Violation of pseudospin symmetry in nucleon-nucleus scattering: exact relations

An exact determination of the size of the pseudospin symmetry violating part of the nucleon-nucleus scattering amplitude from scattering observables is presented. The approximation recently used by Ginocchio turns out to underestimate the violation of pseudospin symmetry. Nevertheless the conclusion of a modestly broken pseudospin symmetry in proton-208Pb scattering at EL=800MeV remains valid.Comment: 8 pages, 2 figure

Implications of Pseudospin Symmetry on Relativistic Magnetic Properties and Gamow - Teller Transitions in Nuclei

Recently it has been shown that pseudospin symmetry has its origins in a relativistic symmetry of the Dirac Hamiltonian. Using this symmetry we relate single - nucleon relativistic magnetic moments of states in a pseudospin doublet to the relativistic magnetic dipole transitions between the states in the doublet, and we relate single - nucleon relativistic Gamow - Teller transitions within states in the doublet. We apply these relationships to the Gamow - Teller transitions from $^{39}Ca$ to its mirror nucleus $^{39}K$.Comment: 17 pages, 2 figures, to be published in PRC. Slightly revised text with one reference adde

Dynamical Symmetries of Dirac Hamiltonian

Several dynamical symmetries of the Dirac Hamiltonian are reviewed in a systematic manner and the conditions under which such symmetries hold. These include relativistic spin and orbital angular momentum symmetries, SO(4)\times SU_{\sigma}(2) symmetry for the Dirac Hydrogen atom, SU(3)\times SU_{\sigma}(2) symmetry for the relativistic simple harmonic oscillator. The energy spectrum in each case is calculated from group-theoretic considerations.Comment: 15 pages, V3 typos removed and some new material include

JJ-pairing interaction, number of states, and nine-jj sum rules of four identical particles

In this paper we study $J$-pairing Hamiltonian and find that the sum of eigenvalues of spin $I$ states equals sum of norm matrix elements within the pair basis for four identical particles such as four fermions in a single-$j$ shell or four bosons with spin $l$. We relate number of states to sum rules of nine-$j$ coefficients. We obtained sum rules for nine-$j$ coefficients $$and$$ summing over (1) even $J$ and $K$, (2) even $J$ and odd $K$, (3) odd $J$ and odd $K$, and (4) both even and odd $J,K$, where $j$ is a half integer and $l$ is an integer.Comment: 6 pages, no figure, updated version, to be published. Physical Review C, in pres

Number of Spin II States of Identical Particles

In this paper we study the enumeration of number (denoted as ${D_I}$) of spin $I$ states for fermions in a single-$j$ shell and bosons with spin $l$. We show that $D_I$ can be enumerated by the reduction from SU$(n+1)$ to SO(3). New regularities of $D_I$ are discerned.Comment: 3 pages, no figures. to be publishe

General pairing interactions and pair truncation approximations for fermions in a single-j shell

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.Comment: a latex text file and 2 figures, to be publishe

Relativistic Mean Field Approach and the Pseudo-Spin Symmetry

Based on the Relativistic Mean Field (RMF) approach the existence of the broken pseudo-spin symmetry is investigated. Both spherical RMF and constrained deformed RMF calculations are carried out employing realistic Lagrangian parameters for spherical and for deformed sample nuclei. The quasi - degenerate pseudo-spin doublets are confirmed to exist near the fermi surface for both spherical and deformed nuclei.Comment: 9 pages RevTex, 4 p.s figures, to appear in Phys. Rev. C as R.

A First-Landau-Level Laughlin/Jain Wave Function for the Fractional Quantum Hall Effect

We show that the introduction of a more general closed-shell operator allows one to extend Laughlin's wave function to account for the richer hierarchies (1/3, 2/5, 3/7 ...; 1/5, 2/9, 3/13, ..., etc.) found experimentally. The construction identifies the special hierarchy states with condensates of correlated electron clusters. This clustering implies a single-particle (ls)j algebra within the first Landau level (LL) identical to that of multiply filled LLs in the integer quantum Hall effect. The end result is a simple generalized wave function that reproduces the results of both Laughlin and Jain, without reference to higher LLs or projection.Comment: Revtex. In this replacement we show how to generate the Jain wave function explicitly, by acting with the generalized ls closed-shell operator discussed in the original version. We also walk the reader through a classical 1d caricature of this problem so that he/she can better understand why 2s+1, where s is the spin, should be associated with the number of electrons associated with the underlying clusters or composites. 11 page

Seniority conservation and seniority violation in the g_{9/2} shell

The g_{9/2} shell of identical particles is the first one for which one can have seniority-mixing effects. We consider three interactions: a delta interaction that conserves seniority, a quadrupole-quadrupole (QQ) interaction that does not, and a third one consisting of two-body matrix elements taken from experiment (98Cd) that also leads to some seniority mixing. We deal with proton holes relative to a Z=50,N=50 core. One surprising result is that, for a four-particle system with total angular momentum I=4, there is one state with seniority v=4 that is an eigenstate of any two-body interaction--seniority conserving or not. The other two states are mixtures of v=2 and v=4 for the seniority-mixing interactions. The same thing holds true for I=6. Another point of interest is that the splittings E(I_{max})-E(I_{min}) are the same for three and five particles with a seniority conserving interaction (a well known result), but are equal and opposite for a QQ interaction. We also fit the spectra with a combination of the delta and QQ interactions. The Z=40,N=40 core plus g_{9/2} neutrons (Zr isotopes) is also considered, although it is recognized that the core is deformed.Comment: 19 pages, 9 figures; RevTeX4. We have corrected the SDI values in Table1 and Fig.1; in Sect.VII we have included an explanation of Fig.3 through triaxiality; we have added comments of Figs.10-12 in Sect.IX; we have removed Figs.7-