Figure 1

The observed states in ${}^{19}$Mg and ${}^{18}$Na whose energies (in MeV) are shown relative to the respective $1p$ and $2p$ thresholds. The main and the minor ${}^{19}\text{Mg}\to {}^{18}\text{Na}+p$ branches are indicated by dashed and dotted arrows, respectively. The spins and parities given in parentheses are tentative assignments. The energy of ${}^{18}$Na(3${}^{-}$) is taken from Ref. [10].Reuse & Permissions

Figure 2

Schematic drawing of transverse momentum correlations $k_{p1-\text{HI}}-k_{p2-\text{HI}}$ in panels (a), (b) expected for two alternative mechanisms of $2p$ decay (illustrated in the respective top panels) from a parent nucleus $A$ to a daughter nucleus $A$-2: (a) direct three-body decay or simultaneous $2p$ emission, (b) sequential emission of protons via a narrow intermediate state in nucleus $A$-1. (c) Measured angular $\left(p_1{-}^{17}\text{Ne}\right)-\left(p_2{-}^{17}\text{Ne}\right)$ correlations (color boxes with scale shown on the right-hand side). The shadowed arc areas (i–iv) (along $\rho =\text{const}$) indicate locations of simultaneous or sequential $2p$ decays of the most intensively populated states in ${}^{19}$Mg.Reuse & Permissions

Figure 3

(a) Angular $p_1{-}^{17}\text{Ne}$ correlations (solid circles with statistical uncertainties) obtained from the measured ${}^{17}\text{Ne}+p+p$ data shown in Fig. 2c without imposing any gate condition. (b) Angular $p_1{-}^{17}\text{Ne}$ distribution obtained from the same data by selecting the other proton angle, ${\theta }_{p2-\mathrm{Ne}}$, within the range from 10 to 36 mrad, which corresponds to the assumed g.s. of ${}^{19}$Mg. The solid curve represents the Monte Carlo simulation of the detector response to ${}^{19}{\text{Mg}}_{\text{g.s.}}\to {}^{17}\text{Ne}+p+p$ with a $2p$-decay energy of 0.75(5) MeV. The histogram represents the assumed background deduced from the data for a ${\theta }_{p2-\mathrm{Ne}}$ gate from 110 to 180 mrad; it contributes 15$\%$ to the peak at angles from 10 to 36 mrad. (c) Angular $p_1{-}^{17}\text{Ne}$ distribution projected by choosing the ${\theta }_{p2-\mathrm{Ne}}$ gate from 65 to 180 mrad. The solid line is the simulation of the final-state interaction of protons with ${}^{17}$Ne due to the 1.55-MeV resonance in ${}^{18}$Na.Reuse & Permissions

Figure 4

Angular $p{-}^{17}\text{Ne}$ correlations (solid circles with statistical uncertainties) selected from the ${}^{17}\text{Ne}+p+p$ data by choosing the arc gates (i–iv) shown in Fig. 2c. (a) The $2p$ decay of the ${}^{19}$Mg g.s. selected by gate (i), that is, the condition $20<\rho <45$ mrad. The solid curve shows the best-fit simulation of the three-body model using a $2p$-decay energy of $Q_{2p}=0.76\left(6\right)$ MeV. (b) The $2p$ decay of the ${}^{19}$Mg “first-excited” state selected by the gate (ii), $50<\rho <65$ mrad. The solid curve displays the simulation of the sequential $2p$ decay of the state at 2.14 MeV via two intermediate states in ${}^{18}$Na, the g.s. at $Q_{1p}=1.23$ MeV (dash-dotted line), and the 2${}^{-}$ state at 1.55 MeV (dashed line). (c) The $2p$ decay of the “second-excited” state in ${}^{19}$Mg selected by gate (iii), $65<\rho <80$ mrad. The solid line is the best-fit simulation of the sequential $2p$ decay of the ${}^{19}$Mg state at 2.9 MeV via the 2${}^{-}$ and 3${}^{-}$ states in ${}^{18}$Na (the dash-dotted and dashed curve, respectively). (d) The $2p$ decay of the suggested high-lying state in ${}^{19}$Mg at $Q_{2p}=5.5$ MeV selected by gate (iv), $90<\rho <115$ mrad. The solid curve represents the best-fit simulation of the decay of this state by sequential $1p$ emission via ${}^{18}$Na${}^{*}\left(2^{-}\right)$. (e) Angular $p{-}^{17}\text{Ne}$ correlations selected by choosing the arc gate between areas (iii) and (iv) shown in Fig. 2c, that is, the condition $80<\rho <90$ mrad. The dashed curve shows the simulation of the sequential $2p$ decay of the suggested excited state in ${}^{19}$Mg via ${}^{18}$Na${}^{*}\left(2^{-}\right)$, with the fitted values $Q_{2p}=3.6\left(2\right)$ MeV and $\Gamma <0.2$ MeV. The dash-dotted curve represents the contribution due to the $2p$ decay of the neighboring ${}^{19}$Mg state at $Q_{2p}=5.5$ MeV. The solid curve is the sum fit.Reuse & Permissions

Figure 5

Intensity distributions of $2p$ decays from ${}^{19}$Mg (arbitrary yields corresponding to the color scale shown on the right-hand side) as a function of the total $2p$-decay energy $E_T$ and the parameter $\varepsilon \sim E_p/E_T$. The distributions are calculated with a three-body model assuming a single resonance in the intermediate nucleus ${}^{18}$Na with energy $E_r$ and width ${\Gamma }_r$. (a) Decays by taking into account the g.s. of ${}^{18}$Na at $E_r=1.23$ MeV with ${\Gamma }_r=0.1$ MeV. (b) Decays via the 1${}_2^{-}$ state in ${}^{18}$Na at $E_r=2.03$ MeV, ${\Gamma }_r=0.9$ MeV [10].Reuse & Permissions