Applications of the collective model to some axially symmetric deformed even-even nuclei

Abstract EN

The rotational energies of deformed even-even nuclei, which have axes of symmetry, are investigated.

A new simple formula, which determines the energy of the rotational state of a deformed even-even nucleus in terms of its total angular momentum and its reciprocal moment of inertia , is given.

The new formula is fitted for the even-even isotopes of the hafnium: 168Hf, 170Hf, 172Hf and 174Hf, uranium: 232U, 234U, and 236U, and plutunium: 238Pu, 240Pu, and 242Pu nuclei.

The required reciprocal values of the cranking moments of inertia of these isotopes are calculated by using the concept of the single-particle Schroedinger fluid and are in excellent agreement with the corresponding experimental values.

Moreover, the calculated values of the rotational energies of the mentioned ten isotopes are in good agreement with the corresponding experimental values and are better than those obtained by using previous formulas.

Furthermore, the ratio of the excitation energies of the first and the first excited states, , is also calculated for these nuclei.

Finally, new simple formulas for calculating the energies of the -band and the γ-band vibrational states are given and used for these nuclei.