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A Differential Equation for the Transition Probability B(E2) and the Resulting Recursion Relations connecting Even-Even Nuclei

We obtain here a new relation for the reduced electric quadrupole transition probability B(E2) of a given nucleus in terms of its derivatives with respect to neutron and proton numbers based on a similar local energy relation in the Infinite Nuclear Matter (INM) model of Atomic Nuclei, which is essentially built on the foundation of the Hugenholtz-Van Hove Theorem of many-body theory. Obviously such a relation in the form of a differential equation is expected to be more powerful than the usual algebraic difference equations. Although the relation for B(E2) has been perceived simply on the basis of a corresponding differential equation for the local energy in the INM model, its theoretical foundation otherwise has been clearly demonstrated. We further exploit the differential equation in using the very definitions of the derivatives to obtain two different recursion relations for B(E2) , connecting in each case three neighboring even-even nuclei from lower to higher mass numbers and vice-verse. We demonstrate their numerical validity using available data throughout the nuclear chart and also explore their possible utility in predicting B(E2) values.