104 research outputs found
Non-Scissors-Mode Behaviour of Isovector Magnetic Dipole Orbital Transitions Involving Isospin Transfer
We study the response of isovector orbital magnetic dipole (IOMD) transitions
to the quadrupole-quadrupole () interaction, to the
isospin-conserving pairing interaction (ICP) and to combinations of both. We
find qualitatively different behaviours for transitions in which the final
isospin differs from the initial isospin versus cases where the two isospins
are the same. For even-even nuclei with ground states
such as and , the summed IOMD from the ground
state to all the states in the space does not
vanish when the interaction is turned off. The pairing interaction
(ICP) alone leads to a finite transition rate. For nuclei with
ground states such as and , the summed IOMD
vanish when the interaction is turned off, as is expected in
a good scissors-mode behaviour. However this is not the case for the
corresponding sum of the IOMD transitions. In (but not
in ) the sum of the IOMD transitions is remarkably
insensitive to the strengths of both the and the ICP interactions.
In an energy weighted-sum is similarly insensitive. All our
calculations were carried out in the space.Comment: 19 pages (including 5 figures). submitted to Nucl. Phys.
Effects of the Spin-Orbit and Tensor Interactions on the and Excitations in Light Nuclei
The effects of varying the spin-orbit and tensor components of a realistic
interaction on excitation rates and are studied on nuclei in the
and shells. Not only the total but also the spin and orbital
parts separately are studied. The single-particle energies are first calculated
with the same interaction that is used between the valence nucleons. Later this
stringent condition is relaxed somewhat and the level is raised relative
to . For nuclei up to , much better results i.e stronger
rates are obtained by increasing the strength of the spin-orbit interaction
relative to the free value. This is probably also true for , but
presents some difficulties. The effects of weakening the tensor
interaction are also studied. On a more subtle level, the optimum spin-orbit
interaction in the lower half of the shell, as far as excitations
are concerned, is substantially larger than the difference
in . A larger spin-orbit splitting
is also needed to destroy the triaxiality in . Also studied are how
much orbital and spin strength lies in an observable region and how much
is buried in the grass at higher energies. It is noted that for many nuclei the
sum is very close to , indicating
that the summed cross terms are very small.Comment: 39 pages, revtex 3.
Analytic expressions for the single particle energies with a quadrupole-quadrupole interaction and the relation to Elliott's SU(3) model
We present an analytical proof and a generalization of the Fayache-Sharon-Zamick relation between single particle energy splitting and the SU(3) limit in Elliott's model
Orbital M1 versus E2 strength in deformed nuclei: A new energy weighted sum rule
Within the unified model of Bohr and Mottelson we derive the following linear
energy weighted sum rule for low energy orbital 1 excitations in even-even
deformed nuclei S_{\rm LE}^{\rm lew} (M_1^{\rm orb}) \cong (6/5) \epsilon
(B(E2; 0^+_1 \rightarrow 2_1^+ K=0)/Z e^2^2) \mu^2_N with B(E2) the E2
strength for the transition from the ground state to the first excited state in
the ground state rotational band, the charge r.m.s. radius squared and
the binding energy per nucleon in the nuclear ground state. It is
shown that this energy weighted sum rule is in good agreement with available
experimental data. The sum rule is derived using a simple ansatz for the
intrinsic ground state wave function that predicts also high energy 1
strength at 2 carrying 50\% of the total moment of the
orbital M1 operator.Comment: REVTEX (3.0), 9 pages, RU924
Description of single and double analog states in the f7/2 shell: The Ti isotopes
The excitation energies of single analog states in even-odd Ti isotopes and
double analog states in even-even Ti isotopes are microscopically described in
a single j-shell formalism. A projection procedure for generalized BCS states
has been used. As an alternative description a particle-core formalism is
presented. The latter picture provides a two-parameter expression for
excitation energies, which describes fairly well the data in four odd and three
even isotopes of Ti.Comment: 14 pages,7 figures, 2 tables. To appear in Phys. Rev.
Allowed Gamow-Teller Excitations from the Ground State of 14N
Motivated by the proposed experiment , we study the
final states which can be reached via the allowed Gamow-Teller mechanism. Much
emphasis has been given in the past to the fact that the transition matrix
element from the ground state of to the ground state of is very close to zero, despite the fact that all
the quantum numbers are right for an allowed transition. We discuss this
problem, but, in particular, focus on the excitations to final states with
angular momenta and . We note that the summed strength to the
states, calculated with a wide variety of interactions, is
significantly larger than that to the final states.Comment: Submitted to Phys. Rev.
Partial Dynamical Symmetries in the g9/2 Shell-Progress and Puzzles
We present analytic proofs of the properties of four particle states in the
g9/2 shell which have seniority v=4 and angular momentum I=4 or 6.We show in
particular that the number of pairs with angular momentum I is equal to one for
these states
The Interference Term between the Spin and Orbital Contributions to M1 Transitions
We study the cross-correlation between the spin and orbital parts of magnetic
dipole transitions M1 in both isoscalar and isovector channels. In particular,
we closely examine certain cases where is very close to , implying a cancellation of the summed
interference terms. We gain some insight into this problem by considering
special cases approaching the SU(3) limit, and by examining the behaviour of
single-particle transitions at the beginning and towards the end of the s-d
shell.Comment: 9 pages of latex file and no figure
Shell-model test of the rotational-model relation between static quadrupole moments Q(2^+_1), B(E2)'s, and orbital M1 transitions
In this work, we examine critically the relation between orbital magnetic
dipole (scissors mode) strength and quadrupole deformation properties. Assuming
a simple K=0 ground state band in an even-even nucleus, the quantities Q(2^+_1)
(i.e., the static quadrupole moment) and B(E2)_{0_1 \to 2_1} both are described
by a single parameter--the intrinsic quadrupole moment Q_0. In the shell model,
we can operationally define Q_0(Static) and Q_0(BE2) and see if they are the
same. Following a brief excursion to the sd shell, we perform calculations in
the fp shell. The nuclei we consider ({44,46,48}Ti and {48,50}Cr) are far from
being perfect rotors, but we find that the calculated ratio
Q_0(Static)/Q_0(BE2) is in many cases surprisingly close to one. We also
discuss the collectivity of orbital magnetic dipole transitions. We find that
the large orbital B(M1) strength in {44}Ti relative to {46}Ti and {48}Ti cannot
be explained by simple deformation arguments.Comment: 12 pages, RevTeX4. Sections II (Quadrupole properties in the
sd-shell) and V (Random interaction studies) added. Minor changes throughout
the text and 48Cr added to present Table IV, as well as results for the
lowest 100 state
- âŠ