On the collective modes of infinite nuclear matter

In this paper we study the longitudinal collective vibrations of infinite nuclear matter in the long wavelength limit. We present an alternative method for solving the Landau equations which allows analytical expressions for the response function, the odd sum rules and the strength of the modes. We solve the theory for a selection of Skyrme interactions and we also consider the properties of the ground state of the system specifically associated with the four collective states which exist in nuclear matter. The relationship between the quantum mechanical response function and the corresponding classical hydrodynamical quantity is explored and the approximate results obtained through sum rules are compared with the exact solutions of the RPA equations. Finally the Landau parameters obtained with the Skyrme forces are tested against the antisymmetry property of the forward particle-hole scattering amplitude on the Fermi surface and the enhancement factor in the photonuclear dipole sum rule.     

Analysis of Boltzmann-Langevin dynamics in nuclear matter

The Boltzmann-Langevin dynamics of harmonic modes in nuclear matter is analyzed within linear-response theory, both with an elementary treatment and by utilizing the frequency-dependent response function. It is shown how the source terms agitating the modes can be obtained from the basicBL correlation kernel by a simple projection onto the associated dual basis states, which are proportional to the RPA amplitudes and can be expressed explicitly. The source terms for the correlated agitation of any two such modes can then be extracted directly, without consideration of the other modes. This facilitates the analysis of collective modes in unstable matter and makes it possible to asses the accuracy of an approximate projection technique employed previously.     

Analysis of Boltzmann-Langevin dynamics in nuclear matter

The Boltzmann-Langevin dynamics of harmonic modes in nuclear matter is analyzed within linear-response theory, both with an elementary treatment and by utilizing the frequency-dependent response function. It is shown how the source terms agitating the modes can be obtained from the basic BL correlation kernel by a simple projection onto the associated dual basis states, which are proportional to the RPA amplitudes and can be expressed explicitly. The source terms for the correlated agitation of any two such modes can then be extracted directly, without consideration of the other modes. This facilitates the analysis of collective modes in unstable matter and makes it possible to asses the accuracy of an approximate projection technique employed previously.     

On the role of the Δ(1232) on the transverse nuclear response in the (e,e′) reaction

The transverse nuclear response to an electromagnetic probe which is limited to create (or destroy) a particle-hole (ph) or delta-hole (Δh) pair is analyzed. Correlations of the random phase approximation (RPA) type and self-energy insertions are considered. For RPA correlations we have developed a scheme which includes explicitly the Δ and the exchange terms. Self-energy insertions over ph and Δh bubbles are studied. Several residual interactions based on a contact plus a (π + ϱ)-meson exchange potential are used. All calculations are performed in non-relativistic nuclear matter. The main effect of the Δ is to reduce the intensity over the nuclear quasi-elastic peak. Exchange RPA terms are very important, while the terms with self-energy insertions depend strongly on the residual interaction employed. Our results are compared with data for ⁴⁰Ca at momentum transfer q = 410 and q = 550 MeV/c, where the longitudinal response is also briefly discussed.     

Collective excitations in the unitary correlation operator method and relativistic QRPA studies of exotic nuclei

The collective excitation phenomena in atomic nuclei are studied in two different formulations of the random-phase approximation (RPA): (i) RPA based on correlated realistic nucleon-nucleon interactions constructed within the unitary correlation operator method (UCOM) and (ii) relativistic RPA derived from effective Lagrangians with density-dependent meson-exchange interactions. The former includes the dominant interaction-induced short-range central and tensor correlations by means of unitary transformation. It is shown that UCOM-RPA correlations induced by collective nuclear vibrations recover a part of the residual long-range correlations that are not explicitly included in the UCOM Hartree-Fock ground state. Both RPA models are employed in studies of the isoscalar giant monopole resonance in closed-shell nuclei across the nuclide chart, with an emphasis on the sensitivity of its properties on the constraints for the range of the UCOM correlation functions. Within the relativistic quasiparticle RPA (RQRPA) based on the relativistic Hartree-Bogolyubov model, the occurrence of pronounced low-lying dipole excitations is predicted in nuclei towards the proton drip line. From the analysis of the transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance. The text was submitted by the authors in English.     

核物质和夸克物质的对称能（英文）

对称能表征了同位旋非对称强相互作用物质状态方程的同位旋相关部分,它对于理解核物理和天体物理中的许多问题有重要意义。简要总结了关于核物质和夸克物质对称能研究的最新进展。对于核物质对称能,通过对核结构,核反应以及中子星的研究,目前对其亚饱和密度的行为已有比较清楚的认识,同时,对饱和密度附近对称能的约束也取得了很好的研究进展。但如何确定核物质对称能的高密行为仍然是一个挑战。另一方面,在极端高重子数密度条件下,强相互作用物质将以退禁闭的夸克物质状态存在。同位旋非对称夸克物质可能存在于致密星内部,也可能产生于极端相对论重离子碰撞中。对最近关于夸克物质对称能对夸克星性质的影响以及重夸克星的存在对夸克物质对称能的约束的研究工作进行了介绍,结果表明同位旋非对称夸克物质中上夸克和下夸克可能感受到很不一样的相互作用,这对于研究极端相对论重离子碰撞中部分子动力学的同位旋效应有重要启发。The symmetry energy characterizes the isospin dependent part of the equation of state of isospin asymmetric strong interaction matter and it plays a critical role in many issues of nuclear physics and astrophysics. In this talk, we briefly review the current status on the determination of the symmetry energy in nucleon (nuclear) and quark matter. For nuclear matter, while the subsaturation density behaviors of the symmetry energy are relatively well-determined and significant progress has been made on the symmetry energy around saturation density, the determination of the suprasaturation density behaviors of the symmetry energy remains a big challenge. For quark matter, which is expected to appear in dense matter at high baryon densities, we briefly review the recent work about the effects of quark matter symmetry energy on the properties of quark stars and the constraint of possible existence of heavy quark stars on quark matter symmetry energy. The results indicate that the u and d quarks could feel very different interactions in isospin asymmetric quark matter, which may have important implications on the isospin effects of partonic dynamics in relativistic heavy-ion collisions.     

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.     

Isospin dynamics in heavy ion collisions: From Coulomb barrier to quark gluon plasma

Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this report, we present a selection of new reaction observables in dissipative collisions particularly sensitive to the symmetry term of the nuclear Equation of State (Iso-EoS). We will first discuss the Isospin Equilibration Dynamics. At low energies, this manifests via the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation, with the symmetry term acting as a restoring force. At higher beam energies, Iso-EoS effects will be seen in Imbalance Ratio Measurements, in particular from the correlations with the total kinetic energy loss. For fragmentation reactions in central events, we suggest to look at the coupling between isospin distillation and radial flow. In Neck Fragmentation reactions, important Iso-EoS information can be obtained from the correlation between isospin content and alignment. The high density symmetry term can be probed from isospin effects on heavy ion reactions at relativistic energies (few AGeV range). Rather, isospin sensitive observables are proposed from nucleon/cluster emissions, collective flows and meson production. The possibility to shed light on the controversial neutron/proton effective mass splitting in asymmetric matter is also suggested. A large symmetry repulsion at high baryon density will also lead to an “earlier” hadron-deconfinement transition in n-rich matter. A suitable treatment of the isovector interaction in the partonic EoS appears very relevant.     

Correlations in hypernuclear matter

We investigate short-range correlations in nuclear and hypernuclear matter. Self-energies due to short-range correlations and their influence on the nucleon and Λ -hyperon spectral functions are described in an approach accounting for a realistic treatment of mean-field dynamics and a self-consistently derived quasi-particle interaction. Landau-Migdal theory is used to derived the short-range interaction from a phenomenological Skyrme energy density functional, subtracting the long-range pionic contributions to the nucleonic spectral functions. We discuss our results for different hyperon-baryon ratios to show the influence of strangeness on the correlations in hypernuclear matter.     

Microscopic three-body force for asymmetric nuclear matter

Brueckner calculations including a microscopic three-body force have been extended to isospin-asymmetric nuclear matter. The effects of the three-body force on the equation of state and on the single-particle properties of nuclear matter are discussed with a view to possible applications in nuclear physics and astrophysics. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs. isospin asymmetry β = (N - Z)/A is fulfilled in the whole asymmetry range 0≤β≤1 up to high densities. The three-body force provides a strong enhancement of the symmetry energy which increases with density in good agreement with the predictions of relativistic approaches. The Lane's assumption that proton and neutron mean fields linearly vary vs. the isospin parameter is violated at high density due to the three-body force, while the momentum dependence of the mean fields turns out to be only weakly affected. Consequently, a linear isospin split of the neutron and proton effective masses is found for both cases with and without the three-body force. The isospin effects on multifragmentation events and collective flows in heavy-ion collisions are briefly discussed along with the conditions for direct URCA processes to occur in the neutron star cooling. Received: 18 February 2002 / Accepted: 16 May 2002     

The Random Phase Approximation: Its role in restoring symmetries lacking in the Hartree-Fock approximation

Hartree-Fock wave-functions often lack symmetries possessed by the Hamiltonian. It is often said that the Random Phase Approximation (RPA) restores the missing symmtries. Since the RPA does not readily lead to explicit wave-functions, it is not a trivial matter to verify this assertion. We analyse the situation, and show that, while RPA restores symmetry in some respects, it does not do so completely. Besides the normal RPA, we discuss the generalisation of RPA that describes modes in isobars of the given nucleus. This is needed to enable us to discuss the case of isospin symmetry, which is analysed in detail.     

The Collective Excitation Spectra of σ, ω and π Mesons in Nuclear Matter

The recent progress on the study of the collective excitation in relativistic nuclear matter is reviewed. The collective excitation modes are derived by meson propagators in nuclear matter. The mesons we studied are σ, ω, γ and π mesons. For pion, we derived not only the relativistic particle-hole, delta-hole excitations but also antiparticle excitations, suchas particle-antiparticle, antidelta-particle, delta-antiparticle excitations. By calculating the dispersion relation and the spin-isospin-dependent response function, the effects of all these excitation are studied.     

Stability and instability of a hot and dilute nuclear droplet

The diabatic approach to dissipative collective nuclear motion is reformulated in the local-density approximation in order to treat the normal modes of a spherical nuclear droplet analytically. In a first application the adiabatic isoscalar modes are studied and results for the eigenvalues of compressional (bulk) and pure surface modes are presented as function of density and temperature inside the droplet, as well as for different mass numbers and for soft and stiff equations of state. We find that the region of bulk instabilities (spinodal regime) is substantially smaller for nuclear droplets than for infinite nuclear matter. For small densities below 30% of normal nuclear matter density and for temperatures below 5 MeV all relevant bulk modes become unstable with similar growth rates. The surface modes have a larger spinodal region, reaching out to densities and temperatures way beyond the spinodal line for bulk instabilities. Essential experimental features of multifragmentation, like fragmentation temperatures and fragment-mass distributions (in particular the power-law behavior) are consistent with the instability properties of an expanding nuclear droplet, and hence with a dynamical fragmentation process within the spinodal regime of bulk and surface modes (spinodal decomposition). Received: 4 September 2000 / Accepted: 14 November 2000     

Isovector part of nuclear energy density functional from chiral two- and three-nucleon forces

A recent calculation of the nuclear energy density functional from chiral two- and three-nucleon forces is extended to the isovector terms pertaining to different proton and neutron densities. An improved density-matrix expansion is adapted to the situation of small isospin asymmetries and used to calculate in the Hartree-Fock approximation the density-dependent strength functions associated with the isovector terms. The two-body interaction comprises of long-range multi-pion exchange contributions and a set of contact terms contributing up to fourth power in momenta. In addition, the leading-order chiral three-nucleon interaction is employed with its parameters fixed in computations of nuclear few-body systems. With this input one finds for the asymmetry energy of nuclear matter the value A(?? ₀) ? 26.5 MeV, compatible with existing semi-empirical determinations. The strength functions of the isovector surface and spin-orbit coupling terms come out much smaller than those of the analogous isoscalar coupling terms and in the relevant density range one finds agreement with phenomenological Skyrme forces. The specific isospin and density dependences arising from the chiral two- and three-nucleon interactions can be explored and tested in neutron-rich systems.     

Response of asymmetric nuclear matter to isospin-flip probes

We investigate the RPA response of asymmetric nuclear matter to external fields which induce charge exchange between nucleons, both at zero and finite temperature. Closed expressions are obtained for the RPA response in each spin channel when the nucleon–nucleon interaction is of the Skyrme type. Exchange terms are fully taken into account. We consider the transferred momentum, asymmetry and temperature as the relevant parameters of our study. Special emphasis is given to the role of neutron excess in relation to the collective states at low momentum.     

Quenching and hardening in the transverse quasi-elastic peak

We study in the RPA framework the collective response of symmetric, infinite nuclear matter to a spin-isospin sensitive probe with both σ · q and σ × q couplings. The two responses, similar in the low-q region, differ markedly for moderate momenta (?1 fm^?1). Indeed the collective effect manifests itself quite differently in the two responses; whereas the longitudinal one displays a softening and an enhancement (due to the attractive character of the associated particle-hole force), the transverse response is quenched and hardened with respect to the free Fermi gas. The existing experimental data, which we analyze, are compatible with our results. We also explore the total strengths and find that for repulsive forces they are appreciably reduced by the RPA correlations. A large part of this quenching comes from the Δ-excitation (LLEE effect), but some reduction is still present even when the nucleonic degrees of freedom are neglected. This illustrates a violation of strength conservation brought about by the RPA correlations in the spin-isospin channel.     

Nuclear compressibilities

We discuss the relation between the compressibility of nuclear matter and the frequencies of the collective monopole vibrations of nuclei. We analyse some of the problems which arise when one extrapolates from properties of finite nuclei to those of infinite nuclear matter. The best way to perform this extrapolation is to use a theory capable of describing both systems on the same footing. Self-consistent calculations using phenomenological effective interactions realize such a program. The general properties of these effective interactions are discussed. The theory we used is described; we emphasize that it accounts for both the properties of the ground states of nuclei and the small amplitude collective vibrations. Simple models of compression modes in infinite nuclear matter and in nuclei are presented; they illustrate various features of the collective modes in both systems. In particular we discuss the role of the shell structure and the effects of the nuclear surface. Results of extensive self-consistent calculations of the breathing mode of nuclei are presented and many features of the mode are analyzed. The role of the single particle spectrum on the frequencies of the collective modes is studied. Finally we briefly review the experimental situation on the monopole excitations of nuclei.We show that experimental data are compatible with a well defined value of the compression modulus of nuclear matter: K_∞ = 210±30 MeV.     

Collective description of nuclear double beta decay transitions

A consistent treatment of the intrinsic and collective coordinates relevant for the calculation of matrix elements describing nuclear double beta decay transitions is introduced. The method, which was originally developed for the case of nuclear rotations, is adapted to include isospin and number of particles degrees of freedom. To illustrate its main features we apply the formalism to the case of Fermi transitions in a simplified model. From the corresponding results we conclude that the uncertainties found in many existing double beta decay calculations might be largely due to the mixing of physical and spurious effects in the treatment of isospin dependent interactions.     

The case of RIB at intermediate energies: Isospin effects on nuclear dynamics

In the reaction dynamics of intermediate-energy radioactive beams we can probe highly asymmetric nuclear matter in compressed as well as dilute phases. In this report some predictions are presented, based on analytical results as well as on reaction simulations. We suggest a series of experiments with RIB aimed to shed light on isospin properties of nuclear interactions in the medium. Received: 1 May 2001 / Accepted: 4 December 2001     

同位旋非对称核物质性质与扩展的BHF方法(III)HVH定理与费米能量

在扩展的同位旋相关的Brueckner—Hartree—Fock理论框架内,在整个同位旋自由度范围内研究了质量算子的空穴线展开中不同等级近似下非对称核物质中Hugenholtz—Van Hove定理的满足程度,并计算了中子和质子的费米能量.结果表明为了使Hugenholtz-Van Hove定理达到令人满意的满足程度,需要同时考虑质量算子中的重排贡献和重正修正,从而指出了基态关联对于非对称核物质中单粒子性质的重要性.