SCHRÖDINGER FLUID AND THE QUADRUPOLE MOMENTS OF THE DOUBLY EVEN NUCLEI IN THE sd- SHELL

The concept of the single-particle Schrödinger fluid is applied to the doubly even deformed nuclei in the -shell in order to obtain the cranking and the rigid body moments of inertia of these nuclei. Variations of the reciprocal moments of inertia of the twelve doubly even nuclei, namely: 18O, 20Ne, 22Ne, 24Mg, 26Mg, 28Si, 30Si, 32Si, 32S, 34S, 36Ar, and 40Ar with respect to the deformation parameter β are carried out in order to obtain the best agreement between the calculated values and the corresponding experimental values. Direct relationships between the moments of inertia and the quadrupole moment of an axially symmetric deformed nucleus are derived. Accordingly, the quadrupole moments of the mentioned nuclei are obtained as functions of their moments of inertia. The obtained values of the measured quadrupole moments by using the cranking moments of inertia for all the considered nuclei are in good agreement with the corresponding experimental values. Concerning the obtained measured quadrupole moments according to the rigid body model, agreement with the corresponding experimental values occur only for the five nuclei 18O, 20Ne, 22Ne, 24Mg, and 26Mg.