10 research outputs found
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.Comment: contribution to XVIIth European Conference of Few-Body Problems in
Physics, Evora, Portugal Sept 2000, to be published in Nucl. Phys.
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 , 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.Comment: 7 pages, no figures, to appear in Physical Review
Dirac-Foldy term and the electromagnetic polarizability of the neutron
We reconsider the Dirac-Foldy contribution to the neutron electric
polarizability. Using a Dirac equation approach to neutron-nucleus scattering,
we review the definitions of Compton continuum (), classical
static (), and Schr\"{o}dinger () polarizabilities
and discuss in some detail their relationship. The latter is the
value of the neutron electric polarizability as obtained from an analysis using
the Schr\"{o}dinger equation. We find in particular , where is the magnitude of the magnetic moment
of a neutron of mass . However, we argue that the static polarizability
is correctly defined in the rest frame of the particle, leading to
the conclusion that twice the Dirac-Foldy contribution should be added to
to obtain the static polarizability .Comment: 11 pages, RevTeX, to appear in Physical Review
Black-hole concept of a point-like nucleus with supercritical charge
The Dirac equation for an electron in the central Coulomb field of a
point-like nucleus with the charge greater than 137 is considered. This
singular problem, to which the fall-down onto the centre is inherent, is
addressed using a new approach, based on a black-hole concept of the singular
centre and capable of producing cut-off-free results. To this end the Dirac
equation is presented as a generalized eigenvalue boundary problem of a
self-adjoint operator. The eigenfunctions make complete sets, orthogonal with a
singular measure, and describe particles, asymptotically free and
delta-function-normalizable both at infinity and near the singular centre
. The barrier transmission coefficient for these particles responsible for
the effects of electron absorption and spontaneous electron-positron pair
production is found analytically as a function of electron energy and charge of
the nucleus. The singular threshold behaviour of the corresponding amplitudes
substitutes for the resonance behaviour, typical of the conventional theory,
which appeals to a finite-size nucleus.Comment: 22 pages, 5 figures, LATEX requires IOPAR