arXiv subjects
Publications and source records attributed to J. N. Ginocchio.
Pseudospin symmetry is a relativistic symmetry of the Dirac Hamiltonian with scalar and vector mean fields equal and opposite in sign. This symmetry imposes constraints on the Dirac eigenfunctions. We examine extensively the Dirac eigenfunctions of realistic relativistic mean field calculations of deformed nuclei to determine if these eigenfunctions satisfy these pseudospin symmetry constraints.
We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = Jmax pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular for those with total angular momenta I le 2j. For I=0 eigenstates of four fermions in a single-j shell we show that there is only one non-zero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems.
At a critical point of a second order phase transition the intrinsic energy surface is flat and there is no stable minimum value of the deformation. However, for a finite system, we show that there is an effective deformation which can describe the dynamics at the critical point. This effective deformation is determined by minimizing the energy surface after projection onto the appropriate symmetries. We derive analytic expressions for energies and quadrupole rates which provide good estimates for these observables at the critical point.
A generalized M1 sum rule for orbital magnetic dipole strength from excited symmetric states to mixed-symmetry states is considered within the proton-neutron interacting boson model of even-even nuclei. Analytic expressions for the dominant terms in the B(M1) transition rates from the first and second $2^+$ states are derived in the U(5) and SO(6) dynamic symmetry limits of the model, and the applicability of a sum rule approach is examined at and in-between these limits. Lastly, the sum rule is applied to the new data on mixed-symmetry states of 94Mo and a quadrupole d-boson ratio $nd(0^+_1)/nd(2^+_2) \approx 0.6$ is obtained in a largely parameter-independent way
We review recent developments that show that pseudospin symmetry is an approximate relativistic symmetry of the Dirac Hamiltonian with realistic nuclear mean field potentials.
We show that a natural explanation for characteristic features (angular momentum and radial quantum numbers) of pseudospin doublets and intruder levels in nuclei can be obtained by combining the relativistic attributes of pseudospin symmetry with known properties of Dirac bound states.
The identification of pseudospin symmetry as a relativistic symmetry of the Dirac Hamiltonian is used to explain the structure of radial nodes occurring in pseudospin doublets and to illuminate the special status of nodeless intruder states in nuclei.
Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates.
We use the empirical evidence that F-spin multiplets exist in nuclei for only selected states as an indication that F-spin can be regarded as a partial symmetry. We show that there is a class of non-F-scalar IBM-2 Hamiltonians with partial F-spin symmetry, which reproduce the known systematics of collective bands in nuclei. These Hamiltonians predict that the scissors states have good F-spin and form F-spin multiplets, which is supported by the existing data.
We show that the generators of pseudospin symmetry are the non - relativistic limit of the generators of an SU(2) symmetry which leaves invariant the Dirac Hamiltonian with scalar and vector potentials equal in magnitude but opposite in sign, $V_V = - V_S$. Furthermore, within this framework, we demonstrate that this symmetry may be approximately conserved for realistic scalar and vector potentials.
Sum rules for the total- and scissors-mode M1 strength in odd-A nuclei are derived within the single-j interacting boson-fermion model. We discuss the physical content and geometric interpretation of these sum rules and apply them to ^{167}Er and ^{161}Dy. We find consistency with the former measurements but not with the latter.