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Testing Validity of the Isobaric Multiplet Mass Equation in T=3 Isospin Septet
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作者 LIU Junhao HUA Xiang ZHAO Xi 《原子核物理评论》 北大核心 2025年第2期218-222,共5页
The validity of the isobaric multiplet mass equation(IMME)is of foundamental importance due to the basic concept of isospin.Recently,a serious breakdown was found in the A=54,T=3,isospin septet,the largest isospin sys... The validity of the isobaric multiplet mass equation(IMME)is of foundamental importance due to the basic concept of isospin.Recently,a serious breakdown was found in the A=54,T=3,isospin septet,the largest isospin system where the validity of IMME have been tested up to now.Inspired by this work,I revist the mass of some isobaric analogue states with the help of recent results from advanced mass measurement experiment.It is found that the IMME holds well in A=50 and 46 isospin septet and the coefficients of IMME also follow the systematic trends.Mass excess value for^(50)Ni and^(46)Fe,is predicted to be-3932(20)keV and 898(67)keV,respectively. 展开更多
关键词 isospin IMME nuclear mass βdecay proton drip-line
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Isospin- and momentum-dependent interaction in isospin-dependent quantum molecular dynamics 被引量:1
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作者 刘建业 郭文军 +3 位作者 任中洲 邢永忠 左维 李希国 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第8期1738-1745,共8页
An isospin-dependent quantum molecular dynamical model (IQMD) is developed, with the isospin degree of freedom in the momentum-dependent interaction(MDI) included in IQMD, to obtain an isospin- and momentum-depend... An isospin-dependent quantum molecular dynamical model (IQMD) is developed, with the isospin degree of freedom in the momentum-dependent interaction(MDI) included in IQMD, to obtain an isospin- and momentum-dependent interaction (IMDI) in IQMD. We investigate the effect of IMDI on the isospin fractionation ratio and its dynamical mechanism in the intermediate energy heavy ion collisions. It is found that the IMDI induces the significant reductions in the isospin fractionation ratio for all of beam energies, impact parameters, neutron-proton ratios and mass number of colliding systems. However, the strong dependence of isospin fractionation ratio on the symmetrical potential is preserved, with the isospin degree of freedom included in the MDI, i.e. the isospin fractionation ratio is still a good probe for extracting the information about the equation of state of isospin asymmetrical nuclear matter. 展开更多
关键词 heavy ion collision isospin fractionation ratio isospin and momentum dependent interaction isospin effect
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Isospin effects on intermediate mass fragments at intermediate energy-heavy ion collisions 被引量:8
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作者 Li Li Fang-Yuan Wang Ying-Xun Zhang 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2022年第5期68-77,共10页
In this study,we investigated the isospin properties of intermediate mass fragments(IMFs)for the central collisions of^(112,124)Sn+^(112,124)Sn at a beam energy of50 MeV per nucleon using an improved quantum molecular... In this study,we investigated the isospin properties of intermediate mass fragments(IMFs)for the central collisions of^(112,124)Sn+^(112,124)Sn at a beam energy of50 MeV per nucleon using an improved quantum molecular dynamics model(ImQMD)coupled with a sequential decay model(GEMINI).Three observables were analyzed:(1)the average center-of-mass kinetic energy per nucleon<Ec.m./A>of fragments as a function of their charge number Z;(2)the average neutron number to proton number ratio(<N>/Z)of fragments with a given charge number Z as a function of their center-of-mass kinetic energy per nucleon(Ec.m./A);and(3)the average total neutron number to total proton number ratio(ΣN/ΣZ)and double ratio(DR(N/Z))of IMFs with Z=3-8 as a function of their center-of-mass kinetic energy per nucleon Ec.m./A.Our calculations revealed that the sensitivity of the isospin properties of IMFs relative to the stiffness of the symmetry energy remains even after sequential decay.By comparing the calculations ofΣN/ΣZ and DR(N/Z)with the data,it was found that the soft symmetry energy,i.e.,γ=0.5,is favored. 展开更多
关键词 Symmetryenergy Intermediatemass fragments isospin effects
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Isospin and Symmetry Structure in ^(36)Ar 被引量:3
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作者 BAI Hong-Bo ZHANG Jin-Fu CAO Wan-Cang LLi-Jun Zhaorigt DONG Hong-Fei Department of Physics,Chifeng University,Chifeng 024001,ChinaLI Yan-Song Department of Physics,Tsinghua University,Beijing 100084,China 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第12期1067-1071,共5页
The interacting boson model-3(IBM-3) has been used to study the isospin excitation states and electromag-netic transitions for ^(36)Ar nucleus.The mixed symmetry states and superdeformed band at low spin are also anal... The interacting boson model-3(IBM-3) has been used to study the isospin excitation states and electromag-netic transitions for ^(36)Ar nucleus.The mixed symmetry states and superdeformed band at low spin are also analyzed.The theoretical calculations are in agreement with experimental data,and the ^(36)Ar is superdeformed rotational nucleusclose to the SU(3) limit.The present calcula,tions indicate that the 2_4^+ state is the lowest mixed symmetry state and thelowest isospin T=1 excitation state and at about 6.2 MeV,and the bandhead of superdeformed band is 0_2^+ state. 展开更多
关键词 IBM-3 energy level isospin mixed symmetry states electromagnetic transitions
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Probing neutron–proton effective mass splitting using nuclear stopping and isospin mix in heavy-ion collisions in GeV energy region 被引量:3
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作者 Fan Zhang Jun Su 《Nuclear Science and Techniques》 SCIE CAS CSCD 2020年第8期35-42,共8页
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 molecu... 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 mn*>mp*case,the mn*<mp*parameter results in a stronger stopping for protons but a weaker stopping for tritons.The calculations of the isospin tracer show that the mn*>mp*parameter results in a higher isospin mix than the mn*<mp*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. 展开更多
关键词 Neutron–proton effective mass splitting Nuclear stopping isospin mix
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Secondary decay effects of the isospin fractionation in the projectile fragmentation at GeV/nucleon 被引量:3
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作者 Chen-Chen Guo Jun Su Long Zhu 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2020年第12期122-128,共7页
The isospin fractionations in 124Sn,107Sn+120Sn at 600 MeV/nucleon,and 136Xe,124Xe+208Pb at 1000 MeV/nucleon are investigated by the isospin-dependent quantum molecular dynamics model coupled with the statistical code... The isospin fractionations in 124Sn,107Sn+120Sn at 600 MeV/nucleon,and 136Xe,124Xe+208Pb at 1000 MeV/nucleon are investigated by the isospin-dependent quantum molecular dynamics model coupled with the statistical code GEMINI.The yield ratio as a function of the binding energy difference for light mirror nuclei 3H/3He,7Li/7Be,11B/11C,and 15N/15O is applied to estimate the ratio between neutrons and protons in the gas of the fragmenting system.By comparing the estimated values resulting from the simulations with and without the GEMINI code,it was found that the secondary decay distorts the signal of the isospin fractionation.To minimize the secondary decay effects,the yield ratio of the light mirror nuclei 3H/3He as well as its double ratio between two systems with different isospin asymmetries of the projectiles is recommended as robust isospin observables. 展开更多
关键词 Quantum molecular dynamics model(QMD) isospin fractionation Secondary decay effect
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Probing the medium effect and isospin dependence of the in-medium nucleon-nucleon cross section in heavy ion collisions
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作者 刘建业 郭文军 邢永忠 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第11期3305-3311,共7页
Probing in-medium nucleon-nucleon (NN) cross section σ1/NN(α) in heavy ion collisions has been investigated by means of the isospin-dependent quantum molecular dynamics (IQMD) with the isospin- and momentum-de... Probing in-medium nucleon-nucleon (NN) cross section σ1/NN(α) in heavy ion collisions has been investigated by means of the isospin-dependent quantum molecular dynamics (IQMD) with the isospin- and momentum-dependent interaction (IMDI(T)). It is found that there are the very obvious medium effect and the sensitive isospin-dependence of nuclear stopping R on the in-medium NN cross section α1/NN(α) in the nuclear reactions induced by halo-neutron projectile and the same-mass stable projectile. However, R induced by the neutron-halo projectile is obviously lower than that induced by the corresponding stable projectile. In particular, there is a very obvious dependence of R on the medium effect of σ1/NN(α) in the whole beam energy region for the above two kinds of projectiles. Therefore, the comparison between the results of R's in the reactions induced by the neutron-halo projectile and the corresponding same-mass stable projectile is a more favourable probe for extracting the information of σ1/NN(α) because of adding a new judgement. 展开更多
关键词 isospin effect neutron-halo projectile nuclear reaction nucleon-nucleon cross section nuclear stopping
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Roles of Isospin in Evaporation Residue Cross Section as a Probe of Nuclear Dissipation
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作者 CHEN Na YE Wei 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第3期739-742,共4页
The influence of isospin on the excess of evaporation residue cross section over its standard statistical-model value for nuclei ^194pb, ^200Pb, and ^206pb is studied via a Langevin equation coupled with a statistical... The influence of isospin on the excess of evaporation residue cross section over its standard statistical-model value for nuclei ^194pb, ^200Pb, and ^206pb is studied via a Langevin equation coupled with a statistical decay model. The magnitude of this excess for a low-isospin fissioning nucleus is shown to be larger and its dependence on the nuclear viscosity coefficient to be stronger than those of a high-isospin fissioning nucleus. These results suggest that to obtain a more accurate information of viscosity coefficient inside the saddle point by measuring evaporation residue cross sections, we had better choose those compound systems with small isospin. 展开更多
关键词 evaporation residue cross section isospin effect nuclear dissipation Langevin equation
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Effects of Isospin on Pre-scission Particle Multiplicity of Heavy Systems and ItsExcitation Energy Dependence
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作者 YEWei CHENNa 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第5期751-756,共6页
Isospin effects on particle emission of fissioning isobaric sources and isotopic sources , and its dependence on the excitation energy are studied via Smoluchowski equations. It is shown that with increasing the isos... Isospin effects on particle emission of fissioning isobaric sources and isotopic sources , and its dependence on the excitation energy are studied via Smoluchowski equations. It is shown that with increasing the isospin of fissioning systems, charged-particle emission is not sensitive to the strength of nuclear dissipation. In addition, we have found that increasing the excitation energy not only increases the influence of nuclear dissipation on particle emission but also greatly enhances the sensitivity of the emission of pre-scission neutrons or charged particles to the isospin of the system. Therefore, in order to extract dissipation strength more accurately by taking light particle multiplicities it is important to choose both a highly excited compound nucleus and a proper kind of particles for systems with different isospins. 展开更多
关键词 isospin effect pre-scission particle multiplicity excitation energy fission diffusion model
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A Simple Approach to Study the Isospin Effect in Mass Splitting of Three-Nucleon Systems by Using Hyperspherical Functions
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作者 H.Feizi A.A.Rajabi M.R.Shojaei 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第7期141-145,共5页
In this work, the binding energy and wavefunctions of three-nucleon systems are obtained by using hy-perspherical harmonic approach. We have used a mathematical modification method to obtain the eigenvalues and eigenf... In this work, the binding energy and wavefunctions of three-nucleon systems are obtained by using hy-perspherical harmonic approach. We have used a mathematical modification method to obtain the eigenvalues and eigenfunctions of Schrdinger equation for three-nucleon systems in calculation. Next, we have used a simple approach to obtain the difference between binding energy of 3H and 3He where gives us mass splitting of three-nucleon systems. We have compared our results with the other works and experimental values. 展开更多
关键词 three nucleon systems binding energy H.H method isospin
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Isospin-conserving hadronic decay of the D_(s1)(2460) into D_(s)π^(+)π^(-)
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作者 Meng-Na Tang Yong-Hui Lin +2 位作者 Feng-Kun Guo Christoph Hanhart Ulf-G.Meißner 《Communications in Theoretical Physics》 SCIE CAS CSCD 2023年第5期119-127,共9页
The internal structure of the charm-strange mesons D_(s0)^(*)(2317)and D_(s1)(2460)are the subject of intensive studies.Their widths are small because they decay dominantly through isospinbreaking hadronic channels D_... The internal structure of the charm-strange mesons D_(s0)^(*)(2317)and D_(s1)(2460)are the subject of intensive studies.Their widths are small because they decay dominantly through isospinbreaking hadronic channels D_(s0)^(*)(2317)^(+)→D_(s)^(+)π^(0) and D _(s1)(2460)^(+)→D_(s)^(*+)π^(0).The D_(s1)(2460)can also decay into the hadronic final states D_(s)^(+)ππ,conserving isospin.In that case there is,however,a strong suppression from phase space.We study the transition D_(s1)(2460)^(+)→D_(s)^(+)π^(+)π^(-)in the scenario that the D_(s1)(2460)is a D^(*)K hadronic molecule.The ππ final state interaction is taken into account through dispersion relations.We find that the ratio of the partial widths of the Γ(D_(s1)(2460)^(+)→D_(s)^(+)π^(+)π^(-)) / Γ(D_(s1)(2460)^(+)→D_(s)^(*+)π^(0))obtained in the molecular picture is consistent with the existing experimental measurement.More interestingly,we demonstrate that theπ+π−invariant mass distribution shows a double bump structure,which can be used to disentangle the hadronic molecular picture from the compact state picture for the D_(s1)(2460)^(+).Predictions on the B_(s1)^(0)→B_(s)^(0)π^(+)π^(-)are also made. 展开更多
关键词 hadronic molecule isospin symmetry heavy quark flavor symmetry
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A New Approach to Mesons’ States and Their Dependence on Spin and Isospin: A Mathematical Study
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作者 Alireza Heidari Seyedali Vedad Mohammadali Ghorbani 《Journal of Modern Physics》 2012年第5期412-419,共8页
The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the authors’ name: Alireza Heidari... The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the authors’ name: Alireza Heidari and Seyedali Vedad. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.5 412-419, 2012, has been removed from this site. 展开更多
关键词 MESON SPIN isospin QUARK Antiquark
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1-3 In-medium and Isospin Effects on Pion Production in Heavy-ion Collisions Near Threshold Energies
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作者 Feng Zhaoqing 《IMP & HIRFL Annual Report》 2015年第1期5-7,共3页
Properties of hadrons in nuclear medium is interest in studying the Quantum Chromodynamics (QCD) structure in dense matter, in particular related to the chiral symmetry restoration, phase-transition from quark-gluon p... Properties of hadrons in nuclear medium is interest in studying the Quantum Chromodynamics (QCD) structure in dense matter, in particular related to the chiral symmetry restoration, phase-transition from quark-gluon plasma to hadrons, dynamics of hypernucleus formation, nuclear equation of state (EoS), etc. High energy heavy-ion collisions in terrestrial laboratory provide a unique possibility to study the in-medium properties of hadrons in dense nuclear matter and to extract the high-density behavior of the nuclear symmetry energy (isospin asymmetri part of EoS). The dynamics of pseudoscalar mesons in heavy-ion collisions and the in-medium properties in dense nuclear matter have been investigated with the Lanzhou quantum molecular dynamics (LQMD) transport model[1]. 展开更多
关键词 isospin PRODUCTION THRESHOLD ENERGIES
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Isospin splitting of nucleon effective mass and isospin effect in heavy-ion collisions 被引量:3
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作者 FENG Zhaoqing 《Nuclear Science and Techniques》 SCIE CAS CSCD 2013年第5期19-23,共5页
Two different isospin splittings of nucleon effective mass in nuclear medium as the form of mn*>mp* and mn*<mp* have been implemented in an isospin and momentum dependent transport model.Their impacts on the iso... Two different isospin splittings of nucleon effective mass in nuclear medium as the form of mn*>mp* and mn*<mp* have been implemented in an isospin and momentum dependent transport model.Their impacts on the isospin emission in heavy-ion collisions is investigated thoroughly.It is found that the yield ratios of energetic neutrons to protons squeezed out during the compression stage of two colliding nuclides are sensitive to the isospin splitting.The elliptic flows of free nucleons are also to be promising observables for extracting the nucleon effective mass splitting.Further experimental measurements are being expected,in particular at the CSR-CEE platform in Lanzhou.Several observables are proposed for constraining the density dependence of symmetry energy,such as the transverse flow difference of neutrons and protons,double ratios of n/p and π-/π+,excitation functions of π-/π+ and K0/K+. 展开更多
关键词 核子有效质量 同位旋效应 重离子碰撞 劈裂 企业社会责任 高能中子 交通工具 排放影响
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Directed flow of isospin sensitive fragments within a modified clusterization algorithm in heavy-ion collisions 被引量:1
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作者 KUMAR Sanjeev MA Yugang 《Nuclear Science and Techniques》 SCIE CAS CSCD 2013年第5期44-49,共6页
By extending the minimum spanning tree(MST)clusterization algorithm for the binding energy cut,the isospin asymmetry dependence of directed flow for isospin sensitive isobar pairs(neutrons-protons,3H-3He) is studied f... By extending the minimum spanning tree(MST)clusterization algorithm for the binding energy cut,the isospin asymmetry dependence of directed flow for isospin sensitive isobar pairs(neutrons-protons,3H-3He) is studied from low towards high incident energies.The modified clusterization method(MSTB) has the advantage to identify the fragments at quite early time.It enhances(reduces) the production of free nucleons(fragments) over MST method.The directed flow of isobaric pair3H-3He is more sensitive towards isospin asymmetry caused by MSTB than isobaric pair n-p.This sensitivity becomes quite strong towards the high incident energy and neutron-rich reaction system.In conclusion,the inclusion of binding energy in clusterization method for the flow studies has been uniquely important for understanding the isospin physics,especially for high density behavior of symmetry energy. 展开更多
关键词 集群化 同位旋 敏感性 重离子碰撞 流量 算法 修改 入射能量
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Sub-barrier fusion cross sections: role of Pauli blocking and isospin asymmetry
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作者 Weiwen Deng Kaixuan Cheng Chang Xu 《Chinese Physics C》 2025年第5期211-219,共9页
Heavy-ion fusion reactions are relevant to numerous important issues in the stellar environment as well as in the synthesis of new nuclides and superheavy elements. In this study, the role of Pauli blocking and the is... Heavy-ion fusion reactions are relevant to numerous important issues in the stellar environment as well as in the synthesis of new nuclides and superheavy elements. In this study, the role of Pauli blocking and the isospin effect in sub-barrier fusion reactions is investigated using the well established coupled-channel method. An isospindependent Pauli blocking potential is proposed to better address the deep sub-barrier fusion hindrance problem. We find that the Pauli blocking effect manifests itself strongly for isospin symmetric targets and is reduced for targets with large isospin asymmetries. The agreement between experimental and theoretical fusion cross sections is improved for both the ^(12)C-target and ^(16)O-target systems. 展开更多
关键词 fusion hindrance coupled-channel method isospin effect
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Isospin effects of the Skyrme potential and the momentum dependent interaction at intermediate energy heavy ion collisions
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作者 郭文军 刘建业 《Chinese Physics C》 SCIE CAS CSCD 北大核心 2008年第3期172-176,共5页
We improve the isospin dependent quantum molecular dynamical model by including isospin effects in the Skyrme potential and the momentum dependent interaction to obtain an isospin dependent Skyrme potential and an iso... We improve the isospin dependent quantum molecular dynamical model by including isospin effects in the Skyrme potential and the momentum dependent interaction to obtain an isospin dependent Skyrme potential and an isospin dependent momentum interaction. We investigate the isospin effects of Skyrme potential and momentum dependent interaction on the isospin fractionation ratio and the dynamical mechanism in intermediate energy heavy ion collisions. It is found that the isospin dependent Skyrme potential and the isospin dependent momentum interaction produce some important isospin effects in the isospin fractionation ratio. 展开更多
关键词 heavy ion collision isospin fractionation ratio isospin effect isospin dependent momentuminteraction isospin dependent Skyrme potential
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Isospin effects of projectile fragmentation in a Boltzmann-Langevin approach 被引量:2
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作者 BingLi Na Tang Feng-ShouZhang 《Chinese Physics C》 SCIE CAS CSCD 2021年第8期90-98,共9页
The isospin effects of projectile fragmentation at intermediate energies are investigated using an isospin-dependent Boltzmann-Langevin model.The collisions of mass-symmetric reactions including 58Fe,58Ni+58Fe,and Ni ... The isospin effects of projectile fragmentation at intermediate energies are investigated using an isospin-dependent Boltzmann-Langevin model.The collisions of mass-symmetric reactions including 58Fe,58Ni+58Fe,and Ni at intermediate energies,in the 30 to 100 MeV/A range,are studied for different symmetry energies.Yield ratios of the isotopic,isobaric,and isotonic pairs of fragments from the intermediate-mass region using three symmetry energies are extracted as functions of the N/Z ratio of the composite systems in the entrance channel and the incident energies.It is found that the yield ratios are sensitive to symmetry energies,especially for neutron-rich systems,and the calculations using soft symmetry energy are closer to the experimental data.The isospin effect is stronger for the soft symmetry energy,owing to the competition of the repulsive Coulomb force and the symmetry energy attractive force on the proton.For the first time,the splits are presented,revealing a transition from the isospin equilibrium at lower energies to translucency at intermediate energies.The results show a degree of transparency in that intermediate mass fragments undergo a transition from dependence on the composite systems in the entrance channel to reliance on the projectile and target nuclei. 展开更多
关键词 symmetry energy projectile fragmentation isospin-dependent Boltzmann-Langevin model isospin effect
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Pion properties at finite isospin chemical potential with isospin symmetry breaking
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作者 吴祖庆 平加伦 宗红石 《Chinese Physics C》 SCIE CAS CSCD 2017年第12期67-75,共9页
Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons,... Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 〈 0 and μI 〉0 in the phase diagram, and different values for the charged pion mass(or decay constant) and neutral pion mass(or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses. 展开更多
关键词 finite temperature and finite isospin chemical potential isospin symmetry breaking properties of meson
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Coexistence of isospin I=0 and I=1 pairings in asymmetric nuclear matter
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作者 Yi-Jun Yan Xin-Le Shang +1 位作者 Jian-Min Dong Wei Zuo 《Chinese Physics C》 SCIE CAS CSCD 2021年第7期225-231,共7页
The coexistence of neutron-neutron(n-n),proton-proton(p-p),and neutron-proton(n-p)pairings is investigated by adopting an effective density-dependent contact pairing potential.These three types of pairings can coexist... The coexistence of neutron-neutron(n-n),proton-proton(p-p),and neutron-proton(n-p)pairings is investigated by adopting an effective density-dependent contact pairing potential.These three types of pairings can coexist only if the n-p pairing is stronger than the n-n and p-p pairings for the isospin asymmetric nuclear matter.In addition,the existence of n-n and p-p pairs might enhance n-p pairings in asymmetric nuclear matter when the n-p pairing strength is significantly stronger than the n-n and p-p ones.Conversely,the n-p pairing is reduced by the n-n and p-p pairs when the n-p pairing interaction approaches n-n and p-p pairings. 展开更多
关键词 COEXISTENCE isospin singlet pairing isospin triplet pairing asymmetric nuclear matter
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