Theory of non-adiabatic cranking and nuclear collective motion

The cranking model is extended to the case of a general non-adiabatic motion. The time-dependent many-body Schrödinger equation is solved, where the time dependence of the collective motion is determined by the classical Lagrange equations of motion. The Lagrangian is obtained from the expectation value of the energy. In the case of one collective degree of freedom the condition that the expectation value of the energy is constant in time is sufficient to determine the collective motion. An iteration procedure is applied, of which the zeroth order is shown to be the common cranking formula. In an alternative approach the energy conservation is expressed in differential form. This leads in the case of one collective degree of freedom to a set of coupled, non-linear first-order differential equations in time for the expansion coefficients of the many-body wave function and for the collective variable. As an illustrative example we solve the case of two coupled linear harmonic oscillators.     

An extended time-dependent mean-field theory for strongly correlated nuclear systems

We perform an extension of the time-dependent mean-field theory by an explicit inclusion of strong two-body correlations of short range on a level of microscopic reversibility relating them to realistic nucleon-nucleon forces. Invoking a least action principle for correlated basis functions, equations of motion for the correlation functions and the single-particle model wave function are derived to the lowest order of the FAHT cluster expansion. Higher order effects as well as longrange correlations we consider only to the extent to which they contribute to the mean field via a readjusted phenomenological effective two-body interaction. The corresponding correlated stationary problem is investigated and appropriate initial conditions to describe a heavy ion reaction are proposed. The single-particle density matrix is evaluated. Norm, energy and particle number conservation are proved. Possible simplifications are discussed. Standard TDHF appears as a limiting case if the range of the explicitly considered part of the bare nucleon-nucleon interaction goes to zero.     

ATDHF versus TDHF in a soluble model

The equations of motion for a system of interacting fermions with SU(3) symmetry are established in TDHF and ATDHF approximations. These equations are presented in a form such that the comparison between different approximations can be made in an analytic way. The problem of coupling between large and small amplitude modes is also discussed.     

Particle transfer reactions with the time-dependent Hartree-Fock theory using a particle number projection technique

A particle-number projection technique is used to calculate transfer probabilities in the 16O+208Pb reaction below the fusion barrier. The time evolution of the many-body wave function is obtained with the time-dependent Hartree-Fock (TDHF) mean-field theory. The agreement with experimental data for the sum of the proton-transfer channels is good, considering that TDHF has no parameter adjusted on the reaction mechanism. Some perspectives for extensions beyond TDHF to include cluster transfers are discussed.     

Dynamics of nuclear fluid: (I). Foundation

Starting with the time-dependent Hartree-Fock (TDHF) formulation of the many-body problem, we cast the equation into a set of conservation laws of classical type. Besides the equation of continuity, TDHF leads to an equation of motion which is analogous to the Euler equation in classical fluid dynamics. The forces do not come from the collective kinetic stress alone, but also from a density-dependent chemical potential, the surface tensional force which depends on density differences and the Coulomb interaction. With an assumed Navier-Stokes generalization of the stress tensor, such a set of differential equations provides a powerful tool for the study of complicated collective motions of nuclear systems such as those involved in heavy-ion reactions and nuclear fission. In the static case, the equation of motion leads to the Thomas-Fermi model of a finite nucleus as formulated by Bethe.     

Phase particle integrations of the nuclear vlasov equation

The non-linear Vlasov equation, describing the time development of the one-body Wigner distribution function, is integrated as an initial value problem by following the trajectories of notional phase particles which evolve along its hamiltonian characteristic curves. Initial conditions are generated by galilean transformations of the self-consistent solutions of the static equation obtained assuming a Thomas-Fermi form for the Wigner distribution.Fusion, deep inelastic collisions and fragmentation are all exhibited depending on the bombarding energy per nucleon, in qualitative agreement with the results of comparable TDHF calculations. A simple criterion for determining the boundaries between these phenomena, based on classical penetration of the collective mean field by the phase particles, is found not to be accurate, presumably due to an inadequate allowance for the effects of self-consistency.     

Accuracy of the Time-Dependent Hartree–Fock Approximation for Uncorrelated Initial States

This article concerns the time-dependent Hartree–Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find that the TDHF approximation is accurate when there are sufficiently many particles and the initial many-particle state is any Gibbs equilibrium state for noninteracting fermions (with Slater determinants as a special example). Assuming a bounded two-particle interaction, we obtain a bound on the error of the TDHF approximation, valid for short times. We further show that the error of the TDHF approximation vanishes at all times in the mean field limit.     

Enhancement of electron density in the interaction of high-power electromagnetic waves with inhomogeneous magnetized plasma

Propagation characteristics of a high-power electromagnetic wave through an inhomogeneous magnetized plasma is investigated. Considering the momentum transfer equations for electrons and ions and taking into account the ponderomotive force, the distribution of electron density and dielectric permittivity are obtained. Using non-linear dielectric permittivity and Maxwell's equations in the absence of external current and charge densities, non-linear wave equations are achieved. The results indicate that the external static magnetic field can modify the profiles of both the electric and magnetic fields. It is also shown that the external static magnetic field enhances the amplitude of the electron density and the non-linear dielectric permittivity.     

Reheating in tachyonic inflationary models: Effects on the large scale curvature perturbations

We investigate the problem of perturbative reheating and its effects on the evolution of the curvature perturbations in tachyonic inflationary models. We derive the equations governing the evolution of the scalar perturbations for a system consisting of a tachyon and a perfect fluid. Assuming the perfect fluid to be radiation, we solve the coupled equations for the system numerically and study the evolution of the perturbations from the sub-Hubble to the super-Hubble scales. In particular, we analyze the effects of the transition from tachyon driven inflation to the radiation dominated epoch on the evolution of the large scale curvature and non-adiabatic pressure perturbations. We consider two different potentials to describe the tachyon and study the effects of two possible types of decay of the tachyon into radiation. We plot the spectrum of curvature perturbations at the end of inflation as well as at the early stages of the radiation dominated epoch. We find that reheating does not affect the amplitude of the curvature perturbations in any of these cases. These results corroborate similar conclusions that have been arrived at earlier based on the study of the evolution of the perturbations in the super-Hubble limit. We illustrate that, before the transition to the radiation dominated epoch, the relative non-adiabatic pressure perturbation between the tachyon and radiation decays in a fashion very similar to that of the intrinsic entropy perturbation associated with the tachyon. Moreover, we show that, after the transition, the relative non-adiabatic pressure perturbation dies down extremely rapidly during the early stages of the radiation dominated epoch. It is these behavior which ensure that the amplitude of the curvature perturbations remain unaffected during reheating. We also discuss the corresponding results for the popular chaotic inflation model in the case of the canonical scalar field.     

Two-body collisions and time dependent Hartree-Fock theory

The time-dependent Hartree-Fock (TDHF) theory is generalized in order to include the effect of two-body collisions (i.e. the residual interaction). This is achieved by adding a collision integral into the TDHF equations, similar to the one ordinarily used in the Boltzmann equation. It is shown, that two-body collisions arise from the imaginary part of the effective interaction between two nucleons whereas the Hartree-Fock field is associated to the real part of the same interaction. There is thus no double counting when the collisions are added to a single particle field. Various approximations for the collision integral are discussed and their accuracy evaluated. Special effort is made in order to obtain conserving approximations. It is shown that for discrete fields, energy as well as momentum conservation is achieved by off-shell scattering processes. In the light of a previous paper, it is argued that two-body collisions should dominate the irreversible processes above some critical energy (roughly 200 MeV per nucleon). Below this energy the irreversible effects due to the single particle field and the collisions are expected to be of the same order of magnitude.     

General semi-classical method for collective motion and its connection with the Rowe-Basserman and marumori theories,and adiabatic limits

In recent work, we have shown that in the adiabatic limit (large amplitude, small momentum), time-dependent Hartree-Fock theory (TDHF) yields a well-defined theory of large-amplitude collective motion which provides an essentially unique construction for a collective hamiltonian. An alternative theory, put forward by Rowe and Basserman and by Marumori is, apparently, not restricted to small momenta. We describe a general framework for the study of collective motion in the semi-classical limit without limitation on the size of coordinates or momenta, which includes all previous methods as limiting cases. We find it convenient, as in the past, to consider two general systems: first, a system with n degrees of freedom and no special permutation symmetry, and, second, a system of fermions described in TDHF. For both systems the problem can be formulated as a search for a hamiltonian flow confined to a finite-dimensional hypersurface in a phase space, which itself may be finite- or infinite-dimensional. Though, in general, there are no exact solutions to this problem, we can formulate consistent approximation schemes corresponding to both the adiabatic and Rowe-Basserman, and Marumori limits. We also show how to extend the momentum expansion, which underlies the adiabatic approximation, to higher orders in the momentum. We thereby confirm the structure of the theory found in our previous work.     

Time-dependent solutions with localized energy of the Einstein system of equations and a nonlinear scalar field

A soliton-like time-dependent solution in the form of a running wave is derived of a self-consistent system of the gravitational field equations of Einstein and Born-Infeld type of equations of a nonlinear scalar field in a conformally flat metric. This solution is localized in space and possesses a localized energy. It is shown that both the gravitational field and the nonlinearity of the scalar field are essential to the presence of such a localized solution. In recent years various classical particle models have been widely discussed which are static or time-independent solutions of nonlinear equations with localization in space and which possess a finite field energy. In particular, soliton solutions [1], solutions in the form of eddies [2], and so on have been derived and investigated. All these solutions were treated in a flat space-time. It is of interest to derive the analogous particle-like solutions with the gravitational field taken into account; in particular it is of interest to investigate the roles of the gravitational field in connection with the formation of localized objects. These problems have been discussed in [3] in the static case. We will present below a soliton-like time-dependent solution in the form of a solitary running wave as an example of the inter-action of a Born-Infeld type of nonlinear scalar field and an Einstein gravitational field in a conformally flat metric.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 12–17, May, 1979.     

Quantum Invariant Theory and Non-Adiabatic Non-Abelian Phase Factor

An alternative formulation is proposed for the calculation of the non-adiabatic non-Abelian connection and phase factor by making use of the invariant theory and invariantrelated unitary transformation method. In order to illustrate the formulation, we study the non-adiabatic non-Abelian phase associated with the motion of a charged particle in a timedependent magnetic field (the time-dependent Landau level problem).     

螺旋线行波管注波互作用时域理论

研究了螺旋线行波管中电子注与高频场互作用的时域理论.电子对场的作用由高频场方程和空间电荷场方程模拟,场对电子注的作用由运动方程模拟.在螺旋导电面模型下利用安培环路定理和法拉第电磁感应定律得到了时域高频场方程.利用空间电荷波模型处理空间电荷场,得到了空间电荷场方程.将高频场和空间电荷场代入洛伦兹力方程,得到了运动方程.利用耦合阻抗处理高频场方程的激励源,使得高频场方程的求解能够借助诸如HFSS或HFCS等高频模拟软件来实现,增强了时域理论的灵活性.基于上述理论,编写软件数值模拟某螺旋线行波管,验证了时域理论的可行性.