Simple relations for the excitation energiesE2and the transition probabilitiesB(E2)of neighboring doubly even nuclides

For even-even nuclei, the excitation energy $E2\mathrm{}$ and the reduced transition probability $B\left(E2\mathrm{}\right)\mathrm{}$ between the ground state and the first excited $2^{+}$ state have been considered. On the basis of different models, it is shown that for a nucleus [$N$, $Z$] the relations $E2[N, Z]+E2[N+2, Z+2]-E2[N+2, Z]-E2[N, Z+2]\approx 0$ and $B\left(E2\mathrm{}\right)[N, Z]+B\left(E2\mathrm{}\right)[N+2, Z+2]-B\left(E2\mathrm{}\right)[N+2, Z]-B\left(E2\mathrm{}\right)[N, Z+2]\approx 0$ hold good, except in certain specified regions. The validity of these difference equations is tested with the available experimental data. The difference equation of Ross and Bhaduri is shown to follow from our approach. Some predictions of unmeasured $E2\mathrm{}$ and $B\left(E2\mathrm{}\right)\mathrm{}$ values have been made.