Effective Mass Splitting Research Articles

Nuclear symmetry energy in terms of single-nucleon potential and its effect on the proton fraction of β-stable npeμ matter

Momentum and density dependence of single-nucleon potential uτ (k, ρ, β) is analyzed using a density dependent finite range effective interaction of the Yukawa form. Depending on the choice of the strength parameters of exchange interaction, two different trends of the momentum dependence of nuclear symmetry potential are noticed which lead to two opposite types of neutron and proton effective mass splitting. The 2nd-order and 4th-order symmetry energy of isospin asymmetric nuclear matter are expressed analytically in terms of the single-nucleon potential. Two distinct behavior of the density dependence of 2nd-order and 4th-order symmetry energy are observed depending on neutron and proton effective mass splitting. It is also found that the 4th-order symmetry energy has a significant contribution towards the proton fraction of β-stable npeμ matter at high densities.

Influence of Skyrme-type interaction on HICs observables

A new version of the improved quantum molecular dynamics model has been developed by including Skyrme type momentum dependent interaction. 12 Skyrme like parameter sets {K0, S0, L, m ∗, m ∗} are adopted in the transport model code to calculate the isospin diffusion, single and double ratios of transverse emitted nucleons, neutron proton isoscaling ratios. The calculations and correlation analysis evidence that isospin diffusion observable at lower beam energy is sensitive to the slope of symmetry energy and m ∗. The high energy neutrons and protons yield ratios from reactions at different incident energies provide a sensitive observable to study the nucleon effective mass splitting, at higher beam energy. The properties of isospin asymmetric nuclear equation of state is of fundamental importance in our understanding of nature’s asymmetric objects including neutron stars as well as heavy nuclei with very different number of neutrons and protons. Currently, there exist, lot of effective interaction parameter sets [1, 2], for fitting the ground-state properties of stable nuclei, symmetric and asymmetric nuclear matter. It also leads very different neutron Equation of state which may have different nuclear matter (NM) parameters, such as incompressibility K0, isoscalar effective mass m ∗ ,s ymmetry energy coef fi cientS0, slope of symmetry energy L and isovector effec

The detector system of the Daya Bay reactor neutrino experiment

The Daya Bay experiment was the first to report simultaneous measurements of reactor antineutrinos at multiple baselines leading to the discovery of ν¯e oscillations over km-baselines. Subsequent data has provided the world׳s most precise measurement of sin22θ13 and the effective mass splitting Δmee2. The experiment is located in Daya Bay, China where the cluster of six nuclear reactors is among the world׳s most prolific sources of electron antineutrinos. Multiple antineutrino detectors are deployed in three underground water pools at different distances from the reactor cores to search for deviations in the antineutrino rate and energy spectrum due to neutrino mixing. Instrumented with photomultiplier tubes, the water pools serve as shielding against natural radioactivity from the surrounding rock and provide efficient muon tagging. Arrays of resistive plate chambers over the top of each pool provide additional muon detection. The antineutrino detectors were specifically designed for measurements of the antineutrino flux with minimal systematic uncertainty. Relative detector efficiencies between the near and far detectors are known to better than 0.2%. With the unblinding of the final two detectors’ baselines and target masses, a complete description and comparison of the eight antineutrino detectors can now be presented. This paper describes the Daya Bay detector systems, consisting of eight antineutrino detectors in three instrumented water pools in three underground halls, and their operation through the first year of eight detector data-taking.

Covariance analysis of symmetry energy observables from heavy ion collision

Using covariance analysis, we quantify the correlations between the interaction parameters in a transport model and the observables commonly used to extract information of the Equation of State of Asymmetric Nuclear Matter in experiments. By simulating 124Sn + 124Sn, 124Sn + 112Sn and 112Sn + 112Sn reactions at beam energies of 50 and 120 MeV per nucleon, we have identified that the nucleon effective mass splitting is most strongly correlated to the neutrons and protons yield ratios with high kinetic energy from central collisions especially at high incident energy. The best observable to determine the slope of the symmetry energy, L, at saturation density is the isospin diffusion observable even though the correlation is not very strong (∼0.7). Similar magnitude of correlation but opposite in sign exists for isospin diffusion and nucleon isoscalar effective mass. At 120 MeV/u, the effective mass splitting and the isoscalar effective mass also have opposite correlation for the double n/p and isoscaling p/p yield ratios. By combining data and simulations at different beam energies, it should be possible to place constraints on the slope of symmetry energy (L) and effective mass splitting with reasonable uncertainties.

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.

Toward relativistic mean-field description of [formula omitted]–nucleus reactions

In this work we study the antinucleon–nucleus optical potential in the framework of the non-linear derivative (NLD) model with momentum dependent mean-fields. We apply the NLD model to interaction of antinucleons (N¯) in nuclear matter and, in particular, to antiproton scattering on nuclei. In nuclear matter a strong suppression of the N¯-optical potential at rest and at high kinetic energies is found and caused by the momentum dependence of relativistic mean-fields. The NLD results are consistent with known empirical N¯–nucleus observations and agree well with antiproton–nucleus scattering data. This makes the NLD approach compatible with both, nucleon and antinucleon Dirac phenomenologies. Furthermore, in nuclear matter an effective mass splitting between nucleons and antinucleons is predicted.

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.

Study of spin polarized nuclear matter and finite nuclei with finite range simple effective interaction

The properties of spin polarized pure neutron matter and symmetric nuclear matter (SNM) are studied using the finite range simple effective interaction, upon its parametrization revisited. Out of the total twelve parameters involved, we now determine ten of them from nuclear matter (NM), against the nine parameters in our earlier calculation, as required in order to have predictions in both spin polarized NM and finite nuclei in unique manner being free from uncertainty found using the earlier parametrization. The information on the effective mass splitting in polarized neutron matter of the microscopic calculations is used to constrain the one more parameter, that was earlier determined from finite nucleus, and in doing so the quality of the description of finite nuclei is not compromised. The interaction with the new set of parameters is used to study the possibilities of ferromagnetic and antiferromagnetic transitions in completely polarized SNM. Emphasis is given to analyse the results analytically, as far as possible, to elucidate the role of the interaction parameters involved in the predictions.

Layer-dependent electronic structure of an atomically heavy two-dimensional dichalcogenide

The first direct measurements are reported of the evolution of the thickness-dependent electronic band structure of monolayers of a material of much current interest. Angle-resolved photoemission is performed on the few-layer single-crystal dichalcogenide WSe${}_{2}$, which is in a class of graphene-like semiconductors with a desirable band gap in the visible frequency range. These results strongly support the presence of a predicted transition from an indirect (bulk or bilayer) to direct (one monolayer) band gap. Values are obtained for the effective mass and spin-orbit splitting of few-layer WSe${}_{2}$, parameters which are very important for transport studies and device applications.

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

Constraints on nucleon effective mass splitting with heavy ion collisions

A new version of the improved quantum molecular dynamics model has been developed to include standard Skyrme interactions. Four commonly used Skyrme parameter sets, SLy4, SkI2, SkM* and Gs are adopted in the transport model code to calculate the isospin diffusion observables as well as single and double ratios of transverse emitted nucleons. While isospin diffusion observables are sensitive to the symmetry energy term, they are not very sensitive to the nucleon effective mass splitting parameters in the interactions. Our calculations show that the high energy neutrons and protons and their ratios from reactions at different incident energies provide a robust observable to study the momentum dependence of the symmetry potential which leads to the effective mass splitting. However the sensitivity of effective mass splitting effect on the double n/p yield ratios decreases with increasing beam energy, even though high energy protons and neutrons are produced more abundantly at high beam energy. Our calculations show that the optimum incident energy to study nucleon effective masses is between 100–200 MeV per nucleon.

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.