QCD inequalities for the nucleon mass and the free energy of baryonic matter

The positivity of the integrand of certain Euclidean space functional integrals for two flavor QCD with degenerate quark masses implies that the free energy per unit volume for QCD with a baryon chemical potential mu(B) (and zero isospin chemical potential) is greater than the free energy with an isospin chemical potential mu(I)=(2 mu(B)/N(c)) (and zero baryon chemical potential). The same result applies to QCD with any number of heavy flavors in addition to the two light flavors so long as the chemical potential is understood as applying to the light quark contributions to the baryon number. This relation implies a bound on the nucleon mass: there exists a particle X in QCD (presumably the pion) such that M(N)> or =(N(c) m(X)/2 I(X)) where m(X) is the mass of the particle and I(X) is its isospin.     

Pion properties at finite isospin chemical potential with isospin symmetry breaking

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.     

Pion phase transition in chiral symmetry breaking model

We show that in the non-linear σ-model, we have a phase transition when the isospin chemical potential is equal to the meson mass. This result is shown to be generally true in the SU(2)×SU(2) symmetry breaking model.     

Sensitive Probe for Symmetry Potential

Based on both very obvious isospin effect of the neutron-proton number ratio of nucleon emissions （n/p）nud on symmetry potential and （n/p）nucl＇s sensitive dependence on symmetry potential in the nuclear reactions induced by halo-neutron projectiles, compared to the same mass stable projectile, probing symmetry potential is investigated within the isospin-dependent quantum molecular dynamics with isospin and momentum-dependent interactions for different symmetry potentials U;ym and U2^sym. It is found that the neutron-halo projectile induces very obvious increase of （n/p）nucl and strengthens the dependence of （n/p） l on the symmetry potential for all the beam energies and impact parameters, compared to the same mass stable projectile under the same incident channel condition. Therefore （n/p）nucl induced by the neutron-halo projectile is a more favourable probe than the normal neutron-rich and neutron-poor projectiles for extracting the symmetry potential.     

动量相关作用对两体耗散同位旋效应的重要性

利用同位旋相关的量子分子动力学,研究了中能重离子碰撞中动量相关的状态方程对原子核阻止基于两体耗散的同位旋效应的影响.计算结果表明原子核阻止对同位旋相关和同位旋无关的核子–核子碰撞截面(两体耗散)的差值强烈地依赖于动量相关势,即在有动量相关势的情况下原子核阻止对同位旋相关和同位旋无关的核子–核子碰撞截面的差值大于没有动量相关势的情况.这就意味着动量相关作用明显地提高了原子核阻止对于核子–核子碰撞截面的灵敏性.因此,在考虑动量相关势的情况下,原子核阻止可以更准确地作为提取同位旋相关的核子–核子碰撞截面的一个探针.     

Dependence of Isoscaling Parameters on Nucleon-Nucleon Cross Section and Momentum-Dependent Interaction

Inltuences of the isospin dependence of the in-medium nucleon-nucleon cross section and the momentum-dependent interaction （MDI） on the isotope scaling are investigated by using the isospin-dependent quantum molecular dynamics model （IQMD）. The results show that both the isospin dependence of the in-medium nucleon-nucleon cross section and the momentum-dependent interaction affect the isoscaling parameters appreciably and indepen- dently. The inltuence caused by the isospin dependence of two-body collision is relatively larger than that from the MDI in the mean tield. Aiming at exploring the implication of isoscaling behaviour, which the statistical equilibrium in the reaction is reached, the statistical properties in the mass distribution and the kinetic energy distribution of the fragments simulated by IQMD are presented.     

Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter based on improved approximation schemes

We present Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter which are based on improved approximations schemes. The potential matrix elements have been adapted for isospin asymmetric nuclear matter in order to account for the proton-neutron mass splitting in a more consistent way. The proton properties are particularly sensitive to this adaption and its consequences, whereas the neutron properties remains almost unaffected in neutron-rich matter. Although at present full Brueckner calculations are still too complex to apply to finite nuclei, these relativistic Brueckner results can be used as a guidance to construct a density-dependent relativistic mean-field theory, which can be applied to finite nuclei. It is found that an accurate reproduction of the Dirac-Brueckner-Hartree-Fock equation of state requires a renormalization of these coupling functions.     

重离子碰撞中的同位旋效应

根据近年来利用同位旋相关输运理论在中能重离子碰撞同位旋效应研究方面的成果 ,并结合国际上在该问题上的进展 ,综合介绍和分析了中能重离子碰撞中的多重碎裂、原子核阻止和前平衡发射中子-质子比的同位旋效应及其随入射道条件:入射能量、碰撞参数、碰撞系统的质量 ,特别是随中子-质子比的演化过程.讨论了利用以上物理观测量在提取同位旋非对称核物质状态方程知识方面的可能性 ,并对其发展进行了展望. Based on the achievements for the intermediate energy heavy ion collision in our recent work and the progresses in the world, the isospin effects and the dependence of the entrance channel conditions on them in the intermediate energy heavy ion collisions were introduced, analysed and commended. From the calculation results by using isospin dependence quantum molecular dynamics, it is clear to see that the nuclear stopping power strongly depends on the in medium isospin dependence...     

库仑作用对同位旋分馏过程的影响

利用同位旋相关的量子分子动力学模型研究了中能重离子碰撞中库仑作用对同位旋分馏过程的影响.研究结果表明,在所研究的能区,无论是丰(缺)中子碰撞系统或者轻(重)反应系统,库仑作用都使同位旋分馏过程减弱,而这种影响主要来自于库仑作用对质子的排斥作用,使更多的质子发射,从而降低了气相中子–质子比所导致     

No-go theorem for critical phenomena in large-N(c) QCD

We derive some rigorous results on the chiral phase transition in QCD and QCD-like theories with a large number of colors, N(c), based on the QCD inequalities and the large-N(c) orbifold equivalence. We show that critical phenomena and associated soft modes are forbidden in flavor-symmetric QCD at finite temperature T and finite but not so large quark chemical potential μ for any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential μ(B)=N(c)μ is ruled out, if the coordinate (T, μ) is outside the pion condensed phase in the corresponding phase diagram of QCD at a finite isospin chemical potential μ(I)=2μ.     

核子碰撞截面的介质修正对多重碎裂的影响

利用同位旋相关的量子分子动力学模型研究了中能重离子碰撞过程中,同位旋相关的核子碰撞截面的介质修正对于多重碎裂的影响.结果表明:在包括动量相关作用在内的软势的情况下,介质修正明显地提高了自由核子的发射和中等质量碎片的多重性对于核子碰撞截面的同位旋依赖的敏感性.但对于原子核阻止敏感地依赖于核子碰撞截面的同位旋效应而不敏感地依赖于对称势的形式这一性质的影响并不明显,因此,原子核阻止对于核子碰撞截面的同位旋依赖的敏感性主要决定于自由核子碰撞截面的同位旋相关性.     

Isospin- and momentum-dependent interaction in isospin-dependent quantum molecular dynamics

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.     

Isospin breaking in the pion–nucleon scattering lengths

We analyze isospin breaking through quark mass differences and virtual photons in the pion–nucleon scattering lengths in all physical channels in the framework of covariant baryon chiral perturbation theory.     

用中子晕弹核探寻同位旋非对称核物质状态方程

总结和评述了用中子晕弹核探寻同位旋非对称核物质状态方程。 在具有同位旋和动量依赖的同位旋相关量子分子动力学框架内, 采用对比中子晕弹核和相等质量稳定弹核在完全相同入射道条件下物理观测量的差别, 来突出中子晕核明显的同位旋效应和加强物理观测量对于同位旋的灵敏性, 从而提取核物质状态方程。 例如, 与稳定弹核碰撞系统相比, 中子晕弹核明显提高了发射核子的中子\|质子比和增加了它对于对称势的灵敏性, 这两点特征非常有利于提取对称势。 同样, 由于中子晕弹核碰撞系统在低能区（E<60 MeV）由于内部松散结构减弱了核子碰撞力度和动量耗散, 与稳定核碰撞系统相比, 明显提高了原子核阻止; 而在高能区由于两体碰撞同位旋效应的增加, 从而明显提高了原子核阻止。 利用这些特征可以提取核子\|核子碰撞截面的介质效应和同位旋依赖性。 Based on the isospin and momentum dependent quantum molecular dynamics, we use the comparison for the differences between observables in the reactions induced by the halo\|neutron projectile and stable projectile with the same mass under complete same incident channel condition to protrude the isospin effect of halo\|neutron projectile and strengthen the sensitivity of observable on the isospin for extracting the information for the equation of state. For example, the halo\|neutron projectile increases the emitted neutron\|proton ratio and then enhances its sensitivity on the symmetrical potential. Two points above are more favorable than the normal neutron\|rich and neutron\|poor projectiles for extracting the symmetry potential. We also found that the neutron\|halo projectile induces the decrease of nuclear stopping in lower beam energy region and the increase in higher beam energy region, compared to corresponding same mass stable projectile under the same incident channel condition, so that we can use these properties to extract the information for the medium effect and isospin effect of in\|medium nucleon\|nucleon cross section.     

Equation of state and symmetry energy within the stability valley

We apply the direct variational method to derive the equation of state for finite nuclei within the stability valley. The extended Thomas-Fermi approximation for the energy functional with Skyrme forces is used. Applying the leptodermous expansion for the profile nucleon densities, we have studied the neutron coat and the isospin symmetry energy for neutron-rich nuclei. Using the equation of state for the pressure, we derive the region of spinodal instability of finite nuclei and its dependence on the mass number, the asymmetry parameter and the Skyrme force parameters. We suggest the procedure of derivation of the isospin symmetry energy from the analysis of the isospin shift of the chemical potential = - beyond the beta-stability line. We show that both the structure of the neutron coat and the position of the drip line depend significantly on the Skyrme force parameters.     

Isospin effects of the Skyrme potential and the momentum dependent interaction at intermediate energy heavy ion collisions

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.     

Isospin effects of the Skyrme potential and the momentum dependent interaction at intermediate energy heavy ion collisions

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.     

多重碎裂的同位旋效应和动量相关作用的影响

利用同位旋相关的量子分子动力学模型,对中能重离子碰撞过程中多重碎裂对于同位旋自由度和动量相关作用的依赖性进行了研究.结果表明:在相对较高能区,碎片的平均多重性敏感地依赖于介质中核子–核子碰撞截面的同位旋效应,但很弱地依赖于对称势;动量相关作用增强了中等质量碎片多重性对于核子–核子碰撞截面的同位旋依赖的敏感性.中等质量碎片的平均多重性可用作提取介质中同位旋相关的核子–核子碰撞截面的探针.     

QCD at finite isospin density

QCD at finite isospin chemical potential mu(I) has no fermion sign problem and can be studied on the lattice. We solve this theory analytically in two limits: at low mu(I), where chiral perturbation theory is applicable, and at asymptotically high mu(I), where perturbative QCD works. At low isospin density the ground state is a pion condensate, whereas at high density it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum numbers as the pion. This leads us to conjecture that the transition from hadron to quark matter is smooth, which passes several tests. Our results imply a nontrivial phase diagram in the space of temperature and chemical potentials of isospin and baryon number.