GCM analysis of the collective properties of lead isotopes with exact projection on particle numbers

We present a microscopic analysis of the collective behaviour of the lead isotopes in the vicinity of ²⁰⁸Pb. In this study, we rely on a coherent approach based on the Generator Coordinate Method (GCM) including exact projection on N and Z numbers within a collective space generated by means of the constrained Hartree-Fock BCS method. With the same Hamiltonian used in HF + BCS calculations, we have performed a comprehensive study including monopole, quadrupole and octupole excitations as well as pairing vibrations. We find that, for the considered nuclei, the collective modes which modify the most the conclusions drawn from the mean-field theory are the octupole and pairing vibrations. Received: 31 May 2001 / Accepted: 23 August 2001     

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.     

The breathing mode and the nuclear surface

The role of the nuclear surface in the breathing mode of nuclei is analyzed. We discuss a simple model in which the density varies according to a scaling of the coordinates. We show that this model reproduces accurately the results of microscopic calculations in heavy nuclei, and we use it to estimate the contribution of the surface to the effective compression modulus of semi-infinite nuclear matter. The calculation is performed in the framework of an extended Thomas-Fermi approximation and using several effective interactions. It is shown that the surface energy is maximum with respect to variations of the density around saturation density. The reduction of the effective compression modulus due to the surface turns to be proportional to the bulk compression modulus. The magnitude of the effect is compared with results of RPA calculations. Other contributions to the effective compression modulus of finite nuclei are also discussed.     

Deducing the nuclear-matter incompressibility coefficient from data on isoscalar compression modes

Accurate assessment of the value of the incompressibility coefficient, K, of symmetric nuclear matter, which is directly related to the curvature of the equation of state (EOS), is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K as determined from experimental data on isoscalar giant monopole and dipole resonances (compression modes) in nuclei, by employing the microscopic theory based on the random-phase approximation (RPA).     

The compression modes in atomic nuclei and their relevance for the nuclear equation of state

Accurate assessment of the value of the incompressibility coefficient, K _∞, of symmetric nuclear matter, which is directly related to the curvature of the equation of state (EOS), is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K _∞ as determined from experimental data on isoscalar giant monopole and dipole resonances (compression modes) in nuclei by employing the microscopic theory based on the Random Phase Approximation (RPA). The importance of full self-consistent calculations is emphasized. In recent years, a comparision between RPA calculations based on either non-relativistic effective interactions or relativistic Lagrangians has been pursued in great detail. It has been pointed out that these two types of models embed different ansatz for the density dependence of the symmetry energy. This fact has consequences on the extraction of the nuclear incompressibility, as it is discussed. The comparison with other ways of extracting K _∞ from experimental data is highlighted. The text was submitted by the author in English.     

Dynamical effects in finite nuclei and their importance in giant resonance calculations

Dynamical effects on the single-particle self-energy Σ_m(ω), i.e., its ω dependence, are studied microscopically using realistic finite-range NN interactions. In heavy nuclei the coupling of particles to high collective low-lying surface vibrations causes dynamical effects much stronger than in nuclear matter. This result can resolve the discrepancies in previous calculations of giant dipole resonance energies.     

Limiting temperatures and the equation of state of nuclear matter

From experimental observations of limiting temperatures in heavy ion collisions we derive the critical temperature of infinite nuclear matter Tc=16.6+/-0.86. Theoretical model correlations between Tc, the compressibility modulus K, the effective mass m*, and the saturation density rho s are then exploited to derive the quantity (K/m*)1/2 rho -1/3 s. This quantity together with calculations employing Skyrme and Gogny interactions indicates a value of K in moderately excited nuclei that is in excellent agreement with the value determined from giant monopole resonance data.     

核子与核力决定的核形状(英文)

讨论了最近提出的作为量子多体系统重要潜在机制之一的量子自组织,原子核无疑是最好的实例。由于原子核内核子的单粒子和集体运动共存,它们的相互制约决定了核结构。集体模式因其驱动力,如使椭球形变的四极力及其阻力达到平衡形成,而单粒子能量就是产生阻力的一种根源。当存在较大单粒子能隙时,相关的集体运动更易受到阻碍。因此,一般认为,单粒子运动和集体运动是相互对抗的"天敌"。然而,由于核力的多样和复杂性,单极相互作用使单粒子能量改变也能减小其对集体运动的阻碍而加强集体模式,该现象将通过Zr同位素实例加以说明。这就导致了量子自组织的产生:单粒子能量由两种量子液体（质子和中子）和控制阻力的单极相互作用自组织。于是,不同于朗道费米液体理论的结论,原子核不一定像填装了自由核子的刚性瓶。Ⅱ型壳演化即是包含跨准幻壳能隙激发的直观实例。在重核中,量子自组织因其轨道和核子数更多而更为重要。We discuss the quantum self-organization introduced recently as one of the major underlying mechanisms of the quantum many-body systems. Atomic nuclei are actually a good example, because two types of the motion of nucleons, single-particle states and collective modes, interplay in determining their structure. The collective mode appears as a consequence of the balance between the effect of the mode-driving force (e.g., quadrupole force for the ellipsoidal deformation) and the resistance power against it. The single-particle energies are one of the sources to bring about such resistance power:a coherent collective motion is more hindered by larger spacings between relevant single particle states. Thus, the single-particle state and the collective mode are "enemies" against each other in the usual understanding. However, the nuclear forces are rich and complicated enough so as to enhance relevant collective mode by reducing the resistance power by changing single-particle energies for each eigenstate through monopole interactions. This will be demonstrated with the concrete example taken from Zr isotopes. In this way, the quantum self-organization occurs:single-particle energies can be self-organized by (i) two quantum liquids, e.g., protons and neutrons, (ii) monopole interaction (to control resistance). Thus, atomic nuclei are not necessarily like simple rigid vases containing almost free nucleons, in contrast to the naïve Fermi liquid picture a la Landau. Type Ⅱ shell evolution is considered to be a simple visible case involving excitations across a (sub)magic gap. The quantum self-organization becomes more important in heavier nuclei where the number of active orbits and the number of active nucleons are larger.     

Is it possible to enhance the nuclear Schiff moment by nuclear collective modes?

The nuclear Schiff moment is predicted to be enhanced in nuclei with static quadrupole and octupole deformation. The analogous suggestion of the enhanced contribution to the Schiff moment from the soft collective quadrupole and octupole vibrations in spherical nuclei is tested in the framework of the quasiparticle random phase approximation with separable quadrupole and octupole forces applied to the odd ^217–221Ra and ^217–221Rn isotopes. In this framework, we confirm the existence of the enhancement effect due to the soft modes, but only in the limit when the frequencies of quadrupole and octupole vibrations are close to zero. The text was submitted by the authors in English.     

Three-body forces and many-body dynamics

Conventional many-body quantum theory considers, as a rule, a system of particles in the mean field interacting through two-body forces. Recently it was suggested that in nuclear physics many-body forces, first of all three-body ones, are important for saturation of nuclear matter and for many details of nuclear structure. We consider possible influence of three-body forces, regardless of their origin (bare nucleon interactions or effective medium phenomena), on many-body dynamics. The new effects include, but are not limited to, renormalization of pairing and other two-body forces, enhancement of anharmonicity for collective modes, and special features of shell model calculations. The text was submitted by the author in English.     

Infinite matter properties and zero-range limit of non-relativistic finite-range interactions

We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin–orbit terms from the spin–isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin–orbit of the M3Y interaction is not compatible with local gauge invariance. Finally, we show that the zero-range limit of both families of interactions coincides with the specific form of the zero-range Skyrme interaction extended to higher momentum orders and we emphasize from this analogy its benefits.     

Calculation on the nuclear breathing modes

The collective compressional vibrations are described within the hydrodynamical model and the microscopic theory. We present calculations of the excitation energy, width and transition probability of theT=0 andT=1 breathing modes for the spherical nuclei O¹⁶, Ca⁴⁰, Zr⁹⁰, Sn¹²⁰ and Pb²⁰⁸.     

巨单极共振和对称能

基于带有混合同位旋标量-矢量非线性耦合的有效拉格朗日量, 在完全自洽的相对论无规位相近似的框架内, 通过单极压缩模式讨论了核物质的不可压缩性. 比较核²⁰⁸Pb,¹⁴⁴Sm,¹¹⁶Sn和⁹⁰Zr实验和计算的巨单极共振能量, 给出了核物质不可压缩系数的取值范围. 新的同位旋标量-矢量非线性耦合软化核物质的对称能, 但无损于基态性质与实验的一致性. 讨论了对称能的软化对巨单极共振的影响.     

A calculation of some parameters in Migdal's theory of nuclei

Some of the parameters in Migdal's theory of nuclei have been calculated. We used principally Landau's phenomenological approach to obtain the quasi-particle interaction. The energy was calculated by Brueckner's theory. We have used effective interactions which in infinite nuclear matter give the same potential energies in (¹S₀+¹D₂ and (³S₁+³D₁) states as the Hamada-Johnston potential. Other contributions to the binding energy were neglected. The nuclear compressibility K was calculated both from the energy-versus-density curve and from the calculated parameters of Migdal's theory. The results were not in conflict with each other. The values of K obtained were 100–150 MeV, which agrees reasonably well with other calculations in infinite nuclear matter, but they are only about of the values bsed by Migdal and collaborators. We obtained 0.7 for the effective mass and 22–25 MeV for the symmetry energy. The latter result agrees reasonably well with empirical values. An attempt to use the Green function approach in the calculations of the parameters was not successful because of poor convergence, if any.     

Collective modes and f-wave pairing interactions in superfluid (3)He

Precision measurements of collective mode frequencies in superfluid (3)He-B are sensitive to quasiparticle and f-wave pairing interactions. Measurements were performed at various pressures using interference of transverse sound in an acoustic cavity. We fit the measured collective mode frequencies, which depend on the strength of f-wave pairing and the Fermi liquid parameter F(2)(s), to theoretical predictions and discuss what implications these values have for observing new order parameter collective modes.     

Collective excitations and a backbending phenomenon in <Superscript>156</Superscript>Dy

We propose a self-consistent practical method to study collective excitations in rotating nuclei within the cranking + random phase approximation approach. It consists in solving the cranking Hartree-Bogolyubov equations for the modified Nilsson potential + monopole pairing forces. Further, the mean field results are used to construct collective vibrations treated in the random phase approximation (RPA). Special attention is paid to fulfill all conservation laws in the RPA to separate spurious and physical solutions. We demonstrate that the backbending in ¹⁵⁶Dy can be explained as a result of the disappearance of collective γ vibrations of the positive signature in the rotating frame.     

Resonant excitations of the 't Hooft-Polyakov monopole

The spherically symmetric magnetic monopole in an SU(2) gauge theory coupled to a massless Higgs field is shown to possess an infinite number of resonances or quasinormal modes. These modes are eigenfunctions of the isospin 1 perturbation equations with complex eigenvalues, E(n)=omega(n)-igamma(n), satisfying the outgoing radiation condition. For n--> infinity, their frequencies omega(n) approach the mass of the vector boson, M(W), while their lifetimes 1/gamma(n) tend to infinity. The response of the monopole to an arbitrary initial perturbation is largely determined by these resonant modes, whose collective effect leads to the formation of a long living breatherlike excitation with an amplitude decaying at late times as t(-5/6).     

Role of the nuclear surface in a unified description of the damping of single-particle states and giant resonances

The damping widths of single-particle states and of giant resonances are estimated in spherical nuclei, based on the excitation of surface modes.A Skyrme III interaction with an effective mass consistent with that resulting from infinite nuclear matter calculations with “realistic” forces $\text{(m}{}^1\text{/m = 0.76)}$, was utilized. The single-particle basis needed to construct the unperturbed nuclear response function for each multipolarity was obtained, treating this force in the Hartree-Fock approximation. Diagonalizing a schematic interaction in this basis, the surface modes were calculated. They are used to dress the single-particle and single-hole states and to renormalize the vertex interaction, taking into account the proper energy dependence of the couplings.The essential new feature of the present calculation as compared to the calculations reported in ref.¹) is that the energy dependence of the real and imaginary part of the self-energy is taken into account. This is done utilizing a strength function model.About 70 % of the damping widths arise from the coupling to specific intermediate states containing one low-lying collective surface vibration. The rest, from the coupling to many nonspecific states.Qualitative agreement is found with the experimental data for spherical nuclei throughout the mass table for both the single-particle states and the giant resonances. The model seems however to predict widths which are smaller than those experimentally observed.