The Mechanism of $\beta$-Delayed Two-Proton Emission

The nucleus $^{31}$Ar seems to be the most prolific ${\beta}$-2p precursor known to date and is at the same time the one with the largest production yields at ISOLDE, where the most sensitive experiments can be done. Our purpose with this experiment is to study the ${\beta}$-2p branches in detail, search for ${\beta}$-3p events, place them in the decay scheme and obtain information on the decay mechanism for ${\beta}$-2p via the energy distribution and the angular correlation between the two protons. As a by product we shall also resolve existing inconsistencies in the level scheme.\\ \\ The nucleus $^{31}$Ar, produced in a cold plasma ion source unit by the impact of a 1 GeV proton beam of 0.5 Hz frequency, had an average yield over one week of 1.5 $^{31}$Ar atoms/s. The beam passed through the central hole of an annular Si detector ($\Omega$ = 4.3~\%) and stopped in a thin carbon foil tilted 45$^o$ with respect to the beam direction. A 70~\% coaxial HPGe-detector ($\Omega$~=~7.4~\%) was located opposite to the annular detector, and in a plane perpendicular to the beam axis two telescopes were placed, one with Si front and back detectors ($\Omega$~=~3.3~\%) and the other with a gas filled front detector and a Si back detector ($\Omega$~=~2.3~\%). $^{33}$Ar was used for internal proton energy calibration.\\ \\ The analysis from this experiment (IS339) proves that many ${\beta}$-2p branches exist; in fact, many more than expected. Three ${\beta}$-2p branches from the IAS have been identified leading to the ground and first two excited states in $^{29}$P, accounting for 40~\% of the 2p-events. This fragmentation of the strength, which reduces the statistic per branch, makes it difficult to assess the mechanism.\\ \\ Therefore, we have designed and tested a more compact set-up. That allowed us to study the ${\beta}$- 2p branches at different angles with a gain in statistics of a factor of 13 for double hits and with a factor of 50 for a triple hit.