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

Transient field g factor and mean-life measurements with a rare isotope beam of 126Sn

Background: The g factors and lifetimes of the 21+ states in the stable, proton-rich Sn isotopes have been measured, but there is scant information on neutron-rich Sn isotopes. Purpose: Measurement of the g factor and the lifetime of the 21+ state at 1.141 MeV in neutron-rich 126Sn (T1/2=2. 3×105y). Method: Coulomb excitation in inverse kinematics together with the transient field and the Doppler shift attenuation techniques were applied to a radioactive beam of 126Sn at the Holifield Radioactive Ion Beam Facility. Results: g(21+)=-0.25(21) and τ(21+)=1.5(2) ps were obtained. Conclusions: The data are compared to large-scale shell-model and quasiparticle random-phase calculations. Neutrons in the h11/2 and d3/2 orbitals play an important role in the structure of the 21+ state of 126Sn. Challenges, limitations, and implications for such experiments at future rare isotope beam facilities are discussed

Low-level structure of 70^{70}Ge from lifetime and g-factor measurements following α\alpha transfer to a 66^{66}Zn ion beam

The g factor of the 2(1)(+) state in Ge-70 was remeasured using a different experimental approach. Furthermore, for the first time an experimental value (although with a large uncertainty) was obtained for the g factor of the 2(2)(+) state in Ge-70. All this was accomplished by employing the technique of alpha transfer to an energetic Zn-66 ion beam in inverse kinematics combined with transient magnetic fields in ferromagnetic gadolinium. The value of the g(2(1)(+)) factor obtained ranges from +0.32(11) to +0.43(12), subject to certain assumptions. This range of values is in general agreement with the range of values in the literature, where Coulomb excitation and different IMPAC techniques were used. Lifetimes of several low-lying states were redetermined using the Doppler-Shift-Attenuation-Method. The deduced B(E2) values and the g(2(1)(+)) factor are discussed within the framework of large-scale full fp shell model calculations with a closed Ca-40 core and including excitations from the f(7/2) orbital. The results are compared with recent data for Ge-68 and Zn-68

Nuclear structure of the first 2+2^+ state in radioactive 68^{68}Ge based on gg factor and lifetime measurements

The $g$ factor of the $2_1^+$ state of radioactive $^{68}$Ge (T_{1/2}=270 d) has been measured for the first time. The technique used is based on $\alpha$ transfer from a $^{12}C target to energetic$^{64}$Zn projectiles that incorporates the favorable conditions of inverse kinematics as in projectile Coulomb excitation. It also includes features of the transient field technique applied to nuclear spin precessions. Because the reaction cross section is large the method is a significant alternative to Coulomb excitation of low-intensity radioactive ion beams. In addition, we have remeasured the lifetimes of several excited states using the Doppler-shift-attenuation method. In these measurements, the inherent focusing nature of the reaction in the forward direction was optimally exploited for the resulting fast-moving nuclei. The g factor value obtained, g(2_1^+)=+0.55(14), is in good agreement with the collective value, g=Z/A=0.47, and is also consistent with the precise data of the stable even-A Ge isotopes. The newly determined lifetimes partially agree with those quoted in the literature and are of comparable accuracy. The deduced B(E2) values and the new measured$g$factor are well reproduced by some$fp$shell model calculations in which excitations from the$f_{7/2}$ orbital play an important role

Measurements of g(4+/1 , 2+/2) in 70,72,74,76Ge: Systematics of low-lying structures in 30 < Z < 40 and 30 < N < 50 nuclei

Background: The interplay between single-particle and collective excitations in the 30 ?Z? 40 and 30 ?N? 50 even-even isotopes has been examined in light of recent new measurements of magnetic moments of 41+, 22+, and 21+ states. Purpose: The g factors of the 41+ and 22+ states in the 72,74,76Ge isotopes have been measured for the first time and the g(21+) values have been remeasured. Methods: The transient field (TF) technique in inverse kinematics with a variety of targets has been applied, following Coulomb excitation of the relevant states. The data have been analyzed within the framework of the IBA-II model. Large-scale shell-model calculations have been performed within the p3/2,p1/2,f 5/2,g9/2 orbital space for both protons and neutrons with the JUN45 and JJ4B interactions. Results: The measured Ge g factors were compared to the g factors of the low-lying states of the neighboring Zn, Ge, Se, Kr, and Sr isotopes. The results were evaluated in the context of the systematics of g factors in the A?80 region. Conclusions: The predictions based on the classic collective model and the interacting boson model IBA-II agree with the experimental results. No evidence for shell closure was found for neutrons at N=38 or N=40. � 2013 American Physical Society

g factors of the low-lying states in 106 Pd: Examination of the vibrational character of 106 Pd

The transient field (TF) technique in inverse kinematics was used to measure the g factors of the low lying 21+, 41+, and 22+ states in Pd106. The g factor of the 41+ state was determined and the g(21+) and g(22+) factors were remeasured. The values of g(21+) and g(22+) had been determined earlier in integral perturbed angular correlation (IPAC) experiments and the value of the former served to calibrate the TF. The three g factors, g(21+), g(22+), and g(41+), agree with each other and with the collective Z/A value. The uncertainties in the g(22+) and g(41+) factors remain fairly large in spite of long measuring times because of the weak excitation of the two-phonon states. The lifetimes of the 22+ and 41+ states were newly determined from line-shape fits. � 2010 The American Physical Society

Nuclear structure studies of 70 Zn from g -factor and lifetime measurements

The g factors and mean lifetimes of several short-lived low-lying states in 3070Zn40 have been measured using the techniques of projectile Coulomb excitation in inverse kinematics combined with transient magnetic fields and the Doppler-shift attenuation method. The present results have been interpreted within the framework of large-scale shell-model calculations that include the g9/2 orbital. � 2009 The American Physical Society

Structure of the Sr-Zr isotopes near and at the magic N = 50 shell from g -factor and lifetime measurements in 88 40 Zr and 84,86,88 38 Sr

Background: The evolution of and interplay between single-particle and collective excitations in the 40 ?N? 50 range for 38Sr and 40Zr isotopes have been studied. Purpose: Measurement of the g factor of the 21+ and 41+ states in radioactive 88Zr while simultaneously remeasuring the g(21+) factors in the Sr isotopes and extention of the measurements to higher energy states in the Sr isotopes. Lifetimes of states in these nuclei are determined. Methods: The transient field technique in inverse kinematics and line-shape analysis using the Doppler-shift attenuation method are applied. The 88Zr nuclei were produced by the transfer of an ? particle from the 12C nuclei of the target to 84Sr nuclei in the beam. The excited states in the stable 84Sr isotopes were simultaneously populated via Coulomb excitation by 12C in the same target. Coulomb excitation measurements on 86 ,88Sr were carried out with the same apparatus. Results: The resulting g factors and B(E2) values of these nuclei reveal similarities between the two chains of Zr and Sr isotopes. Large-scale shell-model calculations were performed within the p 3/2,f 5/2,p 1/2,g 9/2 orbital space for both protons and neutrons and yielded results in agreement with the experimental data. Conclusions: In this paper the magnetic moments and lifetimes of several low-lying states in 88Zr and 84.86 ,88Sr have been measured and compared to large-scale shell-model calculations. � 2012 American Physical Society