3D calculation of Tucson-Melbourne 3NF effect in triton binding energy

As an application of the new realistic three-dimensional (3D) formalism reported recently for three-nucleon (3N) bound states, an attempt is made to study the effect of three-nucleon forces (3NFs) in triton binding energy in a non partial wave (PW) approach. The spin-isospin dependent 3N Faddeev integral equations with the inclusion of 3NFs, which are formulated as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angle between them, are solved with Bonn-B and Tucson-Melbourne NN and 3N forces in operator forms which can be incorporated in our 3D formalism. The comparison with numerical results in both, novel 3D and standard PW schemes, shows that non PW calculations avoid the very involved angular momentum algebra occurring for the permutations and transformations and it is more efficient and less cumbersome for considering the 3NF.

Atomic Bose-Einstein condensation with three-body interactions and collective excitations

The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms is investigated under the assumption of an attractive two-body and a repulsive three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear Schrodinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the s-wave. The lowest collective mode excitations are determined and their dependences on the number of atoms and on the strength of the three-body force are studied. The addition of three-body dynamics can allow the number of condensed atoms to increase considerably, even when the strength of the three-body force is very small compared with the strength of the two-body force. We study in detail the first-order liquid-gas phase transition for the condensed state, which can happen in a critical range of the effective three-body force parameter.

CORRELATIONS AMONG LOW-ENERGY OBSERVABLES OF THE 4-NUCLEON SYSTEM

Using a simple effective nucleon-trinucleon interaction we predict and study certain new correlations which are expected to exist between low-energy s-wave spin-isospin singlet observables of the four-nucleon system when various potential models yielding essentially identical two- and three-nucleon observables are employed in four-nucleon calculations. The study of such correlations using different realistic potential models is expected to yield information about the nucleon-nucleon and three-nucleon interactions.

Tjon Lines and Scaling Limit in Four-Body Systems

The fixed-slope correlation between tetramer and trimer binding energies, observed by Tjon in the context of nuclear physics, is mainly a manifestation of the dominance of the two-nucleon force in the nuclear potential, which makes the four-body scale on the order of the three-body one. In a more general four-boson case, the correlation between tetramer and trimer binding energies has a non-fixed slope, which expresses the dependence on the new scale. The associated scaling function generates a family of Tjon lines. This conclusion relies on a recent study with weakly-bound four identical bosons, within a renormalized zero-range Faddeev-Yakubovsky formalism. © 2012 Springer-Verlag.

Interação nucleon-nucleon devida à troca de três píons e produção de um píon devida à troca de dois píons

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Scaling in few-body nuclear physics

The nuclear matter calculations with realistic nucleon-nucleon potentials present a general scaling between the nucleon-nucleus binding energy, the corresponding saturation density, and the triton binding energy. The Thomas-Efimov three-body effect implies in correlations among low-energy few-body and many-body observables. It is also well known that, by varying the short-range repulsion, keeping the two-nucleon information (deuteron and scattering) fixed, the four-nucleon and three-nucleon binding energies lie on a very narrow band known as a Tjon line. By looking for a universal scaling function connecting the proper scales of the few-body system with those of the many-body system, we suggest that the general nucleus-nucleon scaling mechanism is a manifestation of a universal few-body effect.

The few scales of nuclei and nuclear matter

The well-known correlations of low-energy three and four-nucleon observables with a typical three-nucleon scale (e.g., the Tjon line) is extended to light nuclei and nuclear matter. Evidence for the scaling between light nuclei binding energies and the triton one are pointed out. We argue that the saturation energy and density of nuclear matter are correlated to the triton binding energy. The available systematic nuclear matter calculations indicate a possible band structure representing these correlations. (c) 2006 Elsevier B.V. All rights reserved.

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.

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.

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.

Three- and Four-Nucleon Bound States in Three Dimensions, Without PW Decomposition

A brief review of a three-dimensional (3D) numerical method to solve few-nucleon bound and scattering states, without the standard partial-wave (PW) decomposition, is presented. The approach is applied to three-and four-nucleon bound states, by considering the solutions of the corresponding Faddeev-Yakubovsky (FY) integral equations in momentum space. Realistic spin-isospin dependent 3D and PW formalism are presented for the alpha particle and the triton binding energies, with numerical results given in both schemes for comparison.

Q-ANALOG REALIZATION OF NUCLEON PAIRING

A q-deformed analogue of zero-coupled nucleon pair states is constructed and the possibility of accounting for pairing correlations examined. For the single orbit case, the deformed pairs are found to be more strongly bound than the pairs with zero deformation, when a real-valued q parameter is used. It is found that an appropriately scaled deformation parameter reproduces the empirical few nucleon binding energies for nucleons in the 1f7/2 orbit and 1g9/2 orbit. The deformed pair Hamiltonian apparently accounts for many-body correlations, the strength of higher-order force terms being determined by the deformation parameter q. An extension to the multishell case, with deformed zero-coupled pairs distributed over several single particle orbits, has been realized. An analysis of calculated and experimental ground state energies and the energy spectra of three lowermost 0+ states, for even-A Ca isotopes, reveals that the deformation simulates the effective residual interaction to a large extent.

Spatial Assessment of Indices for Characterizing the Erosive Force of Rainfall in El Salvador Republic

Soil erosion data in El Salvador Republic are scarce and there is no rainfall erosivity map for this region. Considering that rainfall erosivity is an important guide for planning soil erosion control practices, a spatial assessment of indices for characterizing the erosive force of rainfall in El Salvador Republic was carried out. Using pluviometric records from 25 weather stations, we applied two methods: erosivity index equation and the Fournier index. In all study area, the rainiest period is from May to November. Annual values of erosivity index ranged from 7,196 to 17,856 MJ mm ha(-1) h(-1) year(-1) and the Fournier index ranged from 52.9 to 110.0 mm. The erosivity map showed that the study area can be broadly divided into three major erosion risk zones, and the Fournier index map was divided into four zones. Both methods revealed that the erosive force is severe in all study area and presented significant spatial correlation with each other. The erosive force in the country is concentrated mainly from May to November.

Direct observation of oxidative stress on the cell wall of Saccharomyces cerevisiae strains with atomic force microscopy

We imaged pores on the surface of the cell wall of three different industrial strains of Saccharomyces cerevisiae using atomic force microscopy. The pores could be enlarged using 10 mM diamide, an SH residue oxidant that attacks surface proteins. We found that two strains showed signs of oxidative damage via changes in density and diameter of the surface pores. We found that the German strain was resistant to diamide induced oxidative damage, even when the concentration of the oxidant was increased to 50 mM. The normal pore size found on the cell walls of American strains had diameters of about 200nm. Under conditions of oxidative stress the diameters changed to 400nm.This method may prove to be a useful rapid screening process (45-60 min) to determine which strains are oxidative resistant, as well as being able to screen for groups of yeast that are sensitive to oxidative stress. This rapid screening tool may have direct applications in molecular biology (transference of the genes to inside of living cells) and biotechnology (biotransformations reactions to produce chiral synthons in organic chemistry.

Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness

Engineers often face the challenge of reducing the level of vibrations experienced by a given payload or those transmitted to the support structure to which a vibrating source is attached. In order to increase the range over which vibrations are isolated, soft mounts are often used in practice. The drawback of this approach is the static displacement may be too large for reasons of available space for example. Ideally, a vibration isolator should have a high-static stiffness, to withstand static loads without too large a displacement, and at the same time, a low dynamic stiffness so that the natural frequency of the system is as low as possible which will result in an increased isolation region. These two effects are mutually exclusive in linear isolators but can be overcome if properly configured nonlinear isolators are used. This paper is concerned with the characterisation of such a nonlinear isolator comprising three springs, two of which are configured to reduce the dynamic stiffness of the isolator. The dynamic behaviour of the isolator supporting a lumped mass is investigated using force and displacement transmissibility, which are derived by modelling the dynamic system as a single-degree-of-freedom system. This results in the system dynamics being approximately described by the Duffing equation. For a linear isolator, the dynamics of the system are the same regardless if the source of the excitation is a harmonic force acting on the payload (force transmissibility) or a harmonic motion of the base (displacement transmissibility) on which the payload is mounted. In this paper these two expressions are compared for the nonlinear isolator and it is shown that they differ. A particular feature of the displacement transmissibility is that the response is unbounded at the nonlinear resonance frequency unless the damping in the isolator is greater than some threshold value, which is not the case for force transmissibility. An explanation for this is offered in the paper. (C) 2011 Elsevier Ltd. All rights reserved.