The investigation of nuclear structure and reaction mechanisms for light drip-line nuclei, using intense radioactive beams, is one of the current frontiers of experimental and theoretical nuclear physics [1]. The halos discovered in light drip-line nuclei are fascinating structural phenomena characterized by low separation energies of the valence nucleons in low-angular momentum states. These features result in an extended valence-nucleon wave function far beyond the range of the nucleon-core potential. Traditional shell-model and mean-field models break down, as can be expected in such a dilute structure, while cluster models can reproduce the most general features. Numerous nuclei possessing a neutron-halo structure are observed among light neutron-rich drip-line nuclei (Z 10) [2]. There are, however, only a few proton-halo nuclei or candidates for such. Evidence of oneproton halos has been found for 8 B(g.s.) [3][S p = 136(4) keV, p shell], for an excited state 17 F(1/2 + ) [4][S p = 104.9(3) keV, s shell], and for 12 N(g.s.) [5][S p = 601.2(1.4) keV, p shell]. The 17 Ne nucleus is the only realistic candidate for having atwo-protonhalo [5,6][S 2p = 933.1(0.6) keV, sd shell]. The proton separation energies given here were taken from Ref. [7]. The properties of 17 Ne have been intensively studied both theoretically and experimentally. However, these investigations give contradicting results both in the analyses of experimental data and in the theoretical predictions (see Refs. [8,9] and references therein).
Experimental data for drip-line nuclei are also important ingredients in astrophysical calculations, such as nucleosynthesis, stellar evolution, and supernova dynamics. Here an understanding of the 17 Ne electromagnetic dissociation is of relevance for the rapid proton-capture rp-process, where 15 O (T 1/2 = 122 s) is a waiting-point nucleus to produce heavier elements and the two-proton capture reaction 15 O(2p,γ ) 17 Ne is expected to compete with other reaction branches. However, theoretical calculations of the 15 O(2p,γ ) 17 Ne reaction rate differ by several orders of magnitude among each other [10][11][12].
The purpose of the present paper is to present new experimental data on nuclear and electromagnetic dissociation of 17 Ne to further elucidate its structure.
The present experiment was performed at the GSI Helmholzzentrum für Schwerionenforschung GmbH in Darmstadt, Germany, employing the ALADIN-R3B setup for studies of relativistic beams in inverse and full kinematics. An outline of the experimental setup is shown in Fig. 1. A beam of radioactive 17 Ne isotopes (500 MeV/u), produced in fragmentation reactions of a 20 Ne primary beam, was directed toward lead (199 mg/cm 2 ), carbon (370 mg/cm 2 ), and polyethylene (213 mg/cm 2 ) targets to investigate electromagnetic and nuclear dissociation reactions. The combined measurements with polyethylene and carbon targets allowed us to obtain data for fragmentation of 17 Ne on hydrogen. The reaction products were separated according to their mass and charge by the magnetic field of ALADIN (a large-acceptance dipole magnet). Behind ALADIN two separate branches of detectors were used to measure the coordinates of hits, energy loss, and time-of-flight (TOF) of the heavy ions and protons. A tracker routine was employed to get four-momenta of all outgoing charged particles. This analysis requires a precise knowledge of the magnetic field strength inside and outside the magnet, which was measured at several thousands of grid points [13].
The collected reaction events were subdivided into three groups: (i) inclusive detection of oxygen isotopes (inclusive), (ii) oxygen isotopes in coincidence with one proton (p mult = 1), and (iii) in coincidence with two protons (p mult = 2). As will be shown below, we make the following observations:
(1) Events with p mult = 1 together with 15 O are dominated by one-proton knockout.
(2) Events with p mult = 1 and 14 O have a complex mechanism of fragmentation.
(3) Events with p mult = 2 and 15 O are dominated by inelastic scattering with population of excited states in 17 Ne and diffractive dissociation.
(4) Events with p mult = 2 and 14 O reveal distinct features of one-neutron knockout.
The experimental data gave four-momentum vectors for the oxygen isotopes 13,14,15 O and for the protons. The analysis of p mult = 2 events was done using a Jacobi coordinate system, as described in Ref. [14]. From the four-momentum vectors, the relative energies between 13,14,15 O and the observed proton were obtained (E fp ). Also the internal energies in the threebody systems 13,14,15 O + 2p (E fpp ) were obtained together with the fractional energies fp = E fp /E fpp .
The background stemming from interactions of the beam with the material surrounding the target was obtained in separate measurements with an empty target holder. The probability for detection of one proton ( 1p ) and two protons ( 2p ) in the proton-drift chambers (PDCs) was determined experimentally from coincidences with the proton time-offlight wall, where protons are detected with 100% efficiency in thick plastic scintillators. The probabilities are 1p = 0.859 (5) and 2p = 0.58 (4), and this results in another type of background for events with only one detected proton. There is, namely, a certain probability that two protons may have hit the same wire pair in a PDC, w , and such events would be recognized as single-proton events. The probability for this can be estimated to be w = 2 1p -2p = 0.16 (4). Besides, when the energy deposition of a proton in the PDC is below the detection threshold, events with two protons crossing the detector area are misinterpreted as single-proton events with the probability 2p→1p = 2 1p (1 -1p ). The background in p mult = 1 events arising from two protons crossing the detector area but misinterpreted as a one-proton event was also taken into account.
After corrections for detection efficiencies and subtraction of background, the differential cross sections need to be corrected for the geometrical acceptance. These corrections for differential cross sections, as functions of E fp for p mult = 1 and E fpp for p mult = 2, were obtained from Monte Carlo simulations, comprising the ALADIN-R3B setup response. Hence, total cross sections for different reaction branches were obtained using the number of detected inclusive, p mult = 1, and p mult = 2 events. The basic relation between the total cross sections for inclusive, p mult = 1, and p mult = 2 events is
where σ raw incl , σ raw 1p , and σ raw 2p are the respective cross sections for inclusive, p mult = 1 and p mult = 2 events corrected for detection efficiency but uncorrected for the geometrical acceptance. A f , A 1p , and A 2p are the geometrical acceptances for detection of a fragment, one proton, and two protons. The limited geometrical acceptance A f results in a suppression of the negative tail of the horizontal momentum component (p y ) and was obtained from the fit by only using its positive values. A f was found to be 1.00 for detection of 15 O, 0.90(5) for 14 O, and about 0.5 for 13 O. As an example, Fig. 2 shows this for the CH 2 target.
Equation (1) demonstrates that the absolute values of the total cross sections for different branches of Coulomb and nuclear dissociations of 17 Ne can be obtained by only using the experimentally determined quantities without Monte Carlo simulations, which generally are used for this purpose. Monte Carlo simulations suffer, however, from some unavoidable approximations for the input data describing kinematic properties of fragments in the final state. In particular, when the GENBOD random event generator [15] is used, it generates multiparticle dissociation events according to the Lorentz-invariant phase space, while the present experiment has shown that sequential proton emission, with population of excited states in 16 F, is essential.
The PDCs allow for detection of protons with transverse momenta up to ≈70 MeV/c. The shapes of the transverse momentum distributions for protons obtained from p mult = 1 and p mult = 2 events were found to be indistinguishable within the statistical uncertainties (see Fig. 3).
This thus gives evidence that A 2p = A 2 1p . The geometrical acceptances for single-proton events in coincidence with 14,15 O fragments (A 1p ) were determined for each target separately by using Eq. ( 1) and assuming that A 2p = A 2 1p . The resulting values demonstrate an insensitivity to the target material with χ 2 = 0.34 for 15 O and χ 2 = 0.68 for 14 O. Here χ 2 is the weighted sum of squared differences between A 1p obtained for the individual targets and their weighted mean value. The weighted mean value of A 1p is 0.744 (10) and A 2 1p = 0.553 (15). The assumption that A 2p = A 2 1p was checked by using explicitly Eq. ( 1) and the data from different targets. The corresponding A 1p weighted mean value is 0.759(30), A 2p = 0.514(52), confirming the assumptions of target independence and A 2p = A 2 1p is valid within an uncertainty lower than 10%. The comparison of obtained acceptance factors to the Monte dσ/dp (arb. units) Carlo results shows that the approximations used to describe the fragmentation mechanism are acceptable.
The 15 Ne from 13 O + 2p,t h e 16 Ne from 14 O + 2p triple coincidences and inelastic scattering with excitation of narrow resonances in 17 Ne have been analyzed and the results were 17 Ne impinging on hydrogen ( ), carbon (blue, ), and lead (red, ) targets. The distributions were obtained in inclusive detection of oxygen isotopes (a), and in coincidences with one or two protons: 13,14,15 O+1p (b), and 13,14,15 O+2p (c). Distributions in (b) were corrected for misidentification of two protons as a single one (see text). The empty-target background was subtracted. The scale of the dN/dA distribution is fixed by normalizing the 15 O peaks to unity. The 13 O data (hatched region) were scaled up by the shown factors. published in Refs. [9,16,17]. The present paper is devoted mainly to the disentanglement of different reaction branches in the dissociation of 17 Ne, and to the electromagnetic dissociation resulting in a continuous internal energy spectrum in the 15 O -2p three-body system. 0 1 2 3 4 5 0 1 2 3 4 5 dσ/dp (arb. units) x p (MeV/c) x -200 -200 200 200 00 (a) (b) (c) (d) O 14 O 14 O 15 O 15 p =1 mult p =1 mult p =2 mult p =2 mult FIG. 5. Comparison of transverse momentum distributions for 15 Oand 14 O fragments, and different multiplicities of protons crossing the detector area, p mult = 1andp mult = 2. The Pb data in frames (c) and (d) were left out due to too low statistics. Notation for the different targets is the same as in Fig. 4.
distributions for p mult = 1 are narrow for the light targets but about a factor of 2 larger for the lead target [see Fig. 5(a)]. For all these events, one proton exhibits such a large momentum transfer that it is scattered outside the range of the proton detectors, and accordingly we attribute them to the one-proton knockout mechanism. Single-proton knockout results in the population of excited states in 16 F. The comparison of the E fp spectra obtained with different targets, shown in Fig. 6, illustrates that the relative population of states in 16 F is independent of the reaction target. In the Pb case, proton knockout takes place deep inside the Coulomb field resulting in a strong deflection of the charged particles. The proton-unstable 16 F fragment is passing the region of Coulomb repulsion as one
TABLE I. FWHM in MeV/c for fragment momentum distributions. The data are corrected for the experimental resolution. Target Fragment p mult = 1 p mult = 2 Hydrogen 15 O 142(10) 362(15) 14 O 290(15) 213(8) Carbon 15 O 152(14) 301(6) 14 O broad 213(5) Lead 15 O 430(22) 285(6) dσ/dE (arb .units) fp 0.0 0.2 0.4 0.6 0.8 1.0 0.0 E (MeV) fp 0.4 0.8 1.2 1.6 2.0 Pb C H 0 -1 -3 -2 -FIG. 6. Comparison of relative energy spectra E fp obtained in coincidence between 14,15 O and a proton for p mult = 1 for the three targets. The arrows show the excitation energies of resonance states in 16 F. single object and its decay takes place outside the region of the strong Coulomb field, since the widths of the lowest four resonances in 16 F are less than 100 keV, corresponding to a 1500-fm distance traveled by the excited 16 F during the resonance lifetime. The widths of 15 O momentum distribution s h o w ni nF i g .4(a) for the Pb target is broader than for the lighter targets. The reaction mechanism is interpreted to mainly be due to (1) inelastic scattering with excitation of 17 Ne states and (2) diffractive dissociation to 15 O + 2p without a strong final-state interaction. In this case the two protons are emitted in the forward direction.
The data obtained for 14 Ointhep mult = 1 case, shown in Fig. 5(c), suggest a complex fragmentation mechanism. The momentum distributions are broad for all targets.
One notes in Fig. 4(c) a significant decrease in the yield of 15 O relative to 14 Ointhep mult = 2 case with light targets. This is also seen in the ratio R(x) = σ ( 15 O)/σ ( 14 O) in Table II: R(H ) = 0.95 (16), R(C) = 1.18 (10), and R(Pb) = 6.11(68), where the given uncertainties are statistical. The inelastic scattering and diffractive dissociation reaction mechanisms are predominant for the lead target, while a nucleon knockout mechanism is more probable for the hydrogen and carbon targets.
TABLE II. Total cross sections (mb) for fragmentation of 17 Ne in different targets. The data are corrected for background, detection efficiency, and geometrical acceptance. The indicated uncertainties are statistical. Target Fragment σ incl σ 1p σ 2p Hydrogen 15 O 52.0(3.0) 42.3(1.6) 8.75(59) 14 O 20.4(2.9) 10.4(1.1) 9.7(1.5) Carbon 15 O 117.5(4.0) 98.6(1.6) 20.68(68) 14 O 30.4(3.1) 11.61(87) 17.5(1.3) Lead 15 O 534(22) 296.9(8.5) 227.4(6.9) 14 O 63(20) 17.8(4.1) 37.2(4.0) E (MeV) fpp 02468 dσ/dE (mb/MeV) fpp 0 10 20 30 40 50 0 2 4 6 8 0 1 2 H( Ne, O+p+p) 17 15 C( Ne, O+p+p) 17 15 Pb( Ne, O+p+p) 17 15
FIG. 7. Relative energy spectra for the 15 O + 2p system obtained with hydrogen, carbon, and lead targets. The full drawn curves represent excited states superimposed on a smooth contribution from diffractive dissociation (dashed curves) [9].
The momentum distributions for 14 O with p mult = 2, shown in Fig. 5(d), are significantly narrower than for 14 O with p mult = 1 [Fig. 5(c)]. This is evidence for a neutron knockout mechanism, which leads to the unbound nucleus 16 Ne decaying via two-proton emission with both protons flying in the forward direction.
The total cross sections for fragmentation of 17 Ne on different targets corrected for background, detection efficiency, and geometrical acceptance are presented in Table II.
The experimental 15 O + p + p relative-energy spectra showninFig.7 are due to excited states in 17 Ne superimposed on a smooth contribution to the spectrum from diffractive dissociation (dashed curves) [9]. The nuclear and electromagnetic excitations of narrow resonances in 17 Ne were discussed in Ref. [9] together with the three-body correlations at low energies for the E fpp up to 3.0 MeV. However, as seen in Fig. 7, the fragmentation shows also a strong contribution at higher energies where there is no pronounced resonance structure.
The fractional energy distributions in different relative energy regions are shown in Figs. 8 and 9. These distributions were fitted assuming sequential proton emission with population of the lowest four negative parity states in 16 and Pb [(b), (d)] targets. The least-square fits to the data, assuming population of 16 F(0 -,1 -) states (thin solid lines), 16 F(2 -,3 -)(dashed lines), and a genuine three-body decay (dashed-dotted lines), are shown.
5.0 <E fpp < 8.0 MeV. The signatures of genuine three-body decays start to become evident at E fpp > 3.8 MeV. Only the amplitudes of the components were used as free parameters in the fits.
The shape of the W ( fp ) distribution for a genuine threebody decay was described assuming [s 2 ] → [sp] as the dominating transition:
where E 1 , ℓ 1 (E 2 , ℓ 2 ) are relative 15 O-p energies and angular momenta for the protons. Here the exponential is the Gamow penetrability factor, where G was obtained from a fit to the penetrability factor as a function of energy, calculated using the RCWFN code [18], and where the last two terms represent the phase space. The lowest states 0 -and 1 -in 16 F have the structure 15 O(1/2 -) ⊗ (1s 1/2 ) while 15 O(1/2 -) ⊗ (0d 5/2 ) characterizes the 2 -and 3 -states. The widths of all four states are consistent with single-proton states [19]. Population of d states in 16 F have larger probability than s states for light targets, while in reactions in the lead target mainly s states are populated. The . The least-square fits to the data, assuming population of 16 F(0 -,1 -) states (thin solid lines), 16 F(2 -,3 -)(dashed lines), 16 F(I + ) states (dashed lines), and a genuine three-body decay (dashed-dotted lines), are shown.
relative contributions from different branches in different E fpp energy regions for CH 2 and Pb targets are shown in Table III.
The electromagnetic dissociation (EMD) cross section was obtained by subtracting the nuclear dissociation contribution from the dσ/dE(lead) spectrum. This contribution was taken as the dσ/dE(carbon) contribution scaled by a factor of 1.84 (20). This scaling factor was determined experimentally TABLE III. Decay branches (%) in the fragmentation of 17 Ne on CH 2 a n dP bt a r g e t s . 16 F(I + ) denotes positive parity states in 16 [11] [blue solid line -P (s 2 ) = 5%, dashed line -P (s 2 ) = 48%, dashed-dotted line-P (s 2 ) = 73%], by 2(red) for [22], and by 3 (magenta) for [23]. The dotted lines in (a) demonstrate the influence of experimental energy resolution. The upper limit for 17 Ne(g.s.) → 17 Ne(1/2 + ) resonance transition from [9]i ss h o w n . The hatched zone shows the position of the Gamow window for 15 O(2p,γ ) 17 Ne as a function of E fp at 1 GK temperature. in Ref. [9] by assuming that the electromagnetic dissociation of 17 Ne to 14 O has a negligible cross section. The scaling factor is close to the ratio between the sums of projectile and target matter radii, reflecting that the nuclear disintegration is of surface character. The EMD cross section with 14 O in the final state is close to zero, 1.6(6.6) mb, as expected, and thus confirming the value of the scaling factor. The EMD cross section for 15 O as the reaction product was 305(11) mb, with 115(9) mb in the channel with p mult = 1. From the experimental data dσ/dE fpp and from that the dipole-strength function dB(E1)/dE fpp was calculated by using the virtual photon method [20,21]. The virtual photon numbers were taken from [11]. The obtained differential cross section for electromagnetic dissociation is shown in Fig. 10(a), and the corresponding dipole-strength function dB(E1)/dE fpp in Fig. 10(b). The curves 1 (blue), 2 (red), and 3 (magenta) were obtained in calculations using three different models.
The calculations for curve 1 were based on a three-body model in which only the 15 O-p interaction is taken as important, "the one final-state interaction model" (OFSI) [11]. The results were obtained assuming different weights of the (s 2 ) component in the 17 Ne(g.s.): 5%, 48%, and 73%. The E1 strength function was calculated for [s 2 ] → [sp] and [d 2 ] → [dp] transitions. The calculated cross section increases strongly with the increasing P (s 2 ). In order to get agreement with the experimental data in the region around 4 MeV (maximum of the cross section) the following scaling factors would be required: 0.5 for P (s 2 ) = 5%, 0.25 for P (s 2 ) = 48%, and 0.22 for P (s 2 ) = 73%.
The curves labeled 2 in Fig. 10 show the EMD cross section and dB(E1)/dE fpp distribution obtained from [22]. The E1 strength was calculated for 17 Ne assuming a 15 O + 2p structure with s-and d-wave probabilities P (s 2 ) = 16% and P (d 2 ) = 76%, where the two valence protons are excited from the 0 + ground-state configuration to 1 -continuum states.
Finally each curve 3 in Fig. 10 shows results obtained from [23]. These calculations were made in the framework of the Hartree-Bogoliubov theory and in a relativistic quasiparticle random-phase approximation. The proton pygmy dipole resonance (PDR) was predicted at E fpp = 9.26 MeV. A similar result has been obtained in [24] within a shell model with the self-consistent Skyrme-Hartree-Fock wave functions where the PDR was predicted at around 10 MeV. The common feature for all three calculations is an underestimate of the dissociation cross section in the energy region below 3 MeV. However, as shown in Fig. 10(a), the probability for excitation of the 5/2 - 1 state at resonance energy 0.83 MeV by an E2 transition is large. In our earlier study of population of narrow resonances in 17 Ne [9], evidence was found for 3/2 - 2 and 5/2 - 2 states at resonance energies 1.76 and 2.48 MeV, respectively. Also, two additional states with I π = 3/2 -or 5/2 -were observed in the mirror nucleus 17 N at excitation energies 4.4 and 5.5 MeV [25], which would indicate the presence of isobar-analog states in 17 Ne at resonance energies ≈3 and ≈4 MeV. These facts indicate that the E2 transitions are not negligible in the dissociation of 17 Ne. The result obtained in [22] is within spitting distance of the experimental spectrum above 5 MeV.
The hatched region in Fig. 10(b) shows the position of the Gamow window for 15 O(2p,γ ) 17 Ne at 1 GK temperature. The reaction rate is very sensitive to the dB(E1)/dE value in this energy region where the values obtained in Refs. [22,23] are, by several orders of magnitude, larger than those in [11]. As stated in [10], a significant part of the E1 strength goes to the 17 Ne(1/2 + ) resonance at 0.975 MeV above the 15 O + 2p threshold. The upper limit for 17 Ne(g.s.) → 17 Ne(1/2 + ) transition from [9] is shown in Fig. 10.
A combination of several models, based on the three-body structure of 17 Ne, was used in recent calculations [26]. The E1 strength function was obtained assuming P (s 2 ) = 48% for 17 Ne(g.s.). The E1 strength function is close to the result of the OFSI model [11]. The calculated cross section of the E1 excitation, σ (E1) = 386 mb [26], is close to the one obtained in the present experiment. However, the ratio between the cross sections leading to production of 16 Fi ns wave, σ (E1,s) = 368 mb, and d wave, σ (E1,d) = 18 mb, is 20, while the experimental ratio does not exceed a factor of 2.