On Single Particle Energies and Nuclear g Factors

If we add one neutron to doubly magic ^{100}Sn, we can associate the low lying states in^{101} Sn with single particle states.The the J=5/2^{+} and J= 7/2^{+} states are identified as d_{5/2}and g_{7/2}states respectively...They are separated by an energy of 0.18 MeV.Unfortunately there is a disputeas to the ordering of these states.We examine how the 2 scenarios-- J=5/2^{+} ground state or J=7/2^{+}ground state-- affect spectra of higher Sn isotopes

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

The Original Mixed Symmetry States - 61+6^{+}_{1} and 62+6^{+}_{2} in 48^{48}Ti

The $6^{+}_{1}$ and $6^{+}_{2}$ in $^{48}$Ti form a nearly degenerate doublet. In a single j shell calculation with the matrix elements from experiment the $6^{+}_{1}$ changes sign under the interchange of protons and neutron holes (odd signature) while the $6_{2}^{+}$ does not (even signature). As a consequence the calculated B(E2) $6_{1}^{+}\to 4_{1}^{+}$ is much stronger than the $6_{2}^{+}\to 4_{1}^{+}$ and the Gamow-Teller matrix element to the $6_{2}^{+}$ state vanishes. When using some popular interaction e.g. FPD6 in single j shell the ordering of the even signature and odd signature states gets reversed, so that the Gamow-Teller matrix element to the $6^{+}_{1}$ state vanishes and the $6_{2}^{+}\to 4_{1}^{+}$ E2 transition is the strong one. When configuration mixing is introduced, the E2 transition $6_{2}^{+}\to 4_{1}^{+}$ persists in being large. However the Gamow-Teller strengths reverse, with the large matrix element to the $6_{1}^{+}$ state in agreement with experiment. Static properties $\mu$ and Q for the two $6^{+}$ states are also considered. The experimental B(E2)'s from the $6^{+}$ states to the $4_{1}^{+}$ state are not well known

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 ($J_{\pi},J_{\nu}$)

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.