E0decay of the first excited0+states inMg26andSi30

A new method was used to measure $E0\mathrm{}$ $\pi$-decay branching ratios. A plastic scintillator pair spectrometer of high efficiency (3%) was used. It consists of four detectors. Two of them, very thin, select the electrons; the other two, thick, help to measure their energies. An annular counter ($\Omega =0.10\mathrm{}$ sr), working in coincidence with the spectrometer, allows the selection of the $\pi$ decay relevant to the $0^{+}$ excited state and the determination of its population yield. The reactions ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}(\alpha ,p){}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$(3.58 MeV)($\pi$) and ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(\alpha ,p){}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$(3.79 MeV)($\pi$) have been used to study the $E0\mathrm{}$ $\pi$ decay of the first excited $0^{+}$ state in ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$. Pair spectra from the spectrometer were recorded in coincidence with protons in two-dimensional arrays. From the coincidence spectra the values for $\frac{{\Gamma }_{\pi }}{\Gamma }$ are found to be (5.1 ± 0.7) × ${10}^{-3\mathrm{}}$ and (2.6 ± 0.6) × ${10}^{-3\mathrm{}}$, respectively, for ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$(3.58 MeV) and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$(3.79 MeV). When combined with the available lifetimes of these states, these ratios yield ${〈M〉}_{\pi }=(3.0\mathrm{}\pm 0.25)$ ${\mathrm{fm}}^2$ (${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$ and (1.4 ± 0.2) ${\mathrm{fm}}^2$ (${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$) for the monopole matrix elements.