Effect of three-body interaction on hot asymmetric nuclear matter

The properties of hot asymmetric nuclear matter are studied in the framework of the finite temperature Brueckner－Hartree－Fock theory that is extended to include the contribution of microscopic three-body forces. We give the variation of the critical temperature with the asymmetry parameter and show the effect brought by this three-body repulsive potential on the value of the critical asymmetry of the phase transition for asymmetric nuclear matter. Owing to the additional repulsion provided by three-body forces, this value decreases. In addition, the domain of mechanical instability for hot nuclear matter is also indicated, which gradually shrinks with increasing asymmetry and temperature.     

热核物质中基态关联修正下的单核子势和核子有效质量

以有限温度Brueckner-Hartree-Fock(BHF)方法为基础，利用质量算子的空穴线展开，计算了不同温度和密度下的核物质中单核子势和核子有效质量，特别是研究和讨论了基态关联效应和三体核力贡献对热核物质中单核子势的影响. 研究表明，基态关联和三体核力对单核子势的密度和温度依赖性均有重要影响. 基态关联导致的重排修正具有排斥性，大大减弱了低动量区域单核子势的吸引性，而且基态关联效应对单核子势的贡献随密度增大而增强，随温度升高而减弱. 三体核力对基态关联的影响是导致单核子势中重排项贡献减小. 在高密 关键词： 有限温度BHF方法 质量算子空穴线展开 重排修正 单核子势 有效质量     

热核物质中单核子势的重排项贡献和三体核力效应

在包含三体核力的有限温度Brueckner-Hartree-Fock理论方法基础上, 利用质量算子的空穴线展开, 研究了热核物质中基态关联所导致的对单核子势的重排修正项的密度和温度依赖性, 并讨论了三体核力对重排项的影响. 结果表明：单核子势的重排项贡献具有较强的密度和温度相关性, 重排项贡献随密度增加而增强并随温度升高而减弱. 在计算中引入三体核力会在一定程度上抑制基态空穴关联 效应, 从而导致单核子势的重排项贡献减小, 而且三体核力对重排项贡献的影响随密度增大而增强.     

Three-body forces in nuclei and the σ-model

The expectation value of the three-σ-exchange three-body force is evaluated in nuclear matter and in the triton. Full correlations are included between all three particles, and exchange terms are evaluated. When the parameters of the σ-model are chosen to reproduce the medium-range attraction in the two-nucleon system, one obtains some ?15 MeV per particle (attraction) in nuclear matter if the strength of the three-body force is evaluated in the tree approximation. The contribution to the ground-state energy of the triton is in his case about ?1 MeV. A simple interpolation formula is given, which relates the expectation value of the three-body force to the matter density and number of nucleons in the nucleus. It is concluded that the net strength of the three-body force must be reduced by quantum (loop) corrections.     

Symmetry energy,unstable nuclei and neutron star crusts

We present an upgraded review of our microscopic investigation on the single-particle properties and the EOS of isospin asymmetric nuclear matter within the framework of the Brueckner theory extended to include a microscopic three-body force. We pay special attention to the discussion of the three-body force effect and the comparison of our results with the predictions by other ab initio approaches. Three-body force is shown to be necessary for reproducing the empirical saturation properties of symmetric nuclear matter within nonrelativistic microscopic frameworks, and also for extending the hole-line expansion to a wide density range. The three-body force effect on nuclear symmetry energy is repulsive, and it leads to a significant stiffening of the density dependence of symmetry energy at supra-saturation densities. Within the Brueckner approach, the three-body force affects the nucleon s.p. potentials primarily via its rearrangement contribution which is strongly repulsive and momentum-dependent at high densities and high momenta. Both the rearrangement contribution induced by the three-body force and the effect of ground-state correlations are crucial for predicting reliably the single-particle properties within the Brueckner framework.     

Some Aspects of Nuclear Structure in Relativistic Approach

The nucleon effective interaction in the nuclear medium is investigated in the framework of the DiracBrueckner-Hartree-Fock (DBHF) approach. A new decomposition of the Dirac structure of nucleon self-energy in the DBHF is adopted for asymmetric nuclear matter. The properties of finite nuclei are investigated with the nucleon effective interaction. The agreement with the experimental data is satisfactory. The relativistic microscopic optical potential in asymmetric nuclear matter is investigated in the DBHF approach. The proton scattering from nuclei is calculated and compared with the experimental data. A proper treatment of the resonant continuum for exotic nuclei is studied. The width effect of the resonant continuum on the pairing correlation is discussed. The quasiparticle relativistic random phase approximation based on the relativistic mean-field ground state in the response function formalism is also addressed.     

中子星物质中的K介子凝聚与三体核力效应

利用Brueckner-Hartree-Fock方法，计算了β稳定中子星物质的状态方程以及三体核力的影响，特别是研究了三体核力对中子星物质中K介子凝聚的影响. 结果表明三体核力对β稳定中子星物质中出现K介子凝聚的临界密度以及中子星物质中各种粒子所占的比例均有重要影响. 三体核力的主要作用是降低了中子星物质中出现K介子凝聚的临界密度并使K凝聚相中的核物质更加接近于对称核物质.     

Hot Nuclear Matter Equation of State and Finite Temperature Kaon Condensation

We perform a systematic calculation of the equation of state of asymmetric nuclear matter at finite temperature within the framework of the Brueckner-Hartree-Fock approach with a microscopic three-body force. When applying it to the study of hot kaon condensed matter, we find that the thermal effect is more profound in comparison with normal matter, in particular around the threshold density. Also, the increase of temperature makes the equation of state slightly stiffer through suppression of kaon condensation.     

Decomposition of the equation of state of asymmetric nuclear matter into different spin-isospin channels

We investigate the equation of state of asymmetric nuclear matter and its isospin dependence in various spin-isospin ST channels within the framework of the Brueckner-Hartree-Fock approach extended to include a microscopic three-body force（TBF） . It is shown that the potential energy per nucleon in the isospinsinglet T = 0 channel is mainly determined by the contribution from the tensor SD coupled channel. At high densities,the TBF effect on the isospin-triplet T = 1 channel contribution turns out to be much larger than that on the T =0 channel contribution. At low densities around and below the normal nuclear matter density,the isospin dependence is found to come essentially from the isospin-singlet SD channel and the isospin-triplet T = 1 component is almost independent of isospin asymmetry. As the density increases,the T = 1 channel contribution becomes sensitive to the isospin asymmetry and at high enough densities its isospin dependence may even become more pronounced than that of the T = 0 contribution. The present results may provide some microscopic constraints for improving effective nucleon-nucleon interactions in a nuclear medium and for constructing new functionals of effective nucleon-nucleon interaction based on microscopic many-body theories.     

同位旋非对称核物质性质与扩展的BHF方法(Ⅴ)三体核力对质子和中子单粒子势的影响

在扩展的同位旋相关的Brueckner Hartree Fock理论框架内,研究了三体核力对同位旋非对称核物质中质子与中子的单粒子势及其同位旋依赖性的影响.     

Microscopic Three-Body Force Effect on Nucleon-Nucleon Cross Sectionsin Symmetric Nuclear Matter

We provide a microscopic calculation of neutron-proton and proton-proton cross sections in symmetric nuclear matter at various densities, using the Brueckner-Hartree-Fock approximation scheme with the Argonne V₁₄ potential including the contribution of microscopic three-body force. We investigate separately the effects of three-body force on the effective mass and on the scattering amplitude. In the present calculation, the rearrangement contribution of three-body force is considered, which will reduce the neutron and proton effective mass, and depress the amplitude of cross section. The effect of three body force is shown to be repulsive, especially in high densities and large momenta, which will suppress the cross section markedly.     

核势和核子有效质量的同位旋相关性

在Dirac Brueckner Hartree-Fock (DBHF)理论框架下研究了核子光学势和核子有效质量的同位旋相关性. 非对称核物质的计算采用了DBHF的核子自能的Dirac结构的新的分解方法, 核子自能的实部是用G矩阵在Hartree-Fock近似下计算得到, 而虚部从极化图得到. 用核子的薛定谔等价势可以得到核子矢量有效质量. 研究表明考虑了核势的能量相关性在丰中子核物质情况下核子矢量有效质量比质子的大.     

Three-body force effect on the properties of nuclear matter under the gap and continuous choices within the BHF approach

We have calculated and compared the three-body force effects on the properties of nuclear matter under the gap and continuous choices for the self-consistent auxiliary potential within the Brueckner-Hartree-Fock approach by adopting the Argonne V₁₈ and the Bonn B two-body potentials plus a microscopic three-body force (TBF). The TBF provides a strong repulsive effect on the equation of state of nuclear matter at high densities for both the gap and continuous choices. The saturation point turns out to be much closer to the empirical value when the continuous choice is adopted. In addition, the dependence of the calculated symmetry energy upon the choice of the self-consistent auxiliary potential is discussed.     

中子物质中的3PF2态超流性和微观三体核力效应

利用Brueckner-Hartree-Fock(BHF)和BCS理论方法，计算了纯中子物质中处于³PF₂态的中子对关联能隙，特别是研究并讨论了微观三体核力对³PF₂态中子超流性强弱的影响. 结果表明：三体核力显著地增强了中子物质中³PF₂态中子超流性；当采用BHF单粒子能谱时，三体核力导致相应的对关联能隙峰值由0.22MeV增大到0.50MeV. 关键词： 中子物质 3PF₂超流性')" href="#">³PF₂超流性 三体核力 BCS理论     

The three-body force,off-shell πN scattering and binding energies in nuclear matter

We re-examine the off-shell πN amplitude occurring in the two-pion exchange three-body force, subject to all of the constraints of current algebra. This amplitude is not dominated by the Δ(1231) isobar; instead, if the σ-term is known, it can be determined from on-shell scattering. The resulting contribution to the binding energy of nuclear matter is small but attractive, varying from 0.2 MeV to 1.5 MeV, corresponding to πN σ-terms of 70 MeV to 40 MeV.     

Hot nuclear matter in an extended Brueckner approach

The properties of cold and hot nuclear matter are studied in the frame of the Brueckner theory, extended to finite temperature. The basic task is the evaluation of the two-hole line diagram using the Paris potential supplemented by the introduction of three-body forces, coming from the exchange of π and ρ mesons. The latter have an important saturating effect, but not sufficient to reach correct saturation. The latter is achieved by a phenomenological treatment. The properties of hot nuclear matter, for temperatures around 10 MeV, are investigated. Particular attention is paid to one-body properties. The density and temperature dependence of many quantities, like the single-particle energy spectrum, the optical potential, the effective mass, the non-locality of the single-particle field, the mean free path, is displayed and analyzed. The relative importance of the temperature dependence of the g-matrix and of phase space is investigated, especially in relation with the imaginary part of the optical potential and the mean free path. The temperature dependence of the effective mass is particularly studied. It is shown that the peak due to the so-called core polarization effect disappears rapidly as the matter is heated. The evaluation of the entropy and of the level density parameter a, which are closely related, is discussed, and the failure of the Hartree-Fock approach to reproduce the value of a correctly is explained. Two-body properties are also investigated. The temperature and density dependence of the two-body correlations are displayed. Particular attention is paid to the temperature dependence of the effective interaction. The latter is exhibited in a simple manner. It is shown that the effective force felt by low-energy nucleons does not change by more than a few percent when the temperature goes from 0 to 10 MeV. For high-energy nucleons, the change may be as large as ten percent.     

Three-body force effect on the properties of nuclear matter underthe gap and continuous choices within the BHF approach

We have calculated and compared the three-body force effects on the properties of nuclear matter under the gap and continuous choices for the self-consistent auxiliary potential within the Brueckner-Hartree-Fock approach by adopting the Argonne V₁₈ and the Bonn B two-body potentials plus a microscopic three-body force (TBF). The TBF provides a strong repulsive effect on the equation of state of nuclear matter at high densities for both the gap and continuous choices. The saturation point turns out to be much closer to the empirical value when the continuous choice is adopted. In addition, the dependence of the calculated symmetry energy upon the choice of the self-consistent auxiliary potential is discussed.     

Equation of state of dense nuclear matter

An equation of state for cold nuclear matter for the region of densities ρ_nm−4ρ_nm, where ρ_nm is empirical nuclear-matter density, is constructed. We begin from the detailed calculation of Day and Wiringa for the two-body interactions; these give a saturation density of ∼2ρ_nm. This density is brought down to ρ_nm by the addition of relativistic corrections. Additional binding is obtained from three-body forces. A reasonable picture is obtained with the Day-Wiringa compression modulus for the two-body calculation, but the picture can be further improved by choosing this to be smaller.Our equation of state is similar to that of Friedman and Pandharipande in the region of nuclear matter denstiy ρ_nm, but, due to higher-order terms in the loop correction, is substantially softer at high density. Basically what happens is that the many-body effects saturate with increasing density, leaving only the two-body interactions.With this equation of state, prompt supernova explosions are very powerful when the compression modulus of neutron-rich matter (twice as many neutrons as protons) is ∼150 MeV, which corresponds to K_nm ∼ 190 MeV for symmetric nuclear matter.Analysis shows that hot nuclear matter formed in heavy ion collisions demands a very stiff equation of state. We understand this as arising from the strong velocity dependence in the real part of the optical model potential which follows chiefly from the Lorentz character of the interactions, the vector mean field growing with increasing density and the scalar one decreasing. This gives a substantial repulsive contribution to the energy per particle and produces a stiff effective equation of state for several hundred MeV heavy-ion collisions. With increasing degree of equilibration the magnitude of the repulsive energy decreases since equilibration decreases the effective momentum. Given the strong velocity dependence in the interaction, the hot equation of state can be reconciled with the cool one.     

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.     

Phase transitions,correlations and fluctuations of nuclear multifragmentation

Five different phases of the nuclear equation of state are described: the gas, the liquid, the super heated liquid, the super cooled gas and the mechanically unstable spinodal regions, both for nuclear matter and for the finite nucleus¹⁹⁷Au, with a density, temperature, and momentum dependent mean field derived from the extended Skyrme force. From realistic simulations in r-space and in p-space for these different phases at a finite temperature T=6 MeV, one can sort all kinds of nuclear clusters by a coalescence model. Correlation analyses of the nuclear clusters demonstrate that, both multifragmentation and intermittent patterns come only from the spinodal region, critical behaviour comes mainly from the spinodal region while there is also a small contribution from the super heated liquid and the liquid regions.