The mass parameters for the average mean-field potential

Starting from a mean-field hamiltonian with pairing interaction, we use the generator coordinate method (GCM) and a generalized gaussian overlap approximation to derive a multidimensional collective hamiltonian for large-amplitude motion. Numerical calculations are performed for Nilsson and Woods-Saxon potentials with BCS pairing. The BCS wave function is taken as the generator function and the deformation parameters of the single-particle mean field are used as the generator coordinates. We find that the GCM mass parameters on the average are smaller than those of the cranking (+ BCS) model by a factor of $\text{～}\text{2}\text{3}$. In the present approach, the zero-point energy correction to the collective potential is shown to vanish identically.     

A quantum parity-conserving study on octupole deformation in the light-actinide region

Based on a constrained Hartree-Fock plus BCS calculation with Gogny forces, we construct the collective hamiltonian (GCM+mean field and ATDHF+cranking approach) with the quadrupole and octupole deformations as coordinates. We calculate the 0⁺, 1⁻ splitting as well as the E1 and E3 transition probabilities for ²²²Ra. The agreement with experimental results is very good.     

Microscopic analysis of nuclear collective motions in terms of the boson expansion theory: (I). Formulation

A normal-ordered linked-cluster boson expansion theory, previously worked out by one of the authors (T.K.) and Tamura, has been developed further by reformulating it in a “physical” quasiparticle subspace which contains no spurious particle-number excitation modes. The expansion coefficients of the collective hamiltonian for low-lying quadrupole motions are determined starting from a microscopic fermion hamiltonian including self-consistent higher-order (many-body) interactions derived in our previous work. The contributions from the non-collective states with all possible non-collective one-boson excitations having I^π = 0⁺− 4⁺, which can directly couple to the collective states with one or two phonons, are taken into account in a systematic and compact way.     

Mean-field mass parameters for odd nuclei within the GOA+GCM approach

The GCM mass parameters for the heavy odd-nuclei region within the mean-field hamiltonian approximation have been calculated. The influence of the energy window size, the level crossing and the projection onto good particle number effects have been analyzed.     

On the description of dissipative collective motion

We use a recently developed time-dependent projection method to describe the dissipation of collective motion coupled to an intrinsic system. The underlying physical picture is similar to that of the linear response approach. Our approach is, however, different from the conceptual point of view. We do not resort to a quasistatic picture but use instead a time-dependent projector. Furthermore, we project on a model space which includes the intrinsic hamiltonian in addition to the collective subspace. In this way we obtain a Fokker-Planck equation for the collective variables which is coupled to a transport equation describing the evolution of the temperature of the intrinsic system.     

A comparative study of optic phonon-like excitations in liquid mixtures and molten salts

We report a study of collective excitations in an equimolar Lennard–Jones liquid mixture KrAr and a molten salt NaCl within the parameter-free generalized collective modes (GCM) approach. It is shown that the high-frequency propagating modes in liquid KrAr and molten NaCl correspond to optic phonon-like excitations, caused by fast mass-concentration (charge in NaCl) fluctuations. Dispersion curves for optic collective excitations are discussed.     

Isovector pairing and particle-number fluctuation effects on the spectroscopic factors of one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei

Expressions of the spectroscopic factors(SFs) corresponding to one-particle transfer reactions have been established using a schematic definition.These expressions have been derived by taking into account the isovector neutron-proton(np) pairing correlations and a particle-number projection in the framework of the generalized SharpBCS(SBCS) method.Recently proposed expressions of the projected wave-functions of odd-mass nuclei have been used for this purpose.The formalism has first been tested using the single-particle energies of the schematic picketfence model.It is shown that the np pairing and particle-number fluctuation effects are far from negligible and they depend on the pairing gap parameter values.Their behavior is not the same when the parent nuclei are even-even or odd.Predictions dealing with the SFs corresponding to one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei have then been established within the framework of the realistic Woods-Saxon model.It is shown that the np pairing effect as well as the particle-number projection effect are important and thus have to be included in future calculations of the SF corresponding to these kinds of reactions.     

The generator coordinate spin and isospin projection in the chiral bag plus skyrmion hybrid model

We study the baryon properties in the chiral bag plus skyrmion hybrid model. To describe the physical baryon state, we apply the generator coordinate projection method (GCM) instead of the widely used semiclassical collective coordinate method (CCM). The intrinsic state for the skyrmion is constructed as the coherent state and the valence quarks are treated explicitly. The nucleon and delta masses and the axial coupling constant g_A are investigated. Tha masses are significantly reduced from the large hedgehog mass due to the quantum effects in the GCM and a small g_A in the CCM is enhanced as a result of finite N_c. Agreement with experimental data of these quantities is much improved compared to the semiclassical CCM.     

Non-hydrodynamic collective modes in liquid metals and alloys

A short review of analytical and numerical results, obtained for collective dynamics in liquid metals and alloys within a theoretical approach of Generalized Collective Modes (GCM) is presented. The GCM approach permits to represent dynamic structure factors in wide ranges of wave numbers and frequencies as a sum of contributions from hydrodynamic and non-hydrodynamic processes. The origin of collective modes that make important contributions to dynamic structure factors beyond the hydrodynamic regime in liquid metals and alloys is discussed.     

Quadrupole and higher-order pairing forces

Recent work suggests that the quadrupole pair field may be important in describing certain properties of the crossings of high-spin rotational bands (e.g. crossing frequencies) in quantitative detail. We investigate its relative importance by performing an exact diagonalisation of a cranked deformed hamiltonian containing short-range residual interactions in a single j-shell. The major diflerence between odd and even particle-number crossing frequencies is seen to be described by blocking plus quadrupole pairing (J = 2) along with a significant hexadecapole pairing effect (J = 4). Absolute crossing frequencies are also sensitive to higher J-values. The interactions between the crossing levels are also discussed.     

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     

Loop space Hamiltonians and numerical methods for large-N gauge theories

We consider large-N gauge theories in the hamiltonian, collective field approach. We derive an alternative collective representation which leads to significant reduction when translation invariance is invoked. It allows for a simplified computer simulation of loop rearrangements and the development of numerical techniques in the hamiltonian, loop space formalism. We proceed to give numerical evidence for validity of our representation and outline a general numerical approach for solving large-N QCD in terms of gauge-invariant Wilson loop variables.     

A geometric classical model of collective motion in nuclei

A collective phase space of dimension 12 is introduced to study a classical model of nuclear collective motion. The model employs the 6 components of the coordinate quadrupole and 6 corresponding generalized momenta and can be related to properties of closed-shell nuclei. Vibrational and rotational coordinates are introduced, and purely rotational solutions are studied. The model demonstrates hamiltonian non-rigid motion with a fixed shape of the nucleus. The relation between the coordinate quadrupole tensor and the ellipsoids related to the angular momentum and angular velocity is analyzed for simple forms of the collective potential.     

Disappearance of pairing correlations in a rotating nucleus and the role of particle-number projection discussed within a solvable model

The disappearance of pairing correlations in a rotating nucleus and the role of the particlenumber projection technique are discussed using a simple solvable two-level model. Exact solutions are compared to approximate ones obtained with the independent-quasiparticle method both with and without particle-number projection. Analytical formulas for particle-number projected quantities are obtained. It is shown that pairing correlations tend to disappear in a nucleus which rotates fast enough. It is also argued that the pairing parameter Δ which appears in the particle-number projected wave function does not provide an adequate measure of the pairing correlations in nuclei. The pair-transfer reaction cross section is shown to be related closely to the pairing correlation energy and it is suggested that it can be used as a criterion for the existence of the superfluidity in rotating nuclei.     

Influence of isovector pairing and particle-number projection effects on spectroscopic factors for one-pair like-particle transfer reactions in proton-rich even-even nuclei

Isovector neutron-proton(np) pairing and particle-number fluctuation effects on the spectroscopic factors(SF) corresponding to one-pair like-particle transfer reactions in proton-rich even-even nuclei are studied. With this aim, expressions of the SF corresponding to two-neutron stripping and two-proton pick-up reactions, which take into account the isovector np pairing effect, are established within the generalized BCS approach, using a schematic definition proposed by Chasman. Expressions of the same SF which strictly conserve the particle number are also established within the Sharp-BCS(SBCS) discrete projection method. In both cases, it is shown that these expressions generalize those obtained when only the pairing between like particles is considered. First, the formalism is tested within the Richardson schematic model. Second, it is applied to study even-even proton-rich nuclei using the single-particle energies of a Woods-Saxon mean-field. In both cases, it is shown that the np pairing effect and the particle-number projection effect on the SF values are important, particularly in N =Z nuclei, and must then be taken into account.     

Microscopic descriptions of collective SD bands in the A=190 mass region with the Gogny force

In the framework of microscopic models, we present two methods for describing superdeformed (SD) band properties. The first one is the cranked Hartree-Fock-Bogoliubov (HFB) method, without and with inclusion of particle number projection. The second one is the Gaussian overlap approximation to the generator coordinate method (GCM+GOA) with whichwetreat the five quadrupole collective coordinates. Both methods use the Gogny force. Moments of inertia and excitation energies of SD bands are calculated and compared with experimental results.     

Dissipative hamiltonian systems: A unifying principle

The concept of hamiltonian sysem is generalized to include a wide class of dissipative processes. Evolution of any observable is generated jointly by a hamiltonian, with an entropy-conserving Poisson bracket, and an entropy, with an energy-conserving dissipative bracket. This approach yields many of the standard kinetic equations, such as those representing particle collisions, three-wave interactions, and wave-particle resonances.     

Characterizing turbulence in globally coupled maps with stochastic finite automata

We describe a method to discriminate between ordered and turbulent behavior in a general class of collective systems known as Globally Coupled Maps (GCM). Our method is able to discover an unknown small ordered region inside the turbulent phase of GCM parameter space. The computational nature of the method is the main novelty of our approach; it is another example of how measures based on computational notions of structure may provide new information in the study of dynamical systems.