RELATIVISTIC 3-PARTICLE DYNAMICAL EQUATIONS .2. APPLICATION TO THE TRINUCLEON SYSTEM

We calculate the contribution of relativistic dynamics on the neutron-deutron scattering length and triton binding energy employing five sets trinucleon potential models and four types of three-dimensional relativistic three-body equations suggested in the preceding paper. The relativistic correction to binding energy may vary a lot and even change sign depending on the relativistic formulation employed. The deviations of these observables from those obtained in nonrelativistic models follow the general universal trend of deviations introduced by off- and on-shell variations of two- and three-nucleon potentials in a nonrelativistic model calculation. Consequently, it will be difficult to separate unambiguously the effect of off- and on-shell variations of two- and three-nucleon potentials on low-energy three-nucleon observables from the effect of relativistic dynamics. (C) 1994 Academic Press, Inc.

Asymmetry parameter for nonmesonic hypernuclear decay

We give general expressions for the vector asymmetry in the angular distribution of protons in the nonmesonic weak decay of polarized hypernuclei. From these we derive an explicit expression for the calculation of the asymmetry parameter, a(Lambda), which is applicable to the specific cases of He-5(Lambda) and C-12(Lambda) described within the extreme shell model. In contrast to the approximate formula widely used in the literature, it includes the effects of three-body kinematics in the final states of the decay and correctly treats the contribution of transitions originating from single-proton states beyond the s-shell. This expression is then used for the corresponding numerical computation of a(Lambda) within several one-meson-exchange models. Besides the strictly local approximation usually adopted for the transition potential, we also consider the addition of the first-order nonlocality terms. We find values for a(Lambda) ranging from -0.62 to -0.24, in qualitative agreement with other theoretical estimates but in contradiction with some recent experimental determinations.

Renormalization in non-relativistic quantum mechanics

The importance and usefulness of renormalization are emphasized in non-relativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin exhibits ultraviolet divergence. The use of renormalization techniques in these problems leads to finite converged results for both the exact and perturbative solutions. The renormalization procedure is carried out for the quantum two-body problem in different partial waves for a minimal potential possessing only the threshold behaviour and no form factors. The renormalized perturbative and exact solutions for this problem are found to be consistent with each other. The useful role of the renormalization group equations for this problem is also pointed out.

RELATIVISTIC 3-PARTICLE SCATTERING EQUATIONS

We derive a set of relativistic three-particle scattering equations in the three-particle c.m. frame employing a relativistic three-particle propagator suggested long ago by Ahmadzadeh and Tjon in the c.m. frame of a two-particle subsystem. We make the coordinate transformation of this propagator from the c.m. frame of the two-particle subsystem to the three-particle c.m. frame. We also point out that some numerical applications of the Ahmadzadeh and Tjon propagator to the three-nucleon problem use unnecessary nonrelativistic approximations which do not simplify the computational task, but violate constraints of relativistic unitarity and/or covariance.

Collisions with the Earth: the Moon's contribution

In the present work is analyzed the contribution of the Moon on the collisional process of the Earth with asteroids (NEOs). The dynamical system adopted is the restricted four-body problem Sun-Earth-Moon-particle. Using a simple analytical approach one can verify that, the orbit of an object can be significantly affected by the Moon's gravitational field when their relative velocity is smaller than 5 km/s. Therefore, the present work is based on hypothetical asteroids whose velocities relative to Moon are of the order of 1 km/s. In fact, there are several real objects (NEOs) with such velocities at the point they cross the Earth's orbit. The net results obtained indicate that the Moon helps to avoid collisions (2.6%) more than it contributes to extra collisions (0.6%). (C) 2003 COSPAR. Published by Elsevier Ltd. All rights reserved.

Controlling the Eccentricity of Polar Lunar Orbits with Low-Thrust Propulsion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Universal aspects of Efimov states and light halo nuclei

The parametric region in the plane defined by the ratios of the energies of the subsystems and the three-body ground state, in which Efimov states can exist, is determined. We use a renormalizable model that guarantees the general validity of our results in the context of short-range interactions. The experimental data for one-and two-neutron separation energies, implies that among the halo nuclei candidates, only 20C has a possible Efimov state, with an estimated energy less than 14 KeV below the scattering threshold.

Application of the GPS system for preliminary satellite orbit determination

In this paper, we discuss a method of preliminary orbit determination for an artificial satellite based on the navigation message of the GPS constellation. Orbital elements are considered as state variables and a simple dynamic model, based on the classic two-body problem, is used. The observations are formed by range and range and range-rate with respect to four visible GPS. A discrete Kalman filter with simulated data is used as filtering technique. The data are obtained through numerical propagation (Cowell's method), which considers special perturbations for the GPS satellite constellation and a user satellite. © 1997 COSPAR. Published by Elsevier Science Ltd.

Liquid-gas phase transition in Bose-Einstein condensates with time evolution

We study the effects of a repulsive three-body interaction on a system of trapped ultracold atoms in a Bose-Einstein condensed state. The stationary solutions of the corresponding s-wave nonlinear Schrödinger equation suggest a scenario of first-order liquid-gas phase transition in the condensed state up to a critical strength of the effective three-body force. The time evolution of the condensate with feeding process and three-body recombination losses has a different characteristic pattern. Also, the decay time of the dense (liquid) phase is longer than expected due to strong oscillations of the mean-squared radius.

Virtual states of light non-Borromean halo nuclei

It is shown that three-body non-Borromean halo nuclei like 12Be, 18C, 20C, considered as neutron-neutron-core systems, have p-wave virtual states with energy of about 1.7 times the corresponding neutron-core binding energy. We use a renormalizable model that guarantees the general validity of our results in the context of short range interactions.

Nucleon-nucleon interaction: Central potential and pion production

We show that the tail of the chiral two-pion exchange nucleon-nucleon potential is proportional to the pion-nucleon (πN) scalar form factor and discuss how it can be translated into effective scalar meson interactions. We then construct a kernel for the process NN → πNN, due to the exchange of two pions, which may be used in either three-body forces or pion production in NN scattering. Our final expression involves a partial cancellation among three terms, due to chiral symmetry, but the net result is still important. We also find that, at large internucleon distances, the kernel has the same spatial dependence as the central NN potential and we produce expressions relating these processes directly.

Dynamical calculation of direct muon-transfer rates from thermalized muonic hydrogen to C6+ and O8+

Moun-transfer reactions from muonic hydrogen to carbon and oxygen nuclei employing a full quantum-mechanical few-body description of rearrangement scattering were studied by solving the Faddeev-Hahn-type equations using close-coupling approximation. The application of a close-coupling-type ansatz led to satisfactory results for direct muon-transfer reactions from muonic hydrogen to C6+ and O8+.

Chaos in collapsing Bose-condensed gas

We reinvestigate the dynamics of the grow and collapse of Bose-Einstein condensates in a system of trapped ultracold atoms with negative scattering lengths, and found a new behavior in the long time scale evolution: the number of atoms can go far beyond the static stability limit. The condensed state is described by the solution of the time-dependent nonlinear Schrödinger equation, in a model that includes atomic feeding and three-body dissipation. Our results for the model show that, by changing the feeding parameter and when a substantial depletion of the ground-state exists, a chaotic behavior is found. We consider a criterion proposed by Deissler and Kaneko [Phys. Lett. A 119, 397 (1987)] to diagnose spatiotemporal chaos. ©2000 The American Physical Society.

Efimov state predictions for He2-X triatomic systems

A scale independent approach that was proposed in [1], valid for weakly bound three-boson systems, is used to predict that the three-body molecular system 4He2-7Li supports an Efimov state [2] with binding energy close to 2.31 mK.

Stability of trapped Bose-Einstein condensates

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.