The Effect of Deformation on the Twist Mode

Using $^{12}$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 $[rY^{1}\vec{l}]^{\lambda=2}t_{+}$ where l is the orbital angular momentum. We also consider the $\lambda =1$ case. For $\lambda=0$, the operator vanishes. Whereas in a $\Delta N=0$ Nilsson model the summed strength is independent of the relative P$_{3/2}$ and P$_{1/2}$ occupancy when we allow for different frequencies $\omega_{i}$ 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 $^{43}$Ti ($^{43}$Sc) and $^{44}$Ti. The results for $^{44}$Ti were surprisingly good despite the severity of this approximation. In this approximation degeneracies arose in the T=1/2 I=$({1/2})^-_1$ and $({13/2})^-_1$ states in $^{43}$Sc and the T=1/2 $I=({13/2})_2^-$, $({17/2})^-_1$, and $({19/2})_1^-$ in $^{43}$Sc. The T=0 $3_2^+$, $7_2^+$, $9_1^+$, and $10_1^+$ states in $^{44}$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 ($J_{\pi},J_{\nu}$)

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 - $^{44}$Ti, $^{46}$Ti, and $^{48}$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 $=0$) are investigated. Despite the apparent severity of such a procedure, one gets fairly reasonable spectra. We find that using $=0$ in single j shell calculations degeneracies appear e.g. the $I={1/2} ^{-}$ and ${13/2}^{-}$ states in $^{43}$Sc are at the same excitation energies; likewise the I=$3_{2}^{+}$,$7_{2}^{+}$,9$^{+}_{1}$ and 10$^{+}_{1}$ states in $^{44}$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