The dynamics of the fusion of two nuclei

The prediction of the need for an extra push over the interaction barrier in order to make the heavier nuclei fuse is made the basis of a simple algebraic theory for the energy dependence of the fusion cross section. The predictions are compared with recent experiments. A graphical construction, designed to extract directly the three parameters of the theory, suggests about 33 for the effective fissility (Z²/A)_eff defined as $\text{4Z}{}_1\text{Z}{}_2\text{/A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}{}_1\text{A}{}^{\mathrm{<mtext>case1</mtext><mtext>3</mtext>}}{}_2\text{(A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}{}_1\text{+ A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}{}_2$)] beyond which an extra push is needed, determines the initial rate of increase of the square root of the extra push (in MeV) as about one per unit excess of (Z²/A)_eff over 33 and indicates an effective centrifugal repulsion opposing fusion (in cases when angular momentum is present) not very different from that expected for two spheres rolling on each other without sliding.