‎optimized q-cascade approach for stable cadmium isotope purification using newton-raphson and direct substitution methods‎

In this study, the objective was to separate cadmium isotopes using the q-cascade approach. the optimal value of the parameter m* was determined by minimizing the function (∑lε02)/2p within the q-cascade. to overcome computational challenges, the newton-raphson solver and direct substitution algorithm were employed to solve the system of nonlinear equations. the direct substitution method was used to provide a suitable initial guess for the newton-raphson method. validation of the developed algorithms using stable cadmium isotopes showed that the value of m* undergoes slight changes with variations in the target isotope concentration in the product and waste streams. for enriching cd-106 in the product, m* was approximately 108.5, corresponding to the average molar mass of cd-106 and cd-111. as the target isotope concentration in the product increases, the number of enrichment stages increases more steeply compared to the number of stripping stages. similarly, increasing the cd-116 enrichment in the waste leads to a larger increase in the number of stripping stages compared to enrichment stages.