  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.
