PLB140601140601S0370-2693(26)00453-310.1016/j.physletb.2026.140601The AuthorsFig. 1Spectra of oxygen, fluorine, and neon isotopic chains with A=12−16. All energies are given with respect to the 8C core. The energies are given in MeV. Experimental data are taken from Ref. [20] for 13F, Ref. [18] for 14F, Ref. [13] for 15F, Ref. [25] for 15Ne, and Refs. [21,70] for 16Ne. The low-lying states of the oxygen isotopes are taken from [63].Fig. 1 dummy alt textFig. 2Calculated low-lying states in 16Ne, 15F and 14O, compared with experimental data taken from Ref. [13] for 15F and Refs. [21,70] for 16Ne. Energies are given in MeV relative to the ground state of 14O. For the resonant state, the box width indicates the decay width (Γ) in units of keV.Fig. 2 dummy alt textFig. 3The spectra of low-lying states in 15Ne, 14F and 13O, shown relative to the ground state of 13O. The presentation is similar to that of Fig. 2. Experimental data are taken from Ref. [18] for 14F and Ref. [25] for 15Ne.Fig. 3 dummy alt textFig. 4The spectra of low-lying states in mirror pair 14F/14B. The excitation energies are related to the ground state. Experimental data of 14B is taken from Ref. [73].Fig. 4 dummy alt textFig. 5The spectra of low-lying states in 14Ne, 13F, 12O, 11N and 10C, shown relative to the 10C ground state. The presentation is similar to that of Fig. 2. Experimental data are taken from Ref. [20].Fig. 5 dummy alt textTable 1Binding energies (relative to the 8C inert core, in MeV) and widths (in keV) of the selected states of A=11−15 nuclei used to optimize the GSM Hamiltonian, with experimental values from [63].Table 1 dummy alt textNucleusStateEEexpΓΓexp11N1/2+−33.886−34.1221343830(30)11N1/2−−33.400−33.392459600(100)12N1+−49.046−49.22412O0+−33.701−33.76813O3/2−−50.753−50.72714O0+−74.094−73.91214F2−−49.087−49.174617910(100)15F1/2+−72.561−72.659265660(20)15Ne3/2−−48.563−48.280590Table 2Optimized parameters of the EFT interaction at leading order (LO) and next-to-leading order (NLO) in natural units.Table 2 dummy alt textLO constantCS0CS1LO value−0.40−0.49NLO constantC1C2C3C4C5C6C7NLO value0.434.420.78−3.64−4.261.813.66Table 3The calculated average occupations of the proton and neutron partial waves for the low-lying states.Table 3 dummy alt textNucleusStateπp3/2πp1/2πs1/2πd5/2πd3/2νp3/2νp1/214O01+0.011.440.240.270.043.830.1715F1/21+0.011.591.100.270.043.840.165/21+0.011.610.181.160.043.820.1816Ne01+0.021.661.590.670.063.840.1621+0.011.780.971.190.043.830.1713O3/21−0.021.320.300.310.052.910.091/21+0.010.990.970.030.002.910.0914F21−0.021.581.020.320.062.920.0811−0.021.600.990.340.062.920.0831−0.021.500.271.170.042.910.0941−0.011.450.281.210.042.910.0915Ne3/21−0.031.591.600.700.082.920.085/21−0.021.740.961.220.062.910.0912O01+0.021.130.450.350.051.870.1302+0.0040.611.370.020.0021.870.1313F1/21+0.011.421.170.340.051.880.121/21−0.011.621.130.210.021.880.125/21+0.011.150.511.290.031.880.1214Ne01+0.031.551.680.660.081.880.12LetterProbing exotic multi-proton emitters: A Gamow shell model study of proton-rich fluorine and neon isotopes beyond the drip lineProbing exotic multi-proton emitters: A Gamow shell model study of proton-rich fluorine and neon isotopes beyond the drip lineN.ChenabJ.G.Li⁎abcjianguo_li@impcas.ac.cnM.R.XieabP.Y.WangdaK.H.LiaeQ.YuanabN.MichelabaState Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000, ChinaState Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences Lanzhou 730000 ChinaState Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000, ChinabSchool of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing, 100049, ChinaSchool of Nuclear Science and Technology, University of Chinese Academy of Sciences Beijing 100049 ChinaSchool of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing, 100049, ChinacSouthern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, Huizhou, 516000, ChinaSouthern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences Huizhou 516000 ChinaSouthern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, Huizhou, 516000, ChinadAdvanced Energy Science and Technology Guangdong Laboratory, Huizhou, 516007, ChinaAdvanced Energy Science and Technology Guangdong Laboratory Huizhou 516007 ChinaAdvanced Energy Science and Technology Guangdong Laboratory, Huizhou, 516007, ChinaeCollege of Physics, Henan Normal University, Xinxiang, 453007, ChinaCollege of Physics, Henan Normal University Xinxiang 453007 ChinaCollege of Physics, Henan Normal University, Xinxiang, 453007, China⁎Corresponding author.Editor: Silvia Monica LenziAbstractWe investigate proton-rich systems beyond the proton drip line, focusing on the notably poorly known 13F and 15Ne and the yet unobserved 14Ne, whose structure properties remain weakly constrained. Using the Gamow shell model (GSM), which consistently incorporates both inter-nucleon correlations and couplings to the particle continuum, we study oxygen, fluorine, and neon isotopes with mass A=12−16. Taking 8C as an inert core, the GSM Hamiltonian based on an effective field theory nucleon-nucleon interaction is optimized for this proton-rich region. The constructed Hamiltonian reproduces the low-lying spectra and decay properties of fluorine and neon isotopes beyond the proton drip line. We quantify many-body configuration and average partial-wave occupancies to elucidate the structural evolution of the drip line nuclei 12–14O, 13–15F, and 14–16Ne. In particular, multi-proton separation energies and spectroscopic factors are analyzed in detail, leading to a prediction for the unresolved ground state of 13F. Furthermore, the candidate 4p emitter 14Ne is theoretically predicted for the first time, providing valuable guidance for future experimental investigations.KeywordsNuclei beyond proton drip lineMulti-proton emissionsGamow shell modelContinuum coupling,Data availabilityData will be made available on request.1IntroductionDrip lines mark the stability limit against particle emission [1–5]. Extremely proton-rich isotopes lying well beyond the proton drip line, such as 13F, 15Ne, and 16Ne, are unbound and decay through multi-proton emission, since no intermediate proton-bound isotopes exist along their proton-emission chains. These proton-emission processes provide valuable insight into the exotic nuclear structure [6–9].The lightest particle-stable nuclei of the oxygen, fluorine, and neon chains are 13O, 17F, and 17Ne, respectively. Numerous isotopes lighter than those isotopes have been established in experiment. In the fluorine chain, 15F, located two neutrons beyond the proton drip line, was first investigated in Refs [10,11]. Then, numerous experimental investigations of 15F were performed, including transfer reaction [12] and elastic resonance scattering in inverse kinematics [13–17]. Further beyond the proton drip line, 14F was first explored through 13O+p resonance scattering [18], and its structure was later investigated using the invariant-mass method [19]. Experimentally, the 3p decay of 13F, which lies four neutrons beyond the proton drip line and ultimately leads to the particle-stable nucleus 10C, has been observed via a charge-exchange reaction [20]. In the neon isotopic chain, 16Ne have been extensively studied through various reaction channels, such as neutron-knockout reactions from 17Ne [21], the 20Ne(4He, 8Li)16Ne transfer reaction [10,22], and pion double-charge exchange reactions [23,24]. The 15Ne was first observed by two-neutron knockout reactions from a 17Ne beam [25].Theoretical models have been employed to investigate unbound proton-rich F and Ne isotopes. Using the potential model, the low-lying resonances in 13F [26], 14F [27] and 15F [28] have been calculated. The low-lying states of 15F have been extensively analyzed through elastic scattering reaction, using approaches such as the resonating group method [29], the multichannel algebraic scattering theory [30], and the coupled-channel Gamow shell model [17]. Moreover, the Gamow shell model (GSM) has also been applied to study 15F and 16Ne [31–33]. Additional theoretical efforts include the ab initio no-core shell model calculation for 14F [34], the S-matrix pole method for 15F [35], the analytic continuation in the coupling constant [36] for 16Ne, and the microscopic three-cluster model in the generator coordinate method for 15Ne [37]. However, systematic investigations of remote isotopes beyond the drip line remain scarce. To date, 14Ne has not been observed experimentally. Furthermore, theoretical studies of nuclei in the vicinity of 13F remain scarce; in particular, microscopic calculations for 13F itself are virtually nonexistent. Therefore, applying state-of-the-art theoretical models to these extremely proton-rich systems is essential for understanding their exotic properties.Nuclei beyond the drip lines belong to open quantum systems, for which particle emission channels are energetically accessible, and continuum coupling becomes unavoidable [6,38,39]. In such systems, continuum effects and inter-nucleon correlations are strongly intertwined and can qualitatively influence nuclear observables. Accurately incorporating these ingredients into a unified many-body description constitutes a major challenge for traditional bound-state nuclear structure models [40,41].Among available theoretical approaches, the GSM [42–47] provides a powerful extension of the traditional shell model to the open quantum system. Building upon the Berggren ensemble [48,49], the GSM employs a completeness relation in the complex-energy plane. Both many-body correlations and continuum coupling are well treated in the GSM calculations. Consequently, it is particularly well suited for weakly bound and unbound nuclei, where phenomena such as halo structures and resonances are prominent. Over the past few years, the GSM has been successfully applied to a wide range of unbound systems and drip line nuclei, demonstrating its predictive power for spectra, widths, and correlation patterns [43,50–55].In the present work, we perform systematic theoretical calculations for the proton-rich Ne, F, and O isotopes using the GSM. The low-lying spectra and decay properties of 12−14O, 13−15F, and 15,16Ne are presented, along with the calculated multi-proton separation energies. Moreover, we analyze the average occupations of different partial waves and the corresponding spectroscopic factors, revealing the role of continuum coupling in shaping the underlying configurations. Furthermore, our calculations predict the unbound nature of 14Ne, providing useful insights for future experimental investigations.2MethodThe GSM employs the one-body Berggren basis [48,49], constructed from a finite-depth potential and comprising bound, resonant, and scattering states, which satisfies the completeness relation for each (l, j) partial wave:(1)∑n|unlj〉〈unlj|+∫L+|uklj〉〈uklj|dk=1^,where |unlj⟩ represents a bound or resonant state, while |uklj⟩ denotes a scattering state along the complex contour L+. All the discrete resonant states in Eq. (1) must be enclosed within the L+ contour. To obtain an eigenproblem analogous to that of the traditional shell model, the L+ contour is discretized using a Gauss–Legendre quadrature [39]. The many-body completeness relation then follows by constructing Slater determinants from the one-body Berggren basis states. The GSM Hamiltonian matrix, which is complex symmetric, is diagonalized using the Jacobi-Davidson method [56,57]. And the resonant states among the many-body continuum state are selected using the overlap approach [53,58]. More details about the GSM framework have been thoroughly explained in Ref. [39,42].The GSM works in a core + valence nucleons framework. The GSM Hamiltonian in the intrinsic nucleon-core cluster orbital shell model (COSM) coordinates [59], can be written as:(2)H^=∑i=1Nval(p^i22μi+U^core(i))+∑i<jNval(V^(i,j)+p^i·p^jMcore),where Nval is the valence nucleons number, μi is the reduced mass of the ith nucleon and Mcore is the mass of the core. The potential U^core denotes the one-body core-nucleon potential, and V^(i,j) is the two-body interaction between valence nucleons. The last term represents the two-body recoil term.In this work, 8C is used as the inert core. While 8C is unbound, its decay width is very narrow (only 130 keV). In the studied nuclei (12−14O, 13−15F, and 14−16Ne), at least two valence protons and two valence neutrons are present. The core’s instability is then mitigated when valence nucleons are added. So the 8C core is effectively bound and inert within a core + valence nucleons framework. The choice of an unbound core is not unprecedented in GSM, for example, 28O was used as the core in previous calculations of 39Mg [60]. For proton-rich nuclei beyond 8C, it is sufficient to restrict the neutron valence space to the harmonic oscillator (HO) p partial waves. The proton valence space is represented by the Berggren basis, which contains the S-matrix poles 0p1/2, 1s1/2, and 0d5/2, as well as the complex contours of the p1/2, p3/2, s1/2, and d5/2 partial waves. The d3/2 partial wave is generated from the HO basis, as its larger centrifugal barrier leads to weaker continuum effects. The full configuration space is prohibitively large and needs to be truncated to render GSM calculations feasible. The GSM calculation using a natural orbital basis is adopted to reduce computational cost and improve convergence. We first performed a GSM calculation within the Berggren basis, and the obtained one-body density matrix is diagonalized to generate the natural orbital basis [61]. Then, we perform the GSM calculations within the constructed natural orbital basis. For calculations of 14−15Ne and 12−14O, at most four scattering states are allowed in the continuum (the 4p–4h truncation) within the natural orbital basis, whereas 16Ne and 15F are carried out with a 3p–3h truncation due to their higher computational demand. For 13−14F, the broad resonances are strongly embedded in the scattering continuum, for which the natural orbitals lead to unstable resonance identification, especially for the widths [62]. We therefore adopt the Berggren basis with a 3p–3h truncation.To estimate the truncation uncertainty, we compared the results obtained in the 3p–3h and 4p–4h truncation spaces. The energy differences are only several tens of keV for 12−14O and remain below 300 keV for 14−16Ne. For the F isotopes, allowing one additional nucleon to occupy a scattering state changes the energy by only 12 keV, while allowing two additional nucleons in scattering states gives an energy difference below 120 keV. And the width uncertainty of F isotopes is below 100 keV. The treatment properly incorporates continuum coupling and ensures reliable numerical accuracy.The core potential is mimicked by a Woods-Saxon (WS) potential with a diffuseness of d=0.65 fm and a radius of R0=3 fm. The WS central potential depth Vo is 42.5 MeV (l=0), 29.8 MeV (l=1), 38.8 MeV (l=2) for proton, and 51.3 MeV (l=0,1) for neutron. The spin-orbit potential depth Vso is fixed at 8.5 MeV for all l > 0 partial waves. The nucleon-nucleon interaction is described by the pionless effective field theory (EFT) interaction [64–68], including the leading-order (LO) and next-to-leading order (NLO) contact terms. In this work, the interaction parameters are optimized by fitting the calculated binding energies of the low-lying states of selected nitrogen, oxygen, fluorine, and neon isotopes (see Table 1) to the corresponding experimental values. The optimized EFT interaction parameters are listed in Table 2. Note that within the pionless EFT framework, the LO interaction is characterized by the spin-independent (CS) and spin-dependent (CT) terms, which can be equivalently expressed as CS0=(CS−3CT) and CS1=(CS+CT) [69]. In this work, we employ the representation in terms of (CS0, CS1) to describe the LO terms, which correspond to the 1S0 and 3S1 channels, respectively. An A-dependence (0.25) on the number of nucleons has been added to the EFT two-body interaction to account for the effect of three-body interactions. The Coulomb interaction for protons is considered exactly, with charge radius Rch=3 fm. The root mean square deviation (RMSD) between the theoretical energies provided by the optimized GSM Hamiltonian and the experimental energies is 0.157 MeV.3ResultsBased on the optimized GSM Hamiltonian, we have performed systematic GSM calculations for the proton-rich O, F, and Ne isotopes with A=12−16. The results are presented in Fig. 1. The GSM calculations reproduce the experimentally established low-lying states in the oxygen, fluorine, and neon isotopic chains with good accuracy. The RMSD between the GSM energy and the corresponding experimental energy for the 17 reference states shown in the figure is 0.759 MeV, where many of them were not part of the optimization. The largest discrepancy is 1.38 MeV for the 2+ state in 12O.The GSM calculations are performed in a valence space including both pole states and scattering states, thereby including continuum coupling. To evaluate the effect of continuum coupling, we compare the GSM results with those obtained in the pole approximation, where only pole states are retained. Continuum coupling reduces the ground-state separation energies by 0.418 MeV in 15F, 0.704 MeV in 14F, and 0.814 MeV in 13F, demonstrating its sizable impact on these proton-rich systems.Furthermore, we have calculated the proton and neutron partial-wave occupancies for the low-lying states of 12−14O, 13−15F, and 14−16Ne, as presented in Table 3. The average occupations reveal a systematic structural evolution. Along the N=4, 5, and 6 isotonic chains, the proton 1s1/2 occupancy increases from the O isotopes to the F and Ne isotopes. Within each nucleus, most higher-lying excited states exhibit enhanced 0d5/2 occupancy relative to the ground state or the lowest-lying states, as seen in 15F(5/2+), 16Ne(2+), 14F(3−,4−), 15Ne(5/2−), and 13F(5/2+). These trends point to a growing competition between the 1s1/2 and 0d5/2 configurations of extremely proton-rich nuclei, indicating stronger orbital rearrangement and sd-shell mixing beyond the proton drip line.States with dominant proton 1s1/2 components couple more strongly to the continuum, since the s-wave carries l=0 and experiences no centrifugal barrier. They therefore tend to appear as broader resonances. By contrast, states with dominant 0d5/2 character are hindered by the l=2 centrifugal barrier and remain comparatively narrower. The widths are clearly demonstrated in the detailed analysis of each O-F-Ne isotonic chain presented below.We next examine each proton-emission chain in detail to explore their distinct structural properties. Fig. 2 shows the calculated level schemes of the N=6 isotones, with energies referenced to the 14O+2p and 14O+p thresholds for 16Ne and 15F, respectively.The low-lying structure of 15F is now well studied [10–15]: the ground state, Jπ=1/2+, lies about 1.2-1.6 MeV above the 14O+p threshold and appears as a broad resonance (Γ ≈ 0.5–1.3 MeV), whereas the first excited state 5/2+ is unbound by about 2.8 MeV and is comparatively narrow (Γ ≈ 0.3 MeV). In our GSM calculation, the 1/2+ and 5/2+ states of 15F are about 1.53 and 3.28 MeV unbound by 1p decay, respectively. Our calculations reproduce the separation energy well. However, relative to existing data, the excitation energy is slightly overestimated by about 500 keV, and the decay widths of the two states are underestimated. For 15F, the ground state is interpreted as mainly π{(1s1/2)1(0p1/2)2}⊗ν(0p3/2)4, and the first excited state as π{(0p1/2)2(0d5/2)1}⊗ν(0p3/2)4. The structure of the ground state can be interpreted as a proton orbiting with l=0 above a 14Og.s. core. Moreover, GSM calculation yields a spectroscopic factor C2S(s1/2)=0.92 for the 15F ground state (1/2+), in close agreement with the IMME-based estimate C2S=0.88 by H. T. Fortune [71]. For the 5/2+ state we obtain C2S(d5/2)=0.94, consistent with C2S=0.92(12) extracted from the transfer reaction on neon [11]. These values corroborate the good single-particle character of the 1/2+ and 5/2+ states in 15F. To further examine mirror symmetry breaking and continuum effects, we compare the low-lying spectra of 15F and its mirror partner 15C. The GSM calculation reproduces the mirror spectrum, although the calculated 5/2+ excitation energy is about 0.48 MeV higher than the experimental value in 15C. The mirror energy difference of the 5/2+ state obtained in our GSM is 526 keV, which is close to the experimental values of 603 keV.For 16Ne, experimental studies indicate that the ground state lies about 1.34-1.47 MeV above the14Og.s.+2p threshold, with uncertainties of several tens of keV, and first excited state lies at about 3.16 MeV above the same threshold with a narrow width [10,21–23,25,72]. For 16Ne, the ground state is unbound by 1.627 MeV with respect to the 14O+2p threshold in GSM calculation, close to the experimental value of 1.466(20) MeV [21]. The first 2+ state is predicted at 4.685 MeV, whereas experiment reports 3.16(2) MeV [70], with a deviation of  ≈ 1.5 MeV. Structurally, the 16Neg.s. is dominated by π{(1s1/2)2(0p1/2)2}⊗ν(0p3/2)4, with small admixtures of π{(0p1/2)2(0d5/2)2}⊗ν(0p3/2)4 (10%) and π{(1s1/2)2(0d5/2)2}⊗ν(0p3/2)4 (7%). While the first 2+ state is primarily π{(0p1/2)2(1s1/2)1(0d5/2)1}⊗ν(0p3/2)4.Having established the N=6 benchmarks (14O–15F–16Ne), we now turn to the more neutron-deficient N=5 chain (13O–14F–15Ne). As shown in Fig. 3, the energies are plotted relative to the ground state of 13O. 13O is the lightest particle-stable oxygen isotope, whereas 14F and 15Ne are unbound and will decay to 13O via 1p and 2p emission, respectively.For 14F, our GSM calculation gives the single-proton separation energy Sp=1.66 MeV, highly consistent with the experimental value of 1.56 MeV [18]. We place the 3− level about 0.2 MeV above the assignment of Ref. [18], close to an experimentally unobserved region; consistently, the invariant-mass analysis locates this resonance  ∼ 0.5 MeV higher [19], and the estimate of Sherr and Fortune is  ∼ 0.6 MeV higher [27]. The calculated energies for the 1− and 4− states are slightly underestimated relative to the experiment, with a maximum deviation of 0.8 MeV. Our calculation gives the main configuration of 13Og.s. as: π(0p1/2)2⊗ν(0p3/2)3. For 14F, the first two states are dominant by π{(1s1/2)1(0p1/2)2}⊗ν(0p3/2)3. For the narrower states 4− and 3−, the main configurations are π{(0p1/2)2(0d5/2)1}⊗ν(0p3/2)3. As the excitation energy increases, valence protons in the s1/2 orbital tend to be excited to the d5/2 orbital.We now compare the spectroscopic factors from our GSM calculation with those of Sherr and Fortune in Ref. [27]: For the ground state 2g.s.−, both calculations indicate a nearly pure s-wave resonance: C2S=0.88 in this work versus  ∼ 0.98 of Sherr and Fortune. For the 1− state, we obtain C2S=0.85, notably larger than predicted  ∼ 0.55, implying a stronger s–wave single–particle strength in our model, yet still less pure than 2g.s.−. For the 3− and 4−, the spectroscopic factors to the 13Og.s.+d5/2 channel are 0.93 and 0.96, respectively—well above the predicted 0.62(12) and 0.54(10). Our calculation supports a cleaner d5/2 single-particle character. These discrepancies likely reflect differences in the treatment of continuum coupling and the choice of potential parameters, indicating the model sensitivity of extracted spectroscopic strengths.The mirror-symmetry breaking in the 14F/14B mirror pair is also investigated, as shown in Fig. 4. Overall, the GSM calculation reproduces the low-lying spectra reasonably well. The calculated orbital occupations and dominant configurations of the mirror states are nearly identical, indicating that these states have very similar underlying structures. The remaining differences mainly arise from continuum coupling effects associated with the extended s-wave component, which are more pronounced in the proton-rich nucleus 14F. As a result, the calculated excitation energies of the 3− and 4− in 14F are shifted higher than their counterparts in 14B. The results show that continuum coupling provides a non-negligible binding contribution on the s-wave component in the proton-rich unbound nucleus, consistent with the situation in the mirror pair 16F/16N [51].The 15Ne was studied in two-neutron knockout reactions, and the ground state is unbound by 2.522(66) MeV above the 13O+2p decay threshold [25]. Our GSM calculation predicts the 15Ne ground state to be unbound by 2.19 MeV with respect to the 13O+2p threshold and places the 5/2− level 4.72 MeV above 13Og.s.. The calculated 15Ne spectrum agrees with experimental data within 400 keV. The GSM calculation gives that the ground state 15Ne is dominated by the proton configuration π{(1s1/2)2(0p1/2)2}⊗ν(0p3/2)3 (44.2%), with smaller admixtures π{(1s1/2)2(0d5/2)2}⊗ν(0p3/2)3 (10.3%) and π{(0p1/2)2(0d5/2)2}⊗ν(0p3/2)3 (10.3%); the residual strength is among the higher scattering components. Average occupancies in Table 3 indicate a 13O core coupled mainly to 1s1/2 protons with a modest 0d5/2 admixture, consistent with the experimental s-wave fraction of 63(5)% [25]. For the 5/2− excited state, strength is redistributed toward the 0d5/2 orbital with a slight reduction of the 1s1/2 component.For the more proton-rich N=4 isotonic chain, 12O is unbound with respect to the 10C+2p threshold and decays by 2p emission. Fig. 5 presents the calculated and experimental low-lying spectra of the N=4 isotones, with energies referenced to the 10Cg.s.. Experimental data of 10C, 11N and 12O are taken from [63].For 13F, a resonance was observed in the invariant-mass study and probably corresponds to a 5/2+ excited state [20]. In this work, our GSM calculations give three low-lying states of 13F, including the observed excited state 5/2+, the expected ground state 1/2+, and a candidate 1/2− excitation. GSM calculations predict the ground state 1/2+ is located 3.59 MeV above the threshold for 3p decay to 10Cg.s., with decay width of 1.2 MeV. For the 1/2− excited state, the decay energy is about 4.64 MeV with Γ=0.835 MeV. And for the 5/2+ excited state, the decay energy is about 4.91 MeV with Γ=0.732 MeV, about 2.15 MeV lower and markedly narrower than the experimental value [20] [E=7.06(9) MeV, Γ=1.01(27) MeV]. Relative to the 12O+p threshold, our GSM calculation yields Er(1/2+)=2.12 MeV, Er(1/2−)=3.18 MeV, and Er(5/2+)=3.44 MeV. The estimates of Fortune and Sherr [26] give Er(1/2+)=2.40 MeV with Γ=0.60(11) MeV and Er(5/2+)=4.94 (or 5.26) MeV with Γ=0.3–0.4 MeV. Our results place the 1/2+ and 5/2+ states lower by  ∼ 0.28 MeV and  ∼ 1.5–1.8 MeV, respectively, compared to that results in Ref. [26]. We obtain a 1/2−−5/2+ spacing of  ≈ 0.27 MeV, and Ref. [26] anticipated the separation in 13F comparable to that in 13Be.In 13F, the 1/2+ state is primarily π{(1s1/2)1(0p1/2)2}⊗ν(0p3/2)2 (35.6%), with a admixture of π{(0p1/2)2(s˜1/2)1}⊗ν(0p3/2)2 (19.8%). The orbital occupation (Table 3) likewise indicates the 1/2+ state has a configuration corresponding to a single valence proton in the 1s1/2 orbital outside the 12Og.s. core. Accordingly, the GSM calculation for the spectroscopic factor of 12Og.s.+s1/2 provides a large value, as C2S=0.89. The excited 1/2− state is dominated by π{(1s1/2)2(0p1/2)1}⊗ν(0p3/2)2. For the 5/2+ excited state, the enhanced 0d5/2 occupation, as shown in Table 3, contains sizable d5/2 scattering components, indicating stronger coupling to the continuum. The spectroscopic factor of the 1/2− state for the 12Og.s.+p1/2 channel is 0.84, while it is 0.93 for the 5/2+ state in the 12Og.s.+d5/2 channel.Additionally, the GSM calculation allows one to assess the ground state of the unbound 14Ne, which has not yet been observed experimentally and is expected to be unbound with respect to 4p emission. The 14Neg.s. is predicted to be 4.73 MeV above the 10C+4p threshold, with a decay width of 175 keV. The main configuration is π{(1s1/2)2(0p1/2)2}⊗ν(0p3/2)2 (50.0%), with a small admixture of π{(1s1/2)2(0d5/2)2}⊗ν(0p3/2)2 (13.2%). Nevertheless, the spectroscopic factors suggest a possible structural origin of the predicted narrow width. The dominant one-proton overlap is associated with the hindered 13F(1/2−)+p1/2 channel, for which the decay energy is small because the 13F(1/2−) state lies close to the 14Ne ground state.In GSM calculations, the calculated widths can be affected by both model-space truncation and the use of natural orbitals, especially for nuclei with several valence nucleons, such as 15Ne and 14Ne. In these cases, the natural orbitals are generated from a strongly truncated Berggren basis because of the rapidly increasing computational cost, which may affect the decay widths but the corresponding energies remain rather stable. Thus, the narrow width predicted for the 14Ne ground state should be viewed as a model prediction rather than a high-precision result, with the qualitative implication that 14Ne is a promising candidate for 4p emission.4SummarySystematic investigations of nuclei far beyond the proton drip line in the vicinity of 13F, where multi-proton emission is expected, remain scarce. In the present work, we address these open quantum systems within GSM, in which the continuum coupling and inter-nucleon correlations are both well treated, to carry out a comprehensive theoretical study.The GSM Hamiltonian, based on a pionless effective field theory nucleon–nucleon interaction, is optimized, yielding an RMSD of 0.157 MeV for the fitted levels. With this Hamiltonian, we perform a comprehensive study of the low-lying spectra, decay widths, and multi-proton separation energies of 12–14O, 13–15F, and 14–16Ne, focusing in particular on the 3p emitter 13F, the 2p emitter 15Ne, and the candidate 4p emitter 14Ne. Across the oxygen, fluorine, and neon chains with A=12--16, the calculations reproduce the experimental spectra with an overall RMSD of 0.759 MeV. The proton separation energies are well reproduced for 15F and 14F: Sp(15F)=1.53 MeV and Sp(14F)=1.67 MeV, in accord with the experimental values of 1.51(11) and 1.56(4) MeV, respectively. For 13F, we confirm the observed 5/2+ resonance as an excited state with a decay energy of 4.91 MeV relative to the 10C+3p threshold. We further predict a 1/2+ ground state of 13F at  ∼ 3.59 MeV above the 10C+3p threshold and unbound by  ∼ 2.12 MeV with respect to 12O+p. The partial-wave occupancies and spectroscopic factors highlight proton-driven structural evolution and the essential role of continuum coupling in intruder states and configuration mixing. Moreover, the ground state of the experimentally unobserved 14Ne is predicted to lie  ∼ 4.73 MeV above the 10C+4p threshold. Therefore, it is predicted to be a 4p emitter, providing useful insights for future experimental investigations.Declaration of competing interestThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.AcknowledgementThis work has been supported by the National Key R&D Program of China under Grant No. 2023YFA1606403, 2024YFE0109800, and 2024YFE0109802; the National Natural Science Foundation of China under Grant Nos. 12205340, 12175281, 12347106, 12575124, 12441506, and 12405141; the Gansu Natural Science Foundation under Grant Nos. 22JR5RA123 and 25JRRA467. The numerical calculations in this paper have been done at Hefei Advanced Computing Center.References[1]O.SorlinM.G.PorquetNuclear magic numbers: new features far from stabilityProg. Part. Nucl. Phys.612200860267310.1016/j.ppnp.2008.05.001O. Sorlin, M. G. Porquet, Nuclear magic numbers: new features far from stability, Prog. Part. Nucl. Phys. 61 (2) (2008) 602–673. 10.1016/j.ppnp.2008.05.001[2]Y.YeX.YangH.SakuraiB.HuPhysics of exotic nucleiNat. Rev. Phys.712025213710.1038/s42254-024-00782-5Y. Ye, X. Yang, H. Sakurai, B. Hu, Physics of exotic nuclei, Nat. Rev. Phys. 7 (1) (2025) 21–37. 10.1038/s42254-024-00782-5[3]Y.YuY.M.XingY.H.ZhangM.WangX.H.ZhouJ.G.LiH.H.LiQ.YuanY.F.NiuY.N.HuangJ.GengJ.Y.GuoJ.W.ChenJ.C.PeiF.R.XuY.A.LitvinovK.BlaumG.de AngelisI.TanihataT.YamaguchiX.ZhouH.S.XuZ.Y.ChenR.J.ChenH.Y.DengC.Y.FuW.W.GeW.J.HuangH.Y.JiaoY.F.LuoH.F.LiT.LiaoJ.Y.ShiM.SiM.Z.SunP.ShuaiX.L.TuQ.WangX.XuX.L.YanY.J.YuanM.ZhangNuclear structure of dripline nuclei elucidated through precision mass measurements of 23Si, 26P, 27,28S, and 31ArPhys. Rev. Lett.133202422250110.1103/PhysRevLett.133.222501Y. Yu, Y. M. Xing, Y. H. Zhang, M. Wang, X. H. Zhou, J. G. Li, H. H. Li, Q. Yuan, Y. F. Niu, Y. N. Huang, J. Geng, J. Y. Guo, J. W. Chen, J. C. Pei, F. R. Xu, Y. A. Litvinov, K. Blaum, G. de Angelis, I. Tanihata, T. Yamaguchi, X. Zhou, H. S. Xu, Z. Y. Chen, R. J. Chen, H. Y. Deng, C. Y. Fu, W. W. Ge, W. J. Huang, H. Y. Jiao, Y. F. Luo, H. F. Li, T. Liao, J. Y. Shi, M. Si, M. Z. Sun, P. Shuai, X. L. Tu, Q. Wang, X. Xu, X. L. Yan, Y. J. Yuan, M. Zhang, Nuclear structure of dripline nuclei elucidated through precision mass measurements of 23Si, 26P, 27,28S, and 31Ar, Phys. Rev. Lett. 133 (2024) 222501. 10.1103/PhysRevLett.133.222501[4]E.LunderbergP.A.DeYoungZ.KohleyH.AttanayakeT.BaumannD.BazinG.ChristianD.DivaratneS.M.GrimesA.HaagsmaJ.E.FinckN.FrankB.LutherS.MosbyT.NagiG.F.PeasleeA.SchillerJ.SnyderA.SpyrouM.J.StrongmanM.ThoennessenEvidence for the ground-state resonance of 26OPhys. Rev. Lett.108201214250310.1103/PhysRevLett.108.142503E. Lunderberg, P. A. DeYoung, Z. Kohley, H. Attanayake, T. Baumann, D. Bazin, G. Christian, D. Divaratne, S. M. Grimes, A. Haagsma, J. E. Finck, N. Frank, B. Luther, S. Mosby, T. Nagi, G. F. Peaslee, A. Schiller, J. Snyder, A. Spyrou, M. J. Strongman, M. Thoennessen, Evidence for the ground-state resonance of 26O, Phys. Rev. Lett. 108 (2012) 142503. 10.1103/PhysRevLett.108.142503[5]Y.-G.MaMulti-proton emission at the limits of nuclear stability: challenges for extreme open quantum systemsNucl. Sci. Tech.3612202523610.1007/s41365-025-01831-zY.-G. Ma, Multi-proton emission at the limits of nuclear stability: challenges for extreme open quantum systems, Nucl. Sci. Tech. 36 (12) (2025) 236. 10.1007/s41365-025-01831-z[6]Y.JinC.Y.NiuK.W.BrownZ.H.LiH.HuaA.K.AnthonyJ.BarneyR.J.CharityJ.CrosbyD.Dell’AquilaJ.M.ElsonJ.EsteeM.GhazaliG.JhangJ.G.LiW.G.LynchN.MichelL.G.SobotkaS.SweanyF.C.E.TehA.ThomasC.Y.TsangM.B.TsangS.M.WangH.Y.WuC.X.YuanK.ZhuFirst observation of the four-proton unbound nucleus 18MgPhys. Rev. Lett.127202126250210.1103/PhysRevLett.127.262502Y. Jin, C. Y. Niu, K. W. Brown, Z. H. Li, H. Hua, A. K. Anthony, J. Barney, R. J. Charity, J. Crosby, D. Dell’Aquila, J. M. Elson, J. Estee, M. Ghazali, G. Jhang, J. G. Li, W. G. Lynch, N. Michel, L. G. Sobotka, S. Sweany, F. C. E. Teh, A. Thomas, C. Y. Tsang, M. B. Tsang, S. M. Wang, H. Y. Wu, C. X. Yuan, K. Zhu, First observation of the four-proton unbound nucleus 18Mg, Phys. Rev. Lett. 127 (2021) 262502. 10.1103/PhysRevLett.127.262502[7]X.-D.XuI.MukhaJ.G.LiS.M.WangL.AcostaM.BajzekE.CasarejosD.Cortina-GilJ.M.EspinoA.FomichevH.GeisselJ.Gómez-CamachoL.V.GrigorenkoO.KiselevA.A.KorsheninnikovD.KostylevaN.KurzY.A.LitvinovI.MartelC.NociforoM.PfütznerC.Rodríguez-TajesC.ScheidenbergerM.StanoiuK.SümmererH.WeickP.J.WoodsM.V.ZhukovIsospin symmetry breaking disclosed in the decay of three-proton emitter 20AlPhys. Rev. Lett.135202502250210.1103/hkmy-yfdkX.-D. Xu, I. Mukha, J. G. Li, S. M. Wang, L. Acosta, M. Bajzek, E. Casarejos, D. Cortina-Gil, J. M. Espino, A. Fomichev, H. Geissel, J. Gómez-Camacho, L. V. Grigorenko, O. Kiselev, A. A. Korsheninnikov, D. Kostyleva, N. Kurz, Y. A. Litvinov, I. Martel, C. Nociforo, M. Pfützner, C. Rodríguez-Tajes, C. Scheidenberger, M. Stanoiu, K. Sümmerer, H. Weick, P. J. Woods, M. V. Zhukov, Isospin symmetry breaking disclosed in the decay of three-proton emitter 20Al, Phys. Rev. Lett. 135 (2025) 022502. 10.1103/hkmy-yfdk[8]J.L.WangM.R.XieK.H.LiP.Y.WangN.MichelQ.YuanJ.G.LiGamow shell model predictions for six-proton unbound nucleus 20SiPhys. Lett. B872202614003010.1016/j.physletb.2025.140030J. L. Wang, M. R. Xie, K. H. Li, P. Y. Wang, N. Michel, Q. Yuan, J. G. Li, Gamow shell model predictions for six-proton unbound nucleus 20Si, Phys. Lett. B 872 (2026) 140030. 10.1016/j.physletb.2025.140030[9]L.ZhouD.-Q.FangS.-M.WangH.HuaStructure and 2p decay mechanism of 18MgNucl. Sci. Tech.356202410710.1007/s41365-024-01479-1L. Zhou, D.-Q. Fang, S.-M. Wang, H. Hua, Structure and 2p decay mechanism of 18Mg, Nucl. Sci. Tech. 35 (6) (2024) 107. 10.1007/s41365-024-01479-1[10]G.J.KeKelisM.S.ZismanD.K.ScottR.JahnD.J.VieiraJ.CernyF.Ajzenberg-SeloveMasses of the unbound nuclei 16Ne, 15F, and 12OPhys. Rev. C1719781929193810.1103/PhysRevC.17.1929G. J. KeKelis, M. S. Zisman, D. K. Scott, R. Jahn, D. J. Vieira, J. Cerny, F. Ajzenberg-Selove, Masses of the unbound nuclei 16Ne, 15F, and 12O, Phys. Rev. C 17 (1978) 1929–1938. 10.1103/PhysRevC.17.1929[11]W.BenensonE.KashyA.G.LedebuhrR.C.PardoR.G.H.RobertsonL.W.RobinsonT=32 levels in 15F and 15OPhys. Rev. C1719781939194210.1103/PhysRevC.17.1939W. Benenson, E. Kashy, A. G. Ledebuhr, R. C. Pardo, R. G. H. Robertson, L. W. Robinson, $ T=\frac{3}{2} $ levels in 15F and 15O, Phys. Rev. C 17 (1978) 1939–1942. 10.1103/PhysRevC.17.1939[12]A.Lépine-SzilyJ.M.OliveiraD.GalanteG.AmadioR.LichtenthälerH.G.BohlenA.N.OstrowskiA.BlazevicC.BorceaV.GuimarãesV.LapouxG.F.LimaF.de Oliveira SantosN.A.OrrP.Roussel-ChomazT.StollaJ.S.WinfieldSpectroscopy of light proton-rich nuclei:9C and15FNucl. Phys. A734200433133610.1016/j.nuclphysa.2004.01.060A. Lépine-Szily, J. M. Oliveira, D. Galante, G. Amadio, R. Lichtenthäler, H. G. Bohlen, A. N. Ostrowski, A. Blazevic, C. Borcea, V. Guimarães, V. Lapoux, G. F. Lima, F. de Oliveira Santos, N. A. Orr, P. Roussel-Chomaz, T. Stolla, J. S. Winfield, Spectroscopy of light proton-rich nuclei:9C and15F, Nucl. Phys. A 734 (2004) 331–336. 10.1016/j.nuclphysa.2004.01.060[13]W.A.PetersT.BaumannD.BazinB.A.BrownR.R.C.ClementN.FrankP.HeckmanB.A.LutherF.NunesJ.SeitzA.StolzM.ThoennessenE.TryggestadFirst two energy levels in 15FPhys. Rev. C68200303460710.1103/PhysRevC.68.034607W. A. Peters, T. Baumann, D. Bazin, B. A. Brown, R. R. C. Clement, N. Frank, P. Heckman, B. A. Luther, F. Nunes, J. Seitz, A. Stolz, M. Thoennessen, E. Tryggestad, First two energy levels in 15F, Phys. Rev. C 68 (2003) 034607. 10.1103/PhysRevC.68.034607[14]V.Z.GoldbergG.G.ChubarianG.TabacaruL.TracheR.E.TribbleA.AprahamianG.V.RogachevB.B.SkorodumovX.D.TangLow-lying levels in 15F and the shell model potential for drip-line nucleiPhys. Rev. C69200403130210.1103/PhysRevC.69.031302V. Z. Goldberg, G. G. Chubarian, G. Tabacaru, L. Trache, R. E. Tribble, A. Aprahamian, G. V. Rogachev, B. B. Skorodumov, X. D. Tang, Low-lying levels in 15F and the shell model potential for drip-line nuclei, Phys. Rev. C 69 (2004) 031302. 10.1103/PhysRevC.69.031302[15]F.Q.GuoJ.PowellD.W.LeeD.LeitnerM.A.McMahanD.M.MoltzJ.P.O’NeilK.PerajarviL.PhairC.A.RamseyX.J.XuJ.CernyReexamination of the energy levels of 15F by 14O+1H elastic resonance scatteringPhys. Rev. C72200503431210.1103/PhysRevC.72.034312F. Q. Guo, J. Powell, D. W. Lee, D. Leitner, M. A. McMahan, D. M. Moltz, J. P. O’Neil, K. Perajarvi, L. Phair, C. A. Ramsey, X. J. Xu, J. Cerny, Reexamination of the energy levels of 15F by $ ^{14}{\rm O}+^{1}{\rm H} $ elastic resonance scattering, Phys. Rev. C 72 (2005) 034312. 10.1103/PhysRevC.72.034312[16]F.de GranceyA.MercenneF.de Oliveira SantosT.DavinsonO.SorlinJ.C.AngéliqueM.AssiéE.BerthoumieuxR.BorceaA.ButaI.CelikovicV.ChudobaJ.M.DaugasG.DumitruM.FadilS.GrévyJ.KienerA.Lefebvre-SchuhlN.MichelJ.MrazekF.NegoitaJ.OkołowiczD.PantelicaM.G.PellegritiL.PerrotM.PłoszajczakG.RandisiI.RayO.RoigF.RotaruM.G.Saint LaurentN.SmirnovaM.StanoiuI.StefanC.StodelK.SuboticV.TatischeffJ.C.ThomasP.UjićR.WolskiAn above-barrier narrow resonance in 15FPhys. Lett. B7582016263110.1016/j.physletb.2016.04.051F. de Grancey, A. Mercenne, F. de Oliveira Santos, T. Davinson, O. Sorlin, J. C. Angélique, M. Assié, E. Berthoumieux, R. Borcea, A. Buta, I. Celikovic, V. Chudoba, J. M. Daugas, G. Dumitru, M. Fadil, S. Grévy, J. Kiener, A. Lefebvre-Schuhl, N. Michel, J. Mrazek, F. Negoita, J. Okołowicz, D. Pantelica, M. G. Pellegriti, L. Perrot, M. Płoszajczak, G. Randisi, I. Ray, O. Roig, F. Rotaru, M. G. Saint Laurent, N. Smirnova, M. Stanoiu, I. Stefan, C. Stodel, K. Subotic, V. Tatischeff, J. C. Thomas, P. Ujić, R. Wolski, An above-barrier narrow resonance in 15F, Phys. Lett. B 758 (2016) 26–31. 10.1016/j.physletb.2016.04.051[17]V.Girard-AlcindorA.MercenneI.StefanF.de Oliveira SantosN.MichelM.PłoszajczakM.AssiéA.LemassonE.ClémentF.FlavignyA.MattaD.RamosM.RejmundJ.DudouetD.AckermannP.AdsleyM.Assun ç aoB.BastinD.BeaumelG.BenzoniR.BorceaA.J.BostonD.BrugnaraL.CáceresB.CederwallI.CelikovicV.ChudobaM.CiemalaJ.ColladoF.C.L.CrespiG.D’AgataG.De FranceF.DelaunayC.DigetC.Domingo-PardoJ.EberthC.FougèresS.FranchooF.GaltarossaA.GeorgiadouJ.GibelinS.GiraudV.GonzálezN.GoyalA.GottardoJ.GoupilS.GrévyV.GuimaraesF.HammacheL.J.Harkness-BrennanH.HessN.JovančevićD.S.Judson OliverO.KamalouA.KamenyeroJ.KienerW.KortenS.KoyamaM.LabicheL.LalanneV.LapouxS.LeblondA.LefevreC.LenainS.LeoniH.LiA.Lopez-MartensA.MajI.MateaR.MenegazzoD.MengoniA.MeyerB.MillionB.MonteagudoP.MorfouaceJ.MrazekM.NiikuraJ.PiotZ.PodolyakC.PortailA.PulliaB.QuintanaF.RecchiaP.ReiterK.RezynkinaT.RogerJ.S.RojoF.RotaruM.D.SalsacA.M.Sánchez BenítezE.SanchisM.ŞenyigitN.de SérévilleM.SicilianoJ.SimpsonD.SohlerO.SorlinM.StanoiuC.StodelD.SuzukiC.TheisenD.ThisseJ.C. ThomasP.UjicJ.J.Valiente-DobónM.ZielińskaNew narrow resonances observed in the unbound nucleus 15FPhys. Rev. C1052022L05130110.1103/PhysRevC.105.L051301V. Girard-Alcindor, A. Mercenne, I. Stefan, F. de Oliveira Santos, N. Michel, M. Płoszajczak, M. Assié, A. Lemasson, E. Clément, F. Flavigny, A. Matta, D. Ramos, M. Rejmund, J. Dudouet, D. Ackermann, P. Adsley, M. Assun ç ao, B. Bastin, D. Beaumel, G. Benzoni, R. Borcea, A. J. Boston, D. Brugnara, L. Cáceres, B. Cederwall, I. Celikovic, V. Chudoba, M. Ciemala, J. Collado, F. C. L. Crespi, G. D’Agata, G. De France, F. Delaunay, C. Diget, C. Domingo-Pardo, J. Eberth, C. Fougères, S. Franchoo, F. Galtarossa, A. Georgiadou, J. Gibelin, S. Giraud, V. González, N. Goyal, A. Gottardo, J. Goupil, S. Grévy, V. Guimaraes, F. Hammache, L. J. Harkness-Brennan, H. Hess, N. Jovančević, D. S. Judson Oliver, O. Kamalou, A. Kamenyero, J. Kiener, W. Korten, S. Koyama, M. Labiche, L. Lalanne, V. Lapoux, S. Leblond, A. Lefevre, C. Lenain, S. Leoni, H. Li, A. Lopez-Martens, A. Maj, I. Matea, R. Menegazzo, D. Mengoni, A. Meyer, B. Million, B. Monteagudo, P. Morfouace, J. Mrazek, M. Niikura, J. Piot, Z. Podolyak, C. Portail, A. Pullia, B. Quintana, F. Recchia, P. Reiter, K. Rezynkina, T. Roger, J. S. Rojo, F. Rotaru, M. D. Salsac, A. M. Sánchez Benítez, E. Sanchis, M. Şenyigit, N. de Séréville, M. Siciliano, J. Simpson, D. Sohler, O. Sorlin, M. Stanoiu, C. Stodel, D. Suzuki, C. Theisen, D. Thisse, J. C. Thomas, P. Ujic, J. J. Valiente-Dobón, M. Zielińska, New narrow resonances observed in the unbound nucleus 15F, Phys. Rev. C 105 (2022) L051301. 10.1103/PhysRevC.105.L051301[18]V.Z.GoldbergB.T.RoederG.V.RogachevG.G.ChubarianE.D.JohnsonC.FuA.A.AlharbiM.L.AvilaA.BanuM.McCleskeyJ.P.MitchellE.SimmonsG.TabacaruL.TracheR.E.TribbleFirst observation of 14FPhys. Lett. B6925201030731110.1016/j.physletb.2010.07.054V. Z. Goldberg, B. T. Roeder, G. V. Rogachev, G. G. Chubarian, E. D. Johnson, C. Fu, A. A. Alharbi, M. L. Avila, A. Banu, M. McCleskey, J. P. Mitchell, E. Simmons, G. Tabacaru, L. Trache, R. E. Tribble, First observation of 14F, Phys. Lett. B 692 (5) (2010) 307–311. 10.1016/j.physletb.2010.07.054[19]R.J.CharityK.BrownT.WebbL.G.SobotkaInvariant-mass spectroscopy of 10B, 11C, 14F, 16F, and 18NaPhys. Rev. C107202305430110.1103/PhysRevC.107.054301R. J. Charity, K. Brown, T. Webb, L. G. Sobotka, Invariant-mass spectroscopy of 10B, 11C, 14F, 16F, and 18Na, Phys. Rev. C 107 (2023) 054301. 10.1103/PhysRevC.107.054301[20]R.J.CharityT.B.WebbJ.M.ElsonD.E.M.HoffC.D.PruittL.G.SobotkaK.W.BrownG.CerizzaJ.EsteeW.G.LynchJ.ManfrediP.MorfouaceC.SantamariaS.SweanyC.Y.TsangM.B.TsangY.ZhangK.ZhuS.A.KuvinD.McNeelJ.SmithA.H.WuosmaaZ.ChajeckiObservation of the exotic isotope 13F located four neutrons beyond the proton drip linePhys. Rev. Lett.126202113250110.1103/PhysRevLett.126.132501R. J. Charity, T. B. Webb, J. M. Elson, D. E. M. Hoff, C. D. Pruitt, L. G. Sobotka, K. W. Brown, G. Cerizza, J. Estee, W. G. Lynch, J. Manfredi, P. Morfouace, C. Santamaria, S. Sweany, C. Y. Tsang, M. B. Tsang, Y. Zhang, K. Zhu, S. A. Kuvin, D. McNeel, J. Smith, A. H. Wuosmaa, Z. Chajecki, Observation of the exotic isotope 13F located four neutrons beyond the proton drip line, Phys. Rev. Lett. 126 (2021) 132501. 10.1103/PhysRevLett.126.132501[21]K.W.BrownR.J.CharityL.G.SobotkaZ.ChajeckiL.V.GrigorenkoI.A.EgorovaY.L.ParfenovaM.V.ZhukovS.BedoorW.W.BuhroJ.M.ElsonW.G.LynchJ.ManfrediD.G.McNeelW.ReviolR.ShaneR.H.ShowalterM.B.TsangJ.R.WinkelbauerA.H.WuosmaaObservation of long-range three-body coulomb effects in the decay of 16NePhys. Rev. Lett.113201423250110.1103/PhysRevLett.113.232501K. W. Brown, R. J. Charity, L. G. Sobotka, Z. Chajecki, L. V. Grigorenko, I. A. Egorova, Y. L. Parfenova, M. V. Zhukov, S. Bedoor, W. W. Buhro, J. M. Elson, W. G. Lynch, J. Manfredi, D. G. McNeel, W. Reviol, R. Shane, R. H. Showalter, M. B. Tsang, J. R. Winkelbauer, A. H. Wuosmaa, Observation of long-range three-body coulomb effects in the decay of 16Ne, Phys. Rev. Lett. 113 (2014) 232501. 10.1103/PhysRevLett.113.232501[22]C.J.WoodwardR.E.TribbleD.M.TannerMass of 16NePhys. Rev. C271983273010.1103/PhysRevC.27.27C. J. Woodward, R. E. Tribble, D. M. Tanner, Mass of 16Ne, Phys. Rev. C 27 (1983) 27–30. 10.1103/PhysRevC.27.27[23]G.R.BurlesonG.S.BlanpiedG.H.DawA.J.ViescasC.L.MorrisH.A.ThiessenS.J.GreeneW.J.BraithwaiteW.B.CottingameD.B.HoltkampI.B.MooreC.F.MooreIsospin quintets in the 1p and s−d shellsPhys. Rev. C2219801180118310.1103/PhysRevC.22.1180G. R. Burleson, G. S. Blanpied, G. H. Daw, A. J. Viescas, C. L. Morris, H. A. Thiessen, S. J. Greene, W. J. Braithwaite, W. B. Cottingame, D. B. Holtkamp, I. B. Moore, C. F. Moore, Isospin quintets in the 1p and $ s-d $ shells, Phys. Rev. C 22 (1980) 1180–1183. 10.1103/PhysRevC.22.1180[24]K.FöhlR.BilgerH.ClementJ.GräterR.MeierJ.PätzoldD.SchaplerG.J.WagnerO.WilhelmW.KlugeR.WieserM.SchepkinR.AbelaF.ForoughiD.RenkerPionic double charge exchange on N=Z doubly closed shell nucleiPhys. Rev. Lett.7919973849385210.1103/PhysRevLett.79.3849K. Föhl, R. Bilger, H. Clement, J. Gräter, R. Meier, J. Pätzold, D. Schapler, G. J. Wagner, O. Wilhelm, W. Kluge, R. Wieser, M. Schepkin, R. Abela, F. Foroughi, D. Renker, Pionic double charge exchange on $ \mathit{N}\phantom{\rule {0ex}{0ex}}=\phantom{\rule {0ex}{0ex}}\mathit{Z} $ doubly closed shell nuclei, Phys. Rev. Lett. 79 (1997) 3849–3852. 10.1103/PhysRevLett.79.3849[25]F.WamersJ.MarganiecF.AksouhY.AksyutinaH.Álvarez-PolT.AumannS.Beceiro-NovoK.BoretzkyM.J.G.BorgeM.ChartierA.ChatillonL.V.ChulkovD.Cortina-GilH.EmlingO.ErshovaL.M.FraileH.O.U.FynboD.GalavizH.GeisselM.HeilD.H.H.HoffmannH.T.JohanssonB.JonsonC.KaragiannisO.A.KiselevJ.V.KratzR.KulessaN.KurzC.LangerM.LantzT.Le BleisR.LemmonY.A.LitvinovK.MahataC.MüntzT.NilssonC.NociforoG.NymanW.OttV.PaninS.PaschalisA.PereaR.PlagR.ReifarthA.RichterC.Rodriguez-TajesD.RossiK.RiisagerD.SavranG.SchriederH.SimonJ.StrothK.SümmererO.TengbladH.WeickC.WimmerM.V.ZhukovFirst observation of the unbound nucleus 15NePhys. Rev. Lett.112201413250210.1103/PhysRevLett.112.132502F. Wamers, J. Marganiec, F. Aksouh, Y. Aksyutina, H. Álvarez-Pol, T. Aumann, S. Beceiro-Novo, K. Boretzky, M. J. G. Borge, M. Chartier, A. Chatillon, L. V. Chulkov, D. Cortina-Gil, H. Emling, O. Ershova, L. M. Fraile, H. O. U. Fynbo, D. Galaviz, H. Geissel, M. Heil, D. H. H. Hoffmann, H. T. Johansson, B. Jonson, C. Karagiannis, O. A. Kiselev, J. V. Kratz, R. Kulessa, N. Kurz, C. Langer, M. Lantz, T. Le Bleis, R. Lemmon, Y. A. Litvinov, K. Mahata, C. Müntz, T. Nilsson, C. Nociforo, G. Nyman, W. Ott, V. Panin, S. Paschalis, A. Perea, R. Plag, R. Reifarth, A. Richter, C. Rodriguez-Tajes, D. Rossi, K. Riisager, D. Savran, G. Schrieder, H. Simon, J. Stroth, K. Sümmerer, O. Tengblad, H. Weick, C. Wimmer, M. V. Zhukov, First observation of the unbound nucleus 15Ne, Phys. Rev. Lett. 112 (2014) 132502. 10.1103/PhysRevLett.112.132502[26]H.T.FortuneR.SherrPredictions for the first two positive-parity states of 13FPhys. Rev. C86201203430110.1103/PhysRevC.86.034301H. T. Fortune, R. Sherr, Predictions for the first two positive-parity states of 13F, Phys. Rev. C 86 (2012) 034301. 10.1103/PhysRevC.86.034301[27]R.SherrH.T.FortuneLow-lying resonances in 14F and 14BPhys. Lett. B6994201128128210.1016/j.physletb.2011.04.018R. Sherr, H. T. Fortune, Low-lying resonances in 14F and 14B, Phys. Lett. B 699 (4) (2011) 281–282. 10.1016/j.physletb.2011.04.018[28]H.T.FortuneR.SherrComment on “Predicting narrow states in the spectrum of a nucleus beyond the proton drip line”Phys. Rev. Lett.99200708920110.1103/PhysRevLett.99.089201H. T. Fortune, R. Sherr, Comment on “Predicting narrow states in the spectrum of a nucleus beyond the proton drip line”, Phys. Rev. Lett. 99 (2007) 089201. 10.1103/PhysRevLett.99.089201[29]D.BayeP.DescouvemontF.LeoMicroscopic cluster model analysis of 14O+p elastic scatteringPhys. Rev. C72200502430910.1103/PhysRevC.72.024309D. Baye, P. Descouvemont, F. Leo, Microscopic cluster model analysis of $ ^{14}{\rm O}+p $ elastic scattering, Phys. Rev. C 72 (2005) 024309. 10.1103/PhysRevC.72.024309[30]L.CantonG.PisentJ.P.SvenneK.AmosS.KarataglidisPredicting narrow states in the spectrum of a nucleus beyond the proton drip linePhys. Rev. Lett.96200607250210.1103/PhysRevLett.96.072502L. Canton, G. Pisent, J. P. Svenne, K. Amos, S. Karataglidis, Predicting narrow states in the spectrum of a nucleus beyond the proton drip line, Phys. Rev. Lett. 96 (2006) 072502. 10.1103/PhysRevLett.96.072502[31]N.MichelJ.G.LiF.R.XuW.ZuoProton decays in 16Ne and 18Mg and isospin-symmetry breaking in carbon isotopes and isotonesPhys. Rev. C103202104431910.1103/PhysRevC.103.044319N. Michel, J. G. Li, F. R. Xu, W. Zuo, Proton decays in 16Ne and 18Mg and isospin-symmetry breaking in carbon isotopes and isotones, Phys. Rev. C 103 (2021) 044319. 10.1103/PhysRevC.103.044319[32]S.ZhangZ.XuS.WangContinuum effect on mirror symmetry breaking within the gamow frameworksSymmetry172202516910.3390/sym17020169S. Zhang, Z. Xu, S. Wang, Continuum effect on mirror symmetry breaking within the gamow frameworks, Symmetry 17 (2) (2025) 169. 10.3390/sym17020169[33]K.H.LiJ.G.LiN.MichelH.H.LiN.ChenC.W.MaW.ZuoGamow shell model for dynamic Thomas-Ehrman shift in 16Ne/16C and 18Mg/18CPhys. Rev. C111202501430210.1103/PhysRevC.111.014302K. H. Li, J. G. Li, N. Michel, H. H. Li, N. Chen, C. W. Ma, W. Zuo, Gamow shell model for dynamic Thomas-Ehrman shift in 16Ne/16C and 18Mg/18C, Phys. Rev. C 111 (2025) 014302. 10.1103/PhysRevC.111.014302[34]P.MarisA.M.ShirokovJ.P.VaryAb initio nuclear structure simulations: the speculative 14F nucleusPhys. Rev. C81201002130110.1103/PhysRevC.81.021301P. Maris, A. M. Shirokov, J. P. Vary, Ab initio nuclear structure simulations: the speculative 14F nucleus, Phys. Rev. C 81 (2010) 021301. 10.1103/PhysRevC.81.021301[35]A.M.MukhamedzhanovB.F.IrgazievV.Z.GoldbergY.V.OrlovI.QaziBound, virtual, and resonance S-matrix poles from the Schrödinger equationPhys. Rev. C81201005431410.1103/PhysRevC.81.054314A. M. Mukhamedzhanov, B. F. Irgaziev, V. Z. Goldberg, Y. V. Orlov, I. Qazi, Bound, virtual, and resonance S-matrix poles from the Schrödinger equation, Phys. Rev. C 81 (2010) 054314. 10.1103/PhysRevC.81.054314[36]T.OishiM.KimuraAnalytic continuation in coupling constant applied to two-proton emittersPhys. Rev. C112202501430510.1103/ckxc-r2c3T. Oishi, M. Kimura, Analytic continuation in coupling constant applied to two-proton emitters, Phys. Rev. C 112 (2025) 014305. 10.1103/ckxc-r2c3[37]P.DescouvemontMicroscopic three-cluster study of light exotic nucleiPhys. Rev. C99201906430810.1103/PhysRevC.99.064308P. Descouvemont, Microscopic three-cluster study of light exotic nuclei, Phys. Rev. C 99 (2019) 064308. 10.1103/PhysRevC.99.064308[38]X.-Y.XuS.-Q.FanQ.YuanB.-S.HuJ.-G.LiS.-M.WangF.-R.XuProgress in ab initio in-medium similarity renormalization group and coupled-channel method with coupling to the continuumNucl. Sci. Tech.3512202421510.1007/s41365-024-01585-0X.-Y. Xu, S.-Q. Fan, Q. Yuan, B.-S. Hu, J.-G. Li, S.-M. Wang, F.-R. Xu, Progress in ab initio in-medium similarity renormalization group and coupled-channel method with coupling to the continuum, Nucl. Sci. Tech. 35 (12) (2024) 215. 10.1007/s41365-024-01585-0[39]N.MichelW.NazarewiczM.PłoszajczakT.VertseShell model in the complex energy planeJ. Phys. G Nucl. Part. Phys.361200801310110.1088/0954-3899/36/1/013101N. Michel, W. Nazarewicz, M. Płoszajczak, T. Vertse, Shell model in the complex energy plane, J. Phys. G Nucl. Part. Phys. 36 (1) (2008) 013101. 10.1088/0954-3899/36/1/013101[40]L.ZhouS.-M.WangD.-Q.FangY.-G.MaRecent progress in two-proton radioactivityNucl. Sci. Tech.338202210510.1007/s41365-022-01091-1L. Zhou, S.-M. Wang, D.-Q. Fang, Y.-G. Ma, Recent progress in two-proton radioactivity, Nucl. Sci. Tech. 33 (8) (2022) 105. 10.1007/s41365-022-01091-1[41]S.-L.JinJ.-G.LiY.GaoR.-Z.HuF.-R.XuFull configuration interaction quantum Monte Carlo in nuclear structure calculationsNucl. Sci. Tech.3611202521210.1007/s41365-025-01790-5S.-L. Jin, J.-G. Li, Y. Gao, R.-Z. Hu, F.-R. Xu, Full configuration interaction quantum Monte Carlo in nuclear structure calculations, Nucl. Sci. Tech. 36 (11) (2025) 212. 10.1007/s41365-025-01790-5[42]N.MichelM.PłoszajczakGamow Shell Model: The Unified Theory of Nuclear Structure and Reactions, Lecture Notes in PhysicsVol. 9832021Springer, Cham, SwitzerlandN. Michel, M. Płoszajczak, Gamow Shell Model: The Unified Theory of Nuclear Structure and Reactions, Lecture Notes in Physics, Vol. 983, Springer, Cham, Switzerland, 2021.[43]N.MichelW.NazarewiczM.PłoszajczakK.BennaceurGamow shell model description of neutron-rich nucleiPhys. Rev. Lett.89200204250210.1103/PhysRevLett.89.042502N. Michel, W. Nazarewicz, M. Płoszajczak, K. Bennaceur, Gamow shell model description of neutron-rich nuclei, Phys. Rev. Lett. 89 (2002) 042502. 10.1103/PhysRevLett.89.042502[44]J.RotureauN.MichelW.NazarewiczM.PłoszajczakJ.DukelskyDensity matrix renormalization group approach for many-body open quantum systemsPhys. Rev. Lett.97200611060310.1103/PhysRevLett.97.110603J. Rotureau, N. Michel, W. Nazarewicz, M. Płoszajczak, J. Dukelsky, Density matrix renormalization group approach for many-body open quantum systems, Phys. Rev. Lett. 97 (2006) 110603. 10.1103/PhysRevLett.97.110603[45]G.PapadimitriouA.T.KruppaN.MichelW.NazarewiczM.PłoszajczakJ.RotureauCharge radii and neutron correlations in helium halo nucleiPhys. Rev. C84201105130410.1103/PhysRevC.84.051304G. Papadimitriou, A. T. Kruppa, N. Michel, W. Nazarewicz, M. Płoszajczak, J. Rotureau, Charge radii and neutron correlations in helium halo nuclei, Phys. Rev. C 84 (2011) 051304. 10.1103/PhysRevC.84.051304[46]Y.JaganathenR.M.I.BetanN.MichelW.NazarewiczM.PłoszajczakQuantified Gamow shell model interaction for psd-shell nucleiPhys. Rev. C96201705431610.1103/PhysRevC.96.054316Y. Jaganathen, R. M. I. Betan, N. Michel, W. Nazarewicz, M. Płoszajczak, Quantified Gamow shell model interaction for psd-shell nuclei, Phys. Rev. C 96 (2017) 054316. 10.1103/PhysRevC.96.054316[47]J.LiY.MaN.MichelB.HuZ.SunW.ZuoF.XuRecent progress in gamow shell model calculations of drip line nucleiPhysics34202197799710.3390/physics3040062J. Li, Y. Ma, N. Michel, B. Hu, Z. Sun, W. Zuo, F. Xu, Recent progress in gamow shell model calculations of drip line nuclei, Physics 3 (4) (2021) 977–997. 10.3390/physics3040062[48]T.BerggrenOn the use of resonant states in eigenfunction expansions of scattering and reaction amplitudesNucl. Phys. A1092196826528710.1016/0375-9474(68)90593-9T. Berggren, On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes, Nucl. Phys. A 109 (2) (1968) 265–287. 10.1016/0375-9474(68)90593-9[49]T.BerggrenP.LindResonant state expansion of the resolventPhys. Rev. C47199376877810.1103/PhysRevC.47.768T. Berggren, P. Lind, Resonant state expansion of the resolvent, Phys. Rev. C 47 (1993) 768–778. 10.1103/PhysRevC.47.768[50]J.-G.LiB.-S.HuS.ZhangF.-R.XuUnbound 28O, the heaviest oxygen isotope observed: a cutting-edge probe for testing nuclear modelsNucl. Sci. Tech.35220242110.1007/s41365-024-01373-wJ.-G. Li, B.-S. Hu, S. Zhang, F.-R. Xu, Unbound 28O, the heaviest oxygen isotope observed: a cutting-edge probe for testing nuclear models, Nucl. Sci. Tech. 35 (2) (2024) 21. 10.1007/s41365-024-01373-w[51]N.MichelJ.G.LiL.H.RuW.ZuoCalculation of the Thomas-Ehrman shift in 16F and 15O(p, p) cross sections within the Gamow shell modelPhys. Rev. C1062022L01130110.1103/PhysRevC.106.L011301N. Michel, J. G. Li, L. H. Ru, W. Zuo, Calculation of the Thomas-Ehrman shift in 16F and 15O(p, p) cross sections within the Gamow shell model, Phys. Rev. C 106 (2022) L011301. 10.1103/PhysRevC.106.L011301[52]K.FossezJ.RotureauN.MichelW.NazarewiczContinuum effects in neutron-drip-line oxygen isotopesPhys. Rev. C96201702430810.1103/PhysRevC.96.024308K. Fossez, J. Rotureau, N. Michel, W. Nazarewicz, Continuum effects in neutron-drip-line oxygen isotopes, Phys. Rev. C 96 (2017) 024308. 10.1103/PhysRevC.96.024308[53]N.MichelW.NazarewiczM.PłoszajczakJ.OkołowiczGamow shell model description of weakly bound nuclei and unbound nuclear statesPhys. Rev. C67200305431110.1103/PhysRevC.67.054311N. Michel, W. Nazarewicz, M. Płoszajczak, J. Okołowicz, Gamow shell model description of weakly bound nuclei and unbound nuclear states, Phys. Rev. C 67 (2003) 054311. 10.1103/PhysRevC.67.054311[54]K.H.LiN.ChenJ.G.LiH.H.LiM.R.XieC.W.MaW.ZuoGamow shell model calculations for the Thomas-Ehrman shift in the new isotope 21AlPhys. Rev. C111202503432710.1103/PhysRevC.111.034327K. H. Li, N. Chen, J. G. Li, H. H. Li, M. R. Xie, C. W. Ma, W. Zuo, Gamow shell model calculations for the Thomas-Ehrman shift in the new isotope 21Al, Phys. Rev. C 111 (2025) 034327. 10.1103/PhysRevC.111.034327[55]N.ChenJ.G.LiK.H.LiN.MichelP.Y.WangW.ZuoGamow shell model study of the 17Ne(p, p) reaction and of isospin symmetry breaking in 18NaPhys. Rev. C112202503431910.1103/8mt5-2k1zN. Chen, J. G. Li, K. H. Li, N. Michel, P. Y. Wang, W. Zuo, Gamow shell model study of the 17Ne(p, p) reaction and of isospin symmetry breaking in 18Na, Phys. Rev. C 112 (2025) 034319. 10.1103/8mt5-2k1z[56]G.L.G.SleijpenH.A.Van der VorstA Jacobi–Davidson iteration method for linear eigenvalue problemsSIAM J. Matrix Anal. Appl.172199640142510.1137/S0895479894270427G. L. G. Sleijpen, H. A. Van der Vorst, A Jacobi–Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl. 17 (2) (1996) 401–425. 10.1137/S0895479894270427[57]G.L.G.SleijpenA.G.L.BootenD.R.FokkemaH.A.van der VorstJacobi-davidson type methods for generalized eigenproblems and polynomial eigenproblemsBIT Numer. Math.363199659563310.1007/BF01731936G. L. G. Sleijpen, A. G. L. Booten, D. R. Fokkema, H. A. van der Vorst, Jacobi-davidson type methods for generalized eigenproblems and polynomial eigenproblems, BIT Numer. Math. 36 (3) (1996) 595–633. 10.1007/BF01731936[58]N.MichelH.M.AktulgaY.JaganathenToward scalable many-body calculations for nuclear open quantum systems using the Gamow shell modelComput. Phys. Commun.247202010697810.1016/j.cpc.2019.106978N. Michel, H. M. Aktulga, Y. Jaganathen, Toward scalable many-body calculations for nuclear open quantum systems using the Gamow shell model, Comput. Phys. Commun. 247 (2020) 106978. 10.1016/j.cpc.2019.106978[59]Y.SuzukiK.IkedaCluster-orbital shell model and its application to the He isotopesPhys. Rev. C38198841041310.1103/PhysRevC.38.410Y. Suzuki, K. Ikeda, Cluster-orbital shell model and its application to the He isotopes, Phys. Rev. C 38 (1988) 410–413. 10.1103/PhysRevC.38.410[60]K.FossezJ.RotureauN.MichelQ.LiuW.NazarewiczSingle-particle and collective motion in unbound deformed 39MgPhys. Rev. C94201605430210.1103/PhysRevC.94.054302K. Fossez, J. Rotureau, N. Michel, Q. Liu, W. Nazarewicz, Single-particle and collective motion in unbound deformed 39Mg, Phys. Rev. C 94 (2016) 054302. 10.1103/PhysRevC.94.054302[61]L.BrillouinLa méthode du Champ Self-ConsistentVol. 711993Hermann et CieL. Brillouin, La méthode du Champ Self-Consistent, Vol. 71, Hermann et Cie, 1993.[62]K.FossezJ.RotureauN.MichelM.PłoszajczakCan tetraneutron be a narrow resonance?Phys. Rev. Lett.119201703250110.1103/PhysRevLett.119.032501K. Fossez, J. Rotureau, N. Michel, M. Płoszajczak, Can tetraneutron be a narrow resonance?, Phys. Rev. Lett. 119 (2017) 032501. 10.1103/PhysRevLett.119.032501[63]http://www.nndc.bnl.gov/ensdf.[64]E.EpelbaumH.-W.HammerU.-G.MeißnerModern theory of nuclear forcesRev. Mod. Phys.8120091773182510.1103/RevModPhys.81.1773E. Epelbaum, H.-W. Hammer, U.-G. Meißner, Modern theory of nuclear forces, Rev. Mod. Phys. 81 (2009) 1773–1825. 10.1103/RevModPhys.81.1773[65]H.-W.HammerS.KönigU.van KolckNuclear effective field theory: status and perspectivesRev. Mod. Phys.92202002500410.1103/RevModPhys.92.025004H.-W. Hammer, S. König, U. van Kolck, Nuclear effective field theory: status and perspectives, Rev. Mod. Phys. 92 (2020) 025004. 10.1103/RevModPhys.92.025004[66]H.-W.HammerA.NoggaA.SchwenkColloquium: three-body forces: from cold atoms to nucleiRev. Mod. Phys.85201319721710.1103/RevModPhys.85.197H.-W. Hammer, A. Nogga, A. Schwenk, Colloquium: three-body forces: from cold atoms to nuclei, Rev. Mod. Phys. 85 (2013) 197–217. 10.1103/RevModPhys.85.197[67]L.ContessiA.LovatoF.PederivaA.RoggeroJ.KirscherU.van KolckGround-state properties of 4He and 16O extrapolated from lattice QCD with pionless EFTPhys. Lett. B772201783984810.1016/j.physletb.2017.07.048L. Contessi, A. Lovato, F. Pederiva, A. Roggero, J. Kirscher, U. van Kolck, Ground-state properties of 4He and 16O extrapolated from lattice QCD with pionless EFT, Phys. Lett. B 772 (2017) 839–848. 10.1016/j.physletb.2017.07.048[68]J.KirscherN.BarneaD.GazitF.PederivaU.van KolckSpectra and scattering of light lattice nuclei from effective field theoryPhys. Rev. C92201505400210.1103/PhysRevC.92.054002J. Kirscher, N. Barnea, D. Gazit, F. Pederiva, U. van Kolck, Spectra and scattering of light lattice nuclei from effective field theory, Phys. Rev. C 92 (2015) 054002. 10.1103/PhysRevC.92.054002[69]J.G.LiN.MichelW.ZuoF.R.XuUnbound spectra of neutron-rich oxygen isotopes predicted by the Gamow shell modelPhys. Rev. C103202103430510.1103/PhysRevC.103.034305J. G. Li, N. Michel, W. Zuo, F. R. Xu, Unbound spectra of neutron-rich oxygen isotopes predicted by the Gamow shell model, Phys. Rev. C 103 (2021) 034305. 10.1103/PhysRevC.103.034305[70]K.W.BrownR.J.CharityL.G.SobotkaL.V.GrigorenkoT.A.GolubkovaS.BedoorW.W.BuhroZ.ChajeckiJ.M.ElsonW.G.LynchJ.ManfrediD.G.McNeelW.ReviolR.ShaneR.H.ShowalterM.B.TsangJ.R.WinkelbauerA.H.WuosmaaInterplay between sequential and prompt two-proton decay from the first excited state of 16NePhys. Rev. C92201503432910.1103/PhysRevC.92.034329K. W. Brown, R. J. Charity, L. G. Sobotka, L. V. Grigorenko, T. A. Golubkova, S. Bedoor, W. W. Buhro, Z. Chajecki, J. M. Elson, W. G. Lynch, J. Manfredi, D. G. McNeel, W. Reviol, R. Shane, R. H. Showalter, M. B. Tsang, J. R. Winkelbauer, A. H. Wuosmaa, Interplay between sequential and prompt two-proton decay from the first excited state of 16Ne, Phys. Rev. C 92 (2015) 034329. 10.1103/PhysRevC.92.034329[71]H.T.FortuneConstraints on energies of 15F(g.s.), 15O(12+,T=32), and 16F(0+,T=2)Phys. Rev. C74200605431010.1103/PhysRevC.74.054310H. T. Fortune, Constraints on energies of 15F(g.s.), 15O($ {\frac{1}{2}}^{+},T=\frac{3}{2} $), and 16F($ {0}^{+},T=2 $), Phys. Rev. C 74 (2006) 054310. 10.1103/PhysRevC.74.054310[72]I.MukhaK.SümmererL.AcostaM.A.G.AlvarezE.CasarejosA.ChatillonD.Cortina-GilI.A.EgorovaJ.M.EspinoA.FomichevJ.E.García-RamosH.GeisselJ.Gómez-CamachoL.GrigorenkoJ.HofmannO.KiselevA.KorsheninnikovN.KurzY.A.LitvinovE.LitvinovaI.MartelC.NociforoW.OttM.PfütznerC.Rodríguez-TajesE.RoecklM.StanoiuN.K.TimofeyukH.WeickP.J.WoodsSpectroscopy of proton-unbound nuclei by tracking their decay products in-flight: one- and two- proton decays of 15F, 16Ne, and 19NaPhys. Rev. C82201005431510.1103/PhysRevC.82.054315I. Mukha, K. Sümmerer, L. Acosta, M. A. G. Alvarez, E. Casarejos, A. Chatillon, D. Cortina-Gil, I. A. Egorova, J. M. Espino, A. Fomichev, J. E. García-Ramos, H. Geissel, J. Gómez-Camacho, L. Grigorenko, J. Hofmann, O. Kiselev, A. Korsheninnikov, N. Kurz, Y. A. Litvinov, E. Litvinova, I. Martel, C. Nociforo, W. Ott, M. Pfützner, C. Rodríguez-Tajes, E. Roeckl, M. Stanoiu, N. K. Timofeyuk, H. Weick, P. J. Woods, Spectroscopy of proton-unbound nuclei by tracking their decay products in-flight: one- and two- proton decays of 15F, 16Ne, and 19Na, Phys. Rev. C 82 (2010) 054315. 10.1103/PhysRevC.82.054315[73]F.Ajzenberg-SeloveEnergy levels of light nuclei A = 13–15Nucl. Phys. A52311991119610.1016/0375-9474(91)90446-DF. Ajzenberg-Selove, Energy levels of light nuclei A = 13–15, Nucl. Phys. A 523 (1) (1991) 1–196. 10.1016/0375-9474(91)90446-D