Two-body Observables Research Articles

Quark effects in nuclei: One- and two-body observables

We analyze the observability of quark effects in nuclei. We describe the calculation of one- and two-body (at the quark level) observables, paying special attention to the two-body case. We discuss the physics involved with a simplified quantum-mechanical model of the world in which quarks carry no flavor degrees of freedom and space is one dimensional. We then apply our techniques to a relatistic calculation of the Coulomb energy for a deuteron-like system.

Variational extension of the time-dependent mean-field approach

We investigate an application of the variational principle of Balian and Vénéroni for density operators and observables. Our choice for the trial spaces incorporates correlations in the density operator. It allows one to calculate the expectation values of both one-body and two-body observables. We derive a set of coupled equations which extends the TDHF formalism and determines the evolution of the partition function, the one-body density, and the second cumulant (it corresponds also to a truncation of the quantal counterpart of the BBKGY equations). By restricting further the trial space for the two-body observables, the variational principle generates simpler equations which still include the effects of a selected class of correlations on the evolution of the one-body density.

A time dependent RPA-theory for heavy ion reactions

The time dependent Hartree Fock theory (TDHF) is generalized by incorporating 2p-2h correlations into the TDHF Slater determinant in order to improve the description of two-body observables. To this end a time dependent RPA theory (TDRPA) is formulated using the quasi boson approximation. The approach turns out to be readily applicable requiring only minor changes in the present time TDHF codes. The theory is exemplified by considering the spreading width of the fragment particle number in a nucleus-nucleus collision. The TDRPA states are furthermore used to formulate a scattering theory for heavy ion collisions which incorporates the quantum corrections of orderh2 by means of a gaussian parametrization of the scattering form factor.

Microscopic calculation of the nonlinear current fluctuations of a metallic resistor: The problem of heating in perturbation theory

The effect of a constant electric field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}$ on the low-temperature Johnson noise of a metallic resistor is calculated by nonequilibrium diagrammatic perturbation theory. The expansion, in powers of ${E}^{2}$, is shown to diverge, and the divergence is associated with accumulating Joule heat. An insight into how to treat a steady state properly when there is heating is provided by the Boltzmann equation. A vertex function that corresponds to a steady-state solution of this equation is identified. With this vertex function it is possible to evaluate not only one-particle operators, for which the Boltzmann equation is sufficient, but also troublesome contributions to the current fluctuations and other two-body observables for which a many-body approach is required. The calculated corrections to the current correlations agree qualitatively, but not quantitatively, with simple phenomenological agruments. In particular, it is not possible to describe the leading effects of the electric field solely in terms of a variable local temperature. The model calculation illustrates and sheds some light on several problems that only appear when nonlinear deviations from thermal equilibrium must be considered: the complicated effects to which heat generation leads, the identification and treatment of these effects in perturbation theory, and the difficulties these effects pose for hypothetical generalizations of the fluctuation dissipation theorem. Some possible connections between the calculation and $\frac{1}{f}$ noise are also briefly explored. In particular, recent experiments that may confirm the conclusion of this calculation, that systems in which there is only impurity scattering do not exhibit $\frac{1}{f}$ noise, are noted.

Photodisintegration cross sections of the deuteron

Employing a variety of local static potentials, the bremsstrahlung-weighted and integrated cross sections for the photodisintegration of the deuteron are calculated. The effect of variation of the tensor force in the two-nucleon Yale potential in a manner as to affect only the D state probability of the deuteron, while leaving the values of the other two-body observables unchanged, is studied. It is found that though the contribution of the central, tensor, and spin–orbit components of the two-nucleon potentials to the integrated cross section may vary significantly, the integrated cross section does not change by more than a few percent. The sensitivity of the integrated cross section to the short-distance features of the two-nucleon local potentials is also studied.

Triton calculations with phase-equivalent nucleon-nucleon interactions

Abstract Haftel and Tabakin have recently generated a series of potentials by applying a unitary transformation to the Reid potential. The new potentials have a short-range non-locality but reproduce exactly the two-body observables calculated with the Reid potential. We have used several of these potentials to calculate the triton binding energy, rms radius, S-, D- and S'-state admixture probability and charge form factor. We find that these triton observables are sensitive to the short-range part of the nucleon-nucleon interaction, and we conclude that the triton can be used confidently to test phenomenological and field-theoretically derived models of the short range portion of the nucleon-nucleon interaction.

Introduction to Many-Body Formalism

An elementary approach is presented to the many-body formalism needed to understand simple models of superfluid systems. In the framework of occupation number space-particle conserving operators that represent single-body and two-body observables are constructed in an intuitive manner. It is then shown that this formalism when applied to such observables as single-particle energy and two-body interaction potential yields results which are physically plausible. The basic formalism for the understanding of many-body systems is thereby presented without recourse to a complete development of quantum field theory.

On the distinguishability of equivalent potentials

We explore the possibility of discriminating between equivalent potentials (i.e., potentials reproducing the same phase shifts and bound state energies for the two-body problem) by making use of three-body amplitudes. Working with a simple model of a two-body target, and making approximations characteristic of a high-energy treatment, we find that the three-body amplitude can be decomposed into two parts; one sensitive to the nature of the two-body force, the other expressible in terms of two-body observables. When the two-body interaction terminates exactly beyond a certain distance a, the first part arises entirely from the overlap of the target particles if they are regarded as spheres of radius a. By consideration of effective range theory we have also given a brief discussion of potentials with infinitely long tails. For such interactions the second part of the composite amplitude is always zero. In order to avoid extensive digressions into the problem of potential construction (for potentials belonging to assigned classes) we have restricted specific discussion to the two classes for which this problem has been solved, namely, local and nonlocal separable potentials.