We consider the ground state of a harmonically trapped Bose-Einstein
condensate within the Gross-Pitaevskii theory including the effective-range
corrections for a two-body zero-range potential. The resulting non-linear
Schr\"odinger equation is solved analytically in the Thomas-Fermi approximation
neglecting the kinetic energy term. We present results for the chemical
potential and the condensate profiles, discuss boundary conditions, and compare
to the usual Thomas-Fermi approach. We discuss several ways to increase the
influence of effective-range corrections in experiment with magnetically
tunable interactions. The level of tuning required could be inside experimental
reach in the near future.Comment: 8 pages, RevTex4 format, 5 figure
