464 research outputs found
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
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
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 to its mirror nucleus .Comment: 17 pages, 2 figures, to be published in PRC. Slightly revised text
with one reference adde
Number of Spin States of Identical Particles
In this paper we study the enumeration of number (denoted as ) of spin
states for fermions in a single- shell and bosons with spin . We show
that can be enumerated by the reduction from SU to SO(3). New
regularities of are discerned.Comment: 3 pages, no figures. to be publishe
-pairing interaction, number of states, and nine- sum rules of four identical particles
In this paper we study -pairing Hamiltonian and find that the sum of
eigenvalues of spin states equals sum of norm matrix elements within the
pair basis for four identical particles such as four fermions in a single-
shell or four bosons with spin . We relate number of states to sum rules of
nine- coefficients. We obtained sum rules for nine- coefficients
summing
over (1) even and , (2) even and odd , (3) odd and odd ,
and (4) both even and odd , where is a half integer and is an
integer.Comment: 6 pages, no figure, updated version, to be published. Physical Review
C, in pres
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-
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