Coulomb and nuclear excitations of narrow resonances in 17 Ne

New experimental data for dissociation of relativistic 17 Ne projectiles incident on targets of lead, carbon, and polyethylene targets at GSI are presented. Special attention is paid to the excitation and decay of narrow resonant states in 17 Ne. Distributions of internal energy in the 15 O + p + p three-body system have been determined together with angular and partial-energy correlations between the decay products in different energy regions. The analysis was done using existing experimental data on 17 Ne and its mirror nucleus 17 N. The isobaric multiplet mass equation is used for assignment of observed resonances and their spins and parities. A combination of data from the heavy and light targets yielded cross sections and transition probabilities for the Coulomb excitations of the narrow resonant states. The excitation of 17 Ne at relativistic energies

New experimental data for dissociation of relativistic 17 Ne projectiles incident on targets of lead, carbon, and polyethylene targets at GSI are presented. Special attention is paid to the excitation and decay of narrow resonant states in 17 Ne. Distributions of internal energy in the 15 O + p + p three-body system have been determined together with angular and partial-energy correlations between the decay products in different energy regions. The analysis was done using existing experimental data on 17 Ne and its mirror nucleus 17  The proton dripline nucleus 17 Ne is a candidate for a twoproton Borromean halo nucleus [1], with a 15 O core surrounded by two valence protons. The protons are expected to predominantly possess a mixed (1s 1/2 ) 2 and (0d 5/2 ) 2 configuration. There is, however, no real consensus about the relative strength of the s and d configurations, neither experimentally nor theoretically. Estimates based on experimental values for interaction cross-section and momentum distributions of fragments in one-proton knockout [2][3][4][5], the magnetic dipole moment [6], first-forbidden β + -decay [7,8], Coulomb energy difference between the mirror nuclei 17 Ne and 17 N [9][10][11][12][13], as well as pure theoretical investigations [14][15][16], provide widely differing results. Different evaluations of the amount of (1s 1/2 ) 2 in the 17 Ne ground-state wave function, P(s 2 ), range from 15% to 100%. There are also strong contradictions between different theoretical models for Coulomb dissociation of 17 Ne [17][18][19][20].
A theoretical study [21] points to the importance of the determination of electric transition strengths to elucidate the twoproton halo properties. The authors emphasise in particular the importance of reduced electric transition probabilities from the 17 Ne ground state to low-lying states as for example This paper presents a new comparative study of nuclear and Coulomb excitation of 17 Ne at relativistic energies using polyethylene (CH 2 ), carbon, and lead targets.
The experiment was performed at the GSI Helmholzzentrum für Schwerionenforschung GmbH in Darmstadt, employing the R 3 B-LAND setup for measurements in inverse and full kinematics. The reaction products, from 17 Ne interaction, were first detected in a pair of silicon-strip detectors and then separated in the magnetic field of the large dipole magnet (ALADIN). After the magnet, two branches of detectors were used to measure the position, energyloss, and time-of-flight, one for heavy ions (two fibre detectors and a ToF-wall) and another for protons (two drift chambers PDC and a ToF-wall). The trajectories of charged particles through the magnetic field of ALADIN were reconstructed for particle identification and determination of their momentum vectors. The charge of the particles was directly measured via their energy loss in the siliconstrip detectors and ToF-walls, while their mass was obtained from measurements of Bρ using the reconstructed deflection angle in the ALADIN magnet. This analysis is based on knowledge of the magnetic field inside and outside the ALADIN magnet, measured along all three coordinate axes at many thousands of grid points.
The γ -rays emitted by the de-exciting fragments were detected in the 4π gamma spectrometer, Crystal Ball, placed around the target. A sketch of the positions of the charged-particle detectors in the experimental setup is shown in Fig. 1 of Ref. [22].
The 17 Ne beam was directed towards a secondary 199 mg/cm lead target, used to induce electromagnetic excitation of 17 Ne. The experiment also took data with a 370 mg/cm 2 carbon target as well as a 213 mg/cm 2 polyethylene target, to study nuclearinduced breakup. The background was determined in runs with an empty target.
Triple coincidences between 15 O and two protons were selected. The intrinsic two-proton detection efficiency was 57.8(3.1)%. The detection efficiency was determined from losses of two-proton events due to too small energy deposited in the PDCs, losses during the reconstruction of proton trajectories in the magnetic field of ALADIN, and losses due to the spatial resolution in the PDCs.
The losses due to PDC resolution are increasing with the decreasing internal energy in the three-body system. However even at the energy of the 17 Ne(5/2 − ) resonance the change in the detection efficiency was found to be smaller than its uncertainty. The magnetic spectrometer provided large difference in proton trajectories. Quadruple coincidences, including γ -ray detectors, showed that contributions from excited states in 15 O are negligible.
The momentum vectors of the protons and the 15 O fragments were obtained in the rest frame of the beam. As in Ref. [22] and its Eq. (1), Jacobi coordinates in the Y-system were used in the analysis. The internal kinetic energy, E f pp , in the three-body 15 O + p + p system, as well as the fractional energies f p = E f p /E f pp in the fragment-proton subsystem and the angle θ f p between the two vectors p f p and p p− f p , was determined for each event. The analysis was done in two consecutive loops through each event, by selecting one detected proton as the first one in the first loop and then changing to the opposite order in the second loop. The data were corrected for acceptance. The overall acceptance, including momentum cuts due to the finite size of detectors and dead wires in the proton drift chambers, was calculated in a Monte-Carlo simulation under the assumption of isotopic three-body decay. The acceptance function on E f pp is shown in Fig. 3 of Ref. [22]. The experimental energy resolution was found to be close to a Gaussian shape with a dispersion σ = 1. The experimental excitation energy spectra, E * = E f pp + S 2p ( 17 Ne), shown in Fig. 1, are well described as resulting from the contribution of several excited states in 17 Ne, superimposed on a smooth background, shown as dashed lines. This background corresponds to non-resonant dissociation and may also contain contributions from unresolved resonances. Based on experimental results [25], the widths of the resonance structures were assumed as determined entirely by the experimental resolution. A leastsquares fit was performed using the functional minimisation and error analysis code MINUIT [24]. The smooth background, shown as dashed lines in Fig. 1, corresponds to non-resonant dissociation and may also contain contributions from unresolved resonances. Extrapolation of this smooth background into the region of resonances was done by using information from the W ( f p ) distributions (see Fig. 5).
Five resonance-like structures corresponding to excitations of narrow resonant states in 17 Ne are observed in the data from the CH 2 and C targets, while only three are identified in the data from the Pb target (see Fig. 1 and Table 1). The level structure of 17 Ne has been studied earlier using the three-neutron transfer reaction 20 Ne( 3 He, 6 He) [25]. These results were used as a first guidance in our interpretation together with the available experimental information about the structure of excited states in the mirror nucleus 17 N [26]. Atomic masses and energy levels of the A = 17, T = 3/2 isobaric multiplets taken from Refs. [27,28] were also used together with the isobaric multiplet mass equation (IMME) and the Thomas-Ehrman shifts (TESs) for the classification of the states.
(1) The first peak in the spectrum is due to an unresolved doublet consisting of two narrow states at 1.764(12) MeV (I π = 5/2 − ) and at 1.908(15) MeV (1/2 + ) [25]. The relative contribu-  Table 1. tions of these two states were obtained from an analysis of the three-body correlations in the energy region 0 The second peak at E * = 2.652 MeV (see Table 1) is close in energy to the observed excited state at 2.651(12) MeV [25]. This state was interpreted to be an I π = 5/2 + state. However, a 5/2 + state is unlikely to be fed in a Pb target by Coulomb excitation due to the small strength of the required E3 or M2 transitions. Hence, the possibility that the observed peak is due to an unresolved doublet cannot be excluded. Overlapping states with the spin-parity, 5/2 + 1 and 5/2 − 2 , were proposed (see Ref. [25] and references therein). However, in this case an unusually large negative cubic-term coefficient is required (d = −25 keV) in the isobaric multiplet mass equation (IMME) for the 5/2 − 2 iso-quartet and furthermore the Thomas-Ehrman shift for the 5/2 − 2 state is surprisingly large in this case (≈ 1 MeV). 1 An alternative hypothesis is an unresolved doublet of 5/2 + 1 and 3/2 − 2 states. The parabolic IMME was used in the analysis (see Table 2). The position of the 17 (14) keV. The structure of the analog states in the mirror nucleus 17 N has shown that the 3/2 − 1 and 3/2 − 2 states have wave functions [26] with a 14% configuration with one valence proton in the s-shell for 3/2 − 1 and 86% for 3/2 − 2 [26]. A similar structure is expected for the analog states in 17 Ne. Thus a small value for TES(3/2 − 1 ) and a large for TES(3/2 − 2 ) can be explained as a large asymmetry in the weights of the configuration with one valence nucleon in the s-shell and the large spatial extension of the s-wave proton wave function. 2 (3) The excitation energy of the third peak, at E * = 3.415(38) MeV, is close to the observed position of the 9/2 − state at E * = 3.548(20) MeV [25], but the energy difference and the fact that there is no sign of a 7/2 − state, which should have similar structure as the 9/2 − state [26], excludes such an assign- 1 The Thomas-Ehrman shift, TES(I π ), was defined as the difference between the distances from 7/2 − to I π states in the mirror nuclei 17 Ne and 17 N. The 7/2 − states were chosen as reference since the Coulomb-energy shifts for these states, having three-body structure with two valence nucleons in the d-shell, are expected to be small. 2 Note also a large negative TES for positive-parity states. These states cannot be incorporated in the three-body models generally used for the description of 17 Ne structure and reactions involving this nucleus. An explanation of the experimental parity-dependence of the Coulomb-energy shifts of the A = 17 iso-quartet was suggested, e.g., in Ref. [13], using a model with five valence nucleons around the 12 C core.

Table 1
Excitation energies (MeV) and cross sections (mb) with statistical error bars for observed resonance structures in 17 Ne excitation spectra. The number N refers to the structures shown in Fig. 1.    17 Ne level scheme is rather intricate, which makes the analysis knotty. The three-neutron transfer reaction has a selectivity to excitation of states with a definite structure and some states may therefore be missed. A comparison with the level scheme of mirror nucleus, 17 N, suggests that this state could be the second 5/2 − state. The analysis given in Ref. [26] for the 5/2 − 2 state in 17 N, gave a weight of 72% for a configuration with a single proton in the s-shell, a structure similar to that of the 3/2 − 2 state. The present value TES(5/2 − The analysis of the narrow resonant states in the low energy region, based on the discussion above, is shown in Fig. 2 and the results are given in Table 3. Cross sections for excitation of energy levels in the 1 H( 17 Ne(g.s.), 17 Ne(I π )) reaction were obtained from the relation: σ (CH 2 ) = σ (C) + 2σ (H). The data demonstrate different selectivity for the different targets. Thus, for the hydrogen target, positive-parity states have lower excitation probability compared to those with negative-parity. The partial decay scheme with dominating decay branches is shown in Fig. 6.
In order to extract more information from the data, the lowenergy part of the E f pp spectrum was divided into three separate regions, as show in Fig. 2, where the fractional energy spectrum W ( f p ) and the angular distribution W (θ f p ) were constructed and analysed. A sequential decay via an intermediate narrow resonance in 16 F at r = E r /E f pp appears in the W (E f p ) distribution as two peaks at r and 1 − r . A 2 He decay, or diproton emission, would   be characterised by an asymmetric angular W (θ f p ) distribution, increasing when θ f p gets close to 180 • . In the present analysis W (θ f p ) was found to be close to isotropic, within statistical uncertainties, which excludes a significant 2 He emission. The shapes of the W ( f p ) distributions are well described by assuming sequential decays through the first four excited states in 16 F. The parameters for these states were taken from Ref. [23]. The partial W ( f p ) shapes are strongly influenced by the experimental resolution and were calculated in Monte-Carlo simulations. The MINUIT A doublet with 5/2 + and 3/2 − 2 states was identified in the energy region 1.4 ≤ E f pp ≤ 2.2 MeV (region II in Fig. 2). The difference in excitation energy of these two states is much smaller than the experimental resolution and the difference in shape of W ( f p ) for the decay branches is marginal. The penetrability through the Coulomb and centrifugal barriers for the decay of 5/2 + to 3 − is about 20 times smaller than that for the decay to the 2 − state. Further, this ratio is around 1000 for the decay of 3/2 − 2 state. The main decay branches for both states are therefore expected to proceed via the 16 F(2 − ) state. The analysis of W ( f p ) from a carbon target gave a decay branch of 86(2)% while the rest can be attributed to the feeding of the 16 F(3 − ) state. The W ( f p ) from CH 2 and Pb targets were fitted with an assumption that the 17 Ne(5/2 + ) and 17 Ne(3/2 − 2 ) states decay predominantly through 16 F(2 − ) and 16 F(0 − ) states. Contributions from the 16 F(2 − ) branch were 74(2)% for CH 2 and 41(4)% for Pb targets, see Fig. 4. The rest can be attributed to feeding mainly of the 16 F(0 − ) state with a small contribution from the 16 F(3 − ) branch. In the case of the Pb target, the main part of the 16 F(0 − ) branch is coming from a continuous E f pp spectrum.
In the energy region 2.2 ≤ E f pp ≤ 3.0 MeV a contribution from the 17 Ne(5/2 − 2 ) state is expected. The decay branches from this resonance should proceed mainly by emission of = 0 protons, feeding dominantly 2 − and 3 − states in 16 F. The population of 0 − and 1 − states in the resonance decay requires emission of = 2 protons and is expected to be small due to penetrability factors. Still there are sizeable contributions in the W ( f p ) distribution from feeding to these states, especially pronounced for the Pb target, as shown in Fig. 5. These parts of the distributions were treated as a physical background.
The ratio between the feedings σ (2 − )/σ (3 − ) ≈ 1 was obtained for both the CH 2 and the C target. For the Pb target, keeping this ratio fixed, the W ( f p ) cannot be reproduced, which shows that these events cannot be considered as having their origin in the decay of the 5/2 − 2 state. They were therefore also considered as coming from a continuous E f pp spectrum. The distribution was well fitted with only three decay branched to the 0 − , 1 − and 2 − states in 16 F.
The cross sections for Coulomb excitation of resonant states, σ C , were obtained by subtracting the nuclear contribution from the cross sections measured with the lead target scaled with a factor 1.84 (20). The scaling factor was determined experimentally. It was assumed that Coulomb dissociation to 14 O has a very small, if not zero, cross section and the scaling factor was determined as the ratio of ( 17 Ne, 14 O) cross sections obtained with Pb and C targets. The scaling factor is close to the ratio between nuclear radii of projectile and target, (A 1/3 , reflecting that the nuclear disintegration is of surface character. In this analysis it was assumed that the 5/2 + state is not Coulomb excited. Excitation of this state with a large cross section by a M2 or E3 transition or in a multi-step process is unlikely. Cross sections for Coulomb excitation of the identified narrow resonances are given in Table 1. For the state at E * = 5.210(79) MeV and a lead target the excitation stems dominantly from Coulomb interaction.
The transition probabilities B(π λ) from the ground to an excited state in the projectile, where π = E or M stands for an electric or magnetic transition with multipolarity λ, were calculated by the virtual-photon method for intermediate energies [29,30]. The cross section for Coulomb excitation of a narrow resonance at E * is where N(π λ) is the number of virtual photons at excitation energy E * . This expression is used to calculate the transition probability based on the measured cross section σ π λ C (E * ) (in fm 2 ).
The formalism described in Refs. [29,30] is used to calculate N(π λ). In Ref. [30] the effect of strong absorption is incorporated from the outset (see Eqs. (13)-(15)), while a minimal impact parameter B cut has to be used when the analytical semi-classical method from Ref. [29] (Eqs. (2.5.5)) is applied. Calculations using the semi-classical method with B cut = 10.8 fm give the same result as Eqs. (13)- (15) in Ref. [30]. The resulting N(π λ) and B(π λ) values are given in Table 4. The Coulomb excitation of the first two excited states in 17 Ne was studied earlier [31] and the transition probability  Table 4.
The B(E2) values from Ref. [31] without this correction factor were, however, used in Refs. [21,32] as a confirmation of the proposed 17 Ne wave function. The corrected value B(E2, 1/2 − → 5/2 − ) is about twice larger than that obtained in the present experiment. This might be connected with the assumption, made in Ref. [31], that the detected events were from pure Coulomb excitation. In the present experiment it is shown that nuclear excitation contributes to the cross section with about 50%, see Tables 3 and 4. Table 4 Coulomb excitation cross sections, σ C , in mb, for narrow resonant states in 17 Ne, virtual-photon numbers and transition probabilities B(π λ) in (e 2 fm 2λ ). The lowest row gives B(E2) for 5/2 − resonance calculated with Eq. (1) using σ C and N(E2) from Table I in Ref. [31].
In conclusion, new experimental data on dissociation of 17 Ne into 15 O + 2p studied at GSI with a relativistic 17 Ne beam impinging on lead, carbon, and polyethylene targets are presented. The main attention is paid to the excitation and decay of narrow resonant states in 17 Ne, for which cross sections were measured. Three-body correlations were used to determine the relative contributions to unresolved resonances. The data obtained from lead and carbon targets allowed the determination of cross sections and transition probabilities for Coulomb excitation. The reduced electric quadrupole transition probability B(E2, 1/2 − → 5/2 − ) = 90(18) e 2 fm 4 was derived by using the virtual-photon method. The measured B(E2) value was compared to the model calculations.
Finally, the observation of a resonance at E * = 5.210(79) MeV ten-tatively interpreted as 3/2 + state, mainly Coulomb excited, is of special interest and should be a subject of further investigations. The excitation of positive parity states implies that three-body models without inclusion of the core intrinsic structure are not able to fully describe the reaction mechanism. Theoretical methods are urgently needed to describe excitation spectra and reaction mechanisms, including techniques beyond three-body models.