Intrinsic sphape of nuclei
A transformation of coordinates, introduced a decade ago by Dzublik et al. and by Zickendraht, allow us to go from the 3A-3 Jacobi coordinates χ i S , i =1,2,3;ς=1,2,3, A-1 of an A body system to the Euler angles ϑ k , k = 1,2,3 associated with the standard 0(3) group, the 3A-9 coordinates α which are a subset of the (A-1)(A-2)/2 associated with an 0(A-1) group, and,three extra parameters ρ k , k =1,2,3. The latter give a measure of the deformation along the three principal axes in the frame of reference fixed in the body.
In the present note we discuss the deformation of the three body system by considering the expectation values of both the invariants of the inertia tensor and of the ρ k 2 . We compare the results in a basis of harmonic oscillator states for the three body system that reaches up to 22 quanta.
KeywordsEuler Angle Body System Secular Equation Inertia Tensor Ground State Wave Function
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