Static deformation energy calculations: from microscopical to semiclassical theories

Various methods of calculating static potential energy surfaces are reviewed. Their uncertainties and limitations for the prediction of fission barriers of heavy nuclei are evaluated. The relations of the Strutinsky shell-correction method to the microscopical Hartree-Fock theory, on the one hand, and to semiclassical approaches, on the other hand, are discussed. Some representative experimental results are compared with the theoretical predictions, and the differences are related to the uncertainties in the theoretical results themselves. (author)