Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the Interacting Boson Approximation model

摘要

Using the contraction of the SU(3) algebra to the algebra of the rigidrotator in the large boson number limit of the Interacting Boson Approximation(IBA) model, a line is found inside the symmetry triangle of the IBA, alongwhich the SU(3) symmetry is preserved. The line extends from the SU(3) vertexto near the critical line of the first order shape/phase transition separatingthe spherical and prolate deformed phases, and lies within the Alhassid--Whelanarc of regularity, the unique valley of regularity connecting the SU(3) andU(5) vertices amidst chaotic regions. In addition to providing an explanationfor the existence of the arc of regularity, the present line represents thefirst example of an analytically determined approximate symmetry in theinterior of the symmetry triangle of the IBA. The method is applicable toalgebraic models possessing subalgebras amenable to contraction. This conditionis equivalent to algebras in which the equilibrium ground state (and itsrotational band) become energetically isolated from intrinsic excitations, astypified by deformed solutions to the IBA for large numbers of valencenucleons.