Neutron-proton Effective Mass Splitting Research Articles

Neutron-proton effective mass splitting in neutron-rich matter

Neutron-proton effective mass splitting in neutron-rich matter

Influence of the treatment of initialization and mean-field potential on the neutron to proton yield ratios

In this work, we first investigate how to reproduce and how well one can reproduce the Woods-Saxon density distribution of initial nuclei in the framework of the improved quantum molecular dynamics model. Then, we propose a new treatment for the initialization of nuclei which is correlated with the nucleonic mean-field potential by using the same potential energy density functional. In the mean field potential, the three-body force term is accurately calculated. Based on the new version of the model, the influences of precise calculations of the three-body force term, the slope of symmetry energy, the neutron-proton effective mass splitting, and the width of the wave packet on heavy ion collision observables, such as the neutron to proton yield ratios for emitted free nucleons $[R(n/p)]$ and for coalescence invariant nucleons $[{R}_{ci}(n/p)]$ for $^{124}\mathrm{Sn}+^{112}\mathrm{Sn}$ at the beam energy of 200 MeV per nucleon, are discussed. Our calculations show that the spectra of neutron to proton yield ratios $[R(n/p)]$ can be used to probe the slope of symmetry energy ($L$) and the neutron-proton effective mass splitting. In detail, the $R(n/p)$ in the low kinetic energy region can be used to probe the slope of symmetry energy ($L$). With a given $L$, the inclination of $R(n/p)$ to kinetic energy (${E}_{k}$) can be used to probe the effective mass splitting. In the case where the neutron-proton effective mass splitting is fixed, $R(n/p)$ at high kinetic energy can also be used to learn the symmetry energy at suprasaturation density.

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.

Probing neutron–proton effective mass splitting using nuclear stopping and isospin mix in heavy-ion collisions in GeV energy region

The ramifications of the effective mass splitting on the nuclear stopping and isospin tracer during heavy-ion collisions within the gigaelectron volt energy region are studied using an isospin-dependent quantum molecular dynamics model. Three isotope probes, i.e., a proton, deuteron, and triton, are used to calculate the nuclear stopping. Compared to the $$m_\text {n}^{*} > m_\text {p}^{*}$$ case, the $$m_\text {n}^{*} < m_\text {p}^{*}$$ parameter results in a stronger stopping for protons but a weaker stopping for tritons. The calculations of the isospin tracer show that the $$m_\text {n}^{*} > m_\text {p}^{*}$$ parameter results in a higher isospin mix than the $$m_\text {n}^{*} < m_\text {p}^{*}$$ parameter. The rapidity and impact parameter dependences of the isospin tracer are also studied. A constraining of the effective mass splitting using the free nucleons with high rapidity and in a central rather than peripheral collision is suggested.

Nucleon effective mass splitting and density-dependent symmetry energy effects on elliptic flow in heavy ion collisions at Elab= 0.09 ~ 1.5 GeV/nucleon * * Supported in part by the National Natural Science Foundation of China (11875125, 11947410, 11847315, 11505057); the Zhejiang Provincial Natural Science Foundation of China (LY18A050002, LY19A050001) and the Ten Thousand Talent Program of Zhejiang province (2018R52017)

By incorporating an isospin-dependent form of the momentum-dependent potential in the ultra-relativistic quantum molecular dynamics (UrQMD) model, we systematically investigate effects of the neutron-proton effective mass splitting = and the density-dependent nuclear symmetry energy on the elliptic flow in + collisions at beam energies from 0.09 to 1.5 GeV/nucleon. It is found that at higher beam energies ( 0.25 GeV nucleon) with the approximately 75 MeV difference in slopes of the two different , and the variation of ranging from –0.03 to 0.03 at saturation density with isospin asymmetry , the has a stronger influence on the difference in between neutrons and protons, i.e., , than has. Meanwhile, at lower beam energies ( 0.25 GeV nucleon), is sensitive to both the and the . Moreover, the influence of on is more evident with the parameters of this study when using the soft, rather than stiff, symmetry energy.

Reexamining the isospin-relaxation time in intermediate-energy heavy-ion collisions

Isospin relaxation times characterizing isospin transport processes between the projectile and the target with different $N/Z$ ratios and that between the neck and the spectator with different isospin asymmetries and densities in intermediate-energy heavy-ion collisions are studied within an isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model using the lattice Hamiltonian approach. The respective roles and time scales of the isospin diffusion and drift as the major mechanisms of isospin transport in intermediate-energy heavy-ion collisions are discussed. Effects of nuclear symmetry energy and neutron-proton effective mass splitting on the isospin relaxation times are examined.

Constraining simultaneously nuclear symmetry energy and neutron-proton effective mass splitting with nucleus giant resonances using a dynamical approach

With a newly improved isospin- and momentum-dependent interaction and an isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, we have investigated the effects of the slope parameter $L$ of the nuclear symmetry energy and the isospin splitting of the nucleon effective mass $m_{n-p}^*=(m_n^*-m_p^*)/m$ on the centroid energy of the isovector giant dipole resonance and the electric dipole polarizability in $^{208}$Pb. With the isoscalar nucleon effective mass $m_s^*=0.7m$ constrained by the empirical optical potential, we obtain a constraint of $L=64.29\pm11.84 (\rm MeV)$ and $m_{n-p}^*= (-0.019 \pm 0.090)\delta$, with $\delta$ being the isospin asymmetry of nuclear medium. With the isoscalar nucleon effective mass $m_s^*=0.84m$ extracted from the excitation energy of the isoscalar giant quadruple resonance in $^{208}$Pb, we obtain a constraint of $L=53.85\pm10.29 (\rm MeV)$ and $m_{n-p}^*= (0.216 \pm 0.114)\delta$.

Mass-splitting effect on flows in heavy-ion collisions in the Fermi-energy domain

In this work, based on one updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model in which the Skyrme-like (parabolic) isospin- and momentum-dependent interaction is included, the effect of the neutron-proton effective mass splitting (NPEMS) on flows in heavy-ion collisions at the Fermi-energy domain (between 40 and 100 MeV/nucleon) is focused. Using various Skyrme interactions (all exhibiting similar values of isoscalar incompressibility but very different NPEMS), both rapidity- and transverse-momentum-dependent directed and elliptic flows of free neutrons and protons are calculated. Our calculations show that the effect of NPEMS on the flows of free nucleons is more obvious at ${E}_{\mathrm{lab}}=100\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}/\mathrm{nucleon}$ than at $40 \mathrm{MeV}/\mathrm{nucleon}$. At ${E}_{\mathrm{lab}}=100\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}/\mathrm{nucleon}$, the directed flows of both neutrons and protons are easily affected by the NPEMS, while the elliptic flow of protons is not very sensitive to the NPEMS at both energies. It is suggested that the directed flow is better than the elliptic flow for probing the NPEMS.

Reexamination of the neutron-to-proton-ratio puzzle in intermediate-energy heavy-ion collisions

Incorporating a newly improved isospin- and momentum-dependent interaction in the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model IBUU11, we have investigated relative effects of the density dependence of nuclear symmetry energy $E_{sym}(\rho)$ and the neutron-proton effective mass splitting $m^*_n-m^*_p$ on the neutron/proton ratio of free nucleons and those in light clusters. It is found that the $m^*_n-m^*_p$ has a relatively stronger effect than the $E_{sym}(\rho)$ and the assumption of $m^*_n\leq m^*_p$ leads to a higher neutron/proton ratio. Moreover, this finding is independent of the in-medium nucleon-nucleon cross sections used. However, results of our calculations using the $E_{sym}(\rho)$ and $m^*_n-m^*_p$ both within their current uncertainty ranges are all too low compared to the recent NSCL/MSU double neutron/proton ratio data from central $^{124}$Sn+$^{124}$Sn and $^{112}$Sn+$^{112}$Sn collisions at 50 and 120 MeV/u, thus calling for new mechanisms to explain the puzzlingly high neutron/proton ratio observed in the experiments.

Neutron–proton effective mass splitting in neutron-rich matter and its impacts on nuclear reactions

The neutron–proton effective mass splitting in neutron-rich nucleonic matter reflects the spacetime nonlocality of the isovector nuclear interaction. It affects the neutron/proton ratio during the earlier evolution of the Universe, cooling of proto-neutron stars, structure of rare isotopes and dynamics of heavy-ion collisions. While there is still no consensus on whether the neutron–proton effective mass splitting is negative, zero or positive and how it depends on the density as well as the isospin-asymmetry of the medium, significant progress has been made in recent years in addressing these issues. There are different kinds of nucleon effective masses. In this mini-review, we focus on the total effective masses often used in the non-relativistic description of nuclear dynamics. We first recall the connections among the neutron–proton effective mass splitting, the momentum dependence of the isovector potential and the density dependence of the symmetry energy. We then make a few observations about the progress in calculating the neutron–proton effective mass splitting using various nuclear many-body theories and its effects on the isospin-dependence of in-medium nucleon–nucleon cross-sections. Perhaps, our most reliable knowledge so far about the neutron–proton effective mass splitting at saturation density of nuclear matter comes from optical model analyses of huge sets of nucleon–nucleus scattering data accumulated over the last five decades. The momentum dependence of the symmetry potential from these analyses provide a useful boundary condition at saturation density for calibrating nuclear many-body calculations. Several observables in heavy-ion collisions have been identified as sensitive probes of the neutron–proton effective mass splitting in dense neutron-rich matter based on transport model simulations. We review these observables and comment on the latest experimental findings.

Neutron–proton effective mass splitting in neutron-rich matter at normal density from analyzing nucleon–nucleus scattering data within an isospin dependent optical model

The neutron–proton effective mass splitting in asymmetric nucleonic matter of isospin asymmetry δ and normal density is found to be mn−p⁎≡(mn⁎−mp⁎)/m=(0.41±0.15)δ from analyzing globally 1088 sets of reaction and angular differential cross sections of proton elastic scattering on 130 targets with beam energies from 0.783 MeV to 200 MeV, and 1161 sets of data of neutron elastic scattering on 104 targets with beam energies from 0.05 MeV to 200 MeV within an isospin dependent non-relativistic optical potential model. It sets a useful reference for testing model predictions on the momentum dependence of the nucleon isovector potential necessary for understanding novel structures and reactions of rare isotopes.

Neutron-proton effective mass splitting in terms of symmetry energy and its density slope

Using a simple density-dependent finite-range effective interaction having Yukawa form, the density dependence of isoscalar and isovector effective masses is studied. The isovector effective mass is found to be different for different pairs of like and unlike nucleons. Using HVH theorem, the neutron-proton effective mass splitting is represented in terms of symmetry energy and its density slope. It is again observed that the neutron-proton effective mass splitting has got a positive value when isoscalar effective mass is greater than the isovector effective mass and has a negative value for the opposite case. Furthermore, the neutron-proton effective mass splitting is found to have a linear dependence on asymmetry β. The second-order symmetry potential has a vital role in the determination of density slope of symmetry energy but it does not have any contribution on neutron-proton effective mass splitting. The finite-range effective interaction is compared with the SLy2, SKM, f−, f0, and f+ forms of interactions.

Symmetry energy dependence of light fragment production in heavy-ion collisions

We study the pre-equilibrium light cluster emission in low to intermediate energy heavy ion collisions in transport simulations as a means to obtain information about the density and momentum dependence of the nuclear symmetry potential, i.e. about the asy-stiffness and the neutron-proton effective mass splitting of the symmetry energy. We find that the study of n/p and t/He-3 ratios as a function of the energy of the emitted particles may allow to disentangle these two behaviors The t/He-3 ratios appear to carry similar information as the n/p ratios, making this a promising option for experimental investigations. More n-rich systems enhance the sensitivity to the symmetry energy, while double ratios between n-rich and n-poor systems tend to reduce it. A preliminary comparison to experimental data for the Xe-136, Xe-124 + (124, 112) Sn systems is also shown.

Nuclear collective flows as a probe to the neutron–proton effective mass splitting

The isospin-dependent quantum molecular dynamics model is used to investigate the nuclear collective flow observables in semicentral 197Au+197Au collisions at 400A MeV. It is found that the calculated results can reproduce both the experimental data and the other theoretical calculations. We find that the cluster production influences the rapidity dependence of directed flow of protons but less influences the results of tritons. Neutron–proton differential collective flows have larger values when taking the neutron effective mass less than the one of protons as compared with the case of neutron effective mass greater than the one of protons at larger rapidities and transverse momenta. Thus neutron–proton differential collective flows are proposed to be a useful probe to the neutron–proton effective mass splitting and the momentum-dependent symmetry potential.

Constraining neutron-proton effective mass splitting and density dependence of nuclear symmetry energy using heavy-ion collisions

Constraining neutron-proton effective mass splitting and density dependence of nuclear symmetry energy using heavy-ion collisions

Symmetry Energy Dependence of Light Fragment Production in Heavy Ion Collisions

We study the pre-equilibrium light cluster emission in low to intermediate energy heavy ion collisions in transport simulations as a means to obtain information about the density and momentum dependence of the nuclear symmetry potential, i.e. about the asy-stiffness and the neutron-proton effective mass splitting of the symmetry energy. We find that the study of n/p and t/He-3 ratios as a function of the energy of the emitted particles may allow to disentangle these two behaviors The t/He-3 ratios appear to carry similar information as the n/p ratios, making this a promising option for experimental investigations. More n-rich systems enhance the sensitivity to the symmetry energy, while double ratios between n-rich and n-poor systems tend to reduce it. A preliminary comparison to experimental data for the Xe-136, Xe-124 + (124, 112) Sn systems is also shown.

Neutron-proton effective mass splitting in a Boltzmann-Langevin approach

Neutron-proton effective mass splitting in a Boltzmann-Langevin approach

Hartree-Fock-Bogoliubov nuclear mass model with 0.50 MeV accuracy based on standard forms of Skyrme and pairing functionals

We present a new Hartree-Fock-Bogoliubov nuclear mass model based on standard forms of Skyrme and pairing functionals, which corresponds to the most accurate mass model we ever achieved within the framework of the nuclear energy density functional theory. Our new mass model is characterized by a model standard deviation ${\ensuremath{\sigma}}_{\mathrm{mod}}=0.500$ MeV with respect to essentially all the 2353 available mass data for nuclei with neutron and proton numbers larger than 8. At the same time, the underlying Skyrme functional yields a realistic description of infinite homogeneous nuclear matter properties, as determined by realistic calculations and by experiments; these include in particular the incompressibility coefficient, the pressure in charge-symmetric nuclear matter, the neutron-proton effective mass splitting, the stability against spin and spin-isospin fluctuations, as well as the neutron-matter equation of state.

Constraining the neutron–proton effective mass splitting using empirical constraints on the density dependence of nuclear symmetry energy around normal density

According to the Hugenholtz–Van Hove theorem, nuclear symmetry energy Esym(ρ) and its slope L(ρ) at an arbitrary density ρ are determined by the nucleon isovector (symmetry) potential Usym(ρ,k) and its momentum dependence ∂Usym∂k. The latter determines uniquely the neutron–proton effective k-mass splitting mn−p⁎(ρ,δ)≡(mn⁎−mp⁎)/m in neutron-rich nucleonic matter of isospin asymmetry δ. Using currently available constraints on the Esym(ρ0) and L(ρ0) at normal density ρ0 of nuclear matter from 28 recent analyses of various terrestrial nuclear laboratory experiments and astrophysical observations, we try to infer the corresponding neutron–proton effective k-mass splitting mn−p⁎(ρ0,δ). While the mean values of the mn−p⁎(ρ0,δ) obtained from most of the studies are remarkably consistent with each other and scatter very closely around an empirical value of mn−p⁎(ρ0,δ)=0.27⋅δ, it is currently not possible to scientifically state surely that the mn−p⁎(ρ0,δ) is positive within the present knowledge of the uncertainties. Quantifying, better understanding and then further reducing the uncertainties using modern statistical and computational techniques in extracting the Esym(ρ0) and L(ρ0) from analyzing the experimental data are much needed.

Neutron–proton effective mass splitting and thermal evolution in neutron-rich matter

The thermal evolution of properties of neutron-rich asymmetric nuclear matter such as entropy density, internal energy density, free energy density and pressure is studied in the non-relativistic mean field theory using finite range effective interactions. In this framework, the thermal evolution of nuclear matter properties is directly connected to the neutron and proton effective mass properties. Depending on the magnitude of neutron–proton effective mass splittings, two distinct behaviours in the thermal evolution of nuclear matter properties are noticed.