$\beta$-decay of $^{8}$B into highly excited states of $^{8}$Be: Isospin mixing and proton-halo contributions

This thesis work deals with the study of the decay of the proton-halo nucleus $8$B. The data were obtained in an experiment performed at ISOLDE@CERN. The goal of this study is to determine the $\beta$-strength to highly excited states of $^{8}$Be. Of particular interest is the isospin mixing of the 2$^{+}$ doublet at 16.6 and 16.9 MeV excitation energy. The $\beta$-decay process is the only that allows to simultaneously address the two isospin components of the states (T=1 and T=0). This has not been measured before. Also, the second objective is the so far unobserved electron-capture delayed-proton-emission branch expected to proceed via the 17.6 MeV state. The states of interest are unbound. After the $\beta$-decay: the doublet in $^{8}$Be breaks up into two $\alpha$ and the 17.6 MeV state in $^{8}$Be preferentially decays via proton emission to $^{7}$Li. We have measured $\alpha$-$\alpha$ coincidences from the break-up of $^{8}$Be with a compact detector set-up comprised of 5 DSSD detectors, 4 of them backed by a Silicon pad to perform particle identification. We have corrected the$\alpha$-$\alpha$ spectrum for different effects and it have been analysed within the R-matrix formalism. In addition, we have implemented a technique to unfold alpha spectra. From the R-matrix analysis we have estimated the isospin mixing of the two aforementioned states, it was found that each of the states has almost 50% mixture of isospin T=0 and T=1. Furthermore, using Monte Carlo simulations and a thorough analysis of the low part of the spectrum, we have been able to establish an experimental upper limit for the proton decay branch of 2.5 × 10$^{−6}$ with a confidence level of 99.9%, improving the existing limit by a factor of ten.