  A theoretical description of the influence of surface irregularities (such as
wedge-like cracks) on the Bean-Livingston energy barrier is presented. A
careful quantitative estimate of the field of the first vortex entry H* into a
homogeneous bulk superconductor with crack-like defects is obtained. This
estimate is based on an exact analytical solution for the Meissner current
distribution in a bulk superconductor with a single two-dimensional infinitely
thin crack. This thin crack is characterized by the lowest H* value, and, thus,
appears to be the best gate for vortex entry.
