We present the temperature and density dependence of symmetry energy for nuclear matter at finite temperature based on the approach of the thermodynamics with Skyrme energy density functional. We first classify the Skyrme interactions into 7 groups according to the range of neutron and proton effective mass in neutron matter limit(99.99 per cent neutron in the matter). We find that there is obvious correlation between the temperature dependence of the symmetry energy and the splitting of the neutron and proton effective mass. For some Skyrme interactions with $m^{*}_{n}>m^{*}_{p}$ and strong splitting of the neutron and proton effective mass in asymmetric nuclear matter, a transition of the temperature dependence of symmetry energy from decreasing with temperature at low densities to increasing with temperature at high densities appears. For other Skyrme interactions, we do not observe such phenomenon. Our study show that the symmetry energy in hot asymmetric matter not only depends on symmetry potential part but also on the splitting of the neutron and proton effective mass to a certain extent.
Varied signature splitting phenomena in odd proton rare earth nuclei are investigated. Signature splitting as functions of $K$ and $j$ in the angular momentum projection theory is explicitly shown and compared with those of the particle rotor model. The observed deviations from these rules are due to the band mixings. The recently measured $^{169}$Ta high spin data are taken as a typical example where fruitful information about signature effects can be extracted. Six bands, two of which have not yet been observed, were calculated and discussed in detail in this paper. The experimentally unknow…
The latest experimental data on nuclei at $^{132}$Sn permit us for the first time to determine the spin-orbit splittings of neutrons and protons in identical orbits in this neutron-rich doubly-magic region and compare the case to that of $^{208}$Pb. Using the new results, which are now consistent for the two neutron-rich doubly magic regions, a theoretical analysis defines the isotopic dependence of the mean field spin-orbit potential and leads to a simple explicit expression for the difference between the spin-orbit splittings of neutrons and protons. The isotopic dependence is explained in t…
We study the spin-orbit splitting ($ls$-splitting) for the proton d-orbits in 23F in the Hartree-Fock framework with the tensor force in the exchange channel. 23F has one more proton around the neutron-rich nucleus 22O. A recent experiment indicates that the ls-splitting for the proton d-orbits in 23F is reduced from that in 17F. Our calculation shows that the ls-splitting in 23F becomes smaller by about a few MeV due to the tensor force. This effect comes from the interaction between the valence proton and the occupied neutrons in the 0d5/2 orbit through the tensor force and makes the ls-spli…
On the basis of relativistic mean field calculations, we predict that the spin-orbit splitting of $p_{3/2}$ and $p_{1/2}$ neutron orbits depends sensitively on the magnitude of the proton density near the center of the nucleus, and in particular on the occupation of $s_{1/2}$ proton orbits. We focus on two exotic nuclei, $^{46}$Ar and $^{206}$Hg, in which the presence of a pair of $s_{1/2}$ proton holes is predicted to cause the splitting between the $p_{3/2}$ and $p_{1/2}$ neutron orbits near the Fermi surface to be much smaller than in the nearby doubly-magic nuclei $^{48}$Ca and $^{208}$Pb.…
Within the framework of an isospin and momentum dependent transport model, the emissions of isospin particles (nucleons and light clusters) squeezed out in heavy-ion collisions are investigated as probes of the poorly known symmetry energy at high baryon density. Two different mass splittings of neutrons and protons in nuclear medium as $m_{n}^{\ast}>m_{p}^{\ast}$ and $m_{n}^{\ast}<m_{p}^{\ast}$ are used in the model and their influence on the isospin emission in heavy-ion collisions is discussed thoroughly. The competition between the stiffness and the momentum dependence of the symmetry pote…
A systematic and specific pattern due to the effects of the tensor forces is found in the evolution of spin-orbit splittings in neutron drops. This result is obtained from relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. It forms an important guide for future microscopic derivations of relativistic and nonrelativistic nuclear energy density functionals.
We discuss the one-body potentials for protons and neutrons obtained from Dirac-Brueckner-Hartree-Fock calculations of neutron-rich matter, in particular their dependence upon the degree of proton/neutron asymmetry. The closely related symmetry potential is compared with empirical information from the isovector component of the nuclear optical potential.
Spin-polarized symmetric nuclear matter is studied within the Dirac-Brueckner-Hartree-Fock approach. We pay particular attention to the difference between the one-body potentials of upward and downward polarized nucleons. This is formally analogous to the "Lane potential" for isospin-asymmetric nuclear matter. We point out the necessity for additional information on this fundamentally important quantity and suggest ways to constrain it.
Calculations of nuclear masses, using nuclear density functional theory, are presented for even-even nuclei spanning the nuclear chart. The resulting binding energy differences can be interpreted in terms of valence proton-neutron interactions. These are compared globally, regionally, and locally with empirical values. Overall, excellent agreement is obtained. Discrepancies highlight neglected degrees of freedom and can point to improved density functionals.
Isospin-breaking effects in nuclear matter are studied in the framework of a medium-modified Skyrme model. The proposed effective Lagrangian incorporates both the medium influence of the surrounding nuclear environment on the single nucleon properties and an explicit isospin-breaking effect in the mesonic sector. The approach predicts that the neutron-proton mass difference decreases in isospin-symmetric nuclear matter but by a very small amount only.
The difference in elliptic flow $v_{2}$ between protons and antiprotons, produced in $^{197}\text{Au}+^{197}\text{Au}$ collisions at center-of-mass energies $\sqrt{s_{NN}}=5-12~\text{GeV}$, is studied within a modified version of the ultrarelativistic quantum molecular dynamics (UrQMD) model. Two different model scenarios are compared: the cascade mode and the mean field mode which includes potential interactions for both formed and pre-formed hadrons. The model results for the elliptic flow of protons and the relative $v_{2}$ difference between protons and antiprotons obtained from the mean f…
We investigate the $^1S_0$ neutron and proton superfluidity in isospin asymmetric nuclear matter. We have concentrated on the isospin dependence of the pairing gaps and the effect of a microscopic three-body force. It is found that as the isospin asymmetry goes higher, the neutron $^1S_0$ superfluid phase shrinks gradually to a smaller density domain, while the proton one extends rapidly to a much wider density domain. The three-body force turns out to weaken the neutron $^1S_0$ superfluidity slightly, but it suppresses strongly the proton $^1S_0$ superfluidity at high densities in nuclear mat…
A new Skyrme functional has been developed with tensor term guided by ab initio relativistic Brueckner-Hartree-Fock (RBHF) studies on neutron-proton drops. Instead of extracting information on the tensor force from experimental single-particle energy splittings, the RBHF calculations do not contain beyond mean-field effects such as particle-vibration coupling and therefore the information on the tensor force can be obtained without ambiguities. The new functional gives a good description of nuclear ground-state properties as well as various giant resonances. The description for the evolution o…
We study the nuclear stopping in high energy nuclear collisions using the constituent quark model. It is assumed that wounded nucleons with different number of interacted quarks hadronize in different ways. The probabilities of having such wounded nucleons are evaluated for proton-proton, proton-nucleus and nucleus-nucleus collisions. After examining our model in proton-proton and proton-nucleus collisions and fixing the hadronization functions, it is extended to nucleus-nucleus collisions. It is used to calculate the rapidity distribution and the rapidity shift of final state protons in nucle…
Based on an improved isospin- and momentum-dependent interaction, we have studied the qualitative effect of isospin splitting of nucleon effective mass on the specific shear viscosity of neutron-rich nuclear matter from a relaxation time approach. It is seen that for $m_n^\star>m_p^\star$, the relaxation time of neutrons is smaller and the neutron flux between flow layers is weaker, leading to a smaller specific shear viscosity of neutron-rich matter compared to the case for $m_n^\star<m_p^\star$. The effect is larger in nuclear matter at higher densities, lower temperatures, and larger isospi…
Isospin-breaking effects in the baryonic sector are studied in the framework of a medium-modified Skyrme model. The neutron-proton mass difference in infinite, asymmetric nuclear matter is discussed. In order to describe the influence of the nuclear environment on the skyrmions, we include energy-dependent charged and neutral pion optical potentials in the s- and p-wave channels. The present approach predicts that the neutron-proton mass difference is mainly dictated by its strong part and that it strongly decreases in neutron matter.
The change of the probability of proton emission in nuclear photoeffect due to an intense coherent (laser) field is discussed near the threshold, where the hindering effect of the Coulomb field of the remainder nucleus is essential. The ratio of laser-assisted and laser free differential cross section is deduced and found to be independent of the polarization state of the $γ$ field and the two types of initial nuclear state considered. The numerical values of this ratio are given at some characteristic parameters of the intense field.
Within Bombaci's phenomenological single-nucleon potential model we study the neutron-proton effective mass splitting $m_n^*- m_p^*$ in neutron-rich matter. It is shown that an effective mass splitting of $m_n^*<m_p^*$ leads to a symmetry potential that is inconsistent with the energy dependence of the Lane potential constrained by the nucleon-nucleus scattering experimental data.
We calculate the mean free path of protons and neutrons in symmetric and asymmetric nuclear matter, based on microscopic in-medium nucleon-nucleon cross sections. Those are obtained from calculations of the G-matrix including relativistic "Dirac" effects. The dependence of the mean free path on energy and isospin asymmetry is discussed. We conclude by suggesting possible ways our microscopic predictions may be helpful in conjunction with studies of rare isotopes.
The location of the proton dripline in a new phenomenological mass formula is calculated. Predictions of different mass formulas for the dripline are compared. The implications of the new mass formula for rapid proton nucleosynthesis beyond $^{56}$Ni are discussed. It is seen that the new formula indicates that masses up to A=80 are easily synthesized in a typical X-ray burst.
A shell-model study of proton-neutron pairing in f - p shell nuclei using a parametrized hamiltonian that includes deformation and spin-orbit effects as well as isoscalar and isovector pairing is reported. By working in a shell-model framework we are able to assess the role of the various modes of proton-neutron pairing in the presence of nuclear deformation without violating symmetries. Results are presented for $^{44}$Ti, $^{46}$Ti and $^{48}$Cr.
An experimental observation of proton decay would be a spectacular proof of grand unification. Currently, the best constraint on the proton lifetime for the p->e+ pi0 decay channel, coming from the Super-Kamiokande experiment, reaches 8*10^33 years. To improve the measurement, much bigger detectors should be constructed. Moreover, a better description of the bound-nucleon states and of the propagation of the proton-decay products through nuclear matter have to be developed. In this article special attention is paid to the argon nucleus because a liquid argon detector is a promising candidate f…
In the present work, we systematically study the proton radioactivity half-lives of 33 spherical nuclei based on the relationship between the Skyrme parameters and the macroscopic quantities of nuclear matter. Using the two-potential approach with the spherical Skyrme-Hartree-Fock model, the correlation between proton radioactivity half-life and macroscopic quantities was analyzed. Moreover, we obtained a new Skyrme parameter set by fitting the two most weighted macroscopic quantities. Compared with Skyrme parameters MSL0 and the theoretical model of proton radioactivity UDLP, the theoretical …
We introduce a Hartree-Fock-Bogoliubov mean-field approach to treat the problem of proton emission from a deformed nucleus. By substituting a rigid rotor in a particle-rotor-model with a mean-field we obtain a better description of experimental data in $^{141}$Ho. The approach also elucidates the softening of kinematic coupling between particle and collective rotation, the Coriolis attenuation problem.
A shell-model study of proton-neutron pairing in $2p1f$ shell nuclei using a parametrized hamiltonian that includes deformation and spin-orbit effects as well as isoscalar and isovector pairing is reported. By working in a shell-model framework we are able to assess the role of the various modes of proton-neutron pairing in the presence of nuclear deformation without violating symmetries. Results are presented for $^{44}$Ti, $^{45}$Ti, $^{46}$Ti, $^{46}$V and $^{48}$Cr to assess how proton-neutron pair correlations emerge under different scenarios. We also study how the presence of a one-body …
We investigate the effects of charge independence and charge symmetry breaking in neutron-rich matter. We consider neutron and proton properties in isospin-asymmetric matter at normal densities as well as the high-density neutron matter equation of state and the bulk properties of neutron stars. We find charge symmetry and charge independence breaking effects to be very small.
Dynamics of strange particles produced in proton induced nuclear reactions near threshold energies has been investigated within the Lanzhou quantum molecular dynamics (LQMD) transport model. The in-medium modifications on particle production in dense nuclear matter are considered through corrections on the elementary cross sections via the effective mass and the mean-field potentials. It is found that the attractive antikaon-nucleon potential enhances the subthreshold $\bar{K}$ production and also influences the structure of inclusive spectra. The strangeness production is strongly suppressed …
We show that the non-spherical charge distribution of the proton manifests itself in hydrogen hyperfine splitting as an increase (in absolute value) of the proton Zemach radius and polarization contributions.
Hyperfine splitting in Bi$^{82+}$ and Pb$^{81+}$ ions was calculated using continuum RPA approach with effective residual forces. To fix the parameters of the theory the nuclear magnetic dipole moments of two one- particle and two one-hole nuclei around $^{208}$Pb were calculated using the same approach. The contribution from velocity dependent two-body spin- orbit residual interaction was calculated explicitly. Additionally, the octupole moment of $^{209}$Bi and the hfs in muonic bismuth atom were calculated as well in the same approach. All the calculated observables, except the electronic h…
We present the leading-order prediction of baryon chiral perturbation theory for the proton polarizability contribution to the 2S hyperfine splitting in muonic hydrogen, and compare with the results of dispersive calculations.
The multiple scattering of high-energy particles in a thick target is fromulated in an impact parameter representation. A formalism similar but not identical to that of Moliere is obtained. We show that calculations of particle beam broadening due to multiple Coulomb scattering alone can be given in closed form. The focus of this study is on whether or not the broadening of the Coulomb angular distribution prevents the retrieval of nuclear-interaction information from mesauring the angular distributions of charged partiles scattered from a thick target. For this purpose, we study multiple scat…
The thermal evolution of properties of neutron rich asymmetric nuclear matter such as entropy density, internal energy density, free energy density and pressure are 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.
The half-lives of proton radioactivity of proton emitters are investigated theoretically by using KDE0v1 Skyrme interaction. The total barrier potential in the proton radioactive nuclei is calculated as the sum of the nuclear, Coulomb and centrifugal contributions. The Hartree-Fock nuclear density distributions is used in calculating the nuclear as well as the Coulomb interaction potentials. The quantum mechanical tunneling probability is calculated within the WKB approximation. These calculations provide reasonable estimates for the observed proton radioactivity lifetimes.
The elastic and inelastic scattering of protons from mirror nuclei $^{18}$Ne and $^{18}$O are studied in a folding model approach. For comparison, two different effective interactions are folded with Hartree-Fock densities to obtain the nuclear interaction potentials. Both of them provide equivalent descriptions to the data and the deformation parameters extracted from inelastic scattering are reasonable. The density dependence parameters obtained from nuclear matter calculations and used for present analysis also provide a good estimate for the nuclear mean free path. The present formalism un…
The dynamics of $η$ meson produced in proton-induced nuclear reactions via the decay of N$^{\ast}(1535)$ has been investigated within the Lanzhou quantum molecular dynamics transport model (LQMD). The in-medium modifications of the $η$ production in dense nuclear matter are included in the model, in which an attractive $η$-nucleon potential is implemented. The impact of the $η$ optical potential on the $η$ dynamics is investigated. It is found that the attractive potential leads to the reduction of high-momentum (kinetic energy) production from the spectra of momentum distributions and inclusi…
We present the derivation of the formulas for the proton structure-dependent terms in the hyperfine splitting of muonic hydrogen. We use compatible conventions throughout the calculations to derive a consistent set of formulas that reconcile differences between our results and some specific terms in earlier work. Convention conversion corrections are explicitly presented, which reduce the calculated hyperfine splitting by about 46 ppm. We also note that using only modern fits to the proton elastic form factors gives a smaller than historical spread of Zemach radii and leads to a reduced uncert…
We present a precise determination of the polarizability and other proton structure dependent contributions to the hydrogen hyperfine splitting, based heavily on the most recent published data on proton spin dependent structure functions from the EG1 experiment at the Jefferson Laboratory. As a result, the total calculated hyperfine splitting now has a standard deviation slightly under 1 part-per-million, and is about 1 standard deviation away from the measured value. We also present results for muonic hydrogen hyperfine splitting, taking care to ensure the compatibility of the recoil and pola…
We show how the charge symmetry of strong interactions can be used to relate the proton and neutron asymptotic normalization coefficients (ANCs) of the one nucleon overlap integrals for light mirror nuclei. This relation extends to the case of real proton decay where the mirror analog is a virtual neutron decay of a loosely bound state. In this case, a link is obtained between the proton width and the squared ANC of the mirror neutron state. The relation between mirror overlaps can be used to study astrophysically relevant proton capture reactions based on information obtained from transfer re…
We calculate the proton-nucleus total reaction cross sections at different energies of incident protons within the optical limit approximation of the Glauber theory. The isospin effect has been taken into account. The nucleon distribution is obtained in the framework of macroscopic nuclear models in a way depending on the equation of state of uniform nuclear matter near the saturation density. We find that at an energy of order 40 MeV, the reaction cross section calculated for neutron- rich isotopes significantly increases as the parameter L characterizing the density dependence of the symmetr…
Starting from the striking similarity of proton-neutron multiplets in 134Sb and 210Bi, we perform a shell-model study of nuclei with two additional protons or neutrons to find out to what extent this analogy persists. We employ effective interactions derived from the CD-Bonn nucleon-nucleon potential renormalized by use of the V-low-k approach. The calculated results for 136Sb, 212Bi, 136I, and 212At are in very good agreement with the available experimental data. The similarity between 132Sn and 208Pb regions is discussed in connection with the effective interaction, emphasizing the role of c…
The interaction of orbital electrons with the charge and magnetic moment of the nucleus polarizes it, and the detailed description requires a careful treatment of the nuclear vector polarizability. We present a complete and closed form expression for the resulting contribution to hyperfine splitting in light atomic systems.
Within an isospin and momentum dependent transport model, the dynamics of isospin particles (nucleons and light clusters) in Fermi-energy heavy-ion collisions are investigated for constraining the isospin splitting of nucleon effective mass and the symmetry energy at subsaturation densities. The mass splitting of $m^{*}_{n}>m^{*}_{p}$ and $m^{*}_{n}<m^{*}_{p}$ in nuclear matter and the different stiffness of symmetry energy are used in the model. The single and double neutron to proton ratios of free nucleons and light particles are thoroughly investigated in the isotopic nuclear reactions of …
Nuclear structure corrections of orders $Zα\, E_F$ and $(Zα)^2 E_F$ are calculated for the hyperfine splitting of the muonic deuterium. The obtained results disagree with previous calculations and lead to a $5\,σ$ disagreement with the current experimental value of the $2S$ hyperfine splitting in $μ$D.
The nuclear neutron-proton contact is introduced, generalizing Tan's work, and evaluated from medium energy nuclear photodisintegration experiments. To this end we reformulate the quasi-deuteron model of nuclear photodisintegration and establish the bridge between the Levinger constant and the contact. Using experimental evaluations of Levinger's constant we extract the value of the neutron-proton contact in finite nuclei and in symmetric nuclear matter. Assuming isospin symmetry we propose to evaluate the neutron-neutron contact through measurement of photonuclear spin correlated neutron-prot…
We derive medium-induced splitting kernels for energetic partons that undergo interactions in dense QCD matter before a hard-scattering event at large momentum transfer $Q^2$. Working in the framework of the effective theory ${\rm SCET}_{\rm G}\,$, we compute the splitting kernels beyond the soft gluon approximation. We present numerical studies that compare our new results with previous findings. We expect the full medium-induced splitting kernels to be most relevant for the extension of initial-state cold nuclear matter energy loss phenomenology in both p+A and A+A collisions.
We investigate the influence of the spatial extent of the proton magnetization and charge densities on the 2S hyperfine splitting in muonic hydrogen. The use of a non-perturbative relativistic Dirac approach leads to corrections of 15% to values obtained from the perturbative treatment encapsulated by the Zemach radius, which surpass the next-leading order contribution in the perturbation series by an order of magnitude.
The neutron-proton effective mass splitting in neutron-rich nucleonic matter reflects the space-time nonlocality of the isovector nuclear interaction. It affects the neutron/proton ratio during the earlier evolution of the Universe, cooling of protoneutron 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 yeas in addressing these …
A recapitulatory analysis of total nuclear cross sections of various nuclei is presented, which yields detailed knowledge on the different physical processes such as potential/resonance scatter and nuclear reactions. The physical base for potential/resonance scatter and the threshold energy resulting from Coulomb repulsion of nuclei are collective/oscillator models. The part pertaining to the nuclear reactions can only be determined by the microscopic theory (Schrödinger equation and strong interactions). The physical impact is the fluence decrease of proton beams in different media and the sc…
Nuclear modification factor ($R_{cp}$) of protons and pions are investigated by simulating Au + Au collisions from 0.8 to 1.8$A$ GeV in a framework of an isospin-dependent quantum molecular dynamics (IQMD) model. $R_{cp}$ of protons rises with the increase of \pt~ at different beam energies owing to radial flow and Cronin effect. The rate of increase of \rcp~ is suppressed at higher beam energies. The significant difference of $R_{cp}$ between protons and pions indicates different medium effects between protons and pions. By changing the in-medium nucleon-nucleon cross section, the $R_{cp}$ of…
The neutron-proton effective $k$-mass splitting in asymmetric nucleonic matter of isospin asymmetry $δ$ and normal density is found to be $m^{*}_{n-p}\equiv(m^{*}_{n}-m^{*}_{p})/m=(0.41 \pm0.15)δ$ 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 p…
We investigate the phase structure of homogeneous and inhomogeneous neutron-proton condensate in isospin asymmetric nuclear matter. At extremely low nuclear density the condensed matter is in homogeneous phase at any temperature, while in general case it is in Larkin-Ovchinnikov-Fulde -Ferrell phase at low temperature. In comparison with the homogeneous superfluid, the inhomogeneous superfluid can survive at higher nuclear density and higher isospin asymmetry.
Relativistic and QED corrections were calculated for hyperfine splitting of the $2S_{1/2}$ ground state in $^{6,7}$Li atoms with an exact account for electronic correlations. The resulting theoretical predictions achieved such a precision level that, by comparison with experimental values, they enable determination of the nuclear properties. In particular, the obtained results show that the $^7$Li nucleus, having a charge radius smaller than $^6$Li, has about a 40% larger Zemach radius. Together with known differences in the electric quadrupole and magnetic dipole moments, this calls for a dee…
The neutron-proton differential flow is shown to be a very useful probe of the isospin-dependence of the nuclear equation of state (EOS). This novel approach utilizes constructively both the isospin fractionation and the nuclear collective flow as well as their sensitivities to the isospin-dependence of the nuclear EOS. It also avoids effectively uncertainties associated with other dynamical ingredients of heavy-ion reactions at intermediate energies.
We consider the proton structure corrections to hydrogen ground-state hyperfine structure, focusing on a state-of-the-art evaluation of the inelastic nucleon corrections--the polarizability corrections--using analytic fits to the most recent data. We find a value for the fractional correction Delta_{pol} of 1.3 \pm 0.3 ppm. This is 1--2 ppm smaller than the value of Delta_{pol}$ one would deduce using hyperfine splitting data and elastic proton structure corrections obtained from modern form factor fits. In addition, we discuss the derivations of the relevant formulas, paying attention to lept…
We present calculations of nuclear structure effects to the Lamb shift in light muonic atoms. We adopt a modern ab-initio approach by combining state-of-the-art nuclear potentials with the hyperspherical harmonics method. Our calculations are instrumental to the determination of nuclear charge radii in the Lamb shift measurements, which will shed light on the proton radius puzzle.
Based on an isospin dependent transport model IBUU, effects of high density behavior of nuclear symmetry energy in the proton-rich reaction $^{22}$Si+$^{22}$Si at a beam energy of 400 MeV/nucleon are studied. It is found that the symmetry energy affects $π^{+}$ production more than $π^{-}$. More interestingly, comparing with neutron-rich reactions, for $π^{-}/π^{+}$ and dense matter's N/Z ratios, effects of symmetry energy in the proton-rich reaction both show contrary behaviors. The practical experiment by using the proton-rich reaction $^{22}$Si+$^{40}$Ca to study nuclear symmetry energy are…
