  We theoretically study the elastic deformation of a fluid membrane induced by
an adhering spherical colloidal particle within the framework of a Helfrich
energy. Based on a full optimization of the membrane shape we find a continuous
binding and a discontinuous envelopment transition, the latter displaying a
potentially substantial energy barrier. A small gradient approximation permits
membrane shape and complex energy to be calculated analytically. While this
only leads to a good representation of the complex geometry for very small
degrees of wrapping, it still gives the correct phase boundaries in the regime
of low tension.
