368 research outputs found

### Effective three-body interactions in nuclei

It is shown that the three-body forces in the $1f_{7/2}$ shell, for which
recently evidence was found on the basis of spectroscopic properties of the Ca
isotopes and $N=28$ isotones, can be most naturally explained as an effective
interaction due to excluded higher-lying shells, in particular the $2p_{3/2}$
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-

### 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

### 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

### Partial conservation of seniority in nuclei

A review is given of the relation between pairing, quasi-spin algebras and
seniority. The former two concepts are closely connected, the relation being
that the quasi-spin formalism allows an efficient solution of the pairing
problem. Seniority is of much wider applicability than either pairing or
quasi-spin and applications can even be extended to encompass the notion of
partial symmetry. A recent application of partial conservation of seniority and
its importance for nuclear isomers is discussed.Comment: 8 pages, 2 figures. Presented at the 17th Nuclear Physics Conference
"Marie and Pierre Curie" on " Symmetry and Symmetry Breaking in Nuclear
Physics", Kazimierz Dolny, 22-26 september 2010, Poland. Accepted for
publication in International Journal of Modern Physics

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