Spectroscopy of excited states of unbound nuclei ${}^{30}\mathrm{Ar}$ and ${}^{29}\mathrm{Cl}$

Several states of proton-unbound isotopes ${}^{30}\mathrm{Ar}$ and ${}^{29}\mathrm{Cl}$ were investigated by measuring their in-flight decay products, ${}^{28}\mathrm{S}$ + proton + proton and ${}^{28}\mathrm{S}$ + proton, respectively. A refined analysis of ${}^{28}\mathrm{S}$-proton angular correlations indicates that the ground state of ${}^{30}\mathrm{Ar}$ is located at $2.{45}_{-0.10}^{+0.05}$ MeV above the two-proton emission threshold. The investigation of the decay mechanism of the ${}^{30}\mathrm{Ar}$ ground state demonstrates that it has the transition dynamics. In the “transitional” region, the correlation patterns of the decay products present a surprisingly strong sensitivity to the two-proton decay energy of the ${}^{30}\mathrm{Ar}$ ground state and the one-proton decay energy as well as the one-proton decay width of the ${}^{29}\mathrm{Cl}$ ground state. The comparison of the experimental ${}^{28}\mathrm{S}$-proton angular correlations with those resulting from Monte Carlo simulations of the detector response illustrates that other observed ${}^{30}\mathrm{Ar}$ excited states decay by sequential emission of protons via intermediate resonances in ${}^{29}\mathrm{Cl}$. Based on the findings, the decay schemes of the observed states in ${}^{30}\mathrm{Ar}$ and ${}^{29}\mathrm{Cl}$ were constructed. For calibration purposes and for checking the performance of the experimental setup, decays of the previously known states of a two-proton emitter ${}^{19}\mathrm{Mg}$ were remeasured. Evidences for one new excited state in ${}^{19}\mathrm{Mg}$ and two unknown states in ${}^{18}\mathrm{Na}$ were found.

Figure 1

Scheme of the FRS ion-optical system. The colored lines represent the calculated trajectories of ${}^{31}\mathrm{Ar}$ ions. The box at F2 denotes the experimental station including reaction target and tracking detectors. The horizontal slits at F2 are displayed. Detectors for the particle identification are represented by the box at F4. See text for details.

Figure 2

Sketch of the detector setup. The secondary beam ${}^{A}Z$ (${}^{31}\mathrm{Ar}$ or ${}^{20}\mathrm{Mg}$) was tracked by position-sensitive detectors TPC1 and TPC2 before impinging on the reaction target. The trajectories of two protons and HI daughter nucleus ${}^{A-3}(Z-2)$ resulting from the decay of $2p$ precursor ${}^{A-1}Z$ (${}^{30}\mathrm{Ar}$ or ${}^{19}\mathrm{Mg}$) were measured by the DSSD array. At F4, the energy deposition of HI in the detector MUSIC was recorded. The time of flight of HI from F2 to F4 ($\sim 35\mathrm{m}$) was measured by using the scintillator detectors SCI1 and SCI2.

Figure 3

Two-dimensional identification plot of $Z$ vs $A/Q$ for the heavy ions detected at F4 during the production measurements with the ${}^{31}\mathrm{Ar}\text{−}{}^{28}\mathrm{S}$ setting. The first half of the FRS was optimized to transport the 620-MeV/u ${}^{31}\mathrm{Ar}$ beam and the second half of the FRS was tuned to transmit the ${}^{28}\mathrm{S}$ ions.

Figure 4

${}^{17}\mathrm{Ne}$-proton angular correlations derived from the measured ${}^{17}\mathrm{Ne}+p+p$ coincidences. (a) Angular correlations ${\theta }_{\mathrm{Ne}\text{−}\mathrm{p}1}\text{−}{\theta }_{\mathrm{Ne}\text{−}\mathrm{p}2}$. (b) Measured ${\rho }_{\theta }$ spectrum for $2p$ decays of ${}^{19}\mathrm{Mg}$. The peak in panel (b) and the arc in panel (a) labeled with the same Roman numeral correspond to each other.

Figure 5

Measured ${}^{17}\mathrm{Ne}\text{−}p$ angular correlations (full circles with statistical errors) derived from the $2p$ decays of known ${}^{19}\mathrm{Mg}$ states. (a) Measured ${}^{17}\mathrm{Ne}\text{−}p$ angular correlations derived from the $2p$ decay of ${}^{19}\mathrm{Mg}$ g.s. gated by (i), $22.5<{\rho }_{\theta }<47.0$ mrad. The solid curve represents the corresponding MC simulation of the detector response to the simultaneous $2p$ decay of the ${}^{19}\mathrm{Mg}$ g.s. with $Q_{2p}=0.87$ MeV. (b) The $2p$ decay of the excited state gated by (ii), $54.0<{\rho }_{\theta }<70.0$ mrad. The solid curve displays the simulation of the sequential $2p$ decay of ${}^{19}\mathrm{Mg}$ state at 2.5 MeV via ${}^{18}\mathrm{Na}$ states at 1.23 MeV (dotted curve) and 1.55 MeV (dashed curve). (c) The $2p$ decays gated by (iii), $70.0<{\rho }_{\theta }<85.5$ mrad. The solid curve is the simulation of the sequential $2p$ decay of ${}^{19}\mathrm{Mg}$ state at 3.2 MeV via the 1.55-MeV (dashed curve) and 2.084-MeV (dotted curve) levels in ${}^{18}\mathrm{Na}$. (d) The $2p$ decays gated by (iv), $90.0<{\rho }_{\theta }<117.0$ mrad. The result of the simulation to the sequential $2p$ emission of ${}^{19}\mathrm{Mg}$ state at 5.1 MeV via the 1.55-MeV state of ${}^{18}\mathrm{Na}$ state is depicted by the solid curve. (e) The $2p$ decay of a new excited state in ${}^{19}\mathrm{Mg}$ gated by (v), $119.0<{\rho }_{\theta }<146.0$ mrad. The dashed and dotted curves are the ${\theta }_{\mathrm{Ne}\text{−}\mathrm{p}}$ distributions obtained by simulations of sequential proton emission of ${}^{19}\mathrm{Mg}$ state at 8.9 MeV via two unknown observed ${}^{18}\mathrm{Na}$ states at 2.5 and 4.0 MeV, respectively. The solid curve shows the summed fit.

Figure 6

${\theta }_{\mathrm{Ne}\text{−}\mathrm{p}}$ distribution derived from the measured ${}^{17}\mathrm{Ne}+p$ coincidences (unfilled histogram) and that deduced from the ${}^{17}\mathrm{Ne}+p+p$ coincidences (gray-filled histogram). The blue dashed lines together with red arrows indicate the peaks which appear in both histograms and these peaks suggest the ${}^{18}\mathrm{Na}$ resonances. Previously known states of ${}^{18}\mathrm{Na}$ are shown by peaks (1), (2), and (3), while the peaks (4) and (5) suggest two new resonances in ${}^{18}\mathrm{Na}$. Corresponding $1p$-decay energies are shown in the upper axis in MeV. The areas under the green and yellow lines indicate the assumed background contributions to the peaks of interest in the unfilled and gray-filled histogram respectively. See text for details.

Figure 7

${}^{28}\mathrm{S}$-proton angular correlations derived from measured ${}^{28}\mathrm{S}+p+p$ coincidences. (a) ${\theta }_{\mathrm{S}\text{−}\mathrm{p}1}$ vs ${\theta }_{\mathrm{S}\text{−}\mathrm{p}2}$ distribution. (b) The corresponding ${\rho }_{\theta }$ spectrum. The peaks and respective arcs labeled with “A–H” suggest the states of ${}^{30}\mathrm{Ar}$. Corresponding $2p$-decay energies are displayed in the upper axis in MeV. See text for details.

Figure 8

Angular correlations ${\theta }_{\mathrm{S}\text{−}\mathrm{p}}$ derived from the measured ${}^{28}\mathrm{S}+p+p$ coincidences by using the ${\rho }_{\theta }$ gates shown in Fig. 7. The corresponding ${\rho }_{\theta }$ ranges for the peaks A, B, C, D1, D2, E, F1, F2, G, and H are $38.5<{\rho }_{\theta }<48.0$ mrad [panel (a)], $48.0<{\rho }_{\theta }<60.0$ mrad [panel (b)], $62.5<{\rho }_{\theta }<67.0$ mrad [panel (c)], $67.0<{\rho }_{\theta }<72.0$ mrad [panel (d1)], $72.0<{\rho }_{\theta }<81.5$ mrad [panel (d2)], $81.5<{\rho }_{\theta }<93.5$ mrad [panel (e)], $93.5<{\rho }_{\theta }<108.0$ mrad [panel (f1)], $108.0<{\rho }_{\theta }<117.5$ mrad [panel (f2)], $120.0<{\rho }_{\theta }<132.0$ mrad [panel (g)], and $134.5<{\rho }_{\theta }<141.5$ mrad [panel (h)], respectively.

Figure 9

Angular correlations ${\theta }_{\mathrm{S}\text{−}\mathrm{p}}$ derived from the measured ${}^{28}\mathrm{S}+p$ double coincidences (unfilled histogram) and that deduced from the ${}^{28}\mathrm{S}+p+p$ triple coincidences (gray-filled histogram). The blue broken lines together with red arrows indicate the peaks which appear in both histograms, and they suggest the possible ${}^{29}\mathrm{Cl}$ resonances, whose $1p$-decay energies are shown in the upper axis in MeV. The areas under the green lines represent the assumed background regions for peaks of interest in the unfilled histogram, while the yellow lines are for the filled histogram.

Figure 10

Proposed decay schemes of the states observed in ${}^{30}\mathrm{Ar}$ and ${}^{29}\mathrm{Cl}$, whose decay energies (in units of MeV) are given relative to their $2p$ and $1p$ thresholds, respectively. The spins and parities given in parentheses are tentative assignments taken from Ref. [13]. The energy of ${}^{28}\mathrm{S}\left(2^{+}\right)$ is taken from Ref. [21].

Figure 11

Partial level schemes of ${}^{29}\mathrm{Cl}$ and ${}^{30}\mathrm{Ar}$ compared with schemes of isobaric mirror partners. Shell-model predictions (labeled with SM USD) for ${}^{29}\mathrm{Mg}$ and results of a cluster potential model (labeled with Cluster) for ${}^{29}\mathrm{Cl}$ are compared with the experimental data. The energies of ${}^{29}\mathrm{Cl}$ are shown relative to the $1p$ threshold. The energies of ${}^{29}\mathrm{Mg}$ states were shifted down by 3.655 MeV in order to compare them with the mirror states in ${}^{29}\mathrm{Cl}$.

Figure 12

Areas of dominance of different decay mechanisms of $2p$ precursors with mass number $A$ dependance of general decay parameters $Q_{2p}\left(A\right)$, $Q_p(A-1)$, and ${\mathrm{\Gamma }}_r(A-1)$. The blue-, green- and yellow-filled areas correspond to the dominating true, democratic, and sequential $2p$-decay mechanisms, respectively. The transition regions are indicated by the gray areas. The ${}^{30}\mathrm{Ar}$ decay (red dot) is located in the transition region.

Figure 13

Two-proton decay width ${\mathrm{\Gamma }}_{2p}$ of ${}^{30}\mathrm{Ar}$ around the transition regions between the true $2p$ and sequential $2p$ emission mechanisms. Panel (a) shows the width as function of the $2p$-decay energy $Q_{2p}\left({}^{30}\mathrm{Ar}\right)$ for a fixed value of $Q_p{(}^{29}\text{Cl})=1.8$ MeV. Panel (b) shows the width of ${}^{30}\mathrm{Ar}$ g.s. as function of $1p$-decay energy of the ${}^{29}\mathrm{Cl}$ subsystem, $Q_p\left({}^{29}\mathrm{Cl}\right)$ for the fixed value of $Q_{2p}{(}^{30}\text{Ar})=2.45$ MeV. The solid, dashed, dotted, and dash-dotted curves correspond to the ${\mathrm{\Gamma }}_p{(}^{29}\text{Cl})$ values of 6.3, 25, 75, and 225 keV, respectively, at $Q_p{(}^{29}\text{Cl})=1.8$ MeV. The hatched areas indicate the transition regions.

Figure 14

Transition from the true-$2p$ decay mechanism to the sequential proton emission mechanism of ${}^{30}\mathrm{Ar}$ ground state. (a) Energy distribution between core and one of the protons calculated by employing improved direct decay model [14], where the $2p$-decay energy of ${}^{30}\mathrm{Ar}$ is varied. (b) Same as panel (a) but with variation of the width of ${}^{29}\mathrm{Cl}$ g.s. In the panels (c) and (d), the experimental ${\theta }_{\mathrm{S}\text{−}\mathrm{p}}$ distribution measured for the decay of ${}^{30}\mathrm{Ar}$ g.s. (gray histogram with statistical uncertainties) is compared with those stemming from respective theoretical distributions in panels (a) and (b) after experimental bias is taken into account via Monte Carlo simulations.

Figure 15

Angular ${\theta }_{\mathrm{S}\text{−}\mathrm{p}}$ distributions derived from the decays of ${}^{30}\mathrm{Ar}$ excited states at 3.9 and at 4.2 MeV above the $2p$ threshold. (a) The data (black dots with statistical uncertainties) are selected from the ${}^{28}\mathrm{S}+p+p$ coincidences by using the ${\rho }_{\theta }$ gate D1 at $67.0<{\rho }_{\theta }<72.0$ mrad. The solid curve displays the simulation of the sequential $2p$ decay of the ${}^{30}\mathrm{Ar}$ state at 3.9 MeV via the ${}^{29}\mathrm{Cl}$ resonances at 1.8 MeV (dashed curve) and 2.9 MeV (dotted curve). (b) $2p$ decays selected by the ${\rho }_{\theta }$ gate D2, $72.0<{\rho }_{\theta }<81.5$ mrad. The solid curve is the simulation of the sequential $2p$ decay of the ${}^{30}\mathrm{Ar}$ state at 4.2 MeV via the 2.3-MeV (dashed curve) and the 2.9-MeV (dotted curve) levels in ${}^{29}\mathrm{Cl}$.

Figure 16

Angular ${\theta }_{\mathrm{S}\text{−}\mathrm{p}}$ distributions reflecting the decays of several excited states in ${}^{30}\mathrm{Ar}$. (a) $2p$ decays selected by the ${\rho }_{\theta }$ gate E, $81.5<{\rho }_{\theta }<93.5$ mrad. The simulation of sequential $2p$ emission from the ${}^{30}\mathrm{Ar}$ excited state at 5.6 MeV via the 3.5-MeV (dashed curve) and the 2.9-MeV (dotted curve) states in ${}^{29}\mathrm{Cl}$ is depicted by the solid curve. (b) $2p$ decays of excited state in ${}^{30}\mathrm{Ar}$ selected by the ${\rho }_{\theta }$ gate F1, $93.5<{\rho }_{\theta }<108.0$ mrad. The dashed and dotted curves are the ${\theta }_{\mathrm{S}\text{−}\mathrm{p}}$ distributions obtained by simulations of $2p$ emission of the ${}^{30}\mathrm{Ar}$ state at 7.9 MeV via two ${}^{29}\mathrm{Cl}$ states at 3.9 and 2.9 MeV, respectively. The solid curve represents the summed fit. (c) Data obtained by imposing the ${\rho }_{\theta }$ gate F2, $108.0<{\rho }_{\theta }<117.5$ mrad. The solid curve displays the ${\theta }_{\mathrm{S}\text{−}\mathrm{p}}$ spectrum obtained from the simulation of sequential proton ejection from the 9.4-MeV ${}^{30}\mathrm{Ar}$ excited state via the ${}^{29}\mathrm{Cl}$ resonance at 3.5 MeV. (d) The $2p$ decays selected by the ${\rho }_{\theta }$ gate G, $120.0<{\rho }_{\theta }<132.0$ mrad. The solid curve shows the simulation of sequential $2p$ emission of the ${}^{30}\mathrm{Ar}$ excited state at 12.6 MeV via the ${}^{29}\mathrm{Cl}$ states at 3.5 MeV (dashed curve) and 5.3 MeV (dotted curve), respectively.