Evidence on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn><mml:mn/></mml:math>bifurcation in ground bands of even-even nuclei and the theoretical explanation with the interacting boson model

All the data available for the ground rotational bands of even-even actinide nuclei and rare-earth nuclei (with band crossing spins ${I}_{c}&gt;~16$) are studied in terms of the staggering parameter, introduced in the discussion of superdeformed bands. Evidence of $\ensuremath{\Delta}I=4$ bifurcation ($\ensuremath{\Delta}I=2$ staggering) is observed in many cases. We study theoretically this bifurcation phenomenon in terms of the interacting boson model (IBM) by using the variation before projection (VBP) method. In our theoretical framework, the staggering phenomenon is found to originate from the finite boson number effect. The IBM explains the opposite signs of the staggering patterns between two neighboring nuclei, which are found experimentally. We perform also the full diagonalization of the IBM Hamiltonian and obtain consistent results with the VBP method. By introducing the $g$ bosons, we are able to reproduce even irregular or localized staggering patterns in the $\ensuremath{\Delta}I=4$ bifurcation spectrum observed in some data.

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