Nucleon-nucleon Cross Section Research Articles

Influence of in-mediumNNcross sections, symmetry potential, and impact parameter on isospin observables

We explore the influence of in-medium nucleon-nucleon cross section, symmetry potential and impact parameter on isospin sensitive observables in intermediate-energy heavy-ion collisions with the ImQMD05 code, a modified version of Quantum Molecular Dynamics model. At incident velocities above the Fermi velocity, we find that the density dependence of symmetry potential plays a more important role on the double neutron to proton ratio $DR(n/p)$ and the isospin transport ratio $R_i$ than the in-medium nucleon-nucleon cross sections, provided that the latter are constrained to a fixed total NN collision rate. We also explore both $DR(n/p)$ and $R_i$ as a function of the impact parameter. Since the copious production of intermediate mass fragments is a distinguishing feature of intermediate-energy heavy-ion collisions, we examine the isospin transport ratios constructed from different groups of fragments. We find that the values of the isospin transport ratios for projectile rapidity fragments with $Z\ge20$ are greater than those constructed from the entire projectile rapidity source. We believe experimental investigations of this phenomenon can be performed. These may provide significant tests of fragmentation time scales predicted by ImQMD calculations.

Isospin-dependent nucleon-nucleon cross section and the collective flow of nucleons in heavy-ion collision at intermediate energy

In this paper, the influences of the different forms of nucleon-nucleon (NN) cross sections on the rapidity distributions and the in-plane flows of nucleons in reactions 60Ca+60Ca and 60Ni+60Ni are studied by using IBUU04 transport model with the moment-dependent symmetry potential. The calculation results indicate that (1) the discrepancies of the rapidity distributions and in-plane flows corresponding to different forms of NN cross sections are large, (2) the sensitivity of the in-plane flow to the NN cross section still holds when the new form of moment-dependent symmetry energy is adopted, and (3) the influence of the N/P ratio of reaction systems on the transverse flow calculated with a certain NN cross section is more obvious when the incident energy is near the balance energy.

Specific viscosity of neutron-rich nuclear matter from a relaxation time approach

The specific viscosity of neutron-rich nuclear matter is studied from the relaxation time approach using an isospin- and momentum-dependent interaction and the nucleon-nucleon cross sections taken as those from the experimental data modified by the in-medium effective masses as used in the IBUU transport model calculations. The relaxation time of neutrons is larger while that of protons is smaller in neutron-rich nuclear matter compared with that in symmetric nuclear matter, and this leads to a larger specific viscosity in neutron-rich nuclear matter. In addition, the specific viscosity decreases with increasing temperature because of more frequent collisions and weaker Pauli blocking effect at higher temperatures. At lower temperatures the specific viscosity increases with increasing density due to the Pauli blocking effect, while at higher temperatures it slightly decreases with increasing density as a result of smaller in-medium effective masses at higher densities.

Energy dependent growth of the nucleon and hydrodynamic initial conditions

Due to gluon saturation, the growth of the inelastic nucleon-nucleon cross section with increasing collision energy $\sqrt{s}$ results in a broadening of the nucleon's density distribution in position space. This leads to a natural smoothing of the initial energy density distribution in the transverse plane of the matter created near midrapidity in heavy-ion collisions. We study this effect for fluctuating initial conditions generated with the Monte Carlo Kharzeev-Levin-Nardi model for $\mathrm{Au}+\mathrm{Au}$ collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). We argue that at the LHC, viscous hydrodynamics is applicable at earlier times than at the RHIC, not only because of the higher temperature but also since the length scale over which the initial pressure fluctuates increases with collision energy.

Influence of transport variables on isospin transport ratios

The symmetry energy in the nuclear equation of state affects many aspects of nuclear astrophysics, nuclear structure, and nuclear reactions. Recent constraints from heavy-ion collisions, including isospin diffusion observables, have started to put constraints on the symmetry energy below nuclear saturation density, but these constraints depend on the employed transport model and input physics other than the symmetry energy. To understand these dependencies, we study the influence of the symmetry energy, isoscalar mean-field compressibility and momentum dependence, in-medium nucleon-nucleon cross sections, and light cluster production on isospin diffusion within the pBUU transport code. In addition to the symmetry energy, several uncertain issues strongly affect isospin diffusion, most notably the cross sections and cluster production. In addition, there is a difference in the calculated isospin transport ratios, depending on whether they are computed using the isospin asymmetry either of the residue or of all forward-moving fragments. Measurements that compare the isospin transport ratios of these two quantities would help place constraints on the input physics, such as the density dependence of the symmetry energy.

N/ZandN/Adependence of the balance energy as a probe of the symmetry energy in heavy-ion collisions

We study the $N/Z$ and $N/A$ dependence of balance energy (${E}_{\text{bal}}$) for isotopic series of Ca having $N/Z$ ($N/A$) varying from 1.0 to 2.0 (0.5 to 0.67). We show that the $N/Z$ ($N/A$) dependence of ${E}_{\text{bal}}$ is sensitive to symmetry energy and its density dependence at densities higher than saturation density and is insensitive toward the isospin dependence of nucleon-nucleon ($\mathit{nn}$) cross section and Coulomb repulsion. We also study the effect of momentum-dependent interactions (MDI) on the $N/Z$ ($N/A$) dependence of ${E}_{\text{bal}}$. We find that although MDI influences the ${E}_{\text{bal}}$ drastically, the $N/Z$ ($N/A$) dependence of ${E}_{\text{bal}}$ remains unchanged on inclusion of MDI.

Probing the sensitivity of the total nucleus-nucleus reaction cross section at intermediate energies to medium effects and isospin asymmetries

This paper presents reaction cross-section predictions. These predictions are the result of a continuous pipeline that originates from a microscopic nuclear interaction. Density parameters and effective nucleon-nucleon cross sections (both involved in the reaction calculations) are by-products of the same equation of state. First, we perform tests of sensitivity to medium effects using reactions involving $^{208}\mathrm{Pb}$, a stable but weakly isospin-asymmetric nucleus. We also show predictions for collisions of some neutron-rich isotopes of calcium and argon. We observe significant sensitivity of the reaction cross section to medium effects but very weak sensitivity to inclusion of isospin asymmetry in the effective nucleon-nucleon cross sections.

Nonequilibrium dynamics in heavy-ion collisions at low energies available at the GSI Schwerionen Synchrotron

The updated ultrarelativistic quantum molecular dynamics (UrQMD) model, a microscopic transport model, is used to study the directed and elliptic collective flows and the nuclear stopping in Au$+$Au collisions at incident energies covered by INDRA and lower-energy FOPI experiments. It is seen clearly that these observables are sensitive to both the potential terms (including isoscalar and isovector parts as well as the momentum dependent term) in the equation of state (EoS) and the collision term [including the Pauli blocking and the medium-modified nucleon-nucleon elastic cross section (NNECS)]. The momentum modifications of both, the mean-field potentials and the density dependent NNECS, are found to affect the collectivity of heavy-ion collisions. At INDRA energies ($\ensuremath{\leqslant}$$150$ MeV/nucleon) the dynamic transport with a soft EoS with momentum dependence and with the momentum-modified density-dependent NNECS describes the directed flow exhibited by hydrogen isotopes ($Z=1$) emitted at midrapidity fairly well.

Neutron density distribution and the halo structure ofC22

The recently measured reaction cross sections for the neutron-rich carbon isotopes ($^{19}\mathrm{C}$, $^{20}\mathrm{C}$, and $^{22}\mathrm{C}$) on a proton target at 40 A MeV are analyzed using the finite range Glauber model (FRGM) and the microscopic optical potential calculated within the Brueckner-Hartree-Fock formalism (BHF). In FRGM nucleon-nucleon cross sections are used, while in the latter (BHF), Hamada-Johnston, Urbana v-14, and the Argonne v-18 internucleon potentials are employed to calculate the microscopic optical potential. The required nucleon density distributions are calculated within the relativistic mean-field (RMF) framework. To test the halo structure, the extended neutron density distribution for $^{22}\mathrm{C}$ is also used. The analysis reveals that the BHF results of all three internucleon potentials are very close to each other, and also agree with the corresponding results of the FRGM. Our results, using RMF densities, are in agreement with the experimental data for all isotopes of carbon except $^{22}\mathrm{C}$, for which we require extended neutron density distribution, indicating a halo structure.

EXCLUSIVE PRODUCTION OF π+π- PAIRS IN PROTON-PROTON AND PROTON-ANTIPROTON COLLISIONS

We report on a detailed investigation of four-body pp → ppπ+π- and [Formula: see text] reactions which constitute an irreducible background to three-body processes pp → ppM, where M is a broad resonance in the π+π- channel, e.g. M = σ, ρ0, f0(980), f2(1275), f0(1500). We include double-diffractive contribution (both pomeron and reggeon exchanges) as well as the pion-pion rescattering contributions. The first process dominates at higher energies and small pion-pion invariant masses while the second becomes important at lower energies and higher pion-pion invariant masses. We compare our results with the experimental data. We make predictions for future experiments at PANDA, RHIC, Tevatron and LHC energies. The two-dimensional distribution in rapidity space of pions (yπ+, yπ-) is particularly interesting. The higher the incident energy, the higher preference for the same-hemisphere emission of pions. The processes considered constitute a sizeable contribution to the total nucleon-nucleon cross section as well as to pion inclusive cross section.

Unitarity of the tree approximation to the Glauber AA amplitude for large A

The nucleus-nucleus Glauber amplitude in the tree approximation is studied for heavy participant nuclei. It is shown that, contrary to previous published results, it is not unitary for realistic values of nucleon-nucleon cross-sections.

Isospin effects in the disappearance of flow as a function of colliding geometry

We study the effect of isospin degree of freedom on the balance energy (E$_{bal}$) as well as its mass dependence throughout the mass range 48-270 for two sets of isobaric systems with N/Z = 1 and 1.4 at different colliding geometries ranging from central to peripheral ones. Our findings reveal the dominance of Coulomb repulsion in isospin effects on E$_{bal}$ as well as its mass dependence throughout the range of the colliding geometry. Our results also indicate that the effect of symmetry energy and nucleon-nucleon cross section on E$_{bal}$ is uniform throughout the mass range and throughout the colliding geometry. We also present the counter balancing of nucleon-nucleon collisions and mean field by reducing the Coulomb and the counter balancing of Coulomb and mean filed by removing the nucleon-nucleon collisions.

NUCLEON-NUCLEON CROSS SECTIONS IN ISOSPIN ASYMMETRIC NUCLEAR MATTER

The in medium nucleon-nucleon (NN) cross sections in isospin asymmetric nuclear matter at various densities are investigated in the framework of Brueckner-Hartree-Fock theory with the Bonn B two-body nucleon-nucleon interaction supplemented with a new version microscopic three-body force (TBF). The TBF depresses the amplitude of cross sections at high density region. At low densities, the proton-proton and neutron-neutron cross sections decrease while the proton-neutron one increases as the asymmetry increases. But the sensitivity of the NN cross sections to the isospin asymmetry are reduced with the increasing density.

Pauli blocking and medium effects in nucleon knockout reactions

We study medium modifications of the nucleon-nucleon (NN) cross sections and their influence on the nucleon knockout reactions. Using the eikonal approximation, we compare the results obtained with free NN cross sections with those obtained with a purely geometrical treatment of Pauli-blocking and with NN obtained with more elaborated Dirac-Bruecker methods. The medium effects are parametrized in terms of the baryon density. We focus on symmetric nuclear matter, although the geometrical Pauli-blocking allows for the treatment of asymmetric nuclear matter. It is shown that medium effects can change the nucleon knockout cross sections and momentum distributions up to 10% in the energy range E=50-300 MeV/nucleon. The effect is more evident in reactions involving halo nuclei.

Finding a Probe for Extracting Information on the Momentum Dependent-Interaction in Heavy Ion Collisions

The effect of momentum-dependent interaction on the kinetic energy spectrum of the neutron-proton ratio ⟨(n/p)gas⟩b (Ek) for 64Zn + 64Zn is studied. It is found that ⟨(n/p)gas⟩b (Ek) sensitively depends on the momentum-dependent interaction and weakly on the in-medium nucleon-nucleon cross section and symmetry potential. Therefore ⟨(n/p)gas⟩b(Ek) is a possible probe for extracting information on the momentum-dependent interaction in heavy ion collisions.

Transport model study of nuclear stopping in heavy-ion collisions over the energy range from0.09Ato160A GeV

Nuclear stopping in heavy-ion collisions over a beam energy range from SIS and AGS up to SPS is studied in the framework of the modified Ultrarelativistic Quantum Molecular Dynamics transport model, in which mean field potentials of both formed and ``preformed'' hadrons (from string fragmentation) and medium-modified nucleon-nucleon elastic cross sections are considered. It is found that nuclear stopping is influenced by both the stiffness of the equation of state and medium modifications of nucleon-nucleon cross sections at SIS energies. At high SPS energies, a two-bump structure is shown in the experimental rapidity distribution of free protons, which can be understood by considering the preformed hadron potentials.

Distinction between Proton-Neutron Density Distribution of Halo Nuclei at the Nuclear Surface via Reaction Cross Sections

Reaction cross sections ( σ R ) for 11Be and 8B on proton targets at 50 A ∼ 120 A MeV have been measured to distinguish between the proton- and neutron- density distributions at the nuclear surface. The σ R is connected with the nucleon density distributions by the Glauber theory. Since the nucleon-nucleon total cross sections in that energy region have a large isospin dependence, the σ R on proton targets should have a large difference between the proton and neutron in the halo structure. The experimental σ R on proton targets are in good agreement with the calculated ones assuming that the tail dominantly consists of a neutron for 11Be and a proton for 8B.

Exclusivepp→ppπ+π−reaction: From the threshold to LHC

We evaluate differential distributions for the four-body $pp\ensuremath{\rightarrow}pp{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ (and $p\overline{p}\ensuremath{\rightarrow}p\overline{p}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$) reaction which constitutes an irreducible background to three-body processes $pp\ensuremath{\rightarrow}ppM$, where $M$ are a broad resonances in the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ channel, e.g., $M=\ensuremath{\sigma}$, ${\ensuremath{\rho}}^{0}$, ${f}_{0}(980)$, ${f}_{2}(1275)$, ${f}_{0}(1500)$. We include both double-diffractive contribution (both Pomeron and Reggeon exchanges) as well as pion-pion rescattering contribution. The first process dominates at higher energies and small pion-pion invariant masses while the second becomes important at lower energies and higher pion-pion invariant masses. The amplitude(s) is(are) calculated in the Regge approach. We compare our results with measured cross sections for the Intersecting Storage Ring and Fermi National Accelerator Laboratory experiments. We make predictions for future experiments at the anti-Proton ANnihilation at DArmstadt (PANDA), Relativistic Heavy Ion Collider, Tevatron, and LHC energies. Differential distributions in invariant two-pion mass, pion rapidities and transverse momenta of pions are presented. The two-dimensional distribution in $({y}_{{\ensuremath{\pi}}^{+}},{y}_{{\ensuremath{\pi}}^{\ensuremath{-}}})$ is particularly interesting. The higher the incident energy, the higher preference for the same-hemisphere emission of pions. The processes considered constitute a sizeable contribution to the total nucleon-nucleon cross section as well as to pion inclusive cross section.

Possible probe on the momentum dependent interaction in the equation of state of nuclear matter

The effects of momentum dependent interaction on the kinetic energy spectrum of the neutron-proton ratiorb(Ek)in the equation of state of nuclear matter was investigated.We found that the kinetic energy spectrum of the neutron-proton ratio rb(Ek) depends sensitively on the momentum dependent interaction and weakly on the in-medium nucleon-nucleon cross section and symmetry potential so that the rb(Ek) is a sensitive physical probe for extracting the information of momentum dependent interaction in the heavy ion collisions. At the same time, the comparing investigate between rb(Ek) for the neutron-rich collision system and the same mass stable collision system gives a important judgment for extracting the information of momentum dependent interaction in the heavy ion collisions.

Isospin Effects on Anisotropic Flows in Intermediate Energy Heavy Ion Collisions

Anisotropic flows per nucleon (v1/A, v2/A, v3/A and v4/A) of light fragments up to the mass number 4 as a function of transverse momentum per nucleon are studied for 55 MeV/nucleon 58 Fe+58 Fe and 58Ni+58 Ni at large impact parameters by the isospin-dependent quantum molecular dynamics model. The effects of symmetry energy and nucleon-nucleon cross sections, which are both isospin-dependent on anisotropic flows, are studied in detail. In comparison of the two systems with or without symmetry potential term, the results show that the strength of flows is sensitive to symmetry potential and nucleon-nucleon cross sections, which mainly cause a repulsion effect in this energy region.