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Deviation from the I(I+1) rule in the even-even isotopes 62Sm, 64Gd, 66Dy,68Er, 70Y b, 72Hf, 74W and 76Os nuclei have been studied with a new approachbased on the idea that the rotational nucleus being stretched out along thesymmetry axis, where such stretching is treated according to quantum mechanics.This approach led to a new formula that describes the dependence of the momentof inertia on the angular momentum, and such formula works well for alleven-even nuclei in the actinide and rare-earth region in the range 2.9<R<3.3.The calculations were carried out with the stretched model where the stretchingof the nucleus with the rotation is quantized. The obtained results with a newderived formula which gives a reasonable agreement with the experimental datefor all I up to 16.

The effect of the quantization of the centrifugal stretching on the  analysis of rotational spectra of even-even deformed nuclei in rare earth and  actinide regions