Solution of Two-Body Bound State Problems with Confining Potentials

The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to remove the singularity of the kernel of the integral equation, a regularized form of the potentials is used. As an application of the method, the mass spectra of heavy quarkonia, mesons consisting from heavy quark and antiquark $(\Upsilon(b\bar{b}), \psi(c\bar{c}))$, are calculated for linear and quadratic confining potentials. The results are in good agreement with configuration space and experimental results.Comment: 6 pages, 5 table

Relativistic three-particle dynamical equations: II. Application to the trinucleon system

We calculate the contribution of relativistic dynamics on the neutron-deuteron 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.Comment: 15 pages, [Text and one postscript figure included, e-mail: [email protected]; Fax: 55-11-288 8224] Report # IFT P.069/9

Charged three-body system with arbitrary masses near conformal invariance

Within an adiabatic approximation to the three-body Coulomb system, we study the strength of the leading order conformaly invariant attractive dipole interaction produced when a slow charged particle $q_3$ (with mass $m_3$) is captured by the first excited state of a dimer [with individual masses and charges $(m_1,q_1$) and ($m_2,q_2=-q_1$)]. The approach leads to a universal mass-charge critical condition for the existence of three-body level condensation, ${(m_1^{-1}+m_2^{-1})}/ {[(m_1+m_2)^{-1}+m_3^{-1}]}>|{q_1}/(24 q_3)|$, as well as the ratio between the geometrically scaled energy levels. The resulting expressions can be relevant in the analysis of recent experimental setups with charged three-body systems, such as the interactions of excitons, or other matter-antimatter dimers, with a slow charged particle.Comment: 5 pages, 1 figure, to appear in Physical Review

Problem of Statistical Model in Deep Inelastic Scattering Phenomenology

Recent Deep Inelastic data leads to an up-down quark asymmetry of the nucleon sea. Explanations of the flavour asymmetry and the di-lepton production in proton-nucleus collisions call for a temperature $T \approx 100$ MeV in a statistical model. This T may be conjectured as being due to the Fulling-Davies-Unruh effect. But it is not possible to fit the structure function itself.Comment: 8 pages, 2 figures, figures on request to [email protected], IFT preprint-IFT P-050/93, Late

Radii in weakly-bound light halo nuclei

A systematic study of the root-mean-square distance between the constituents of weakly-bound nuclei consisting of two halo neutrons and a core is performed using a renormalized zero-range model. The radii are obtained from a universal scaling function that depends on the mass ratio of the neutron and the core, as well as on the nature of the subsystems, bound or virtual. Our calculations are qualitatively consistent with recent data for the neutron-neutron root-mean-square distance in the halo of $^{11}$Li and $^{14}$Be nuclei

Relativistic three-particle dynamical equations: I. Theoretical development

Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, we rederive three dimensional scattering integral equations satisfying constraints of relativistic unitarity and covariance, first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, we derive several three dimensional three-particle scattering equations satisfying constraints of relativistic unitarity and covariance. We relate two of these three-particle equations by a transformation of variables as in the two-particle case. The three-particle equations we derive are very practical and suitable for performing relativistic scattering calculations.Comment: 30 pages, Report # IFT P.070/93, [Text in Latex, e-mail: [email protected] ; FAX: 55-11-288-8224

Path Dependence of the Quark Nonlocal Condensate within the Instanton Model

Within the instanton liquid model, we study the dependence of the gauge invariant two--point quark correlator on the path used to perform the color parallel transport between two points in the Euclidean space.Comment: 4 pages, 5 figure

Two definitions of the electric polarizability of a bound system in relativistic quantum theory

For the electric polarizability of a bound system in relativistic quantum theory, there are two definitions that have appeared in the literature. They differ depending on whether or not the vacuum background is included in the system. A recent confusion in this connection is clarified

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 ultra-cold atoms in Bose-Einstein condensed state. The stationary solutions of the corresponding $s-$wave non-linear Schr\"{o}dinger 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 new characteristic pattern. Also, the decay time of the dense (liquid) phase is longer than expected due to strong oscillations of the mean-square-radius.Comment: 4 eps-figure

Validity of Feynman's prescription of disregarding the Pauli principle in intermediate states

Regarding the Pauli principle in quantum field theory and in many-body quantum mechanics, Feynman advocated that Pauli's exclusion principle can be completely ignored in intermediate states of perturbation theory. He observed that all virtual processes (of the same order) that violate the Pauli principle cancel out. Feynman accordingly introduced a prescription, which is to disregard the Pauli principle in all intermediate processes. This ingeneous trick is of crucial importance in the Feynman diagram technique. We show, however, an example in which Feynman's prescription fails. This casts doubts on the general validity of Feynman's prescription