Proton-proton correlations observed in two-proton decay of ${}^{19}\mathrm{Mg}$ and ${}^{16}\mathrm{Ne}$

Proton-proton correlations were observed for the two-proton decays of the ground states of ${}^{19}\mathrm{Mg}$ and ${}^{16}\mathrm{Ne}$. The trajectories of the respective decay products, ${}^{17}\mathrm{Ne}$+$p+p$ and ${}^{14}\mathrm{O}$+$p+p$, were measured by using a tracking technique with microstrip detectors. These data were used to reconstruct the angular correlations of fragments projected on planes transverse to the precursor momenta. The measured three-particle correlations reflect a genuine three-body decay mechanism and allowed us to obtain spectroscopic information on the precursors with valence protons in the $\mathit{sd}$ shell.

Figure 1

States observed in ${}^{16}\mathrm{Ne}$, ${}^{19}\mathrm{Mg}$ and the corresponding intermediate systems ${}^{15}\mathrm{F}$, ${}^{18}\mathrm{Na}$. Decay energies (in keV) are given relative to the respective $p$ and $2p$ thresholds. Most values have been taken from the literature [9, 10, 11, 12, 13, 14, 15], those in bold print are from the present work.

Figure 2

(a) Cartoon of momentum correlations $k_{p1-\mathrm{HI}}\text{−}{k}_{p2-\mathrm{HI}}$ expected for a direct three-body decay (the area $k_{3R}$) and sequential $2p$ decay (grey boxes with black peaks $k_{2R}$). (b) Sketch of the kinematic enhancement of an angular $p$-HI correlation at the maximum possible angle for a given momentum between the decay products. (c) Corresponding angular $p$-HI distribution.

Figure 3

(a) Angular ($p_1\text{−}{}^{14}$O)-$(p_2\text{−}{}^{14}$O) correlations obtained from the measured ${}^{14}\mathrm{O}$+$p+p$ events (colored boxes with scale shown on right). The grey areas indicate simultaneous and sequential $2p$ emission in analogy to those shown in Fig. 2. (b) Angular $p\text{−}{}^{14}$O distribution (full circles with statistical uncertainties) obtained from the data shown in panel (a) by selecting the other proton angle ${\theta }_{p2-\mathrm{O}}$ within the range from 0 to 45 mrad, which corresponds to the ground state of ${}^{16}\mathrm{Ne}$. The solid curve represents the Monte Carlo simulation of the detector response for ${}^{16}\mathrm{Ne}$ ${}_{\mathrm{gs}}\to {}^{14}$O + $p+p$ with a $2p$-decay energy of 1.35(8) MeV which agrees with the value of 1.4(1) MeV measured in Ref. [11]. The dashed line is a sum fit to the data. The dotted curve indicates the background as explained in the text. (c) Angular $p\text{−}{}^{14}$O distribution obtained from the data shown in (a) by selecting the other proton angle from 120 to 150 mrad, which corresponds to $p\text{−}{}^{14}$O final-state interactions due to the ground and excited states of ${}^{15}\mathrm{F}$. The dashed and dotted curves are the Monte Carlo simulations of the known $1p$ decays of the ground and first excited states of ${}^{15}\mathrm{F}$ with $1p$ decay energies of 1.56(13) and 2.85(4) MeV, respectively [12]. The dash-dotted and dash-dot-dotted curves show the result of fits to the $p\text{−}{}^{14}$O correlation, indicating unknown excited states in ${}^{15}\mathrm{F}$ with $1p$ decay energies of 4.9(2) and 6.4(2) MeV, respectively. The solid line is the sum fit.

Figure 4

(a) Three-body correlations predicted by the three-body model [19] for the $2p$ decay of ${}^{19}\mathrm{Mg}$, plotted as a function of the relative energy between two protons, $E_{p-p}/E$, and the angle ${\theta }_k$ between the relative momenta of the fragments as illustrated in the figure. Extreme cases of $p\text{−}p$ correlations are sketched and related to the corresponding areas in the correlation plot. (b) $p\text{−}p$ energy spectra from the $2p$ decay of ${}^{19}\mathrm{Mg}$ calculated for different weights $W$ of $\mathrm{spd}$-shell configurations in ${}^{19}\mathrm{Mg}$. (c) Typical intensity distributions plotted as a function of ${\theta }_k$ [see (a)] in the rest frame of the $2p$ precursor (solid curve) and its analog in the laboratory system ${\theta }_k^{\text{'}}$ projected on the transverse detector plane (dashed curve).

Figure 5

Angular $p\text{−}p$ correlations from the $2p$ decays of the ground states of ${}^{19}\mathrm{Mg}$ (left) and ${}^{16}\mathrm{Ne}$ (right) obtained from the measured ${}^{17}\mathrm{Ne}$$+p+p$ and ${}^{14}\mathrm{O}$$+p+p$ events, respectively, by selecting both protons from the respective $p\text{−}{}^{17}$Ne(${}^{14}\mathrm{O}$) angular ranges. The solid curves show the three-body model calculations (54% and 88% of $d$-wave configuration in ${}^{16}\mathrm{Ne}$ and ${}^{19}\mathrm{Mg}$, respectively) normalized to the data. The dotted curves show the background contributions estimated as described in the text. The dashed curves are the diproton model predictions, and the dash-dotted curves are the phase-space simulations of the $2p$ decays (isotropic proton emission in the $2p$ precursor's rest frame).

Figure 6

Three-body correlations from the $2p$ decays of the ground states of ${}^{16}\mathrm{Ne}$ and ${}^{19}\mathrm{Mg}$ (full circles with statistical uncertainties) obtained from the measured ${}^{14}\mathrm{O}$ + $p+p$ and ${}^{17}\mathrm{Ne}$ + $p+p$ events by selecting an angle ${\theta }_k^{\text{'}}$ (see text). The solid curves are the three-body model calculations (assuming 54% and 88% of $d$-wave configuration in ${}^{16}\mathrm{Ne}$ and ${}^{19}\mathrm{Mg}$, respectively). The dashed curves are the diproton model predictions, and the dash-dotted curves are the phase-space simulations illustrating the response to an isotropic $2p$ emission in the precursor's rest frames (both simulations are not normalized). The dotted curves show the background contributions estimated from all measured HI + $p+p$ events.