By Aage Bohr

Publication by way of Aage Bohr, Ben R. Mottelson

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4-15)); the part of the energy operator acting in K=O bands is therefore diagonal with respect to I , and can only depend on the combination I:+ 1;. To leading order, the rotational Hamiltonian is of the form where h,(q,p) is a function of the intrinsic variables. The expectation value 2 4 % ROTATIONAL SPECTRA Ch. 4 of the operator (4-43) can be written h2 Erot=---I(I+ 1) 29- (4-44) with the effective moment of inertia Xdefined by 2 4- =(Klh,lK) 2Y - (4-45) The form (4-44) is the familiar expression obtained by quantizing the classical Hamiltonian for a symmetric top.

For such a system, the quantum number r , for states with vanishing electronic angular momentum about the axis, can be expressed in the form r = re1P(12),where rel represents the r quantum number of the electronic wave function, while P(12) represents the spatial exchange of the nuclei. The statistics for the identical nuclei implies the relation P( 12) = ( - l)', where S is the total nuclear spin. For the total rotational angular momentum L, exclusive of the nuclear spins, we therefore 12 3isr ROTATIONAL SPECTRA Ch.

I 1 I I I I ( I I I I 150 160 170 180 190 " 220 230 260 250 * Energy ratios in the ground-state rotational band in even-even nuclei. The figure shows the observed energy ratios EI : E2 for the ground-state rotational bands in even-even nuclei in the regions 1525A5190 and 2245A. -stable isotopes are included. , 1967. The entries in parentheses represent tentative assignments. The horizontal lines give the theoretical energy ratios for the leadingorder expression (4-44). Figure 4-4 The observed bands have the quantum numbers Kvr = 0 + + .

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Nuclear Structure Volume II: Nuclear Deformations by Aage Bohr
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