Phase equivalent potentials for three-body halos

We compare the properties of three-body systems obtained with two-body potentials with Pauli forbidden states and with the corresponding phase equivalent two-body potentials. In the first case the forbidden states are explicitly excluded in the calculation. Differences arise due to the off-shell properties of these on-shell equivalent potentials. We use the adiabatic hyperspherical method to formulate a practical prescription to exclude Pauli forbidden states in three-body calculations. Schematic as well as realistic potentials are used. Almost indistinguishable results are obtained.Comment: 18 pages, 6 figure

Three-Body Halos. II. from Two- to Three-Body Asymptotics

The large distance behavior of weakly bound three-body systems is investigated. The Schr\"{o}dinger equation and the Faddeev equations are reformulated by an expansion in eigenfunctions of the angular part of a corresponding operator. The resulting coupled set of effective radial equations are then derived. Both two- and three-body asymptotic behavior are possible and their relative importance is studied for systems where subsystems may be bound. The system of two nucleons outside a core is studied numerically in detail and the character of possible halo structure is pointed out and investigated.Comment: 16 pages, compressed and uuencoded PosrScript file, IFA-94/3

Characteristics of cases with poor outcomes of rendering medical care to children in six regions of the Russian Federation

Objective: to determine the characteristics of the outcome of the improper care for children, established during the commission of forensic examinations. Material and Methods. The material of this study was commission a forensic medical examination of the archives department of complex expertise of the Bureaus of Forensic Medicine of Moscow; the Moscow, Penza, Samara and Ulyanovsk regions, and the Republic of Mordovia, conducted from 1996 to 2006. The method of this study was a statistical database processing using Excel software application package. Results. The article presents the results of the analysis of 279 forensic medical examinations conducted by committees in the Bureaus of Forensic Medical Examination of Moscow; the Moscow, Penza, Samara and Ulyanovsk regions, and the Republic of Mordovia from 1996 to 2006. The examinations were conducted in connection with poor outcomes of rendering medical care to children. Conclusion. The number of conducted examinations correlates with the population of the region. The parents of the children affected by poor treatment mostly demand the medical staff to be prosecuted and more often make legal claims to the quality of emergency medical care; dissatisfaction with the quality of medical care is more often expressed by the parents of children under 3 years old. Legal claims are more often made against obstetricians-gynecologists, pediatricians, surgeons, infectious disease specialists and anesthesiologists-resuscitators. If the conclusion of the forensic medical examination committee on the nature of the pathological process coincides with the final clinical diagnosis, the provided medical care often turns out to be adequate; in cases of inadequate medical care the risks of moderate and grievous bodily harm as well as the patient's death are high.</p

Scaling predictions for radii of weakly bound triatomic molecules

The mean-square radii of the molecules $^4$He$_3$, $^4$He$_2-^6$Li, $^4$He$_2-^7$Li and $^4$He$_2-^{23}$Na are calculated using a three-body model with contact interactions. They are obtained from a universal scaling function calculated within a renormalized scheme for three particles interacting through pairwise Dirac-delta interaction. The root-mean-square distance between two atoms of mass $m_A$ in a triatomic molecule are estimated to be of de order of ${\cal C}\sqrt{\hbar^2/[m_A(E_3-E_2)]}$, where $E_2$ is the dimer and $E_3$ the trimer binding energies, and ${\cal C}$ is a constant (varying from $\sim 0.6$ to $\sim 1$) that depends on the ratio between $E_2$ and $E_3$. Considering previous estimates for the trimer energies, we also predict the sizes of Rubidium and Sodium trimers in atomic traps.Comment: 7 pages, 2 figure

Low-Energy Universality in Atomic and Nuclear Physics

An effective field theory developed for systems interacting through short-range interactions can be applied to systems of cold atoms with a large scattering length and to nucleons at low energies. It is therefore the ideal tool to analyze the universal properties associated with the Efimov effect in three- and four-body systems. In this "progress report", we will discuss recent results obtained within this framework and report on progress regarding the inclusion of higher order corrections associated with the finite range of the underlying interaction.Comment: Commissioned article for Few-Body Systems, 47 pp, 16 fig

Anatomy of three-body decay III. Energy distributions

We address the problem of calculating momentum distributions of particles emerging from the three-body decay of a many-body resonance. We show that these distributions are determined by the asymptotics of the coordinate-space complex-energy wave-function of the resonance. We use the hyperspherical adiabatic expansion method where all lengths are proportional to the hyperradius. The structures of the resonances are related to different decay mechanisms. For direct decay all inter-particle distances increase proportional to the hyperradius at intermediate and large distances. Sequential three-body decay proceeds via spatially confined quasi-stationary two-body configurations. Then two particles remain close while the third moves away. The wave function may contain mixtures which produce coherence effects at small distances, but the energy distributions can still be added incoherently. Two-neutron halos are discussed in details and illustrated by the $2^+$ resonance in $^{6}$He. The dynamic evolution of the decay process is discussed.Comment: 30 pages, 8 figures, to be published in Nuclear Physics

Efimov Trimers near the Zero-crossing of a Feshbach Resonance

Near a Feshbach resonance, the two-body scattering length can assume any value. When it approaches zero, the next-order term given by the effective range is known to diverge. We consider the question of whether this divergence (and the vanishing of the scattering length) is accompanied by an anomalous solution of the three-boson Schr\"odinger equation similar to the one found at infinite scattering length by Efimov. Within a simple zero-range model, we find no such solutions, and conclude that higher-order terms do not support Efimov physics.Comment: 8 pages, no figures, final versio

Three-body halos. V. Computations of continuum spectra for Borromean nuclei

We solve the coordinate space Faddeev equations in the continuum. We employ hyperspherical coordinates and provide analytical expressions allowing easy computation of the effective potentials at distances much larger than the ranges of the interactions where only s-waves in the different Jacobi coordinates couple. Realistic computations are carried out for the Borromean halo nuclei 6He (n+n+\alpha) for J\pi = 0+-, 1+-, 2+- and 11Li (n+n+9Li) for (1/2)+-, (3/2)+-, (5/2)+-. Ground state properties, strength functions, Coulomb dissociation cross sections, phase shifts, complex S-matrix poles are computed and compared to available experimental data. We find enhancements of the strength functions at low energies and a number of low-lying S-matrix poles.Comment: 35 pages, 14 figure

A Model Study of Discrete Scale Invariance and Long-Range Interactions

We investigate the modification of discrete scale invariance in the bound state spectrum by long-range interactions. This problem is relevant for effective field theory descriptions of nuclear cluster states and manifestations of the Efimov effect in nuclei. As a model system, we choose a one dimensional inverse square potential supplemented with a long-range Coulomb interaction. We study the renormalization and bound-state spectrum of the system as a function of the Coulomb interaction strength. Our results indicate, that the counterterm required to renormalize the inverse square potential alone is sufficient to renormalize the full problem. However, the breaking of the discrete scale invariance through the Coulomb interaction leads to a modified bound state spectrum. The shallow bound states are strongly influenced by the Coulomb interaction while the deep bound states are dominated by the inverse square potential.Comment: 8 pages, 6 figures, EPJ style, published versio

Correlated N-boson systems for arbitrary scattering length

We investigate systems of identical bosons with the focus on two-body correlations and attractive finite-range potentials. We use a hyperspherical adiabatic method and apply a Faddeev type of decomposition of the wave function. We discuss the structure of a condensate as function of particle number and scattering length. We establish universal scaling relations for the critical effective radial potentials for distances where the average distance between particle pairs is larger than the interaction range. The correlations in the wave function restore the large distance mean-field behaviour with the correct two-body interaction. We discuss various processes limiting the stability of condensates. With correlations we confirm that macroscopic tunneling dominates when the trap length is about half of the particle number times the scattering length.Comment: 15 pages (RevTeX4), 11 figures (LaTeX), submitted to Phys. Rev. A. Second version includes an explicit comparison to N=3, a restructured manuscript, and updated figure