4 of 6 The activation energy of 231 Th is 8.3MeV. If a nucleus of 230 Th captures a thermal neutron, determine whether fission is likely to be induced. b) Explain how the likely outcome of the process would change without the contribution of the pairing effect. Include an energy level sketch in your explanation. c) A spherical nucleus of mass number A and of radius R is deformed into an ellipsoid. Rota- tional symmetry about one axis is mantained and the volume is kept constant. a = R(1+ €) is the half-length of the long axis of the ellipsoid and b R/1+ the half-length of the short ones ( < 1 is a small positive number). Show that the surface term in the semi- empirical mass formula for the binding energy changes, up to the second order in ε, to = Es = as A2/3 12/3 (1 + 2/3/2²). 5 where as is the surface term constant. Hint: Use the approximate formula for the surface area of an ellipsoid Sellipsod = 4πT ab + aPcP + bP \1/p 3 where a, b, c are the half-lengths of the principal axes and p = 8/5.

4 of 6 The activation energy of 231 Th is 8.3MeV. If a nucleus of 230 Th captures a thermal neutron, determine whether fission is likely to be induced. b) Explain how the likely outcome of the process would change without the contribution of the pairing effect. Include an energy level sketch in your explanation. c) A spherical nucleus of mass number A and of radius R is deformed into an ellipsoid. Rota- tional symmetry about one axis is mantained and the volume is kept constant. a = R(1+ €) is the half-length of the long axis of the ellipsoid and b R/1+ the half-length of the short ones ( < 1 is a small positive number). Show that the surface term in the semi- empirical mass formula for the binding energy changes, up to the second order in ε, to = Es = as A2/3 12/3 (1 + 2/3/2²). 5 where as is the surface term constant. Hint: Use the approximate formula for the surface area of an ellipsoid Sellipsod = 4πT ab + aPcP + bP \1/p 3 where a, b, c are the half-lengths of the principal axes and p = 8/5.