclear matter

We extend the Brueckner-Hartree-Fock (BHF) approach to include the three-body force (TBF) rearrangement contribution in calculating the neutron and proton single particle (s.p.) properties in isospin asymmetric nuclear matter. We investigate the TBF rearrangement effect on the momentum-dependence of neutron and proton s.p. potentials, the isospin splitting and especially its density dependence of the neutron and proton effective masses, and the isospin symmetry potential in neutron-rich nuclear matter by adopting the realistic Argonne V-18 two-body nucleon-nucleon interaction supplemented with a microscopic TBF. We find that at low densities, the TBF rearrangement effect is fairly weak, whereas the TBF induces a significant rearrangement effect on the s.p. properties at high densities and large momenta. The TBF rearrangement contribution to s.p. potential is shown to be repulsive, and it reduces considerably the attraction of the BHF s.p. potential. The repulsion from the TBF rearrangement turns out to be strongly momentum dependent at high densities and high momenta. As a consequence, it enhances remarkably the momentum dependence of the proton and neutron s.p. potentials and reduces the neutron and proton effective masses. At low densities, the TBF rearrangement effect on symmetry potential is almost negligible, while at high densities, it enlarges sizably the symmetry potential. At high enough densities, it may even change the high-momentum behavior of symmetry potential. In both cases, with and without including the TBF rearrangement contribution, the predicted neutron effective mass is larger than the proton one in neutron-rich matter within the BHF framework; i.e., the predicted isospin splitting of the proton and neutron effective masses in neutron-rich matter is such that m(n)(*)>= m(p)(*), in agreement with the recent Dirac-BHF predictions. The TBF rearrangement contribution reduces remarkably the magnitude of the proton-neutron effective mass splitting at high densities. At high enough densities, inclusion of the TBF rearrangement contribution even suppresses almost completely the effective mass splitting.

Single and double pi(-)/pi(+) ratios in heavy-ion reactions as probes of the high-density behavior of the nuclear symmetry energy

Based on the 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 Sn-132+Sn-124 and Sn-112+Sn-112 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 significantly reduce the systematic errors, it is thus a more effective probe for the high-density behavior of the nuclear symmetry energy.

System size and beam energy effects on probing the high-density behavior of nuclear symmetry energy with pion ratio

Based on the isospin-and momentum-dependent hadronic transport model IBUU04, we have investigated the pi(-)/pi(+) ratio in the following three reactions: Ca-48+Ca-48, Sn-124 +Sn-124 and Au-197+Au-197 with nearly the same isospin asymmetry but different masses, at the bombarding energies from 0.25 to 0.6 A GeV. It is shown that the sensitivity of probing the E-sym (rho) with pi(-)/pi(+) increases with increasing the system size or decreasing the beam energy, showing a correlation to the degree of isospin fractionation. Therefore, with a given isospin asymmetry, heavier system at energies near the pion threshold is preferential to study the behavior Of nuclear symmetry energy at supra-saturation densities.

Non-commutative oscillator with Kepler-type dynamical symmetry

A 3-dimensional non-commutative oscillator with no mass term but with an appropriate momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The trajectories lie on ellipses. The dynamical symmetry allows for an algebraic determination of the bound-state spectrum and extends to o(4,2). (c) 2010 Elsevier B.V. All rights reserved.

Probing balance energy using momentum- and isospin-dependent potential

Using the momentum- and isospin-dependent Boltmann-Uehling-Uhlenbeck (BUU) model, we investigate the transverse flow and balance energy in two isotopic colliding systems Ca-48+Fe-58 and Cr-48+Ni-58 by adopting different symmetry potentials. By comparing the results between the two colliding systems, we find that the difference between the balance energies of two isotopic systems can be considered as a sensitive probe to the density dependence of symmetry energy.

Kinetics and Force Dependence of P-selectin/PSGL-1 Interactions Measured by AFM

Leukocytes roll along the endothelium of postcapillary venules in response to inflammatory and thrombotic processes. The rolling under hydrodynamic shear forces is a first step in directing leukocytes out of the blood stream into sites of inflammation and is mediated by the selectins, a family of extended, modular, and calcium-dependent lectin receptors. The interactions between P-, E-or L-selectins and their count.