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Register a new userRegularities and symmetries of subsets of collective 0+ states
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The energies of subsets of excited 0+ states in geometric collective models are investigated and found to exhibit intriguing regularities. In models with an infinite square well potential, it is found that a single formula, dependent on only the number of dimensions, describes a subset of 0+ states. The same behavior of a subset of 0+ states is seen in the large boson number limit of the Interacting Boson Approximation (IBA) model near the critical point of a first order phase transition, in contrast to the fact that these 0+ state energies exhibit a harmonic behavior in all three limiting symmetries of the IBA. Finally, the observed regularities in 0+ energies are analyzed in terms of the underlying group theoretical framework of the different models.
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A remarkably simple regularity in the energies of 0+ states in a broad class of collective models is discussed. A single formula for all 0+ states in flat-bottomed infinite potentials that depends only on the number of dimensions and a simpler expression applicable to all three IBA symmetries in the large boson number limit are presented. Finally, a connection between the energy expression for 0+ states given by the X(5) model and the predictions of the IBA near the critical point is explored.
In addition to shape oscillations, low-energy excitation spectra of deformed nuclei are also influenced by pairing vibrations. The simultaneous description of these collective modes and their coupling has been a long-standing problem in nuclear structure theory. Here we address the problem in terms of self-consistent mean-field calculations of collective deformation energy surfaces, and the framework of the interacting boson approximation. In addition to quadrupole shape vibrations and rotations, the explicit coupling to pairing vibrations is taken into account by a boson-number non-conserving Hamiltonian, specified by a choice of a universal density functional and pairing interaction. An illustrative calculation for $^{128}$Xe and $^{130}$Xe shows the importance of dynamical pairing degrees of freedom, especially for structures built on low-energy $0^+$ excited states, in $gamma$-soft and triaxial nuclei.
An algebraic model is developed to calculate the T=0 and T=1 ground state binding energies for N=Z nuclei. The method is tested in the sd shell and is then extended to 28-50 shell which is currently the object of many experimental studies.
Geometric configurations of three-$alpha$ particles in the ground- and first-excited $J^pi=0^+$ states of $^{12}$C are discussed within two types of $alpha$-cluster models which treat the Pauli principle differently. Though there are some quantitative differences especially in the internal region of the wave functions, equilateral triangle configurations are dominant in the ground state, while in the first excited $0^+$ state isosceles triangle configurations dominate, originating from $^8{rm Be}+alpha$ configurations.
Dirac Hamiltonian is scaled in the atomic units $hbar =m=1$, which allows us to take the non-relativistic limit by setting the Compton wavelength $% lambda rightarrow 0 $. The evolutions of the spin and pseudospin symmetries towards the non-relativistic limit are investigated by solving the Dirac equation with the parameter $lambda$. With $lambda$ transformation from the original Compton wavelength to 0, the spin splittings decrease monotonously in all spin doublets, and the pseudospin splittings increase in several pseudospin doublets, no change, or even reduce in several other pseudospin doublets. The various energy splitting behaviors of both the spin and pseudospin doublets with $lambda$ are well explained by the perturbation calculations of Dirac Hamiltonian in the present units. It indicates that the origin of spin symmetry is entirely due to the relativistic effect, while the origin of pseudospin symmetry cannot be uniquely attributed to the relativistic effect.
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