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Register a new userRelativistic effect of spin and pseudospin symmetries
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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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We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70s by Smith and Tassie, and Bell and Ruegg. As relativistic symmetries, they have been extensively researched and applied to several physical systems for the last 18 years. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrodinger-like equations, i.e, without a matrix structure. In this paper we use the original formalism of Bell and Ruegg to derive general requirements for the Lorentz structures of potentials in order to have these SU(2) symmetries in the Dirac equation, again allowing for the suppression of the matrix structure of the second-order equation of either the upper or lower components of the Dirac spinor. Furthermore, we derive equivalent conditions for spin and pseudospin symmetries with 2- and 1-dimensional potentials and list some possible candidates for 3, 2, and 1 dimensions. We suggest applications for physical systems in three and two dimensions, namely electrons in graphene.
The dominance (preponderance) of the 0+ ground state for random interactions is shown to be a consequence of certain random interactions with chaotic features. These random interactions, called chaotic random interactions, impart a symmetry property to the ground-state wave function: an isotropy under an appropriate transformation, such as zero angular momentum for rotation. Under this mechanism, the ground-state parity and isospin can also be predicted in such a manner that positive parity is favored over negative parity and the isospin T = 0 is favored over higher isospins. As chaotic random interaction is a limit with no particular dynamics at the level of two interacting particles, this realization of isotropic symmetry in the ground state can be considered as the ultimate case of many-body correlations. A possible relation to the isotropy of the early universe is mentioned.
Following a recent rapid communications[Phys.Rev.C85,021302(R) (2012)], we present more details on the investigation of the relativistic symmetry by use of the similarity renormalization group. By comparing the contributions of the different components in the diagonal Dirac Hamiltonian to the pseudospin splitting, we have found that two components of the dynamical term make similar influence on the pseudospin symmetry. The same case also appears in the spin-orbit interactions. Further, we have checked the influences of every term on the pseudospin splitting and their correlations with the potential parameters for all the available pseudospin partners. The result shows that the spin-orbit interactions always play a role in favor of the pseudospin symmetry, and whether the pseudospin symmetry is improved or destroyed by the dynamical term relating the shape of the potential as well as the quantum numbers of the state. The cause why the pseudospin symmetry becomes better for the levels closer to the continuum is disclosed.
It is shown that the rotational band structure of the cluster states in 12C and 16O can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle for 12C, and a regular tetrahedron for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of alpha-particles. Finally, some first results are presented for odd-cluster nuclei.
In the 70s Smith and Tassie, and Bell and Ruegg independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and applied to several physical systems. Twenty years after, in 1997, the pseudospin symmetry has been revealed by Ginocchio as a relativistic symmetry of the atomic nuclei when it is described by relativistic mean field hadronic models. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrodinger-like equations, i.e, without a matrix structure. In this paper we propose a generalization of these SU(2) symmetries for potentials in the Dirac equation with several Lorentz structures, which also allow for the suppression of the matrix structure of second-order equation equation of either the upper or lower components of the Dirac spinor. We derive the general properties of those potentials and list some possible candidates, which include the usual spin-pseudospin potentials, and also 2- and 1-dimensional potentials. An application for a particular physical system in two dimensions, electrons in graphene, is suggested.
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