Problem 4 [20] Consider the two-group bare homogeneous reactor model. For this configuration, the two- group criticality eigenvalue problem without up-scattering can be written as: DV 6, (F) + 1% (F) = [(v,,),(F)+(v,2,),4(F)], k eff DV(F) + 9,242 (F) 5,1+241 (F) = 0, - D(U). Lets assume that both fast and thermal group scalar flux components can be characterized by the same spatial shape function R(F). The shape function R(F) is the fundamental eigenfunction of the corresponding Helmholtz eigenvalue problem: [VR(F) + B R(F) = 0, VF extr." R(Fextr.) = 0, Vextr. OV ex extr." Using the above problem statement and the corresponding Helmholtz eigenvalue problem, give the following: 'R,g 1) (5 point) Write explicitly all components of g. Explain how 2nd (thermal group) equation was obtained in terms of a,2 2) (5 point) Explain, why the 2nd (thermal group) equation is homogeneous (right hand side of this equation is equal to zero). 3) (10 points) Derive the two-group approximation formula for the effective multiplication factor koff of a bare homogeneous reactor configuration.