New states in 18Na and 19Mg observed in the two-proton decay of 19Mg

PHYSICAL REVIEW C 85, 044325 (2012) New states in 18Na and 19Mg observed in the two-proton decay of 19Mg I. Mukha,1,*L. Grigorenko,1,2,3L. Acosta,4M. A. G. Alvarez,5E. Casarejos,6,7A. Chatillon,1D. Cortina-Gil,6J. M. Espino,5 A. Fomichev,2J. E. Garc´ ıa-Ramos,4H. Geissel,1J. G´ omez-Camacho,5J. Hofmann,1O. Kiselev,1A. Korsheninnikov,3 N. Kurz,1Yu. A. Litvinov,1I. Martel,4C. Nociforo,1W. Ott,1M. Pf¨ utzner,1,8C. Rodr´ ıguez-Tajes,6,9E. Roeckl,1 C. Scheidenberger,1M. Stanoiu,1,10 K. S¨ ummerer,1H. Weick,1and P. J. Woods11 1GSI Helmholtzzentrum f¨ ur Schwerionenforschung, D-64291 Darmstadt, Germany 2Joint Institute for Nuclear Research, RU-141980 Dubna, Russia 3RRC “Kurchatov Institute,” RU-123184 Moscow, Russia 4Department of Applied Physics, University of Huelva, E-21071 Huelva, Spain 5University of Seville, E-41012 Seville, Spain 6University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain 7University of Vigo, E-36310 Vigo, Spain 8Faculty of Physics, University of Warsaw, PL-00681 Warszawa, Poland 9GANIL, CEA/DSM-CNRS/IN2P3, BP 55027-14076 Caen Cedex 05, France 10IFIN-HH, Post Office Box MG-6, Bucharest, Romania 11University of Edinburgh, EH1 1HT Edinburgh, United Kingdom (Received 7 February 2012; revised manuscript received 5 April 2012; published 30 April 2012) Previously unknown states in 18Na and 19Mg have been studied by measuring the trajectories of their decay products with microstrip detectors. Analyzing angular correlations of the fragments provided information on decay energies and widths of the parent states. The ground state of 18Na has been detected and its one-proton decay energy of 1.23(15) MeV determined. Four previously unknown states in 19Mg at 2.1, 2.9, 3.6, and 5.2 MeV have been observed. The competition between simultaneous and sequential two-proton emission of states in 19Mg is discussed, and the conclusion of a direct mechanism of 2pradioactivity of the 19Mg ground state is confirmed. DOI: 10.1103/PhysRevC.85.044325 PACS number(s): 21.10.−k, 21.45.−v, 23.50.+z, 27.20.+n I. INTRODUCTION Two-proton (2p) radioactivity, or the spontaneous decay of an atomic nucleus by 2pemission, has revealed unexpectedly long half-lives for all 2pprecursors investigated so far: 45Fe [1], 48Ni [2], 54Zn [3], 19Mg [4], and 94mAg [5]. The regular occurrence of long-lived 2pprecursors has been explained by a quantum-mechanical theory which describes 2pradioactivity on the basis of a three-body model [6] as simultaneous (ordirect)2pemission through large centrifugal three-body and Coulomb barriers. Experimental data on 19Mg [4]were obtained using an experimental technique to investigate decays of proton-unbound nuclei with lifetimes from 10−9to 10−12 s, as proposed by Mukha and Schrieder [7]. The trajectories of all decay products were tracked with microstrip detectors, making it possible to deduce their decay vertices as well as their angular correlations. Observation of 19Mg and its 2pradioactivity as well as proton-proton correlations from 2pdecays of 19Mg were reported [4,8]. All experimental data have been reproduced quantitatively by the three-body model, considering 19Mg as a p+p+17Ne system that decays by simultaneous 2pemission. In addition to the direct 2pdecay of the 19Mg ground state (g.s.), sequential emission of protons from excited states in 19Mg via intermediate states in 18Na, a twobody subsystem of 19Mg, is possible. To understand this *[email protected] mechanism quantitatively, information on the lowest states in 18Na is required. The first data on 18Na states were ambiguous, allowing the g.s. to be located either 0.42(17) or 1.27(17) MeV above the proton-decay threshold [9]. Recently, the spectroscopic properties of the unbound isotope 18Na were studied by the resonant-elastic-scattering reaction p+17Ne [10]. Four excited states in 18Na were identified while its g.s. remained undetected. The authors of Ref. [10] also proposed an explanation for the half-life value of the 19Mg g.s. in terms of sequential emission of protons via tails of broad excited states in 18Na. In the present article, we extend the analysis of the proton- 17Ne correlations from our 19Mg experiment [4,8]. In contrast to the previous works [9,10], we find unambiguous evidence for the identification of the g.s. of 18Na. We report also newly observed excited states in 19Mg, whose 1pdecays populate states in 18Na. The derived level schemes and decay branches are sketched in Fig. 1. We discuss the interplay of simultaneous and sequential 2pdecays of the 19Mg states and argue in favor of direct 2pemission from the 19Mg g.s. and sequential 2p emission from the excited states of 19Mg. II. EXPERIMENT In our experiment, a beam of 20Mg was produced by fragmentation of 24Mg at the projectile-fragment separator (FRS) [11] with an average intensity of 400 ions s−1and an energy of 450 AMeV. Nuclei of 19Mg were produced by 044325-1 0556-2813/2012/85(4)/044325(6) ©2012 American Physical Society I. MUKHA et al. PHYSICAL REVIEW C 85, 044325 (2012) FIG. 1. The observed states in 19Mg and 18Na whose energies (in MeV) are shown relative to the respective 1pand 2pthresholds. The main and the minor 19Mg→18Na +pbranches are indicated by dashed and dotted arrows, respectively. The spins and parities given in parentheses are tentative assignments. The energy of 18Na(3−)is taken from Ref. [10]. secondary fragmentation of 20Mgona2g/cm2thick 9Be target positioned in the midplane of the FRS. A sketch of the detectors near the latter target is presented in Fig. 1of Ref. [12]. A silicon detector array was positioned downstream of the target. It consisted of four large-area microstrip detectors that measured positions of coincident hits of two protons and a heavy ion (HI). This allowed the reconstruction of all fragment trajectories as well as deriving the coordinates of the corresponding reaction vertex and the angular p-pand p-HI correlations with an angular resolution of 1 mrad. The experimental setup and the data-analysis procedures were recently presented in detail (see Ref. [12]). In particular, we have shown how identification of 2p-precursor states and their decay energies and widths can be obtained from analyzing angular correlations of the decay products. The known properties of four states in 15F, 16Ne, and 19Na were reproduced. Below we re-evaluate our data on direct and sequential decays of 19Mg. III. EXPERIMENTAL RESULTS The identification of the 19Mg g.s. and the measurement of its 2pdecay energy were performed by analyzing angular correlations of protons with respect to 17Ne. Such angular correlations are similar to transverse momentum correlations which are normally used to identify nuclear states and their decay channels [12]. We assumed that all measured channels feed only the g.s. of 17Ne (i.e., no evidence for excitations of the 1.288-MeV state in 17Ne which de-excites by γray emission was found). In the top panels of Figs. 2(a) and 2(b), simultaneous and sequential 2pdecays are shown schematically while the bottom panel illustrates the respective momentum correlations as obtained in our experiment. The 2pdecays of narrow states are arranged along arcs with radius ρ=θ2 p1−Ne +θ2 p2−Ne =const, since two protons share the same total decay energy. This feature can be used to select certain 2p-precursor states, as we have previously demonstrated on 2pdecays of the known states in 16Ne [12]. The measured angular correlations θ(p1-17Ne)-θ(p2-17Ne) shown in Fig. 2(c) display several distinct clusters of events that apparently resemble the schemes displayed in Figs. 2(a) (a) A A-1 A-2 k k p - HI (arb. units) k k p - HI (arb. units) k k p - HI (arb. units) (b) A A-1 A-2 (c) FIG. 2. (Color online) Schematic drawing of transverse momentum correlations kp1-HI-kp2-HI in panels (a), (b) expected for two alternative mechanisms of 2pdecay (illustrated in the respective top panels) from a parent nucleus Ato a daughter nucleus A-2: (a) direct three-body decay or simultaneous 2pemission, (b) sequential emission of protons via a narrow intermediate state in nucleus A-1. (c) Measured angular (p1-17Ne)-(p2-17Ne) correlations (color boxes with scale shown on the right-hand side). The shadowed arc areas (i–iv) (along ρ=const) indicate locations of simultaneous or sequential 2pdecays of the most intensively populated states in 19Mg. and 2(b). In our previous work [4] the small-angle events around θ(p-17Ne) =30 mrad were attributed to the 19Mg g.s., while those at larger angles, above 45 mrad, were tentatively ascribed to a single excited state in 19Mgwitha2p-decay energy of 3.2 MeV. We argue below that the most intense groups may be assigned to sequential 1pdecays of four excited states in 19Mg via low-lying states in 18Na, including, in particular, its g.s. In the first step of the data analysis, we consider angular correlations obtained by gating on angular p2-17Ne slices in a way similar to that of Ref. [4]. Figure 3shows the p1-17Ne correlations obtained by restricting θp2-Ne as indicated on top of each spectrum. The un-gated distribution displayed in Fig. 3(a) shows two intense peaks around 30 and 55 mrad, which we interpret as being due to the “g.s.” and “excited state(s)” (“ex.s.”). Figure 3(b) shows the p1-17Ne correlations corresponding to the lowest g.s. peak in the other pair p2-17Ne. The contribution from the g.s. peak dominates, whereas the ex.s. peak is suppressed, in contrast to the ungated distribution 044325-2 NEW STATES IN 18Na AND 19Mg OBSERVED IN ... PHYSICAL REVIEW C 85, 044325 (2012) FIG. 3. (a) Angular p1-17Ne correlations (solid circles with statistical uncertainties) obtained from the measured 17Ne +p+p data shown in Fig. 2(c) without imposing any gate condition. (b) Angular p1-17Ne distribution obtained from the same data by selecting the other proton angle, θp2-Ne,withintherangefrom10to36mrad, which corresponds to the assumed g.s. of 19Mg. The solid curve represents the Monte Carlo simulation of the detector response to 19Mgg.s. →17Ne +p+pwith a 2p-decay energy of 0.75(5) MeV. The histogram represents the assumed background deduced from the data for a θp2-Ne gate from 110 to 180 mrad; it contributes 15% to the peak at angles from 10 to 36 mrad. (c) Angular p1-17Ne distribution projected by choosing the θp2-Ne gatefrom65to180mrad.Thesolid line is the simulation of the final-state interaction of protons with 17Ne due to the 1.55-MeV resonance in 18Na. displayed in Fig. 3(a). Therefore, the g.s. and ex.s. peaks cannot be explained by emission of protons from one and the same state in 19Mg because in this case both peak integrals should be equal. Moreover, the ex.s. decay always occurs when the second proton is emitted under a large angle with respect to 17Ne [see Fig. 3(c)], which is equivalent to large excitations in 19Mg. The qualitative explanation of this behavior is that the “excited state” peak is due to a 18Na resonance occurring in the p1-17Ne pair. The experimental data are compared to Monte Carlo simulations, assuming two decay mechanisms: (i) simultaneous or direct 2pdecay 19Mg →17Ne +p+paccording to the predictions of the three-body model [13] and (ii) sequential emission of protons from 19Mg via one of the low-lying 18Na levels identified in [10]. In both cases, the 2p-decay energies were obtained by fitting the peaks in the experimental spectra. The peak around 30 mrad in Fig. 3(b) is described by the direct 2pdecay with Q2p=0.75(5) MeV. The peak around 55 mrad in Fig. 3(c) can be interpreted as sequential emission of protons from continuum excited states in 19Mg (9 <Q2p<15 MeV) to a single narrow 18Na state which decays by emission of a 1.5-MeV proton. The latter assumption is based on final-state interaction of protons with 17Ne and is justified by the newly identified 2−resonance in 18Na at 1.55 MeV [10]. As can be seen from Fig. 3(c), the whole spectrum is not described by assuming a single 18Na state, and further analysis of the exclusive data is needed. FIG. 4. (Color online) Angular p-17Ne correlations (solid circles with statistical uncertainties) selected from the 17Ne +p+pdata by choosing the arc gates (i–iv) shown in Fig. 2(c).(a)The2pdecay of the 19Mg g.s. selected by gate (i), that is, the condition 20 <ρ< 45 mrad. The solid curve shows the best-fit simulation of the three-body model using a 2p-decay energy of Q2p=0.76(6) MeV. (b) The 2pdecay of the 19Mg “first-excited” state selected by the gate (ii), 50 <ρ<65 mrad. The solid curve displays the simulation of the sequential 2pdecay of the state at 2.14 MeV via two intermediate states in 18Na, the g.s. at Q1p=1.23 MeV (dash-dotted line), and the 2−state at 1.55 MeV (dashed line). (c) The 2pdecay of the “second-excited” state in 19Mg selected by gate (iii), 65 <ρ< 80 mrad. The solid line is the best-fit simulation of the sequential 2p decay of the 19Mgstateat2.9MeVviathe2 −and 3−states in 18Na (the dash-dotted and dashed curve, respectively). (d) The 2pdecay of the suggested high-lying state in 19Mg at Q2p=5.5 MeV selected by gate (iv), 90 <ρ<115 mrad. The solid curve represents the best-fit simulation of the decay of this state by sequential 1pemission via 18Na∗(2−). (e) Angular p-17Ne correlations selected by choosing the arc gate between areas (iii) and (iv) shown in Fig. 2(c), that is, the condition 80 <ρ<90 mrad. The dashed curve shows the simulation of the sequential 2pdecay of the suggested excited state in 19Mg via 18Na∗(2−), with the fitted values Q2p=3.6(2) MeV and < 0.2 MeV. The dash-dotted curve represents the contribution due to the 2pdecay of the neighboring 19Mg state at Q2p=5.5MeV.The solid curve is the sum fit. 044325-3 I. MUKHA et al. PHYSICAL REVIEW C 85, 044325 (2012) TABLE I. Nuclear levels observed in this work, listed according to isotope, tentative spin-parity Jπassignment, decay channel, 1p/2p decay energy Qexp, and width exp (the latter two given in MeV). Isotope JπDecay Qexp exp Reference 18Na (1)−17Ne +p1.23(15) <0.2 This work 18Na ? 17Ne +p1.27(17) 0.54(13) [9] 18Na 2−17Ne +p1.55(7) 0.25(−15 +25) This work 18Na 2−17Ne +p1.552(5) 0.005(3) [10] 19Mg 1/2−17Ne +p+p0.76(6) 1.14 ×10−10 This work 19Mg (3/2−)17Ne +p+p2.14(23) 0.4(2) This work 19Mg (5/2−)17Ne +p+p2.9(2) 0.6(−4 +6) This work 19Mg (3/2−)17Ne +p+p3.6(2) <0.2 This work 19Mg (3/2−)17Ne +p+p5.5(2) 2.0(8) This work The second step of the data analysis considers angular p-17Ne correlations obtained by selecting arc gates along ρ=const. This method is similar to that applied to 16Ne [12]. The chosen gates are shown in Fig. 2(c). The angular p-17Ne correlation displayed in Fig. 4(a) corresponds to a selection by the lowest arc gate (i), which picks out the g.s. of 19Mg. Under this condition, one observes exclusively the peak due to the g.s. of 19Mg, while the background component is reduced dramatically in comparison with Fig. 3(b).The peak fit performed by assuming the direct 2pdecay of the 19Mg g.s. and neglecting the background contribution yields Q2p=0.76(6) MeV. The angular p-17Ne correlations shown in Figs. 4(b),4(c), and 4(d) were obtained by imposing the larger-arc gates (ii), (iii), and (iv) indicated in Fig. 2(c). They correspond to 2p decays of three excited states in 19Mg. Indications on these intensively populated levels can be observed in Fig. 2(c).The two cases which are easiest to interpret are marked by arc areas (iii) and (iv). In both cases the corresponding p-17Ne correlations show pronounced peaks which we interpret as signatures for 2pdecays from a single state in 19Mg. In both spectra displayed in Figs. 4(c) and 4(d), one of the peaks occurs at the same p-17Ne angle of 55 mrad, which makes sense only for sequential emissions of protons via the same resonance in 18Na. These spectra were fitted by assuming decays 19Mg∗→18Na +p→17Ne +p+pwith four fit parameters corresponding to Q2p(19Mg∗), (19Mg∗) and Q1p(18Na), (18Na). The parameters obtained in both cases for the 18Na resonance are Q1p=1.55(7) MeV and =0.25(−15 +25) MeV, which match the 2−state at 1.55 MeV [10]. For a quantitative reproduction of the spectrum shown in Fig. 4(c), an additional branch (about 25%) via the known 3− state at 2.084 MeV [10] has to be postulated. The properties of the respective parent states in 19Mg at 2.9 and 5.5 MeV are given in rows 7 and 9 of Table I. Evidence for one more excited state in 19Mg can be seen in Fig. 2(c), where there are peaks indicated in the area 80 <ρ<90 mrad, between gates (iii) and (iv). Figure 4(e) presents the angular correlations selected correspondingly. For a quantitative reproduction of the data, two components are needed. The first one is the sequential 2pdecay of the above-mentioned broad 5.5-MeV state via 18Na(2−), whose low-energy tail describes about half of the spectrum. To account for the rest of data, the sequential 2pdecay of an additional state in 19Mg via 18Na(2−) has to be involved. It should be very narrow and is located at Q2p=3.6(2) MeV, as shown in row 8 of Table I. Evidence in favor of the 18Na g.s. was obtained in the decay of the lowest-lying excited state in 19Mg, which is indicated in Fig. 2(c) by arc area (ii). Though these events are not very well separated from the neighboring ones marked by arc (iii), the respective 2p-decay patterns are distinctively different, which can be seen by comparing the respective p-17Ne correlations showninFigs.4(b) and 4(c). The distribution from the 2p decay of the “first-excited state” of 19Mg [Fig. 4(b)] is much broader and does not show any indication of the 1.5-MeV peak which is present in the “second-excited state” 2pdecay spectrum in Fig. 4(c). Such a structure cannot be explained by sequential 2pdecay via any previously known state in 18Na. Thus, the existence of a new level in 18Na has to be suggested. Its properties were derived by fitting the p-17Ne correlations shown in Fig. 4(b), assuming sequential 2pdecay of an unknown state in 19Mg via an unknown intermediate state in 18Na. The parameters of the 18Na resonance derived from a four-parameter fit are listed in row 1 of Table Itogether with the properties (in row 6) of the respective parent state in 19Mg at 2.14 MeV. An additional 2pdecay branch via the 2−state in 18Na is needed to describe the correlations in Fig. 4(b) quantitatively; its relative weight is 35%. The inferred 1p-decay energy of 1.23(15) MeV is slightly lower than the value of 1.3 MeV preliminarily deduced in our previous publication [4] and is close to the 1.27(17)-MeV assignment of the 18Na g.s. suggested tentatively in the invariant-mass measurements [9]. The corresponding mass excess of the 18Na g.s. is therefore 25.02(15) MeV. We note that there is no evidence in our spectra for the other 1ppeak at Q1p=0.42(16) MeV proposed in Ref. [9]. The difference between the experimentally measured mass of 18Na and the corresponding mass predicted by using charge conjugation of its mirror state in 18N (on the basis of charge-symmetric mass relationships [14]) is M(Z,N)=−395(150) keV, which matches reasonably the systematics of proton-unstable nuclei where the average value M(Z,N)=−577(325) keV displays a general shift of the Thomas-Ehrman type [14]. IV. DISCUSSION The theoretical predictions of the g.s. mass and low-lying structure of 18Na are ambiguous. Both shell-model [10,15] 044325-4 NEW STATES IN 18Na AND 19Mg OBSERVED IN ... PHYSICAL REVIEW C 85, 044325 (2012) and relativistic mean-field calculations [16] predict the lowest 0−,1 −, and 2−states to be unbound with decay energies of ∼1.5 MeV. However, they have quite different sets of spectroscopic factors within a configuration space of a proton in the 1d5/2shell coupled to 17Ne, which itself is a mixture of (sd)2and [(sd)2(1p)−1] configurations. The two lowest 1−and 2−states were predicted to be separated by about 200 keV. In Ref. [10], the 2−state in 18Na was identified at 1.552(5) MeV leaving 1−as the only possible assignment for the g.s. of 18Na. Its width was predicted to be 22 keV [10], which is consistent with the upper limit of 200 keV determined in our work. The information obtained on 18Na [10] can be used for assigning tentative Jπvalues to the newly observed 19Mg levels. In particular, the measured width of 0.4 MeV for the 2.14 MeV state in 19Mg and its decay branches agree only with an assignment of Jπ=3/2−because it preferably decays by emitting a proton with an angular momentum of p=0to the 1−and 2−states in 18Na. The corresponding upper-limit estimate (Wigner limit) for the partial proton width yields about 0.1–0.3 MeV. All other spin parities would correspond to p>0 and result in much smaller Wigner limits. Similar considerations lead to the 5/2−assignment for the 2.9-MeV state in 19Mg because it decays predominantly to the 2−and 3−states in 18Na but not to its 1−state. A comparison of the mirror nuclei 19N and 19Mg also supports the 3/2−and 5/2−assignments for the 2.14- and 2.9-MeV states in 19Mg, respectively: The first two excited 3/2−and 5/2−states in 19N are at excitation energies of 1.141 and 1.676 MeV, respectively [17]. We suggest that these levels arise from the coupling of ap1/2neutron hole to the first 2+state of the 20Mg core, in analogy to the conclusion drawn for the (tentative) mirror states in 19N[17]. We note that the possible intense 5/2− excitation of 19Mg is a surprising result for reactions of oneneutron knockout from 20Mg where neutrons are mostly in p1/2and p3/2configurations; this requires further studies. The high-lying excited state in 19Mg at 5.5 MeV emits a proton to 18Na(2+) with the Wigner-limit estimates for its width of 4.6, 2.8, and 0.85 MeV for pof 0, 1, and 2, respectively. This excludes d-wave proton emission, which leaves tentative Jπ of 1/2+,3/2−,5/2−,7/2 +, for the 5.5-MeV state. We compared the observed excitations in 19Mg with shell-model calculations. As we have observed only the 19Mg states which are most-intensively populated in one-neutron removal reactions from 20Mg projectiles, configurations of those states are likely to have large overlaps with the 20Mg g.s. In particular, one-neutron removal from p1/2and p3/2shells can populate 1/2−and 3/2−states in 19Mg, respectively. We calculated the respective spectroscopic factors in the spsdpf -shell space with the WBP interaction of Warburton-Brown [18]usingtheNUSHELL@MSU code [19], and the results are summarized in Table II. From Table II one can see that the g.s. and three excited states of 19Mg are populated strongly. The properties of the first excited state 3/2−in 19Mg, its decay energy and decay branches are reproduced well though the theory does not agree with the data at higher energies, and further investigations are needed. As a final topic, we want to address the question if the observation of broad resonances in 18Na [10] requires TABLE II. Nuclear levels in 19Mg most intensively populated in one-neutron knock-out from 20Mg projectiles according to shellmodel calculations. The 19Mg states are listed according to spin parity Jπ, spectroscopic factor C2Sof overlap 19Mg |20Mg, calculated 2p-decay energy QSM 2p(given in MeV), and partial width i(given in MeV) of a 2p-decay branch ivia the Jπ istate in 18Na. JπC2SQ SM 2pi18Na(Jπ i) 1/2−2.18 0.76a–– 3/2− 10.57 2.44 0.186 1− 0.054 2− 3/2− 20.38 4.35 0.25 1− 0.02 2− 3/2− 30.35 5.21 large 1−,2 − 0.134 1− 2 0.030 2− 2 0.028 3− aThe 2pdecay energies of the 19Mg states are normalized to the experimental value of the 19Mg g.s. reinterpreting the direct (three-body) character of the 2pdecay of the 19Mg g.s. Assie et al. [10] suggest that the 19Mg g.s. decays sequentially via the tails of the broad intermediate resonances in 18Na at 1.84 MeV (Jπ=0−,=0.3 MeV) and 2.03 MeV (Jπ=1−,=0.9 MeV). The essential condition for the sequential-decay mechanism is that the first-emitted proton and the intermediate 18Na state are separated in space before the subsequent decay of this state occurs. Otherwise, the 19Mg decay should be treated as simultaneous 2pemission or direct three-body decay. Goldansky [20] has suggested as a criterion for the direct decay that Q2p+r/2<E r, where Erand rare the energy and the width of the intermediate resonance, respectively. This is clearly fulfilled in our case. The same conclusion was reached in a recent review where the competition between simultaneous and sequential 2pdecay was investigated (see Chap. VII.C.3 in [21]): Any resonance in 19Mg below Q2p=1.5 MeV should decay by direct 2p emission. To illustrate further the interplay between sequential and direct 2p-decay mechanisms, we have performed more calculations within the above-mentioned three-body model for 2pdecays of the 19Mg g.s., which includes both direct and sequential emission mechanisms [22]. For simplicity, we assume only one intermediate resonance in the p+17Ne subsystem. We calculate proton-energy distributions in terms of the parameter ε∼Ep/ET, which describes how the two protons share the total decay energy ET(for a fixed value of Er). Figure 5(a) shows our results for the case that the intermediate resonance represents a state in 18Na with Jπ=1−at Er=1.23 MeV, with a narrow width r=0.1MeV.Atlow energies, the decay protons share the total energy ETin a broad region always centered around ε=0.5, which is a typical feature of the simultaneous (direct) 2pdecay. A sequential decay should manifest itself in the observation that the energy of one proton peaks near and below 1.23 MeV. Such a feature is not present in Fig. 5(a). However, at ET≃1.2·Erone can see a dramatic change of the proton-energy distributions which are 044325-5 I. MUKHA et al. PHYSICAL REVIEW C 85, 044325 (2012) 0.0 0.2 0.4 0.6 (a) 0.8 1.0 ε (b) 0.0 0.2 0.4 0.6 ε 0.8 1.0 FIG. 5. (Color online) Intensity distributions of 2pdecays from 19Mg (arbitrary yields corresponding to the color scale shown on the right-hand side) as a function of the total 2p-decay energy ETand the parameter ε∼Ep/ET. The distributions are calculated with a three-body model assuming a single resonance in the intermediate nucleus 18Na with energy Erand width r. (a) Decays by taking into account the g.s. of 18Na at Er=1.23 MeV with r=0.1 MeV. (b) Decays via the 1− 2state in 18Na at Er=2.03 MeV, r= 0.9MeV[10]. characterized by two distinct and intense peaks corresponding to sequential 2pemission via the 18Na state. With increasing ET, the 1.23-MeV peak represents a decreasing fraction of ET; that is, its position moves along the right narrow ridge toward the left-hand side. The first-emitted proton peak moves complementarily toward the right-hand side. At ET≃2·Er, the proton energies are equal, which is a special case of undistinguishable decay channels. Such a situation requires a separate detailed consideration elsewhere. In Fig. 5(b), we display a similar distribution where now the intermediate resonance in 18Na is assumed to be a broad state (r=0.9MeV)atEr=2.03 MeV, in accordance with the results of Ref. [10]. Though the detailed structure of the distribution is washed out (due to the large width of the intermediate state), one can recognize a general trend similar to the previous case, with two regions corresponding to direct and sequential decays. We conclude from these schematic calculations that in the case of the 19Mg g.s., where ETEr, the direct 2p-emission mechanism dominates while the observed excited states decay sequentially via 18Na. In summary, the unbound g.s. of 18Na and three new excited states in 19Mg have been deduced from the measured angular correlations of their decay products. The data yielded the decay energies and widths of these states. Schematic model calculations support the direct three-body decay mechanism for the g.s. and sequential proton emission for the excited states of 19Mg. ACKNOWLEDGMENTS The authors are grateful to N. K. Timofeyuk for the shell-model calculations and constructive discussions of the data. This work has been supported by Contract EURONS No. EC-I3, FPA2006-13807-C02-01 MEC, and FPA2009-08848 MICINN (Spain). L.V.G. is supported by the FAIR-Russia Research Center by Grants RFBR No. 08-02-00892 and RFBR No. 11-02-00657, Russian Ministry of Industry and Science Grant No. NSh-7235.2010.2, and by the LOEWE program of the State of Hessen (HIC for FAIR), Germany. [1] K. Miernik et al.,Phys.Rev.Lett.99, 192501 (2007). [2] M. Pomorski et al.,Phys.Rev.C83, 061303 (2011). [3] B. Blank et al.,Phys.Rev.Lett.94, 232501 (2005). [4] I. Mukha et al.,Phys.Rev.Lett.99, 182501 (2007). [5] I. Mukha et al.,Nature (London) 439, 298 (2006). [6] L. V. Grigorenko, R. C. Johnson, I. G. Mukha, I. J. Thompson, and M. V. 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