  A new method is introduced to construct approximations to Skyrmions that are
explicit rational functions of the spatial Cartesian coordinates. The scheme
uses ADHM data of a Yang-Mills instanton to produce a Skyrmion with a baryon
number that is equal to the instanton number. The formula for the Skyrmion
involves only the evaluation of the ADHM data, in contrast to the Atiyah-Manton
construction that requires the solution of a differential equation that can
only be solved explicitly in the case of a spherically symmetric Skyrmion.
Examples with baryon numbers one and two are studied in detail. The energy of
the rational Skyrmion with baryon number one is lower than that of the
Atiyah-Manton Skyrmion, which is already within one percent of the energy of
the true numerically computed Skyrmion. A family of baryon number two Skyrmions
is presented, which includes an axially symmetric Skyrmion that smoothly
transforms to a pair of well-separated single Skyrmions as the parameter is
varied.
