Charge Dependent Matrix Element Research Articles

On the Charge-Dependent Matrix Element Between the 9.516 MeV 4+ T = 1 Level and the 8.439 MeV 4+ T = 0 Level of 24Mg

A recent measurement of the ß - y circular polarization asymmetry parameter A on the isospinforbidden ß + decay of the ground state of 24Al to the 8.438 MeV 4+ T= 0 state of 24Mg yields a charge-dependent matrix element ⟨ VCD⟩Mg between the 9.516 MeV 4+ T = 1 state and the 8.439 MeV 4+ T = 0 state of 24Mg of (106 ± 40) keV, which is the largest measured value obtained so far in ß decay. Our calculation using Nilsson’s wavefunctions and a spherical Coulomb potential results in a value of 87 keV for ⟨ VCD⟩Mg . Variation of the value of ⟨ VCD⟩Mg against the deformation parameter ß shows that theory agree very well with the measured ⟨ VCD⟩Mg for ß around 0.5.

Isospin mixing in 2 − levels in 16O

The 15N(p, p) 15N and 15N(p, α 1) 12C(4.439) reactions have been used to measure the proton and α-particle widths of the 16O J π = 2 − levels at excitation energies of 12.530 MeV and 12.9686 MeV. Excitation functions for the reactions were obtained at four angles using a differentially pumped gas target and a proton beam from the Queen's University 4 MV Van de Graaff accelerator. The data were analyzed using the R-matrix formalism, and the proton and α-particle widths of the resonances were determined to be Γ p = 25 ± 3eV, Γ α1 = 72 ± 10 eV and Γ p = 0.99 ± 0.12 keV, Γ α1 = 0.60 ± 0.08 keV for the 12.530 MeV and 12.9686 MeV states respectively. The charge-dependent matrix element responsible for the isospin mixing of the two states is deduced to be 〈 T = 0| H c| T = 1〉 = 181 ± 10 keV.

Isospin mixing inMg24

We have used the ..beta..-..gamma.. circular polarization correlation technique to measure the isospin-forbidden Fermi matrix element for the ..beta../sup +/ decay of /sup 24/Al to the 4/sup +/ T = 1 state in /sup 24/Mg at E/sub x/ = 8.439 MeV. The /sup 24/Al activity was produced by bombarding a natural Mg target with 18 MeV protons. The ..beta..-..gamma.. circular polarization correlation was measured using a novel apparatus which featured good energy resolution in both the ..gamma.. and ..beta.. arms. The circular polarization sensitive ..gamma..-ray detector utilized a transmission-mode Compton polarimeter and a 12.7 cm x 15.2 cm NaI detector. The ..beta.. detector was a telescope with a 700 ..mu..m surface barrier detector and a 5.1 cm x 12.7 cm plastic scintillator. The ..beta..-..gamma.. circular polarization asymmetry A (defined by W(theta,tau) = 1+tauv/cA costheta where tau is the photon helicity) was found to be A = -0.145 +- 0.030. After applying a correction for feeding of the 8.439 MeV state from the analog state this value of A corresponds to a charge dependent matrix element between the 9.5 MeV 4/sup +/ T = 1 and 8.4 MeV T = 0 levels of Vertical Bar Vertical Bar =more » 106 +- 40 keV which is the largest matrix element of H/sub CD/ ever observed in ..beta.. decay. For comparison the charge dependent matrix element between the 9.5 MeV state and the 4.1 MeV 4/sup +/ state, previously measured in /sup 24/Na decays is only 5.4 +- 2.2 keV. Our exceptionally large value occurs because the 9.5 MeV T = 1 and 8.4 MeV T = 0 states have very similar space and spin wave functions. This matrix element is consistent with predictions which ascribe the entire effect to Coulomb forces.« less

Measurement of isospin mixing between the 1 + doublet in 12C using pion inelastic scattering

Pion inelastic scattering has been used to extract the off-diagonal charge dependent matrix element, H 01, between the J π = 1 + doublet of states at 12.71 (T = 0) and 15.11 (T = 1) MeV in 12 C . The reported measurements yield a value, H 01 = 148 ±29 keV, in good agreement with recent electromagnetic measurements.

The [formula omitted] and [formula omitted] reactions: J-transfer determination and isospin mixing in 12C

Use of the 13C(d, t) 12C and 13C(d, 3He) 12B reactions to study the isospin mixing of the 12.71 and 15.11 MeV levels in 12C has depended upon the prediction by Cohen and Kurath that the j = 1 2 transfer to these 1 + states is negligible compared to they j = 3 2 transfer. In this paper evidence from vector analyzing power data for these reactions obtained at 29 MeV is presented. It is concluded that the j = 1 2 component is small but may not be insignificant and contributes approximately 8% of the total yield to these states. Including a j = 1 2 component of this size in the analysis of this data yields a charge dependent matrix element of 0.12 ± 0.03 MeV as compared to a value of 0.14 ± 0.04 MeV obtained if the j = 1 2 component is excluded. Both of these values are smaller than those reported in previous measurements, and are thus closer to the values resulting from the Coulomb interaction alone. While these results do not refute the evidence presented for the presence of charge dependent nuclear forces, the confidence in their presence is reduced.

Isospin-forbidden β-decay of 28Mg

We have measured the branching ratio for the isospin-forbidden Fermi β-decay of 28Mg to the 0.972 MeV 0 +, T = 1 level in 28Al. This decay occurs through an admixture of the 0 +, t = 2 analog state at 5.992 MeV into the anti-analog level at 0.972 MeV. A charge-dependent matrix element of 17.0 −5.8 +4.3 keV is deduced from the observed (0.21 ± 0.12)% branch. Comparisons are made with matrix elements deduced in other nuclei. An analysis based on a simple shell model with fourfold degenerate Orbitals indicates the importance of the two-body Coulomb interaction in isospin mixing in nuclei with more than one valence proton.

The α + α → 8Be double resonance at the 16.6 and 16.9 MeV levels

The elastic scattering 4He(α, α) has been investigated in the energy range 32.6–35.4 MeV. The level parameters of the overlapping 2 + states in 8Be at 16.6 and 16.9 MeV were obtained with a double resonance formalism. In R-matrix theory the level energies and widths are 16623 ± 3 keV, 107.7 ± 0.5 keV and 16925 ± 3 keV, 74.4 ± 0.4 keV, respectively. In complex-eigenvalue theory the resonance energies and widths are 16630 ± 3 keV, 108.5 ± 0.5 keV and 16918 ± 3 keV, 73.6 ± 0.4 keV, respectively. The relation between the parameter sets is discussed. The present results are compared with previous investigations where 8Be is formed as a product nucleus. The isospin mixing of the doublet and the deduced charge-dependent matrix element are discussed with regard to theoretical predictions.

Radiative transitions and isospin mixing inC12

$\ensuremath{\gamma}$-ray decays of the 12.7 and 16.1 MeV states of $^{12}\mathrm{C}$ are investigated in a coincidence study of the $^{10}\mathrm{B}(^{3}\mathrm{He}, p\ensuremath{\gamma})$ reaction. We obtain $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}0}}{\ensuremath{\Gamma}}=(1.93\ifmmode\pm\else\textpm\fi{}0.12)%$, $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}1}}{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}0}}=(15.0\ifmmode\pm\else\textpm\fi{}1.8)%$ and $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\alpha}}}{\ensuremath{\Gamma}}=(97.8\ifmmode\pm\else\textpm\fi{}0.1)%$ for $^{12}\mathrm{C}$(12.7), and $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}1}}{\ensuremath{\Gamma}}=(2.42\ifmmode\pm\else\textpm\fi{}0.29)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ for $^{12}\mathrm{C}$(16.1). Relative $\ensuremath{\gamma}$-ray branching ratios of $^{12}\mathrm{C}$(16.1) were measured using the ${E}_{p}=163$ keV $^{11}\mathrm{B}(p, \ensuremath{\gamma})$ resonance. We find $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}0}}{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}1}}=(4.6\ifmmode\pm\else\textpm\fi{}0.7)%$, $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}}(16.1\ensuremath{\rightarrow}9.6)}{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}1}}=(2.4\ifmmode\pm\else\textpm\fi{}0.4)%$, and $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}}(16.1\ifmmode\pm\else\textpm\fi{}12.7)}{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}1}}=(1.46\ifmmode\pm\else\textpm\fi{}0.25)%$. This information, together with existing data on $M1$ transitions and single nucleon transfer reactions, is used to determine the isospin mixing between the 12.7 and 15.1 MeV levels of $^{12}\mathrm{C}$. A charge dependent matrix element of 110 \ifmmode\pm\else\textpm\fi{} 30 keV is deduced.NUCLEAR REACTIONS $^{10}\mathrm{B}(^{3}\mathrm{He}, p\ensuremath{\gamma})$, $E=4.1$ MeV, $p$, $\ensuremath{\gamma}$ coincidence. Deduced ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}}$ for $^{12}\mathrm{C}$ levels at 12.7, 16.1 MeV. $^{11}\mathrm{B}(p, \ensuremath{\gamma})$, $E=163$ keV resonance. Measured ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}}$ for transitions to 0.0, 4.4, 9.6, and 12.7 MeV in $^{12}\mathrm{C}$.NUCLEAR STRUCTURE $^{12}\mathrm{C}$, deduced isospin mixing between 12.7 and 15.1 MeV levels.

Isospin mixing in 12C

We observe a yield to the 1 + T = 1 level in 12C at 15.11 MeV in the isospin forbidden 12C(d, d') and 10B(α, d) reactions at about 1 % of the yield to the 1 + T = 0 level at 12.71 MeV. Observed yields to the T = 12 + level at 16.11 MeV in both reactions at about half the yield to the 15.11 MeV level preclude attributing this observed isospin violation entirely to final state mixing. From the ratios of the spectroscopic factors for the 12.71 and 15.11 MeV levels in 12C and the ground state of 12B from the 13C(d, t) and 13C(d, 3He) reactions, we find a charge dependent matrix element between the 1 + states in 12C of 179 ± 75 keV.

Large Isospin-Mixing Matrix Element inC12

Isospin mixing between the 12.71-MeV, ${1}^{+}$, $T=0$ and 15.11-MeV, ${1}^{+}$, $T=1$ levels in $^{12}\mathrm{C}$ is measured utilizing two different direct reactions. A consistent value (${\ensuremath{\beta}}^{2}\ensuremath{\sim}0.01$) is obtained from both the isospin-forbidden reaction $^{12}\mathrm{C}(d,{d}^{\ensuremath{'}})^{12}\mathrm{C}^{*}$ and the comparison of the yields in the analog reactions $^{13}\mathrm{C}(d,t)^{12}\mathrm{C}^{*}$ (15.11 MeV) and $^{13}\mathrm{C}(d,h)^{12}\mathrm{B}$ (0.00 MeV). This mixing implies a charge-dependent matrix element between these two levels of approximately 250 keV.

β-γ(CP) correlation studies of 72Ga and spin assignments in 72Ge

Using a transmission polarimeter, measurements have been made of the β-γ circular-polarization correlation parameter A for the 948 keV β- 2202 keV γ-cascade in the decay of 72Ga. The measured value A = −0.142±0.026 is in good agreement with previous scattering polarimeter results. It and a 2 − assignment to the 3036 keV level in 72Ge lead to δ(M2/E1) = +0.036±0.039 for the 2202 keV γ-ray, whereas 3 − yields the charge-dependent matrix element |〈 H C〉| = 45.9±3.3 keV. On the basis of other published studies of 72Ge, the 2 − assignment is strongly favored, and our results are completely consistent with this also. The value A = −0.019±0.018 was measured for the combined 642 keV β-2508 keV γ and 659 keV β-2491 keV γ-cascades. With the assignment of 3 − to the 3342 keV level and 2 − to the 3325 keV level this result yields, for the ΔJ = 0 transition involving the 2508 keV γ-ray, the value if(7.4±2.3) × 10 −3 for the Fermi matrix element, | M V| and |〈 H c〉| = 22.8±7.9keV. These assignments are favored on the basis of an analysis of the γ-ray transition probabilities plus other available evidence. The data are also analysed for alternative assignments to these levels.