Multiparticle emission in the decay of ${}^{31}\mathrm{Ar}$

A multihit capacity setup was used to study the decay of the dripline nucleus ${}^{31}\mathrm{Ar}$, produced at the ISOLDE facility at CERN. A spectroscopic analysis of the $\beta$-delayed three-proton decay of ${}^{31}\mathrm{Ar}$ is presented for the first time together with a quantitative analysis of the $\beta$-delayed 2$p$$\gamma$ decay. A new method for determination of the spin of low-lying levels in the $\beta$$p$ daughter ${}^{30}\mathrm{S}$ using proton-proton angular correlations is presented and used to determine that the spin of the 5.2-MeV level is most likely $3^{+}$ with $4^{+}$ also possible. The half-life of ${}^{31}\mathrm{Ar}$ is found to be 15.1(3) ms. An improved analysis of the Fermi $\beta$ strength including the $\beta$3$p$-decay mode gives a total measured branching ratio of $3.60\left(44\right)\%$, which is lower than the theoretical value found to be $4.24\left(43\right)\%$. Finally, a previously unidentified $\gamma$ transition from the isobaric analog state in the decay of ${}^{33}\mathrm{Ar}$ has been found.

Figure 1

Decay scheme for the $\beta$ decay of ${}^{31}\mathrm{Ar}$, not to scale. Selected proton and $\gamma$ transitions are drawn.

Figure 2

The detector setup used for the experiment consisting of a cube of DSSSDs and two Miniball Ge detectors. The beam enters between DSSSDs 5 and 6 and is stopped in a carbon foil mounted on a small metal holder entering between DSSSDs 3 and 5. The top of the cube with three of the DSSSDs is lifted, following the dotted black line, for better visualization. The two Miniball detectors that were situated outside the cube behind DSSSDs 3 and 4 are not shown in the picture.

Figure 3

$Q_{3p}$ for three-particle events. The histogram shows all the events where the first two particles detected have energies above 800 keV and the third has an energy above 500 keV unless it is in detector 5, where it also has to have an energy above 800 keV. To obtain the histogram in green (gray), events that are most likely not real 3$p$ events were removed as described in the text.

Figure 4

$Q_{3p}$ vs $Q_{3p}-Q_{2p}$. The lines indicate the levels in ${}^{29}\mathrm{P}$. For the black circles $Q_{2p}$ is calculated assuming that the first two particles are the ones with the highest energy and for the green (gray) triangles it is calculated to best fit the five levels in ${}^{29}\mathrm{P}$ shown.

Figure 5

$Q_{2p}$ calculated from the two particles with highest energy. The histogram is from the 41 events in the green (gray) histogram of Fig. 3. The part that is green (gray) is the 19 events around 4.84(29) MeV in the green (gray) histogram of Fig. 3.

Figure 6

The $\gamma$ spectrum gated on one proton with an energy above 800 keV.

Figure 7

The $\gamma$ spectrum gated on two protons. For the black spectrum both protons have energies above 800 keV. The extra events in green (gray) are $\gamma$ rays where one of the protons has an energy between 500 and 800 keV and has not hit detector 5.

Figure 8

Two-proton spectrum made using only detectors 3 and 6 with a lower cutoff of $E>500$ keV. (Left) $Q_{2p}$ vs the energy, $E_i$, of the two particles. (Right) The projection onto the $Q_{2p}$ axis.

Figure 9

The one-proton energy spectrum for detector 3 for high energies.

Figure 10

Two-proton spectrum with lower cutoff, $E_1>800$ keV and $E_2>500$ keV, except for detector 5, where $E_2>800$ keV. (Left) $Q_{2p}$ vs the energy, $E_i$, of the two particles. (Right) The projection onto the $Q_{2p}$ axis.

Figure 11

Energy spectrum for ${}^{30}\mathrm{S}$ calculated for the events from Fig. 10.

Figure 12

Energy of the first particle for transitions going through the 5.2-MeV level in ${}^{30}\mathrm{S}$. The peaks containing most counts are marked by numbers.

Figure 13

Angular distribution of the two protons forming peaks 1 and 4 in Fig. 12 compared with the corresponding fitted 2$p$ simulations for either isotropic (green solid curve) or nonisotropic (red dashed curve) distributions. For better visualization data are here shown using 45 bins, while the fits are made using 90 bins.

Figure 14

The $\gamma$ spectrum of ${}^{33}\mathrm{Ar}$. The numbers corresponds to transitions in the $\beta$-daughter ${}^{33}\mathrm{Cl}$, the Roman numbers to transitions in the $\beta$-granddaughter ${}^{33}\mathrm{S}$ and the * to a transition in the $\beta$-proton daughter ${}^{32}\mathrm{S}$. The letters corresponds to background lines.