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Physical Review C

Dynamics of the nuclear one-body density: Small amplitude regime

Maria Carolina Nemes, A. F. R. de Toledo Piza

Published Feb 1, 1985• 3 citations
Publisher

Abstract

We present a microscopic treatment for the small amplitude limit of the equations of motion for the nuclear one-body density. These were derived previously by means of projection techniques, and allow for the explicit separation of mean-field and collision effects which result from the dynamics of many-body correlations. The form of the nuclear response in the presence of collision effects is derived. An illustrative application to a soluble model is discussed.

DOI
10.1103/physrevc.31.613

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We present a microscopic treatment for the small amplitude limit of the equations of motion for the nuclear one-body density. These were derived previously by means of projection techniques, and allow for the explicit separation of mean-field and collision effects which result from the dynamics of many-body correlations. The form of the nuclear response in the presence of collision effects is derived. An illustrative application to a soluble model is discussed.
We present a formal derivation of the exact dynamics of the one-body density matrix. Its essential ingredients are shown to be the following: (a) a mean field unitary time evolution; (b) irreducible nonunitary corrections to the unitary evolution (collision effects); and (c) effects due to the time evolution of initial state correlation [which contribute to both (a) and (b)]. In the weak coupling limit the collision effects give rise to a term of Boltzmann form. A qualitative discussion of the importance of collision effects for the expectation values of one-body operators and a quantitative illustration in the framework of an exactly soluble model are given. In this case one finds large nonunitary contributions.NUCLEAR STRUCTURE Exact microscopic description of the time evolution of the one body density matrix.
In this article, I provide a simple review on conventional methods and models on the transport phenomenon of nuclear many-body systems. By exploiting the basic idea of time-dependent projection operator, I recommend a novel method to derive the transport equation for collective motion which is embedded on the microscopic dynamics of timedependent single-particle motion. It is emphasized that the microscopic dynamics of single-particle motion should play an important role for understanding the dynamics of nuclear reaction and the synthesis mechanisms of new superheavy elements. The numerical results of energy dissipation and entropy production indicate that the collective motion passes through three stages, such as dephasing/decoherence, statistical relaxation and stationary state. The statistical relaxation is a complex anomalous diffusion process in general. With the aid of above analysis and results, a possible way to define the collective and single-particle variables for the realistic nuclear many-body systems is proposed.
Aiming at exploring microscopic dynamics responsible for the dissipative large-amplitude collective motion, the dynamic response and correlation functions are introduced within the general theory of nuclear coupled-master equations. The theory is based on the microscopic theory of nuclear collective dynamics which has been developed within the time-dependent Hartree-Fock (TDHF) theory for disclosing the complex structure of the TDHF manifold. A systematic numerical method for calculating the dynamic response and correlation functions is proposed. By performing numerical calculation for a simple model Hamiltonian, it is pointed out that the dynamic response function gives important information in understanding the large-amplitude dissipative collective motion which is described by an ensemble of trajectories within the TDHF manifold.
For one decade, several fields in physics as well microscopic as macroscopic benefit from the computational particle-models (astrophysics, electronics, fluids mechanics...). In particular, the nuclear matter offers an interesting challenge as many body problem, owing to the quantal nature of its components and the complexity of the in-medium interaction. Using a model derived from semi-classical Vlasov equation and the projection of the Wigner function on a Gaussian coherent states basis (pseudo-particles), static and dynamical properties of nuclear matter are studied, featuring the growing of bulk instabilities in dilute matter. Using different zero and finite range effective interactions, the effect of the model parameters upon the relation total energy - density - temperature and surface energy of the pseudo-particles fluid is pointed out. The dynamical feature is first based upon a model of the 2-body Uehling-Ulhenbeck collisionnal term. A study of the relaxation of a nucleonic system is performed. At last, the pseudo-particle model is used in order to extract time scale for the growing of density fluctuations. This process is supposed to be a possible way to clusterization during heavy nuclei collisions.
Starting from a recent reformulation of the Markov limit, we apply the mean- field approximation to the resulting Lindblad-type many-electron dynamics, and derive a closed equation of motion for the electronic single-particle density matrix in the presence of one- and two-body scattering mechanisms. The proposed formulation preserves the positive- definite character of the single-particle density matrix. This result is in striking contrast with conventional Markov approaches, where the single-particle mean-field equations can lead to positivity violations and therefore to unphysical results.
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.