Eur. Phys. J. A 42, 421–429 (2009) DOI 10.1140/epja/i2009-10790-9

THE EUROPEAN PHYSICAL JOURNAL A

Regular Article – Experimental Physics

Experimental studies of nuclei beyond the proton drip line by tracking technique I. Mukhaa For the S271 Collaborationb Universidad de Sevilla, Sevilla, Spain Received: 26 November 2008 / Revised: 6 March 2009 c Societ` Published online: 15 May 2009 –  a Italiana di Fisica / Springer-Verlag 2009 ¨ o Communicated by J. Ayst¨ Abstract. A novel experimental technique for measurements of in-flight decays of proton-unbound nuclei with pico-second lifetimes is described on the examples of the recent discovery of 19 Mg and its two-proton (2p) radioactivity and the study of the reference 2p decay of the known isotope 16 Ne. The method of measurements of 2p decays in flight by tracking all fragments with micro-strip detectors has also proven to be a potent tool for obtaining valuable spectroscopic information on exotic isotopes like 19 Mg or 16 Ne. Systematic studies of other 2p emitters predicted theoretically are foreseen with this powerful technique whose sensitivity is larger by factor of 20–30 in comparison with a conventional invariant-mass method. Information about the respective one-proton unbound subsystems can be obtained at the same time by evaluating proton–heavy-fragment correlations, which is illustrated on the example of the spectroscopy of 15 F. This finding opens a way for systematic studies of exotic nuclei beyond the proton drip line, e.g., 69 Br. The properties of such nuclei may be important for the understanding of the element abundance in the Universe and may be used as input data for modeling the rp-process in various astrophysical sites. PACS. 23.50.+z Decay by proton emission – 23.90.+w Other topics in radioactive decay and in-beam spectroscopy

1 Two-proton decays and radioactivity In 1960, proton-rich nuclei with odd or even atomic numbers were predicted [1] to decay through one-proton (1p) and 2p radioactivity, respectively. The experimental observation of one-proton radioactivity was first reported in 1970. Two-proton radioactivity, the spontaneous decay of an atomic nucleus by the emission of two protons, is the most recently discovered nuclear disintegration mode. It has first been reported for 45 Fe with a halflife of about 4 ms [2], which is about 1000 times longer than the quasi-classical estimate of “diproton” (or 2 He) cluster emission. Further observations of 2p radioactivity, e.g. reported for 54 Zn [3], 48 Ni [4] and for 94m Ag [5] where first proton-proton correlations were observed, have

confirmed unexpectedly large half-lives of 2p precursors. The recently developed first quantum-mechanical theory of 2p radioactivity which uses a three-body “core”+p+p model [6] interprets this observation as being due to a considerable influence of Coulomb and centrifugal barriers together with nuclear-structure effects, and is able to predict the regular existence of considerably long-lived 2p precursors. Such a general feature of proton-unbound nuclei with a three-body structure may be of interest for nuclear astrophysics. The inverse reaction to 2p decay, namely 2p radiative capture, is expected to play an important role in the synthesis of heavy elements in the Universe, possibly bridging some “waiting points” in the “hot” rp-process, see e.g. [7,8]. The measurements of 2p decays are the only way of studies of 2p radiative capture so far.

a

On leave from the Kurchatov Istitute, Moscow, Russia; e-mail: [email protected] b GSI Helmholtzzentrum f¨ ur Schwerionenforschung, Darmstadt Germany; Universidad de Sevilla, Spain; Universidad de Huelva, Spain; Joint Institute of Nuclear Research, Dubna, Russia; RRC Kurchatov Institute, Moscow, Russia; IEP Warsaw University, Poland; Universidad de Santiago de Compostela, Spain; University of Mainz, Germany; University of Edinburgh, UK.

2 Tracking technique in studies of in-flight 2p decays applied to 19 Mg and 16 Ne Experiments investigating 2p radioactivity are usually based on the implantation of the radioactive atoms and subsequent detection of their decay. For the first time in studies of radioactivity, the in-flight decay experiment

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suggested in [9] was performed in which all fragments were tracked and the decay vertices as well as the angular correlations of the decay products were deduced from the measured trajectories. This allowed an observation of 2p radioactivity of the previously unknown isotope 19 Mg [10]. The trajectories of all three 2p-decay products, 17 Ne+p+p, were precisely measured by micro-strip detectors, which allowed a reconstruction of the 2p-decay vertices and the fragment correlations [11]. The investigation of 2p emissions from 19 Mg and 16 Ne was performed by using a 591 A MeV beam of 24 Mg accelerated by the SIS facility at GSI Helmholtzzentrum f¨ ur Schwerionenforschung, Darmstadt. The radioactive beams of 20 Mg and 17 Ne were produced at the projectile fragment separator, FRS [12] with average intensities of 400 and 800 ions s−1 and energies of 450 A MeV and 410 A MeV, respectively. The secondary one-neutron removal reactions, (20 Mg, 19 Mg) and (17 Ne, 16 Ne) occurred at the mid-plane of FRS in a secondary 2 g/cm2 thick target of 9 Be. Special magnetic optics settings were applied, the first half of FRS was tuned to be in an achromatic mode by using a wedge-shaped degrader, while the second half was set for the identification of the heavy ions (HI), in particular 17 Ne and 14 O, with high acceptance in angle and momentum. The heavy 2p-decay residuals (17 Ne and 14 O) were unambiguously identified by their time of flight, magnetic rigidity, and energy loss measured with the position-sensitive scintillator detectors and at the second half of FRS. The sketch of the experimental set-up at the FRS may be found in fig. 1 of ref. [10] where it is explained in detail. For illustration purpose, the sketch in fig. 1 shows the close-up of the array of micro-strip detectors used. The four micro-strip double-sided silicon detectors (MSD, [13]) (with an area of 7×4 cm2 and a strip pitch of 100 μm) were arranged in an array with three planes N1 , N2 , F1 positioned 2.6, 8.6, and 29 cm downstream from the secondary target, respectively. This array was used to measure the energy loss and position of coincident hits of two protons and a heavy fragment.

Fig. 1. Sketch illustrating a tracking of 2p decays of 19 Mg with the three planes of micro-strip detectors, N1 , N2 , F1 . The trajectory of each fragment was defined by the three respective sets of hit coordinates.

Fig. 2. Number of micro-strips fired in micro-strip detectors by 400 A MeV protons and 17 Ne ions.

2.1 Tracking of charged particles with micro-strip detectors The procedure of fragment tracking was based on the response of the micro-strip detectors to the proton and HI hits. In fig. 2, a number of micro-strips fired in MSD is shown for protons and 17 Ne ions. As one may see, protons fired mostly one strip of√MSD, thus their position uncertainty was σx = 100/ 12 ≈ 30 μm. The Ne(Mg) ions typically produced clusters of 7(9) strips fired. Their centroids were found with uncertainties of ∼ 14 μm which were determined from a calibration tracking procedure applied for single ions of the beam crossing the three layers of MSD. Such a procedure is illustrated in fig. 3, where the dX, dY differences between the two alternative coordinates (X, Y ) obtained for the 20 Mg ions on the secondary-target plane (see fig. 1) are shown. The dX, dY differences were derived from the two

Fig. 3. Uncertainties of positions of 20 Mg ions on the secondary target in the (X, Y )-transverse directions. The uncertainties are evaluated from the differences between the two alternative (X, Y )-coordinate values of the 20 Mg positions on the target derived from the two alternative 20 Mg trajectories defined by the MSD pairs N1 -F1 and N2 -F1 , see fig. 1.

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Fig. 5. (a) Sketch of transverse momentum correlations kp1-HI -kp2-HI expected for a direct three-body (the grey area with black peak k3R ) and sequential (grey boxes with black peaks k2R ) 2p-decay mechanisms. Arrows indicate directions of the peak tails. (b) Scheme of the kinematical enhancement of an angular p-HI correlation at the maximum possible angle for a given momentum between the decay products. (c) The corresponding ideal angular p-HI distribution peaked at the maximum angle with a low-angle tail.

ing the detector performance and tracking procedure may be found in [10,14–16].

2.2 Identification of 2p-decay channels by using angular proton–heavy-fragment correlations Fig. 4. Upper panel: histogram of minimal distances between trajectories of protons and 17 Ne ions derived from the measured triple 17 Ne+p+p coincidence. Lower panel: histogram of the difference between two decay vertexes along a beam direction defined for the p1 -17 Ne and p2 -17 Ne trajectories which were taken from the same 17 Ne+p1 +p2 event.

alternative trajectories of single 20 Mg defined by the different MSD pairs, N1 -F1 and N2 -F1 (see fig. 1). The main source of the position uncertainties was the relative alignment of the tracking detectors. The distribution in fig. 3 was obtained as the result of the fitting procedure applied for trajectories of 20 Mg with five fit parameters for each tracking detector, namely two spatial (X0 , Y0 ) and three angular (Θ0x , Θ0y , Θ0z ) pedestals. Proton-HI vertices were defined as points where distances between the respective trajectories were minimal (typically less than 150 μm) which is illustrated by the upper panel in fig. 4. The uncertainty of defining a HI+p+p vertex along a beam direction depended on the two proton-HI angles (taken from the same HI+p+p event) and varied typically from 0.3 to 1 mm, see the respective distribution in the lower panel in fig. 4. An uncertainty of a position of a centroid of a vertex distribution (which was assumed to have N events in total) was smaller than√the respective single-event uncertainty by a factor of 1/ N . For example, the centroid of the 19 Mg vertex distribution (about 150 events) was measured with an accuracy of 0.1 mm. Angular uncertainties of decay products were mainly due to the angular straggling of protons in the MSDs and amounted to ∼ 1 mrad. More details concern-

Several reactions can produce triple HI+p+p events in exit channels. Three-body decay kinematics can be completely described by a Dalitz plot which is traditionally used to disentangle different reaction channels. In general, the 2p decays may proceed either via sequential or direct proton emission mechanisms. The first case is usually described as two consecutive 1p decays through an intermediate resonance [17]. In a schematic 2-dimensional (kp1 -HI)–(kp2 -HI) distribution (which is built in analogy to a Dalitz plot) shown in fig. 5(a), the first case should populate peaks k2R located along the arc area with the root-mean-squared proton momentum being constant; the widths of the peaks reflect the width of the intermediate state. Sequential proton emission from a single 2p-parent state via narrow p-HI resonances displays usually double peaks while 2p de-excitation of continuum parent states with p-HI final-state interactions should reveal “slices” as shown in fig. 5(a). In the second case, the simultaneously emitted protons share the 2p-decay energy, with both p-HI spectra being identical and peaked at Q2p /2 [18,19]. Then the area marked k3R in fig. 5 is populated. In all cases, the patterns in fig. 5 should be symmetric due to permutation of protons. The discussed structures can be found in the angular θp1-HI -θp2-HI correlations as well. This is illustrated in fig. 5(b) where protons emitted isotropically in the 1p precursor frame are grouped in a narrow cone in the laboratory frame due to kinematical forward focussing, with the maximum intensity showing up around the largest possible angle. The p-HI angles reflect the transverse proton momentum relative to the HI momentum, and are therefore correlated with the precursor’s decay energy. Thus sequential 2p decays from excited states in parent nuclei

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should be mostly located in peaks with tails along the respective slices in the angular θp1-HI -θp2-HI correlations, in analogy to those sketched in fig. 5(a). In direct 2p decays, the single-proton energy spectrum always exhibits a relatively narrow peak centered close to half of the 2p-decay energy; such energy distribution is a stable feature of this decay mechanism [1,20]. Correspondingly, a bump should appear in the angular correlations in the same way as it should appear along the arc marked by k3R in the scatter plot in fig. 5. This correspondence between angular and momentum correlations has been used to derive the 2p-decay energy of 19 Mg [10]. 2.3 Energy of 2p decay derived from measured angular proton–heavy-fragment correlations In the first measurements of 2p-decay energy by the tracking technique, the reference case of the ground state of 16 Ne was chosen because its 2p-decay energy is known. For the 2p decay of 16 Ne, the angular correlations of each coincident proton with respect to the 14 O momentum, θp1-O -θp2-O , derived from the measured 14 O+p+p coincidence events [11], are shown in fig. 6(a). The events with the smallest angles fall into a distinct cluster around θp-O = 35 mrad while most of the other events are located in the slices centered around 70 and 95 mrad. These two groups can be attributed to the direct 2p decay from the 16 Ne ground state and to the sequential emission of protons from excited states in 16 Ne via the 15 F ground state, respectively. These events will be referred as the “groundstate” and “excited-state” events, respectively. In order to select the “ground-state” events with minimal admixture of the “excited-state” events, a slice projection was made from the measured (p1 -14 O)–(p2 -14 O) correlations in fig. 6(a) by selecting the angle of one of the protons within the range 0–45 mrad, where the 2p decay of the 16 Ne ground state was expected to show up. Figure 6(b) displays the angular correlations θp1-O corresponding to the “ground-state” gate in the other pair θp2-O . The peak around 35 mrad (the suggested “ground state”) dominates the spectrum, whereas very few correlations can be seen between a proton from the “ground state” and another proton at larger angles. This means that the two protons are from the same “ground-state” event, i.e. this peak can be explained by an emission of protons from the ground state in 16 Ne. The data were fit by Monte Carlo simulations of the set-up response to the direct 2p decay 16 Ne → 14 O + p + p by using the GEANT program [21]. The simulations took into account the above-mentioned experimental uncertainties of tracking the fragments and of reconstructing the decay vertices. Low-angle cutoff due to the finite cluster width of a HI-hit in MSD which did not allowed to distinguish protons and HI below about 10 mrad opening angle was taken into account as well. The normalized simulation reproduced the data in the low-angle peak very well. Fitting the 2p-decay energy of 16 Ne in the same way as for 19 Mg [10], the value Q2p = 1.35(8) MeV was found, in very good agreement with the literature value of

Fig. 6. (a) Plot of angular correlations (p1 -14 O)–(p2 -14 O) obtained from the 14 O+p+p events measured with a 17 Ne beam (colored (on-line) boxes with scale shown on the right). The violet areas indicate simultaneous and sequential 2p emission in analogy to those shown in fig. 5. (b) Angular p-14 O distribution (full circles with statistical uncertainties) projected from the data shown in panel (a) by gating the other proton angle θp2-O from 0 to 45 mrad, which corresponds to the selection of the ground state of 16 Ne. The solid curve represents the Monte Carlo simulation of the detector response for 16 Neg.s. → 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 [22]. The dashed line is a sum fit to the data. The dotted curve indicates the background as explained in the text.

1.4(1) MeV [22]. The contribution from the “tail” of the higher states to the ground-state peak was about 20%. The shape of this distribution is assumed to have the same shape as the θp1-O distribution selected within the θp2-O range just outside the ground-state region, from 48 to 160 mrad (the dotted curve). In analogy to 16 Ne, the 2p decay of the unknown isotope 19 Mg was investigated. In fig. 7(a), the angular correlations of protons with respect to 17 Ne (θ(p1 -17 Ne)– θ(p2 -17 Ne)) measured with a 20 Mg beam are shown. The events are grouped into two distinct clusters: a spot about θ(p-17 Ne) = 30 mrad and a broad cross around 55 mrad. These two clusters may be attributed to the simultaneous 2p emission from the 19 Mg ground state and to the sequential decay of excited states in 19 Mg via the 18 Na ground state, respectively. Like in the 16 Ne case, these

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gies were fitted to the peaks appearing in the experimental spectrum. The peak around 30 mrad was fitted by a Q2p value of 0.75(5) MeV. In a similar way the peak around 55 mrad was fitted by assuming a sequential emission of 1.8 MeV protons from an excited state in 19 Mg to the 18 Na ground state and subsequent emission of 1.3 MeV protons, with a total Q2p value of 3.2(2) MeV. Figure 7(b) shows the p1 -17 Ne correlations corresponding to the “groundstate” peak in another pair p2 -17 Ne (the selection gate ranging from 9 to 43 mrad). The contribution from the “ground-state” peak dominates but the “excited state” peak is suppressed. Therefore the “ground state” and “excited state” peaks cannot be explained by a sequential emission of protons from the same state in 19 Mg because both peak’s integrals should be equal otherwise. The derived Q2p value of 0.75 MeV matches the range of 2p-decay energies predicted for 19 Mg [20] while a 2pdecay energy of about 3.2 MeV should result in immediate break-up regardless of the 2p-decay mechanism involved. Thus the only plausible explanation of the p-17 Ne correlations observed inside and outside the target is that the 55 mrad peak can be ascribed to an excited state in 19 Mg, and the 30 mrad peak is related to the 19 Mg ground state. In the procedure to determine the half-life of 19 Mg as described below in sect. 2.5, these two peaks were used as gates for producing the 2p-decay vertex distributions shown in fig. 11. It should be noted that an unambiguous description of the 55 mrad “excited-state” events is not possible due to the lack of a reliable knowledge about the 18 Na excited states [23]. Fig. 7. (a) Angular correlation plot (p1 -17 Ne)–(p2 -17 Ne) obtained from the measured 17 Ne+p+p events (colored (on-line) boxes with scale shown on the right). The grey areas indicate simultaneous and sequential 2p emission in analogy to those shown in fig. 5. (b) Angular p-17 Ne distribution (full circles with statistical uncertainties) projected from the plot shown in panel (a) by selecting the other proton angle θp2-Ne within the range from 9 to 43 mrad, which corresponds to the ground state of 19 Mg. The solid curve represents the Monte Carlo simulation of the detector response for 19 Mgg.s. → 17 Ne + p + p with a 2p-decay energy of 0.75(5) MeV. The histogram indicates the background as explained in the text.

events will be referred as the “ground state” and “excited state”, respectively. As a delayed decay of 19 Mg was searched for, two projections from the measured p-p-17 Ne correlations were made. One was gated on vertices downstream of the target where the radioactivity of the 19 Mg ground state should show up. The other distribution was gated on vertices inside the target. The angular p-17 Ne correlations resulting from inside the target exhibited two peaks on top of a broad distribution while mostly one peak survives in the spectrum downstream from the target. The data were compared to Monte Carlo simulations made with two assumed mechanisms: i) the direct 2p-decay 19 Mg → 17 Ne + p + p [20]; ii) a sequential emission of protons from a suggested narrow state in 19 Mg via the ground state of 18 Na [23]. In both cases, the 2p-decay ener-

2.4 Proton-proton and three-particle correlations in 2p decays: the 19 Mg and 16 Ne cases The method of measuring 2p decays in flight provides new specific observable which can yield valuable spectroscopic information. E.g., p-p correlations were observed for the 2p decays of the ground states of 19 Mg and 16 Ne for the first time [11]. These data were used to reconstruct the angular correlations of fragments projected on planes transverse to the precursor momenta. In general, the three-body correlations can be completely described by two variables (the total decay energy E is assumed to be fixed), e.g., by an energy distribution parameter Ep-p /E (here Ep-p is the relative energy between two protons) and an angle θk between the relative p-p and (pp)-HI momenta. Figure 8 shows such distributions calculated with the three-body model for the 2p decay of 19 Mg [24,20]. The three-body model predicts a distinctive correlation pattern displaying an enhancement at small Ep-p due to final-state interaction and a suppression in the regions of strong Coulomb repulsion (Ep-p /E ∼ 0.5, cos(θk ) ∼ ±1). The predicted energy distributions are sensitive to the structure of the precursor (see the left panel in fig. 8). Similar predictions are available for 16 Ne [25]. In the 2p-decay tracking experiments, the opening angles θp-p between protons were measured whose distribution reflects the Ep-p correlations. Figure 9 shows the experimental angular p-p distributions obtained from triple

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Fig. 8. (Colour on-line) Fragment correlations predicted by the three-body model [20] for the 2p decay of 19 Mg, plotted as a function of the relative energy between two protons, Ep-p /E, and the angle θk between the relative momenta of the frag−−→ −−−→ ments, kp-p and kpp-HI . Left panel: The p-p energy spectra from the 2p decay of 19 Mg calculated for different weights W of s-p-d shell configurations in 19 Mg. Right panel: decay intensity distributions plotted as a function of θk in the rest frame of the 2p precursor (black curve) and its analog in the lab system θk projected on the transverse detector plane (blue curve).

Fig. 9. (Colour on-line) Angular p-p correlations from the 2p decays of 19 Mg (left panel) and 16 Ne (right panel) obtained from the measured 17 Ne+p+p and 14 O+p+p events, respectively, by selecting both protons from the respective p17 Ne(14 O) angular ranges. The black solid curves show the three-body model calculations (88% and 54% of d-wave configuration in 19 Mg and 16 Ne, respectively) normalized to the data. The dotted curves show the background contributions estimated as described in the text. The blue dashed curves are the diproton model predictions, and the red dash-dotted curves are the phase-space simulations of the 2p decays (isotropic proton emission in the 2p precursor’s frame).

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O+p+p and 17 Ne+p+p events gated by the conditions that both protons originate from the “ground states” of 16 Ne and 19 Mg. These gates were inferred from the respective angular p-HI correlations as discussed above. The events representing the “ground-state” 2p decay actually contain contributions from the ground state and background contributions from both excited states of the parent nucleus and fragmentation reactions. The shapes of the background components were evaluated empirically by projecting triple events with the p-HI gates shifted away from the “ground-state” region towards larger angles. The resulting p-p background contributions shown by the dotted curves in fig. 9 constitute about 20% of all p-p correlation data for 16 Ne and 25% for 19 Mg (see fig. 6(b) and fig. 4(c) in [10]); they were subtracted from the original p-p correlations. As one can see in fig. 9, the predictions following from the assumption of a diproton emission fail

Fig. 10. (Colour on-line) Intensities of the 2p decays of 16 Ne and 19 Mg (full circles with statistical uncertainties) obtained from the measured 14 O+p+p and 17 Ne+p+p events as a function of a three-body angle θk (see text). The black curves are the three-body model calculations (assuming 54% and 88% of d-wave configuration in 16 Ne and 19 Mg, respectively). The blue curves are the diproton model predictions, and the red curves are the phase-space simulations illustrating an isotropic 2p emission in the precursor’s frames (both simulations are not normalized). The black dotted curves show the background contributions estimated from all measured HI+p+p events.

to describe both the 16 Ne and 19 Mg data while the threebody model reproduces the shapes of both distributions. In the 19 Mg case, the best description is obtained with the d-wave configuration dominating. The 16 Ne data give evidence for nearly equal s- and d-wave components. In fig. 10, the intensity distributions are displayed as a function of cos(θk ). The Jacobi-projected angle, θk was defined by a line connecting the two points where two protons hit the same detector and by a vector joining the middle between the 2p hits and the point of a related heavy-ion hit, in analogy with the original Jacobi angle θk shown in the right panel of fig. 8. The typical theoretical prediction for such a distribution is shown in the right panel of fig. 8 as well. The diproton model predicts flat angular distributions in contrast to the experimental data in both cases. Only the three-body model can reproduce the characteristic shapes of the observed correlations with the broad bumps around cos(θk ) = 0 (the indicated spikes at cos(θk ) ≈ ±1 predicted by all calculations are less conclusive). Such a shape is a manifestation of the “Coulomb focusing” efficiently repulsing the fragments from large regions of the momentum space. These distributions are weakly sensitive to the assumed structure of the parent states but are an exclusive feature of the three-body model.

2.5 Measurements of radioactive lifetimes The decay vertex distributions derived from the measured trajectories of 2p-decay products were described in sect. 2.1. In the case of in-flight radioactivity measurements, prompt reactions and delayed decays should have different profiles of the respective vertexes. For the illustration purpose, a sketch of two ideal vertex profiles assuming a constant beam velocity across the target is shown in fig. 11a. The dissociation reaction of 20 Mg into the non-resonant 17 Ne+p+p+n continuum should have a

I. Mukha: Experimental studies of nuclei beyond the proton drip line . . .

Fig. 11. (Colour on-line) Profiles of the 2p-decay vertices along the beam direction with respect to the closest MSD. (a) Ideal profiles of prompt (blue line) and delayed (red curve) decays expected in a thick target. (b) Vertex distribution of 17 Ne+p+p events gated by the large p-17 Ne angles (i.e., by the large p-17 Ne energies), which corresponds to short-lived excited states in 19 Mg (black triangles with statistical uncertainties). The blue curve shows the simulations of the detector response ∗ for the prompt 2p decay 19 Mg → 17 Ne+p+p. (c) The same as 17 (b) but gated by the small p- Ne angles corresponding to the “ground state” of 19 Mg. The blue curve depicts a simulation of the prompt 2p decay. The red and black curves are fits to the data assuming a mixture of 25% of the prompt-decay component and 75% of the radioactivity component with T1/2 values of 4 and 8 ps, respectively. The insert shows the probability (as a function of the assumed half-lives) that the simulation histograms match the data.

uniform distribution within the target. The same profile is expected if highly excited, short-lived states of 19 Mg are populated and decay promptly. The population of the 19 Mg ground state and its subsequent (delayed) radioactive decay is expected to exhibit “grow-in” and “decay” curves along the beam direction corresponding to radioactivity; this is analogous to counting decay products as a function of time in a standard radioactivity experiment. In fact, the discussed vertex profile can be converted into a standard radioactivity time distribution by dividing vertex coordinates by a factor of 2p precursor velocity. The vertex profile of the delayed decay is expected to be broader and shifted downstream in comparison with the profile of prompt 2p emission. Due to the limited spatial resolution of the detectors and angular straggling of the decay products both idealized profiles are smeared in reality. Figures 11b and 11c show the experimental vertex profiles obtained from triple 17 Ne+p+p events gated by the

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conditions of “excited-state” and “ground-state” groups from fig. 7(a), respectively. These gates are inferred from the respective angular p-17 Ne correlations as discussed in the context of fig. 7(b) in sect. 2.3. The Monte Carlo simulations [21] of vertex profiles for the 2p decay of the “ex∗ cited state” 19 Mg → 17 Ne + p + p are shown in fig. 11b. The simulations assumed the prompt decays of the excited states of 19 Mg and took into account the above-mentioned experimental position uncertainties in tracking of the fragments and in reconstructing the decay vertices. The simulations reproduce the data with more than 90% probability, according to the statistical Kolmogorov test used in CERN [26]. The small asymmetry of the rising and falling slopes of the vertices is due to the multiple scattering of the fragments in the thick target. This vertex profile (the position of its centroid is marked by the blue vertical line) serves as the reference for estimating the position, width and longitudinal uncertainty of the measured vertex distributions. The uncertainty of its centroid along a beam direction of 0.05 mm has been derived. The vertex profile shown in fig. 11c was produced with the condition that both protons originate from the “ground state” of 19 Mg. The position of its centroid is marked by the red vertical line. This vertex distribution is more broad and it is shifted in downstream direction by about 1 mm in comparison with the reference case displayed in fig. 11b. The shift indicates unambiguously a delayed activity (the uncertainty of its centroid along a beam direction was estimated to be 0.1 mm). Its shape was fitted by a simulation of the 2p radioactivity of 19 Mg by assuming T1/2 = 3.1(10) ps. However, the observed vertex profile cannot be related to the 2p decay of the 19 Mg ground-state alone. The events selected as representing the “ground state” contain contributions from both the ground state and excited states of this nucleus. Therefore, using the angular-correlation data discussed above, a two-component fit of the observed vertex profile shown in fig. 11c was applied, with a mixture of 25% of the T1/2 = 0 component and 75% of the component with T1/2 = 4.0(15) ps. The corresponding fit describes the data with about 95% probability. The uncertainty of this result was defined by the half-life range where the experimental data are described by the simulation with probability above 50%. The possible systematic uncertainty of T1/2 due to the unknown shape of the T1/2 = 0 background was estimated by another fit of the 2p-decay vertices gated by the condition that only one proton belongs to the “ground state” gate in fig. 7(a). The contribution of the T1/2 = 0 component was then about 65%, and the derived T1/2 value of 19 Mg amounts to 6(+2 −4 ) ps. The deduced half-life is compatible with an upper limit of non-observation of 19 Mg (T1/2 < 22 ns) reported in ref. [27].

3 Information on proton-unbound nuclei: the 15 F example In the reviewed studies of 2p decay, information about 1punbound two-body subsystems, e.g., 15,16 F, 18,19 Na, was

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decay may be measured in-flight by detecting the triple Se+p+p coincidence following sequential 2p decays of 70 Kr∗ . 68

4 Summary and outlook

Fig. 12. (Colour on-line) Angular p-14 O distribution obtained from the data shown in fig. 6(a) by selecting the other proton angle from 120 to 150 mrad, which corresponds to p-14 O finalstate interactions due to the resonances in 15 F. The red and blue curves are the Monte Carlo simulations of the known 1p decays of the ground and first-excited states of 15 F with 1pdecay energies of 1.56(13) and 2.85(4) MeV, respectively [28]. The green and pink curves show the result of fits to the large-angle peaks of the p-14 O correlation, indicating unknown excited states in 15 F with 1p-decay energies of 4.9(2) and 6.4(2) MeV, respectively. The black line is the sum fit.

simultaneously obtained. This opened a way for systematic studies of proton-rich exotic nuclei beyond the proton drip line. The properties of such nuclei are important for understanding the element abundance in nature, providing input data for modeling the astrophysical rp-process. For example, fig. 12 displays the angular p-14 O distribution for “excited states” obtained from fig. 6(a) by selecting the angular range of the other proton from 120 to 150 mrad, which corresponds to high-energy continuum states in 16 Ne decaying to 14 O via the low-lying states in 15 F. The Monte Carlo simulation of known oneproton decays 15 F → 14 O + p of the ground and firstexcited states in 15 F with 1p-decay energies of 1.56(13) and 2.85(4) MeV [28] reproduces well the two smallestangle peaks. The two higher-lying peaks indicate 1p decays of unknown excited states in 15 F with derived 1pdecay energies of 4.9(2) and 6.4(2) MeV. Information on the excited states in 19 Mg, 16 Ne, 18 Na and 16 F can be obtained from the measured distributions as well. With the discussed technique, other exotic 1p-unbound nuclei can be studied. For example, properties of the unknown ground state of 69 Br are important for the nuclearastrophysics experiments studying the synthesis of elements during X-ray bursts in rapid proton capture reactions, especially on the N = Z waiting-point nucleus 68 Se (see, e.g., [7,29]). The 69 Br states can be detected in two-proton decays of excited states of 70 Kr produced in a secondary one-neutron knock-out reaction of a radioactive beam of 71 Kr which can first be made in primary fragmentation reactions of a primary beam of 78 Kr. Such a way of population is in analogy with the successful observation of the 15 F spectrum by using the chain of reactions ∗ 24 Mg → 17 Ne → 16 Ne → 15 F + p → 14 O + 2p. The 69 Br

The powerful method of measuring 2p decays in flight by tracking all fragments with micro-strip detectors allowed a breakthrough into a pico-second lifetime scale in studies of radioactivity. The method can provide new specific observables which yield valuable spectroscopic information on parent isotopes. For example, the measured threeparticle correlations from the 2p decays of the ground states of 16 Ne and 19 Mg are described quantitatively by the predictions of the three-body model [20], in contrast to the quasi-classical “diproton” model which fails to depict our observations. These correlations are sensitive to the structure of the decaying nucleus. Thus, the comparison between experiment and theory allows us to obtain spectroscopic information about the parent states. In 16 Ne, the data are consistent with strong s/d mixing [25]. In 19 Mg, the dominating d-shell configuration is the preferable description which is also consistent with the lifetime information [10]. Information about two-body subsystems, e.g., 15 F, is simultaneously obtained. Systematic studies of other 1p and 2p emitters predicted to live in a pico-second time scale [24,30] can be performed with this novel technique. The author is grateful to all co-authors who contributed to the S271 experiment performed at GSI, Darmstadt, Germany and to the corresponding publications [10, 11]. This work has been supported by the contracts EURONS No. EC-I3 and FPA200613807-C02-01 (MEC, Spain).

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