The alpha-alpha interaction is described by a two body potential. It is shown that there is a two body potential of the Woods-Saxon form which gives correctly the energy and the decay width of the $^{8}\mathrm{Be}$ ground state and also the phase shifts for $L=0, 2, 4, \mathrm{and} 6$. The wave function representing the alpha particles in the $^{8}\mathrm{Be}$ ground state has radial quantum number equal to three.NUCLEAR REACTIONS $^{4}\mathrm{He}(\ensuremath{\alpha}, \ensuremath{\alpha})^{4}\mathrm{He}$, ${E}_{\mathrm{c}.\mathrm{m}.}=0.2 \mathrm{to} 15$ MeV. Computation of decay and scattering parameters and comparison with experimental values.