21 research outputs found
The Effect of Deformation on the Twist Mode
Using C as an example of a strongly deformed nucleus we calculate the
strengths and energies in the asymptotic (oblate) deformed limit for the
isovector twist mode operator where l is the
orbital angular momentum. We also consider the case. For
, the operator vanishes. Whereas in a Nilsson model the
summed strength is independent of the relative P and P
occupancy when we allow for different frequencies in the x, y, and
z directions there is a weak dependency on deformation.Comment: 9 page
Unfolding the Effects of the T=0 and T=1 Parts of the Two-Body Interaction on Nuclear Collectivity in the f-p Shell
Calculations of the spectra of various even-even nuclei in the fp shell
({44}Ti, {46}Ti, {48}Ti, {48}Cr and {50}Cr) are performed with two sets of
two-body interaction matrix elements. The first set consists of the matrix
elements of the FPD6 interaction. The second set has the same T=1 two-body
matrix elements as the FPD6 interaction, but all the T=0 two-body matrix
elements are set equal to zero (T0FPD6). Surprisingly, the T0FPD6 interaction
gives a semi-reasonable spectrum (or else this method would make no sense). A
consistent feature for even-even nuclei, e.g. {44,46,48}Ti and {48,50}Cr, is
that the reintroduction of T=0 matrix elements makes the spectrum look more
rotational than when the T=0 matrix elements are set equal to zero. A common
characteristic of the results is that, for high spin states, the excitation
energies are too high for the full FPD6 interaction and too low for T0FPD6, as
compared with experiment. The odd-even nucleus {43}Ti and the odd-odd nucleus
{46}V are also discussed. For {43}Sc the T=0 matrix elements are responsible
for staggering of the high spin states. In general, but not always, the
inclusion of T=0 two-body matrix elements enhances the B(E2) rates.Comment: 15 pages, 14 figures. Submitted to Phys. Rev.
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 ()
Effects of T=0 two body matrix elements on M1 and Gamow-Teller transitions: isospin decomposition
We perform calculations for M1 transitions and allowed Gamow Teller (GT)
transitions in the even-even Titanium isotopes - Ti, Ti, and
Ti. We first do calculations with the FPD6 interaction. Then to study
the effect of T=0 matrix elements on the M1 and GT rates we introduce a second
interaction in which all the T=0 matrix elements are set equal to zero and a
third in which all the T=0 matrix elements are set to a constant. For the
latter two interactions the T=1 matrix elements are the same as for FPD6. We
are thus able to study the effects of the fluctuating T=0 matrix elements on M1
and GT rates
Degeneracies when T=0 Two Body Matrix Elements are Set Equal to Zero and Regge's 6j Symmetry Relations
The effects of setting all T=0 two body interaction matrix elements equal to
a constant (or zero) in shell model calculations (designated as ) are
investigated. Despite the apparent severity of such a procedure, one gets
fairly reasonable spectra. We find that using in single j shell
calculations degeneracies appear e.g. the and
states in Sc are at the same excitation energies; likewise the
I=,,9 and 10 states in Ti. The
above degeneracies involve the vanishing of certain 6j and 9j symbols. The
symmetry relations of Regge are used to explain why these vanishings are not
accidental. Thus for these states the actual deviation from degeneracy are good
indicators of the effects of the T=0 matrix elements. A further indicator of
the effects of the T=0 interaction in an even - even nucleus is to compare the
energies of states with odd angular momentum with those that are even