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M. Bawin

Publications and source records attributed to M. Bawin.

7 recordsLinked to original sources
arXiv2003

The singular inverse square potential, limit cycles and self-adjoint extensions

We study the radial Schroedinger equation for a particle in the field of a singular inverse square attractive potential. This potential is relevant to the fabrication of nanoscale atom optical devices, is said to be the potential describing the dipole-bound anions of polar molecules, and is the effective potential underlying the universal behavior of three-body systems in nuclear physics and atomic physics, including aspects of Bose-Einstein condensates, first described by Efimov. New results in three-body physical systems motivate the present investigation. Using the regularization method of Beane et al., we show that the corresponding ``renormalization group flow'' equation can be solved analytically. We find that it exhibits a limit cycle behavior and has infinitely many branches. We show that a physical meaning for self-adjoint extensions of the Hamiltonian arises naturally in this framework.

quant-ph↗
arXiv2000

Darwin-Foldy term and proton charge radius

In this contribution we study the Dirac equation for a finite size proton in an external electric field with explicit introduction of Dirac-Pauli form factors. Our aim is twofold. On the one hand, we wish to study whether our conclusions regarding the exact cancellation between Dirac form factor and Foldy term contributions occurring for the neutron still hold for the proton. On the other hand, we wish to clearly illustrate some of the specific features of the description of a composite particle like the proton with the Dirac equation.

nucl-th↗
arXiv2000

A Neutral Atom and a Charged Wire: From Elastic scattering to Absorption

We solve the problem of a neutral atom interacting with a charged wire, giving rise to an attractive 1/r^2 potential in two dimensions. We show how a suitable average over all possible self-adjoint extensions of the radial Schroedinger Hamiltonian eventually leads to the classical formula for absorption of the atom, a formula shown to be in agreement with a recent experiment.

quant-ph↗
arXiv1999

Neutron charge radius and the Dirac equation

We consider the Dirac equation for a finite-size neutron in an external electric field. We explicitly incorporate Dirac-Pauli form factors into the Dirac equation. After a non-relativistic reduction, the Darwin-Foldy term is cancelled by a contribution from the Dirac form factor, so that the only coefficient of the external field charge density is $e/6 r^2_{En}$, i. e. the root mean square radius associated with the electric Sachs form factor . Our result is similar to a recent result of Isgur, and reconciles two apparently conflicting viewpoints about the use of the Dirac equation for the description of nucleons.

nucl-th↗
arXiv1996

Dirac-Foldy term and the electromagnetic polarizability of the neutron

We reconsider the Dirac-Foldy contribution $μ^2/m$ to the neutron electric polarizability. Using a Dirac equation approach to neutron-nucleus scattering, we review the definitions of Compton continuum ($\barα$), classical static ($α^n_E$), and Schrödinger ($α_{Sch}$) polarizabilities and discuss in some detail their relationship. The latter $α_{Sch}$ is the value of the neutron electric polarizability as obtained from an analysis using the Schrödinger equation. We find in particular $α_{Sch} = \barα - μ^2/m$ , where $μ$ is the magnitude of the magnetic moment of a neutron of mass $m$. However, we argue that the static polarizability $α^n_E$ is correctly defined in the rest frame of the particle, leading to the conclusion that twice the Dirac-Foldy contribution should be added to $α_{Sch}$ to obtain the static polarizability $α^n_E$.

nucl-th↗
arXiv1995

Strongly coupled positronium in a chiral phase

Strongly coupled positronium, considered in its pseudoscalar sector, is studied in the framework of relativistic quantum constraint dynamics. Case's method of self-adjoint extension of singular potentials, which avoids explicit introduction of regularization cut-offs, is adopted. It is found that, as the coupling constant αincreases, the bound state spectrum undergoes an abrupt change at the critical value α= α_c = 1/2. For α> α_c, the mass spectrum displays, in addition to the existing states for α< α_c, a new set of an infinite number of bound states concentrated in a narrow band starting at mass W=0. In the limit αgoing to α_c from above, these states shrink to a single massless state with a mass gap with the rest of the spectrum. This state has the required properties to represent a Goldstone boson and to signal a spontaneous breakdown of chiral symmetry. It is suggested that the critical coupling constant α_c be viewed as a possible candidate for an ultra- violet stable fixed point of QED, with a distinction between two phases, joined to each other by a first-order chiral phase transition.

hep-ph↗