1. (10 pts) Let's examine the fusion reaction180 + 184s 625m. An appropriate set of Woods-Saxon potential parameters for this collision are Vo = -61.98 MeV, R = 9.135 fm, a = 0.652 fm such that Vws =- Vo 1+exp(r-R . The centrifugal term has the form - h21 (1+1 ) 2ur2 a. (2 pts) Using something like Mathematica, excel, python, etc, plot the coulomb, nuclear and total internuclear potential V(r) as a function of r for I = 0 and 1=20 (also showing the centrifugal potential in this case). Your x axis should be in fm, your y axis in MeV b. (1 pt) For 1 = 0, determine (by reading off the graph or otherwise), the fusion barrier height VB (in MeV) and radius RB (in fm). These values are the center of mass values. c. (2 pts) Using these barrier parameters, and the classical expression for the fusion cross- section, evaluate the fusion cross-section at Ecm = 70 MeV. Now let's think about the two-channel coupled-channels formalism. 144Sm has a vibrational state we'll label | 1). Assuming the excitation energy of this state is zero, and its coupling to the ground state |0) is real and independent of the distance between the nuclei r, the coupling interaction can be written as Vc = F (10)(1| + [1)