418 research outputs found
Effective three-body interactions in nuclei
It is shown that the three-body forces in the shell, for which
recently evidence was found on the basis of spectroscopic properties of the Ca
isotopes and isotones, can be most naturally explained as an effective
interaction due to excluded higher-lying shells, in particular the
orbit.}Comment: 5 pages, 1 tables, accepted for publication in Europhysics Letter
Relations Between Coefficients of Fractional Parentage
For each of the (9/2), (11/2) and (13/2) single j shells we have only one
state with J=j V=3 for a five particle system. For four identical particles
there can be more than one state of seniority four. We note some ``ratio''
relations for the coefficients of fractional parentage for the four and five
identical particle systems
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-
A new effective interaction for the trapped Fermi gas
We apply the configuration-interaction method to calculate the spectra of
two-component Fermi systems in a harmonic trap, studying the convergence of the
method at the unitary interaction limit. We find that for a fixed
regularization of the two-body interaction the convergence is exponential or
better in the truncation parameter of the many-body space. However, the
conventional regularization is found to have poor convergence in the
regularization parameter, with an error that scales as a low negative power of
this parameter. We propose a new regularization of the two-body interaction
that produces exponential convergence for systems of three and four particles.
From the systematics, we estimate the ground-state energy of the
four-particle system to be (5.05 +- 0.024)hbar omega.Comment: 4 pages, 3 figure
Spin-aligned neutron-proton pairs in nuclei
A study is carried out of the role of the aligned neutron-proton pair with
angular momentum J=9 and isospin T=0 in the low-energy spectroscopy of the
nuclei Cd, Ag, and Pd. Shell-model wave functions
resulting from realistic interactions are analyzed in terms of a variety of
two-nucleon pairs corresponding to different choices of their coupled angular
momentum and isospin . The analysis is performed exactly for four holes
(Cd) and carried further for six and eight holes (Ag and
Pd) by means of a mapping to an appropriate version of the interacting
boson model. The study allows the identification of the strengths and
deficiencies of the aligned-pair approximation.Comment: 5 figures, 7 tables, accepted for publication in Physical Review
Relativistic U(3) Symmetry and Pseudo-U(3) Symmetry of the Dirac Hamiltonian
The Dirac Hamiltonian with relativistic scalar and vector harmonic oscillator
potentials has been solved analytically in two limits. One is the spin limit
for which spin is an invariant symmetry of the the Dirac Hamiltonian and the
other is the pseudo-spin limit for which pseudo-spin is an invariant symmetry
of the the Dirac Hamiltonian. The spin limit occurs when the scalar potential
is equal to the vector potential plus a constant, and the pseudospin limit
occurs when the scalar potential is equal in magnitude but opposite in sign to
the vector potential plus a constant. Like the non-relativistic harmonic
oscillator, each of these limits has a higher symmetry. For example, for the
spherically symmetric oscillator, these limits have a U(3) and pseudo-U(3)
symmetry respectively. We shall discuss the eigenfunctions and eigenvalues of
these two limits and derive the relativistic generators for the U(3) and
pseudo-U(3) symmetry. We also argue, that, if an anti-nucleon can be bound in a
nucleus, the spectrum will have approximate spin and U(3) symmetry.Comment: Submitted to the Proceedings of "Tenth International Spring
Seminar-New Quests in Nuclear Structure", 6 page
Alternate Derivation of Ginocchio-Haxton relation [(2j+3)/6]
We address the problem, previously considered by Ginocchio and Haxton (G-H),
of the number of states for three identical particles in a single j-shell with
angular momentum J=j. G-H solved this problem in the context of the quantum
Hall effect. We address it in a more direct way. We also consider the case
J=j+1 to show that our method is more general, and we show how to take care of
added complications for a system of five identical particles.Comment: 7 pages, RevTeX4; submitted to Phys. Rev.
U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator
We show that a Dirac Hamiltonian with equal scalar and vector harmonic
oscillator potentials has not only a spin symmetry but an U(3) symmetry and
that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials
equal in magnitude but opposite in sign has not only a pseudospin symmetry but
a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case.Comment: 8 pages, 0 figures, pusblished in Physical Review Letters 95, 252501
(2005
Degeneracies when T=0 Two Body Interacting Matrix Elements are Set Equal to Zero : Talmi's method of calculating coefficients of fractional parentage to states forbidden by the Pauli principle
In a previous work we studied the effects of setting all two body T=0 matrix
elements to zero in shell model calculations for Ti (Sc) and
Ti. The results for Ti were surprisingly good despite the
severity of this approximation. In this approximation degeneracies arose in the
T=1/2 I= and states in Sc and the T=1/2
, , and in Sc. The T=0
, , , and states in Ti were degenerate as
well. The degeneracies can be explained by certain 6j symbols and 9j symbols
either vanishing or being equal as indeed they are. Previously we used Regge
symmetries of 6j symbols to explain these degeneracies. In this work a simpler
more physical method is used. This is Talmi's method of calculating
coefficients of fractional parentage for identical particles to states which
are forbidden by the Pauli principle. This is done for both one particle cfp to
handle 6j symbols and two particle cfp to handle 9j symbols. The states can be
classified by the dual quantum numbers ()
Fermionic Symmetries: Extension of the two to one Relationship Between the Spectra of Even-Even and Neighbouring Odd mass Nuclei
In the single j shell there is a two to one relationship between the spectra
of certain even-even and neighbouring odd mass nuclei e.g. the calculated
energy levels of J=0^+ states in ^{44}Ti are at twice the energies of
corresponding levels in ^{43}Ti(^{43}Sc) with J=j=7/2. Here an approximate
extension of the relationship is made by adopting a truncated seniority scheme
i.e. for ^{46}Ti and ^{45}Sc we get the relationship if we do not allow the
seniority v=4 states to mix with the v=0 and v=2 states. Better than that, we
get very close to the two to one relationship if seniority v=4 states are
admixed perturbatively. In addition, it is shown that the higher isospin states
do not contain seniority 4 admixtures.Comment: 11 pages, RevTex file and no figures, typos added, references changed
and changed content
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