Force-field parameterization of the galactic cosmic ray spectrum Validation for Forbush decreases

A useful parametrization of the energy spectrum of galactic cosmic rays (GCR) near Earth is offered by the so-called force-field model which describes the shape of the entire spectrum with a single parameter, the modulation potential. While the usefulness of the force-field approximation has been confirmed for regular periods of solar modulation, it was not tested explicitly for disturbed periods, when GCR are locally modulated by strong interplanetary transients. Here we use direct measurements of protons and alpha -particles performed by the PAMELA space-borne instrument during December 2006, including a major Forbush decrease, in order to directly test the validity of the force-field parameterization. We conclude that (1) The force-field parametrization works very well in describing the energy spectra of protons and alpha -particles directly measured by PAMELA outside the Earths atmosphere; (2) The energy spectrum of GCR can be well parameterized by the force-field model also during a strong Forbush decrease; (3) The estimate of the GCR modulation parameter, obtained using data from the world-wide neutron monitor network, is in good agreement with the spectra directly measured by PAMELA during the studied interval. This result is obtained on the basis of a single event analysis, more events need to be analyzed.