${\rm B(E2)}\uparrow (0_{1}^{+} \rightarrow 2_{1}^{+})$ predictions for even–even nuclei in the differential equation model

Abstract

We use the recently developed differential equation model (DEM) for the reduced electric quadrupole transition probability B(E2)↑ for the transition from the ground to the first 2+ state for predicting its values for a wide range of even–even nuclides almost throughout the nuclear landscape from Neon to Californium. This is made possible as the principal equation in the model, namely, the differential equation connecting the B(E2)↑ value of a given even–even nucleus with its derivatives with respect to the neutron and proton numbers, provides two different recursion relations, each connecting three different neighboring even–even nuclei from lower- to higher-mass numbers and vice versa. These relations are primarily responsible in extrapolating from known to unknown terrain of the B(E2)↑-landscape and thereby facilitate the predictions throughout. As a result, we have succeeded in predicting its hitherto unknown value for the adjacent 251 isotopes lying on either side of the known B(E2)↑ database.