Isospin-dependent Boltzmann-Uehling-Uhlenbeck Research Articles

Bayesian inference of in-medium baryon-baryon scattering cross sections from HADES proton flow data

Within a Bayesian statistical framework using a Gaussian Process emulator for an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model simulator of heavy-ion reactions at intermediate energies, we infer from the HADES proton flow data the posterior probability distribution functions of in-medium baryon-baryon scattering cross section modification factor X with respect to free-space and the corresponding incompressibility K of nuclear matter as well as their correlation function. The mean value of X is found to be X=1.32−0.40+0.28 at 68% confidence level assuming the nuclear incompressibility K will not exceed 400 MeV, providing circumstantial evidence for enhanced baryon-braryon scattering cross sections in hot and dense nuclear matter.

Principal Component Analysis of azimuthal flow in intermediate-energy heavy-ion reactions

Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event single-particle azimuthal angle distribution matrices in ultra-relativistic heavy-ion collisions at RHIC-LHC energies indicate that the sine and cosine functions chosen a priori in the traditional Fourier analysis are naturally the most optimal basis for azimuthal flow studies according to the data itself. We perform PCA-SVD analyses of mid-central Au+Au collisions at Ebeam/A=1.23 GeV simulated using an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model to address the following two questions: (1) if the principal components of the covariance matrix of nucleon azimuthal angle distributions in heavy-ion reactions around 1 GeV/nucleon are naturally sine and/or cosine functions and (2) what if any advantages the PCA-SVD may have over the traditional flow analysis using the Fourier expansion for studying the EOS of dense nuclear matter. We find that (1) in none of our analyses the principal components come out naturally as sine and/or cosine functions, (2) while both the eigenvectors and eigenvalues of the covariance matrix are appreciably EOS dependent, the PCA-SVD has no apparent advantage over the traditional Fourier analysis for studying the EOS of dense nuclear matter using the azimuthal collective flow in heavy-ion collisions.

Isospin blocking and its effects in heavy-ion collisions

A concept of \emph{isospin blocking} in the process of isospin diffusion in heavy-ion collisions is raised. Generally, in the process of isospin diffusion, isospin asymmetry would diffuse from the place with large asymmetry to the place with small asymmetry. However, our study shows that the isospin diffusion could be blocked in case the local value of the symmetry energy is larger. We dub this phenomenon ``isospin blocking''. To check this behavior, in the framework of an Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, isospin diffusions in the isotope Sn+Sn reactions at 270 MeV/nucleon are studied. It is shown that the value of the after-diffusion asymmetry is distinctly blocked if the local symmetry energy is large. The effects of the isospin blocking on the isospin asymmetry of dilute and dense matter and the final $\pi^-/\pi^+$ ratio in heavy ion collisions are demonstrated.

High pt squeezed-out n/p ratio as a probe of Ksym of the symmetry energy

By involving the constraints of the slope of nuclear symmetry energy $L$ into the question of determination of the high-density symmetry energy, one needs to probe the curvature of nuclear symmetry energy $K_{\rm{sym}}$. Based on the Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, effects of the curvature of nuclear symmetry energy on the squeezed-out nucleons are demonstrated in the semi-central Au+Au reaction at 400 and 600 MeV/nucleon. It is shown that the squeezed-out isospin-dependent nucleon emissions at high transverse momenta are sensitive to the curvature of nuclear symmetry energy. The curvature of nuclear symmetry energy at saturation density thus can be determined by the high momentum squeezed-out isospin-dependent nucleon emissions experiments from the semi-central Au+Au reaction at 400 or 600 MeV/nucleon.

Blind spots of probing the high-density symmetry energy in heavy-ion collisions

The nuclear symmetry energy, especially at suprasaturation densities, plays crucial roles in many astrophysical studies. However, nowadays the high-density behavior of the symmetry energy is still very controversial in nuclear community. To constrain the high-density behavior of the symmetry energy, neutron-rich nuclei collisions at medium energies are considered to be one of the most effective methods. While probing the high-density symmetry energy by using heavy-ion collisions, blind spots may exist. In the framework of the Isospin-dependent Boltzmann–Uehling–Uhlenbeck (IBUU) transport model, the blind spots of probing the high-density symmetry energy by the n/p ratio in the central Au + Au reaction at 300MeV/nucleon are demonstrated. It is found that the nucleon observable neutron to proton ratio n/p in heavy-ion collisions cannot effectively probe the high-density symmetry energy when the high-density symmetry energy is less density-dependent.

Influence of the nuclear symmetry energy on the collective flows of charged pions

Based on the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we studied charged pion transverse and elliptic flows in semicentral $^{197}\mathrm{Au}+^{197}\mathrm{Au}$ collisions at 600 MeV/nucleon. It is found that ${\ensuremath{\pi}}^{+}\ensuremath{-}{\ensuremath{\pi}}^{\ensuremath{-}}$ differential transverse flow and the difference of ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ transverse flows almost show no effects of the symmetry energy. Their corresponding elliptic flows are largely affected by the symmetry energy, especially at high transverse momenta. The isospin-dependent pion elliptic flow at high transverse momenta thus provides a promising way to probe the high-density behavior of the symmetry energy in heavy-ion collisions at the Facility for Antiproton and Ion Research (FAIR) at GSI, Darmstadt or at the Cooling Storage Ring (CSR) at HIRFL, Lanzhou.

Probing the high-momentum component in the nucleon momentum distribution by nucleon emission from intermediate-energy nucleus-nucleus collisions

The free nucleon emission from intermediate-energy nucleus-nucleus collisions is proposed as a possible probe to study the high-momentum tail (HMT) in nucleon momentum distribution of nuclei. Within the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, the effect of HMT on free nucleon emission from the reactions of a light system $^{12}\mathrm{C}+^{12}\mathrm{C}$ and heavy one $^{124}\mathrm{Sn}+^{124}\mathrm{Sn}$ at the beam energies of 50 and 140 MeV/nucleon was investigated. We show that the probability of free nucleon emission, especially high-energy nucleons, is sensitive to the high-momentum component in nucleon momentum distribution of nuclei. The momentum distribution with HMT can lead to an increase of both high-energy free proton and neutron emission as compared to the free Fermi gas case for both symmetric and asymmetric nuclear systems.

Modeling pion production in heavy-ion collisions at intermediate energies

Pion production in nucleus-nucleus collisions at intermediate energies was modeled in the framework of the Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model. The effects of nucleon-nucleon short-range correlations in initialization and mean-field potential, isospin-dependent in-medium baryon-baryon elastic and inelastic cross sections and pion in-medium effect are all considered in this model. It is found that the ratio and yields of $\pi^{-}$and $\pi^{+}$ in Au+Au reaction at 400 MeV/nucleon reproduce the FOPI/GSI data very well especially with a soft symmetry energy in the present transport model. Predictions on the single and double $\pi^{-}/\pi^{+}$ ratio are made for the isotope reaction systems $^{132}\rm {Sn}+^{124}\rm {Sn}$ and $^{108}\rm {Sn}+^{112}\rm {Sn}$ at 300 MeV/nucleon since related experiments are being carried out at RIKEN/Japan.

Effects of the symmetry energy in the Sn132+Sn124 reaction at 300 MeV/nucleon

Based on the recently updated Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we studied the effects of symmetry energy on the neutron to proton n/p ratio and the $\pi^{-}/\pi^{+}$ ratio in central $^{132}\rm {Sn}+^{124}\rm {Sn}$ reaction at 300 MeV/nucleon. It is found that the n/p ratio and the $\pi^{-}/\pi^{+}$ ratio in central $^{132}\rm {Sn}+^{124}\rm {Sn}$ reaction at 300 MeV/nucleon mainly probe the symmetry energy in the density region 1-1.5 times saturation density. However, the $\pi^{-}/\pi^{+}$ ratio may be able to probe the density-dependent symmetry energy above 1.5 times saturation density by making some kinematic restrictions such as the azimuthal angle and kinetic energy cuts of emitting pions.

Effect ofΔpotential on theπ−/π+ratio in heavy-ion collisions at intermediate energies

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.

Effects of pion potential and nuclear symmetry energy on theπ−/π+ratio in heavy-ion collisions at beam energies around the pion production threshold

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.

Symmetry-energy dependence of the dynamical dipole mode in the Boltzmann-Uehling-Uhlenbeck model

Using an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we have studied the connection between the symmetry energy and features of the dynamical dipole mode in fusion reactions with charge-asymmetric entrance channel. The yield and angular distribution of the prompt photon emission are extracted by a bremsstrahlung approach. The experimental data of $^{36}$Ar+$^{96}$Zr at 16 MeV/nucleon and $^{32}$S + $^{100}$Mo at 9.3 MeV/nucleon are compared with IBUU model calculations, and the soft symmetry energy is found to describe the data reasonably well.

Energy dependence of pion in-medium effects on theπ−/π+ratio in heavy-ion collisions

Within the framework of a thermal model with its parameters fitted to the results from an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we study the pion in-medium effect on the charged-pion ratio in heavy-ion collisions at various energies. We find that due to the cancellation between the effects from pion-nucleon s-wave and p-wave interactions in nuclear medium, the \pi^-/\pi^+ ratio generally decreases after including the pion in-medium effect. The effect is larger at lower collision energies as a result of narrower pion spectral functions at lower temperatures.

Disentangling effects of collision geometry and symmetry energy in U+U collisions

Effects of the collision geometry on experimental observables that are known to be sensitive to the high-density behavior of nuclear symmetry energy are examined in U $+$ U collisions at 0.52 GeV/nucleon using an isospin- and momentum-dependent interaction within the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model. It is found that the neutron-proton differential flow in tip-tip collisions and the difference of neutron and proton elliptic flow in body-body collisions are more sensitive to the symmetry energy at suprasaturation densities compared with collisions of spherical nuclei of the same masses. In addition, the $n/p$ ratio of preequilibrium nucleons is found to be slightly more sensitive to the symmetry energy in tip-tip collisions, and the collision geometry affects the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio significantly.

Can the nuclear symmetry potential at supra-saturation densities be negative?

In the framework of an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, for the central $^{197}\mathrm{Au}+^{197}\mathrm{Au}$ reaction at an incident beam energy of $400$ MeV/nucleon, the effect of nuclear symmetry potential at supra-saturation densities on the preequilibrium clusters emission is studied. It is found that for the positive symmetry potential at supra-saturation densities the neutron-to-proton ratio of lighter clusters with mass number $A\ensuremath{\leqslant}3$ [$(n/p){}_{A\ensuremath{\leqslant}3}$] is larger than that of the heavier clusters with mass number $A>3$ [$(n/p){}_{A>3}$], whereas for the negative symmetry potential at supra-saturation densities the $(n/p){}_{A\ensuremath{\leqslant}3}$ is smaller than the $(n/p){}_{A>3}$. This may be considered as a probe of the negative symmetry potential at supra-saturation densities.

Experimental studies ofN/Zequilibration in peripheral collisions using fragment yield ratios

Peripheral collisions of $^{40}\mathrm{Ca}$ and $^{48}\mathrm{Ca}$ projectiles at 32 MeV/nucleon on $^{112}\mathrm{Sn}$ and $^{124}\mathrm{Sn}$ targets were studied in this work. The fragments of the projectile-like source (quasiprojectile) were collected with a charged-particle multidetector array. The average value of the neutron-to-proton ratio $N/Z$ of the quasiprojectiles formed in the reactions was determined with two approaches. The first is a direct reconstruction approach using isotopically resolved fragments and is hindered by undetected neutrons leading to lower $N/Z$ values. The second approach, based on the assumption of early fragment formation, employs yield ratios of fragment isobars and is not hindered by undetected neutrons. Using this approach, the amount of $N/Z$ mixing that occurred in the quasiprojectiles (compared to a fully $N/Z$ equilibrated system) was found to be approximately $53%$. The experimental results were compared with model calculations. First, the phenomenological DIT (deep inelastic transfer) model was used, followed by the statistical multifragmentation model (SMM). The results of these calculations are in close agreement with the data and indicate that the mean number of undetected neutrons increases with the $N/Z$ of the composite system, accounting for the difference observed between the two approaches of quasiprojectile $N/Z$ determination. Second, the microscopic transport model IBUU (isospin-dependent Boltzmann-Uehling-Uhlenbeck) was employed, providing preliminary results in reasonable agreement with the data. The determination of the degree of $N/Z$ equilibration employing the present fragment yield ratio approach may provide a valuable probe to study the isospin part of the nuclear equation of state in conjunction with detailed microscopic models of the collisions in the Fermi energy regime.