99 research outputs found
Systematics of the Quadrupole-Quadrupole Interaction and Convergence Properties
Our main concern in this work is to show how higher shell admixtures affect
the spectrum of a Q.Q interaction. We first review how, in the valence space,
the familiar SU(3) result for the energy spectrum can be obtained using a
coordinate space Q.Q interaction rather than the Elliott one which is symmetric
in r and p. We then reemphasize that the Elliott spectrum goes as L(L+1) where
L is the orbital angular momentum. While in many cases this is compatible with
the rotational formula which involves I(I+1), where I is the total angular
momentum, there are cases, e.g. odd-odd nuclei, where there is disagreement.
Finally, we consider higher shell admixtures and devise a scheme so as to
obtain results, with the Q.Q interaction, which converge as the model spaces
are increased. We consider not only ground state rotational bands but also
those that involve intruder states.Comment: 13 pages, Revtex, to appear in Annals of Physic
Scissors Modes and Spin Excitations in Light Nuclei including =2 excitations: Behaviour of and
Shell model calculations are performed for magnetic dipole excitations in
and in which all valence configurations plus
excitations are allowed (large space). We study both the orbital
and spin excitations. The results are compared with the `valence space only'
calculations (small space). The cumulative energy weighted sums are calculated
and compared for the =0 to =1 excitations in and
for =1 to both =1 and = =2 excitations in
. We find for the =1 to =1 isovector
{\underline {spin}} transitions in that the summed strength in the
{\underline {large}} space is less than in the {\underline {small}} space. We
find that the high energy energy-weighted isovector orbital strength is smaller
than the low energy strength for transitions in which the isospin is changed,
but for =1 to =1 in the high energy strength
is larger. We find that the low lying orbital strength in is
anomalously small, when an attempt is made to correlate it with the
strength to the lowest states. On the other hand a sum rule of Zheng and
Zamick which concerns the total strength is reasonably satisfied in
both and . The Wigner supermultiplet scheme is a useful
guide in analyzing shell model results. In and with a
interaction the T=1 and T=2 scissors modes are degenerate, with the latter
carrying 5/3 of the T=1 strength.Comment: 51 pages, latex, 9 figures available upon reques
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.
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