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S. A. Coon

Publications and source records attributed to S. A. Coon.

17 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.

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arXiv2003

Charge-Symmetry Breaking and the Two-Pion-Exchange Two-Nucleon Interaction

Charge-symmetry breaking in the nucleon-nucleon force is investigated within an effective field theory, using a classification of isospin-violating interactions based on power-counting arguments. The relevant charge-symmetry-breaking interactions corresponding to the first two orders in the power counting are discussed, including their effects on the 3He-3H binding-energy difference. The static charge-symmetry-breaking potential linear in the nucleon-mass difference is constructed using chiral perturbation theory. Explicit formulae in momentum and configuration spaces are presented. The present work completes previously obtained results.

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arXiv2000

Reworking the Tucson-Melbourne Three-Nucleon Potential

We introduce new values of the strength constants (i.e., $a$, $b$, $c$, and $d$ coefficients) of the Tucson-Melbourne (TM) 2$π$ exchange three nucleon potential. The new values come from contemporary dispersion relation analyses of meson factory $π$N scattering data. We make variational Monte Carlo calculations of the triton with the original and updated three-body forces to study the effects of this update. We remove a short-range -- $π$-range part of the potential due to the $c$ coefficient and discuss the effect on the triton binding energy.

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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.

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arXiv2000

Off-Mass-Shell $π$N Scattering and $pp \to pp π^0$

We adapt the off-shell $π$N amplitude of the Tucson-Melbourne three-body force to the half-off-shell amplitude of the pion rescattering contribution to $pp \to pp π^0$ near threshold. This {\em pion} rescattering contribution, together with the impulse term, provides a good description of the data when the half-off-shell amplitude is linked to the phenomenological invariant amplitudes obtained from meson factory $π$N scattering data.

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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.

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arXiv1999

Particle Mixing and Charge Asymmetric $ΛN$ Forces

We calculate the contributions of a particular set of charge asymmetric $ΛN$ interactions to the difference of the separation energies of $^4_Λ$He and $^4_Λ$H. We use perturbation theory with four-body variational Monte Carlo wave functions calculated from a Hamiltonian with two- and three-hadron forces. We compare with the data and with an earlier calculation made by one of us which employed a two-body wave function of the $Λ$-nucleus type.

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arXiv1999

Isospin violation and meson-exchange models of the nucleon-nucleon interaction

Traditionally isospin violation (charge symmetry breaking and charge dependence) has been modeled by the exchange of mesons between two nucleons. Sources of isospin violation in these models include meson mass differences, meson mixing (of pseudoscalar, vector, and axial-vector mesons) and isospin violating couplings of mesons with nucleons. I will review the calculated results of this theoretical approach and the NN data on isospin violation.

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arXiv1998

Vector Meson Dominance and Rho-Omega Mixing

The scale of a phenomenologically successful charge-symmetry-violating nucleon-nucleon interaction, that attributed to meson exchange with a $ΔI =1$ rho-omega transition, is set by the Coleman-Glashow SU(2) breaking tadpole mechanism. A single tadpole scale has been obtained from symmetry arguments, electromagnetic meson and baryon measured mass splittings, and the observed isospin violating ($ΔI=1$) decay $ω\to π^+π^-$. The hadronic realization of this tadpole mechanism lies in the $I = 1$ $a_0$ scalar meson. We show that measured hadronic and two-photon widths of the $a_0$ meson, with the aid of the Vector Meson Dominance model, recover the universal Coleman-Glashow tadpole scale.

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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 $α^n_E$.

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arXiv1996

$ΔI=1$ axial-vector mixing and charge symmetry breaking

Phenomenological Lagrangians that exhibit (broken) chiral symmetry as well as isospin violation suggest short-range charge symmetry breaking (CSB) nucleon-nucleon potentials with a $\mbox{\boldmath $σ$}_1 \!\cdot\!\mbox{\boldmath $σ$}_2$ structure. This structure could be realized by the mixing of axial-vector ($1^+$) mesons in a single-meson exchange picture. The Coleman-Glashow scheme for $ΔI_{z}=1$ charge symmetry breaking applied to meson and baryon $SU(2)$ mass splittings suggests a universal scale. This scale can be extended to $ΔI=1$ nonstrange CSB transitions $\langle a_1^\circ|H_{em}|f_1\rangle$ of size $-0.005$ GeV$^2$. The resulting nucleon-nucleon axial-vector meson exchange CSB potential then predicts $ΔI=1$ effects which are small.

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arXiv1995

Repulsive Short Range Three-Nucleon Interaction

The three nucleon interaction that arises from pion and the effective scalar and vector meson exchange components of the nucleon-nucleon interaction is constructed and shown to be repulsive. Using several wavefunction models we show that this interaction reduces the calculated binding energy of the trinucleons by about 200 keV. The contributions of intermediate $N$(1440) resonances to this three nucleon interaction and of the $D$-state component in the trinucleon model are estimated, and shown to be small.

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arXiv1993

Nucleon polarization in three-body models of polarized \bbox{^6}Li

Just as $^3\roarrow{\rm He}$ can be approximately characterized as a polarized neutron target, polarized \Li6D has been advocated as a good {\em isoscalar} nuclear target for the extraction of the polarized gluon content of the nucleon. The original argument rests upon a presumed ``alpha + deuteron'' picture of \Li6, with the polarization of the nucleus carried by the polarization of the deuteron. We have calculated the polarization of the constituents of \Li6 as a three-body bound state of $α+ n + p$ interacting with local potentials fitted to the scattering data. It is necessary to include partial waves up to $j=17/2$ (75 channels, or, when including the $T=1$ state, 150 channels) in the Faddeev equations before the energy eigenvalue converges. The longitudinal formfactors are then described well by the wave function. Various combinations of $α$N and NN strong and Coulomb potentials yield a straight line in the charge radius {\em vs.} energy plane which, unlike those of previous calculations, passes through the experimental datum. We find for all cases a polarization of the valence neutron in excess of 90\%. This may make polarized \Li6D an attractive target for many nuclear physics purposes, since its neutrons are effectively 45\% polarized.

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arXiv1993

Momentum and Coordinate Space Three-nucleon Potentials

In this paper we give explicit formulae in momentum and coordinate space for the three-nucleon potentials due to $ρ$ and $π$ meson exchange, derived from off-mass-shell meson-nucleon scattering amplitudes which are constrained by the symmetries of QCD and by the experimental data. Those potentials have already been applied to nuclear matter calculations. Here we display additional terms which appear to be the most important for nuclear structure. The potentials are decomposed in a way that separates the contributions of different physical mechanisms involved in the meson-nucleon amplitudes. The same type of decomposition is presented for the $π- π$ TM force: the $Δ$, the chiral symmetry breaking and the nucleon pair terms are isolated.

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