1999•Physical Review COpen access

Neutron charge radius and the Dirac equation

Michel Bawin, S. A. Coon

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Abstract

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 nonrelativistic 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 ${(e/6)r}_{\mathrm{En}}^{2}$, 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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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 nonrelativistic 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 ${(e/6)r}_{\mathrm{En}}^{2}$, 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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Available abstract

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 nonrelativistic 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 ${(e/6)r}_{\mathrm{En}}^{2}$, 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.

Key concepts: Dirac equation, Two-body Dirac equations, Dirac sea, Physics, Pauli exclusion principle, Dirac (video compression format), Quantum electrodynamics, Charge radius

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