Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

摘要

Using a contraction of the SU(3) algebra to the algebra of the rigid rotator in the large-boson-number limitnof the interacting boson approximation (IBA) model, a line is found inside the symmetry triangle of the IBA,nalong which the SU(3) symmetry is preserved. The line extends from the SU(3) vertex to near the critical linenof the first-order shape/phase transition separating the spherical and prolate deformed phases, and it lies withinnthe Alhassid-Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) verticesnin the midst of chaotic regions. In addition to providing an explanation for the existence of the arc of regularity,nthe present line represents an example of an analytically determined approximate symmetry in the interior of thensymmetry triangle of the IBA. The method is applicable to algebraic models possessing subalgebras amenablento contraction. This condition is equivalent to algebras in which the equilibrium ground state and its rotationalnband become energetically isolated from intrinsic excitations, as typified by deformed solutions to the IBA fornlarge numbers of valence nucleons.