Nucleon-nucleon Cross Section Research Articles

In-medium nucleon-nucleon cross sections from characteristics of nuclear giant resonances and nuclear stopping power

In-medium nucleon-nucleon cross sections from characteristics of nuclear giant resonances and nuclear stopping power

In-medium nucleon-nucleon cross section in nuclear matter

In-medium nucleon-nucleon ($NN$) cross sections at various densities and isospin asymmetries are investigated systematically in the framework of the Brueckner-Hartree-Fock approach. The calculations are base on the exact treatment of the center-of-mass momentum instead of the total momentum approximation employed in previous works. The neutron-proton in-medium cross section is shown to exhibit nearly isospin asymmetry independence. For convenience in application, analytical formulas embodying the medium correction to free $NN$ cross section with parameters calibrated to the calculated results have been provided. Using these formulas, the transverse and elliptic flows of emitted nucleons in heavy-ion collisions are studied within the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model. We find the medium effect of the cross section from the $G$ matrix contributes to the transverse and elliptic flows oppositely to and obviously smaller than that from the effective mass. In addition, the present microscopic in-medium cross sections can significantly revise the predictions of the transverse and elliptic flows compared to the in-medium cross sections previously adopted in transport models for heavy-ion collisions.

Taming the in-medium nucleon-nucleon cross section with a deep neural network method

由于周围核子的影响，介质中核子-核子(NN)截面与散射两核子的状态相关，依赖于核子数总密度、同位旋非对称度、两核子总动量和质心系总动能。并且其依赖形式相当复杂，基于复杂公式的拟合在精度上有不足之处。鉴于机器学习与神经网络在数据拟合方面的优势，本文以微观计算的有效NN截面为数据集，通过深度神经网络方法，获得各种条件下的NN截面。结果表明，机器学习可以很好地拟合介质中的NN截面，同时也展现出机器学习的明显优势。另外，通过机器学习得到的截面可以直接应用到输运模型来研究介质对核反应观测量的影响。

Accessing the in-medium effects on nucleon-nucleon elastic cross section with collective flows and nuclear stopping

A systematic study of the in-medium correction factor (F) on nucleon-nucleon elastic cross section is performed within the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. The effects of the beam energy dependence of F on the directed, elliptic flow and nuclear stopping in 197Au+197Au collisions with energy ranging from 0.09 to 0.8A GeV are explored. It is found that the directed, elliptic flow and nuclear stopping at relatively low energies are very sensitive to F, and the sensitivity gradually weakens with increasing beam energy. The beam energy dependent in-medium correction factor F is deduced from the comparison of the excitation functions of the directed, elliptic flow and nuclear stopping between the calculated results and the FOPI experimental data.

Centrality dependence of electroweak boson production in PbPb collisions at the CERN Large Hadron Collider

Recent data on the nuclear modification of W and Z boson production measured by the ATLAS collaboration in PbPb collisions at $\sqrt{s_{\rm nn}}=5.02$ TeV show an enhancement in peripheral collisions, seemingly contradicting predictions of the Glauber model. The data were previously explained by arguing that the nucleon-nucleon cross section may be shadowed in nucleus-nucleus collisions, and hence suppressed compared to the proton-proton cross section at the same collision energy. This interpretation has quite significant consequences for the understanding of heavy-ion data, in particular in the context of the Glauber model. Instead, we provide an alternative explanation of the data by assuming that there is a mild bias present in the centrality determination of the measurement; on the size of the related systematic uncertainty. Using this assumption, we show that the data is in agreement with theoretical calculations using nuclear parton distribution functions. Finally, we speculate that the centrality dependence of the W$^-$/W$^{+}$ ratio may point to the relevance of a larger skin thickness of the Pb nucleus, which, if present, would result in a few percent larger PbPb cross section than currently accounted for in the Glauber model and may hence be the root of the centrality bias.

Nuclear giant quadruple resonance within a transport approach and its constraint on the nucleon effective mass

We study the nuclear iso-scalar giant quadruple resonance~(ISGQR) based on the Boltzmann-Uehling-Uhlenbeck~(BUU) transport equation. The mean-field part of the BUU equation is described by the Skyrme nucleon-nucleon effective interaction, and its collision term, which embodies the two-particle-two-hole ($2$p-$2$h) correlation, is implemented through the stochastic approach. We find that the width of ISGQR for heavy nuclei is exhausted dominated by collisional damping, which is incorporated into the BUU equation through its collision term, and it can be well reproduced through employing a proper in-medium nucleon-nucleon cross section. Based on further Vlasov and BUU calculations with a number of representative Skyrme interactions, the iso-scalar nucleon effective mass at saturation density is extracted respectively as $m^{*}_{s,0}/m$ $=$ $0.83\pm0.04$ and $m^{*}_{s,0}/m$ $=$ $0.82\pm0.03$ from the measured excitation energy $E_x$ of the ISGQR of $\isotope[208]{Pb}$. The small discrepancy between the two constraints indicates the negligible role of $2$p-$2$h correlation in constraining $m_{s,0}^*$ with the ISGQR excitation energy.

Rapidity distributions of Z = 1 isotopes and the nuclear symmetry energy from Sn+Sn collisions with radioactive beams at 270 MeV/nucleon

The rapidity distributions of hydrogen isotopes emitted from central collisions of neutron-rich 132Sn+124Sn and neutron-deficient 108Sn+112Sn systems at 270 MeV/nucleon were investigated at RIKEN-RIBF. The data are compared with antisymmetrized molecular dynamics (AMD) calculations and the rapidity distributions can be reproduced after adjusting the in-medium nucleon-nucleon cross sections. The double ratios between the two reaction systems taken for the relative yields of deuteron to proton (d/p) and triton to proton (t/p) are further examined in the midrapidity domain, where the adjustments in the AMD calculations do not affect much on them. The d/p and t/p double ratios at midrapidity agree well with the ratio of the system neutron numbers and its squared value, respectively, and the rapidity dependence of these double ratios is consistent with a picture of partial mixing of colliding nuclei. By comparing with the AMD model which shows a strong symmetry energy dependence of the t/p double ratio, the experimental result in the midrapidity domain favors the calculation with a symmetry-energy slope parameter around L=46 MeV rather than L=108 MeV.

Application of machine learning in the determination of impact parameter in the Sn132+Sn124 system

Background: $^{132}$Sn+$^{124}$Sn collisions at the beam energy of 270 MeV$/$nucleon have been performed at the Radioactive Isotope Beam Factory (RIBF) in RIKEN to investigate the nuclear equation of state. Reconstructing impact parameter is one of the important tasks in the experiment as it relates to many observables. Purpose: In this work, we employ three commonly used algorithms in machine learning, the artificial neural network (ANN), the convolutional neural network (CNN) and the light gradient boosting machine (LightGBM), to determine impact parameter by analyzing either the charged particles spectra or several features simulated with events from the ultra-relativistic quantum molecular dynamics (UrQMD) model. Method: To closely imitate experimental data and investigate the generalizability of the trained machine learning algorithms, incompressibility of nuclear equation of state and the in-medium nucleon-nucleon cross sections are varied in the UrQMD model to generate the training data. Results: The mean absolute error $\Delta b$ between the true and the predicted impact parameter is smaller than 0.45 fm if training and testing sets are sampled from the UrQMD model with the same parameter set. However, if training and testing sets are sampled with different parameter sets, $\Delta b$ would increase to 0.8 fm. Conclusion: The generalizability of the trained machine learning algorithms suggests that these machine learning algorithms can be used reliably to reconstruct impact parameter in experiment.

Theoretical uncertainties on the extraction of in-medium NN cross sections by different Pauli blocking algorithms * *This work was partly inspired by the transport code comparison project, and it was supported by the National Natural Science Foundation of China (11875323, 11705163, 11790320, 11790323, 11961141003), the National Key R&D Program of China (2018YFA0404404), the Continuous Basic Scientific Research Project (WDJC-2019-13, BJ20002501)

Three typical Pauli blocking algorithms in quantum molecular dynamics type models are investigated in the nuclear matter, the nucleus, and heavy ion collisions. In nuclear matter, the blocking ratios obtained with the three algorithms are underestimated by 13%-25% compared to the corresponding analytical values. For a finite nucleus, spurious collisions occur around the surface of the nucleus owing to the defects of the Pauli blocking algorithms. In the simulations of heavy ion collisions, the uncertainty of stopping power arising from the different Pauli blocking algorithms is less than 5%. Furthermore, the in-medium effects of nucleon-nucleon (NN) cross sections on the nuclear stopping power are discussed. Our results show that the transport model calculations with free NN cross sections result in the stopping power decreasing with beam energy when the beam energy is less than 300 MeV/u. To increase or decrease the values of the stopping power, the transport model calculations need enhanced or suppressed model dependent in-medium NN cross sections that are expected to be smaller than the true in-medium NN cross sections.

Symmetry potentials and in-medium nucleon-nucleon cross sections within the Nambu–Jona-Lasinio model in relativistic impulse approximation

In the relativistic impulse approximation (RIA), we study symmetry potentials and in-medium nucleon-nucleon (NN) cross sections with the Nambu-Jona-Lasinio (NJL) model that features chiral symmetry. The chiral symmetry that plays a fundamental role in the nonperturbative physics in the strong interaction is anticipated to add restrictive effects on the symmetry potentials and in-medium NN cross sections. For comparison, we also perform the study with the usual relativistic mean-field (RMF) model. The numerical results with the NJL and RMF models are similar at saturation density and below, since a priori fit was made to saturation properties. With the increase of nuclear density, the chiral symmetry starts to be restored partially in the NJL model, resulting in the explicit fall of the scalar density. In a large energy span, the symmetry potential acquires a significant rise for the partial restoration of the chiral symmetry, compared to the one with the RMF model. It is found that the in-medium NN cross sections in the RIA with the NJL and RMF models both increase with the density in the energy region interested in this study, whereas those with the NJL model increase sharply as long as a clear chiral symmetry restoration takes place. The different tendency of observables in density can be transmitted to the different energy dependence in the RIA. The NJL model is shown to have characteristic energy-dependent symmetry potentials and NN cross sections beyond saturation point, apart from the RMF models.

Shadowing in Inelastic Nucleon-Nucleon Cross Section?

Experimental results of inclusive hard-process cross sections in heavy-ion collisions conventionally lean on a normalization computed from Glauber models where the inelastic nucleon-nucleon cross section σ_{nn}^{inel}-a crucial input parameter-is simply taken from proton-proton measurements. In this Letter, using the computed electroweak boson production cross sections in lead-lead collisions as a benchmark, we determine σ_{nn}^{inel} from the recent ATLAS data. We find a significantly suppressed σ_{nn}^{inel} relative to what is usually assumed, show the consequences for the centrality dependence of the cross sections, and address the phenomenon in an eikonal minijet model with nuclear shadowing.

Nucleon-nucleon phase variation and in-medium effects on elastic scattering cross sections

Analytical formulae are used to calculate the phase variation and the slope parameter of the nucleon–nucleon (NN) scattering amplitude in terms of momentum transfer q2. An empirical series is presented to calculate the total NN cross section. The proton–nucleus and nucleus–nucleus elastic differential cross–sections for different reactions at different bombarding energies less than 200 MeV/N have been calculated. The phase variation and the in-medium effect are considered in these calculations using the Glauber model. The calculated cross sections are in reasonable agreement with the experimental data over the whole range of energy considered in this work among light and medium nuclei.

Hard-photon production and its correlation with intermediate-mass fragments in a framework of a quantum molecular dynamics model

Hard photon provides a unique probe for nuclear reaction dynamics. In this work, we embedded incoherent neutron-proton bremsstrahlung photon production channel in a framework of isospin-dependent quantum molecular dynamics (IQMD) model and performed a systematic study of multiplicities of hard photons and intermediate-mass fragments (IMFs). It is found that the IQMD model with the in-medium nucleon-nucleon cross section can reproduce previous experimental data of hard-photon energy spectra better. By investigating the incident energy and centrality dependencies of multiplicities of hard photons and IMFs of $^{40}\mathrm{Ca}+^{40}\mathrm{Ca}$ collisions, it is found that the multiplicity correlation between thermal photons and IMFs can provide valuable information on nuclear liquid-gas phase transition. Additionally, temperatures from the thermal emitting sources are also investigated. The results indicate that hard photons provide some unique information of the thermodynamical state of multifragmentating nuclear system.

Nucleus giant resonances from an improved isospin-dependent Boltzmann-Uehling-Uhlenbeck transport approach

We have studied the isoscalar giant quadruple resonance (ISGQR) and the isovector giant dipole resonance (IVGDR) in $^{208}$Pb based on an improved isospin-dependent Boltzmann-Uehling-Uhlenbeck transport approach using an improved isospin- and momentum-dependent interaction. With the isoscalar nucleon effective mass and the nucleon-nucleon cross section which reproduces respectively the excitation energy and the width of the ISGQR strength function, the slope parameter of the symmetry energy and the neutron-proton effective mass splitting are constrained respectively within $36<L<62$ MeV and $0.08\delta<(m_{n0}^*-m_{p0}^*)/m<0.42\delta$, by comparing the resulting centroid energy of the IVGDR and the electric dipole polarizability with the experimental data. It is found that nucleon-nucleon collisions have considerable effects on the resulting electric dipole polarizability, which needs to be measured more accurately in order to pin down isovector nuclear interactions.

In-medium effects in central heavy ion collisions at intermediate energies

Energy dissipation and cluster production in central nuclear collisions in the Fermi energy range have been investigated using the large INDRA database. A study of the in-medium nucleon-nucleon cross section, ${\ensuremath{\sigma}}_{NN}^{*}$, has been performed by comparing the results of a model with the measured isotropy ratio of the kinetic energy distributions of the detected protons. This analysis has been done for a large variety of systems at various incident energies from 20 to 100 MeV/nucleon and confirms nicely previous results with enhanced statistics in a full Monte Carlo treatment. Most importantly, it is found that ${\ensuremath{\sigma}}_{NN}^{*}$ is drastically reduced as compared to the vacuum values, due partly to Pauli blocking but also to in-medium effects for which mean values and uncertainties are given. Concerning the cluster production, a coalescence model has been developed to study the parallel and perpendicular velocity distributions of the light clusters ($A\ensuremath{\le}4$). For ${A}_{C}=3$ ($^{3}\mathrm{H}, ^{3}\mathrm{He}$), it is found that the mean internal kinetic energy of the nucleons in the cluster is reduced as compared to the vacuum value. These two results shows that any comparison between experimental and theoretical predictions in heavy-ions induced reactions around and above the Fermi energy must take into account these in-medium effects.

Constraining the in-medium nucleon-nucleon cross section from the width of nuclear giant dipole resonance

We develop a new lattice Hamiltonian method for solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation. Adopting the stochastic approach to treat the collision term and using the GPU parallel computing to carry out the calculations allows for a rather high accuracy in evaluating the collision term, especially its Pauli blocking, leading thus to a new level of precision in solving the BUU equation. Applying this lattice BUU method to study the width of giant dipole resonance (GDR) in nuclei, where the accurate treatment of the collision term is crucial, we find that the obtained GDR width of 208Pb shows a strong dependence on the in-medium nucleon-nucleon cross section σNN⁎. A very large medium reduction of σNN⁎ is needed to reproduce the measured value of the GDR width of 208Pb at the Research Center for Nuclear Physics in Osaka, Japan.

Progress of quantum molecular dynamics model and its applications in heavy ion collisions

In this review article, we first briefly introduce the transport theory and quantum molecular dynamics model applied in the study of the heavy ion collisions from low to intermediate energies. The developments of improved quantum molecular dynamics model (ImQMD) and ultra-relativistic quantum molecular dynamics model (UrQMD), are reviewed. The reaction mechanism and phenomena related to the fusion, multinucleon transfer, fragmentation, collective flow and particle production are reviewed and discussed within the framework of the two models. The constraints on the isospin asymmetric nuclear equation of state and in-medium nucleon-nucleon cross sections by comparing the heavy ion collision data with transport models calculations in last decades are also discussed, and the uncertainties of these constraints are analyzed as well. Finally, we discuss the future direction of the development of the transport models for improving the understanding of the reaction mechanism, the descriptions of various observables, the constraint on the nuclear equation of state, as well as for the constraint on in-medium nucleon-nucleon cross sections.

Particle Production in Heavy Ion Collisions at Intermediate Energies

We investigate the influence of the in-medium modifications of nucleon-nucleon cross sections on the particle production in heavy ion collisions at intermediate energies. In particular, it is shown that the pion and kaon yields and their rapidity distributions are strongly affected by the density dependence of the inelastic cross sections. On the other hand, the particle ratios depend less on the in-medium behavior of the inelastic cross sections.

Effects of the in-medium NN cross sections in heavy ion collisions on particle production

The density dependence of the in-medium nucleon-nucleon (NN) cross sections is investigated in terms of particle production in heavy ion collisions (HIC). It is found, in particular, that the in-medium modifications of the inelastic NN cross sections considerably affect the pion yields and improve the comparison with experimental information. Such studies are important in determining the still unknown behavior of the nuclear equation of state (EoS) at supra-normal densities in HIC.

Nuclear transparency in Monte Carlo neutrino event generators

Hadron cascade model is an essential part of Monte Carlo neutrino event generators that governs final state interactions of knocked-out nucleons and produced pions. It is shown that such model enriched with physically motivated modifications of nucleon-nucleon cross section and incorporation of nuclear correlation effects is able to reproduce experimental nuclear transparency data. Uncertainty of nucleon final state interactions effects is estimated and applied to recent neutrino-nucleus cross section measurements that include an outgoing proton in the experimental signal. Conclusions are drawn on a perspective of identification of events that originate from two-body current mechanism.