Regular Article - Theoretical Physics

Cottingham formula and nucleon polarisabilities

¹ Albert Einstein Center for Fundamental Physics, Institut für theoretische Physik, Universität Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
² Institut für Kernphysik, Technische Universität Darmstadt, 64289, Darmstadt, Germany
³ ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291, Darmstadt, Germany
⁴ Institute for Nuclear Theory, University of Washington, Seattle, WA, 98195-1550, USA
⁵ Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, Nussallee 14-16, 53115, Bonn, Germany

^* e-mail: mhofer@uw.edu

Received: 24 June 2015
Accepted: 23 July 2015
Published online: 19 August 2015

Abstract

The difference between the electromagnetic self-energies of proton and neutron can be calculated with the Cottingham formula, which expresses the self-energies as an integral over the electroproduction cross sections – provided the nucleon matrix elements of the current commutator do not contain a fixed pole. We show that, under the same proviso, the subtraction function occurring in the dispersive representation of the virtual Compton forward scattering amplitude is determined by the cross sections. The representation in particular leads to a parameter-free sum rule for the nucleon polarisabilities. We evaluate the sum rule for the difference between the electric polarisabilities of proton and neutron by means of the available parameterisations of the data and compare the result with experiment.