$^{8}$Be, $^{12}$C, $^{16}$O, $^{20}$Ne, $^{24}$Mg, and $^{32}$S nuclei and alpha clustering within a generalized liquid drop model

The potential energy governing the shape and the entrance and decay channels of the 12 C, 16 O, 20 Ne, 24 Mg, and 32 S 4n-nuclei has been determined within a generalized liquid drop model. Different three-dimensional and planar shapes have been investigated: linear chain, triangle, square, tetrahedron, pentagon, trigonal bipyramid, square pyramid, hexagon, octahedron, octogon and cube. The rms radii of the linear chains are higher than the experimental rms radii of the ground states. The binding energies of the planar shapes at the contact point are lower than the ones of the three-dimensional configurations. The a particle plus A-4 daughter configuration leads always to the lowest potential barrier relatively to the sphere configuration.