$\beta$-delayed charged-particle decay of ${}^{22,23}\mathrm{Si}$

The $\beta$ decay of ${}^{22,23}\mathrm{Si}$ by emission of delayed charged particles was investigated in an experiment at the Cyclotron Institute of Texas A&M University by means of an optical-readout time-projection chamber. The previously-known decay of the two isotopes by $\beta$-delayed one- and two-proton emission was confirmed. For the first time, a new, rare, decay mode for ${}^{23}\mathrm{Si}$, $\beta$-delayed three-proton emission, was observed and $\beta$-delayed proton-$\alpha$ emission tentatively identified. Moreover, the $\beta$-decay pattern for the ground state of ${}^{23}\mathrm{Si}$ was studied by means of multireference density-functional-rooted calculations.

Figure 1

Ground-state (g.s.) energies for the $A=22$,23 silicon precursors (dotted lines) [16], particle-separation (dashed lines) [16], and IAS (solid lines) [7, 17] energies for the respective aluminium daughter nuclei ($A=22$,23).

Figure 2

Schematic representation of the OTPC detector and its working principle. The beam-entrance window is highlighted on the side of the chamber (W) and the cathode (C), gating electrode (G) and anode (A) are shown as dotted lines. The GEM foils as dashed lines. The ion enters the chamber with a kinetic energy of about $10A$ MeV and is stopped in the active volume of the chamber. See text for details.

Figure 3

Identification plot $\mathrm{\Delta }E$ versus range for the ion-optics setting centered on ${}^{23}\mathrm{Si}$. Only events contained between the two red lines were considered in the analysis. See text for details.

Figure 4

Top panel: CCD images for example events of (a) $\beta p$, (b) $\beta 2p$, (c) $\beta 3p$, and (d) $\beta p\alpha$ decay of ${}^{23}\mathrm{Si}$. The horizontal track from left to right in each image corresponds to the ${}^{23}\mathrm{Si}$ ion entering the chamber. The tracks emerging from the ion stopping point correspond to the emitted particles. Bottom panels: respective PMT signals for the (e) $\beta p$, (f) $\beta 2p$, (g) $\beta 3p$, and (h) $\beta p\alpha$ decay events. The signal generated by the ${}^{23}\mathrm{Si}$ ion stopped in the chamber is not visible in the histograms displayed in the bottom panel. Only the portion of the PMT signal centered around the time at which the decay happened is shown. In the case of a single particle recorded in the decay, the PMT signal shows the corresponding Bragg peak. In the $\beta p$ event in (a) and (e), the proton was emitted downwards, towards the anode. In the case of more particles emitted at the same time, as is for $\beta 2p$, $\beta 3p$, and $\beta p\alpha$, the PMT signal will be the convolution of the signals corresponding to each of the particles emitted.

Figure 5

Upper panel: Energy spectrum for protons following ${}^{23}\mathrm{Si}\beta$ decay and stopped in the active volume of the OTPC detector. The dashed line shows the proton-stopping efficiency as a function of energy. The dotted vertical lines mark the energy intervals corresponding to the proton groups around 1250 keV (900–1400 keV), 1550 keV (1400–1900 keV), and 2050 keV (1900–2300 keV). Lower panel: expanded low-energy portion of the spectrum. The vertical dotted lines mark the energy intervals for the energy of the proton-groups at about 300 keV (150–350 keV) and 600 keV (500–700 keV). See also Table 2.

Figure 6

Partial decay scheme of ${}^{23}\mathrm{Si}$ illustrating the levels of relevance for its $\beta p$ decay as found in this work. The proton transitions that could be placed in the decay scheme are marked by arrows. The dashed lines show the two possible transitions for the protons at about 1550 keV energy. All the experimental knowledge available on the ${}^{23}\mathrm{Al}$ levels fed in $\beta$ decay completes the picture [24].

Figure 7

Sum-energy spectrum of $\beta 2\mathrm{p}$ events in which both protons stopped in the active volume of the OTPC detector.

Figure 8

Partial decay scheme of ${}^{23}\mathrm{Si}$ illustrating the levels of relevance for its $\beta 2p$ decay. The grey excitation-energy region in ${}^{23}\mathrm{Al}$ between 6550 and 9000 keV, with level(s) marked by a solid line at $\sim 8600$ keV, show the range of excitation energies from which the two protons shown in Fig. 7 are emitted. Intermediate states in ${}^{22}\mathrm{Mg}$ at about 7 MeV excitation involved in the process are highlighted. Dashed lines in ${}^{23}\mathrm{Al}$ show the separation energy for one and for two protons, while dotted lines schematically depict the process of $\beta 2p$ when higher energy protons are emitted (i.e., escaping from the chamber). See text for details.

Figure 9

Opening angle between the two protons for the events shown in Fig. 7 with sum energy above 2 MeV. See text.

Figure 10

Opening angle between the two protons for events in which one or both protons escape the chamber. See text.

Figure 11

PMT trace for the event tentatively identified as $\beta \alpha \mathrm{p}$ decay of ${}^{23}\mathrm{Al}$ and its fit assuming emission of two protons and one alpha and one proton, respectively. See text for details.

Figure 12

Excitation energy spectrum for low lying states and the IAS in ${}^{23}\mathrm{Al}$ from DFT (this work) and shell model (SM) of Ref. [7]. See text for details.

Figure 13

Matrix elements for the g.s. $\beta$ decay of ${}^{23}\mathrm{Si}$ calculated within the DFT-NCCI variant that involves only AMP. Filled (open) symbols label Fermi (GT) matrix elements, respectively. Triangles, circles, and squares mark GT matrix elements between the g.s. of ${}^{23}\mathrm{Si}$ and $I=3/2^{+},5/2^{+}$, and $7/2^{+}$ states in ${}^{23}\mathrm{Al}$ below 15 MeV. Arrows show IAS and low-lying states strongly populated by the GT decay which are discussed in the text.

Figure 14

Top panels: CCD images for example events of (a) $\beta p$ and (b) $\beta 2p$ decay of ${}^{22}\mathrm{Si}$. The horizontal track from left to right in each image corresponds to the ${}^{22}\mathrm{Si}$ ion entering the chamber. The tracks emerging from the ion stopping point correspond to the emitted particles. Bottom panels: respective PMT signals for the (c) $\beta p$ and (d) $\beta 2p$ decay events. The signal generated by the ${}^{22}\mathrm{Si}$ ion stopped in the chamber is not visible in the histograms displayed in the bottom panels. Only the portion of the PMT signal centered around the time at which the decay happened is shown. When a single particle is recorded in the decay, the PMT signal shows the corresponding Bragg peak. In the $\beta p$ event in (a) and (c), the proton was emitted upwards, towards the cathode. In the case of more particles emitted at the same time, as is for $\beta 2p$, the PMT signal will be the convolution of the signals corresponding to each of the particles emitted.

Figure 15

Energy spectrum for protons following ${}^{22}\mathrm{Si}\beta$ decay and stopped in the active volume of the OTPC detector. The dashed line shows the proton-stopping efficiency as a function of energy. The vertical dotted lines mark the energy intervals for the proton-groups reported in Table 3.