One-neutron knockout reaction of 17C on a hydrogen target at 70 MeV/nucleon

First experimental evidence of the population of the first 2- state in 16C above the neutron threshold is obtained by neutron knockout from 17C on a hydrogen target. The invariant mass method combined with in-beam gamma-ray detection is used to locate the state at 5.45(1) MeV. Comparison of its populating cross section and parallel momentum distribution with a Glauber model calculation utilizing the shell-model spectroscopic factor confirms the core-neutron removal nature of this state. Additionally, a previously known unbound state at 6.11 MeV and a new state at 6.28(2) MeV are observed. The position of the first 2- state, which belongs to a member of the lowest-lying p-sd cross shell transition, is reasonably well described by the shell-model calculation using the WBT interaction.

ences in Ref. [4]) and by observing decay neutrons and constructing the invariant mass [5][6][7][8][9][10][11][12]. For one-nucleon knockout case, the momentum spread of the residue reflects the Fermi motion of the nucleon suddenly removed, and is sensitive to the orbital angular momentum (the l value) of the struck nucleon. Furthermore, the cross sections leading to individual final states relate to the occupancy of single-particle orbits, providing a link to details of the nuclear structure.
The present study aims at exploring unbound states in 16 C through an application of the one-neutron knockout technique to a 17 C beam impinged on a proton target, for which simple reaction mechanisms are expected. Focus is placed in a search of lowest-lying cross shell transitions, the location of which reflects the shell gap between p and sd orbits. The neutron-rich carbon (C) isotopes have attracted attention as they often exhibit unique features: none of the odd mass C (heavier than 13 C) has the ground-state spin parity of J π g.s. = 5/2 + , the values which are expected from a naive shell model. There has been a debate about a reduced E2 transition strength (small proton collectivity) for the 2 + 1 state in 16 C [13][14][15][16][17][18]. There is evidence for neutron halo formation for 15 C [19], 19 C [20], and 22 C [21,22]. For some, if not all, of these features, nuclear deformation may play a key role, which occurs in this mass region due to near degeneracy of the νd 5/2 -νs 1/2 orbits: neutrons in these orbits can gain energy by breaking spherical symmetry (the Jahn-Teller effect) [23]. The effect of nuclear deformation will further be signified by large quadrupole transition strengths [24,25] and by a reduction of the major p-sd shell gap [26][27][28]. A recent β-delayed neutron emission study of 17 B [29] has reported low-lying negative parity states in 17 C, among which the lowest one was the J π = 1/2 − state at the excitation energy of E x = 2.71 (2) MeV. The energy of this state, reflecting the p-sd shell gap, turned out to be lower than those of neighboring odd mass C isotopes: E x = 3.10 MeV for the 1/2 − 1 state in 15 C and E x = 3.09 MeV for the 1/2 + 1 state in 13 C [30]. This might indicate an onset of the p-sd shell gap quenching towards heavier C isotopes. To examine this picture in more detail it is worthwhile to accumulate data on cross shell transitions in neighboring isotopes. This Letter reports on new relevant spectroscopic information on 16 C in its unbound E x region. Besides, based on the parallel momentum distribution of the core fragment populated in a final state, it is demonstrated that the width of the distribution provides a good measure of the l value (and thus the parity) of the state populated; for neutron knockout involving a proton target, this has previously been shown based on the transverse momentum distributions in the 1 H( 18 C, 17 C * ) [31] and 1 H( 14 Be, 13 Be * ) [8] reactions with the aid of elaborate reaction mechanism calculations.
Despite relative proximity to stability, information on energy levels of 16 C, particularly that above the neutron threshold (the neutron separation energy of 16 C is S n = 4.250(4) MeV [32]), has been limited. This is partially due to ineffectiveness of β decay for this particular nucleus, as recognized by the absence of a parent nucleus ( 16 B is particle unstable). Early spectroscopic studies on 16 C utilized binary reactions involving transfers of neutrons. The 14 C(t, p) 16 C two-neutron transfer studies [33][34][35][36] have investigated levels below 7 MeV, including six bound states and an unbound state at 6.11 MeV. Since the ground state of 14 C is characterized by neutron p-shell closure, the states populated mostly involved configurations with two sd-shell neutrons, (1s0d) 2 . The 13 C( 12 C, 9 C) 16 C three-neutron transfer study [37] has reported 14 more states up to E x = 17.4 MeV, including states with more complex configurations. Due to kinematical matching [37] states with high angular momenta were favorably populated. Combining information from the recent 15 C(d, p) 16 C reaction study using a radioactive 15 C beam [17], sound J π assignments have been available for bound states. For unbound states only the 8.92-MeV level has received a firm assignment of 5 − [37]. Two earlier oneneutron knockout studies on 17 C using Be targets focused on transitions leading to bound final states in 16 C by means of in-beam γ -ray spectroscopy [3,38]. They provided information not only on excited states of 16 C but also on ground state properties of 17 C, e.g., the spin parity, J π g.s. ( 17 C) = 3/2 + , and no halo formation in spite of the remarkable low neutron separation energy of S n = 0.727(18) MeV [32] due to a high angular momentum of l = 2 for the valence neutron.
The experiment was performed at the RIPS facility [39] of RIKEN. Details of the setup are provided in Refs. [25,40], and a preliminary report of this work has been presented in Ref. [41]. The 17 C beam was produced from a 110-MeV/nucleon 22 Ne beam which impinged on a 6-mm-thick Be target. The typical 17 C beam intensity was 10.2 kcps with a momentum spread of P /P = ±0.1%. The beam profile was monitored by a set of parallel-plate avalanche counters (PPACs) placed upstream of the experimental target. The target was pure liquid hydrogen [42] contained in a cylindrical cell: 3 cm in diameter, 120 ± 2 mg/cm 2 in thickness, and having 6-μm-thick Havar foils for the entrance and exit windows. The average energy of 17 C at the middle of the target was 70 MeV/nucleon. The target was surrounded by a NaI(Tl) scintillator array used to detect γ rays from charged fragments. The fragment was bent by a dipole magnet behind the target, and was detected by a plastic counter hodoscope placed downstream of the magnet. The E and time-of-flight (TOF) information in the hodoscope was used to identify the Z number of the fragment. The trajectory was reconstructed by a set of multi-wire drift chambers (MWDCs) before and after the magnet, which, together with TOF, gave mass identification. Neutrons were detected by two walls of plastic scintillator arrays placed 4.6 and 5.8 m downstream from the target. The neutron detection efficiency was 24.1 ± 0.8% for a threshold setting of 4 MeVee. The relative energy (E rel ) of the final system was calculated from momentum vectors of the charged fragment and the neutron. In deducing the fragment vector, information on the impact point on target in transverse directions (determined by the upstream tracking detectors) was taken into account together with hit information within the MWDC placed behind the target. Neutron coincidence events were classified in terms of E rel and the Fermi momentum of the struck neutron k 3 . In the sudden approximation, the latter corresponds to the transferred momentum to the knockout residue ( 16 C). The detector acceptance was evaluated by a Monte Carlo simulation as a function of E rel and k 3 .  Table 1 States populated by the 1 H( 17 C, 16 C) reaction. Theoretical cross sections were obtained by using the Glauber-model code csc_gm [45] and the shell-model spectroscopic factors calculated with the WBT interaction [46]. Calculations used S eff n involving experimental E x values. (3) a Observed in coincidence with the 0.74-MeV γ ray from 15 C.
b Derived from the energy E x = 6.11 MeV in Ref. [33] by assuming the 15 [30]. This long life time caused the emission point of the de-excitation γ ray to be distributed along the path of the fast-moving decay product. The Doppler correction for the γ ray energy was made by assuming that the decay occurs at 40.7 cm downstream of the target (an average decay point expected from the average beam energy and the known mean life for the isomeric state) in both data reduction and simulation by the geant code [43]. The latter was done fully taking into account realistic geometry of the experiment. A higher energy tail for the photoelectric peak is due to this incomplete Doppler correction procedure. The simulated response, however, reproduced the data well as shown by the green solid line. The photo-peak efficiency over E γ = 0.60-1.12 MeV (γ -ray window) was estimated to be 5.1(3)% by the geant simulation. Fig. 1(b) was obtained by gating on the 5/2 + γ peak with the above window and by correcting for the detection efficiency. The background component was subtracted by assuming (i) that the background portion is the same as that in the γ -ray spectrum in the inset of Fig. 1(b): the portion of the area beneath the dotted line over the γ -ray window, which amounts to 46%, and (ii) that the background shape is characterized by the inclusive spectrum in Fig. 1(a). A peak is clearly seen at E rel = 0.46 MeV in Fig. 1(a). This is also evident in Fig. 1(b), indicating that this peak feeds the 5/2 + state in 15 C after emitting a neutron. Besides, another resonance is visible at E rel ≈ 1.3 MeV in Fig. 1(b). These were observed for the first time. The relative energy spectrum of Fig. 1(a)  Breit-Wigner function [44,25] (for other states, not as well isolated in the present data as this state, only the instrumental resolution was taken into account). In the analysis an excess strength was recognized at E rel ≈ 1.9 MeV. This may correspond to the nearest known state at E x = 6.11 MeV [33,36] if the decay product nucleus 15 C is populated in the ground state (in Fig. 1(a) the response of this strength was created by assuming E rel = 1.86 MeV: the difference between E x = 6.11 MeV and S n for 16 C). A similar fitting analysis using the γ -ray coincidence spectrum in Fig. 1(b), however, did not exclude the possibility that this component is absent from this spectrum. It is quoted that the upper limit on the fraction of 15 C fragments from the decay of the E rel = 1.86-MeV resonance, that were in the 0.74-MeV state is 20% of the strength found in the spectrum in Fig. 1(a). The solid line in Fig. 1(a) shows the result of the fit to the total inclusive spectrum. The background (dotted line) coming from transitions to the continuum and from detecting neutrons not associated with the decay of excited states in 16 C, e.g., neutrons emitted from excited 17 C nuclei that are created by inelastic scattering processes, was simulated by a function a(E rel ) b exp(−cE rel ) with a, b, and c free parameters. The results of the fit are summarized in Table 1. E x was calculated by for the background shape, turned out to be a dominant source of the error: they were 80, 90, and 70% of the errors quoted in Table 1 for E rel , Γ , and σ exp  Fig. 1(b) using the responses for the E rel = 0.46 and 1.29-MeV states, obtained from the fit to the inclusive spectrum in Fig. 1(a). To quantify the character of the latter state, as a state built on the 15 C * (0.74 MeV) excited core, the fit was repeated by changing the strength from the original one. By finding the fractional value at which the χ 2 of the fit alters from the minimum by one unit, a lower limit of 32% was deduced. The extraction of the l value of the knocked-out neutron from a differential quantity for the E rel = 0.46-MeV state is explained later.
To allow discussion in terms of nuclear structure, reaction model calculations based on the Glauber approximation [47] were performed. The one-neutron removal cross section σ th −1n is expressed for a given final state with J π as where A is the projectile mass, N the major oscillator quantum number, C 2 S the spectroscopic factor, and σ sp the single-particle cross section. The quantum numbers of the removed neutron are denoted by nlj. S eff n is the effective separation energy given by the sum of S n of the projectile and E x of the residue. σ sp was calculated by the code csc_gm [45] taking into account both stripping and diffractive processes (effective nature of the nucleon-nucleon (NN) profile function used resulted in small non-zero stripping cross sections) [47]. The elastic S matrix for the collision of the residue (core) with the proton target was calculated by folding the finite-range Gaussian NN profile function [48] with the point proton and neutron densities of the core obtained from the Hartree-Fock (HF) calculation using the SkX interaction [49]. The S matrix for describing the scattering of the valence neutron with the target proton was given by S(b) = 1 − Γ pn (b), here b is the impact parameter of the colliding nucleons, and Γ pn the profile function for proton-neutron scattering. The parameters chosen for the profile function are those describing the N N total and elastic cross sections consistently [48]. The neutron-residue relative motion was calculated in a Woods-Saxon potential. The depth was adjusted so as to reproduce S eff n , for a diffuseness a 0 = 0.7 fm and a reduced radius r 0 specifically chosen to be consistent with the HF calculation [50,51]: r 0 generates a single-particle wave function with a rms neutron-core separation of r sp = [A/(A − 1)] 1/2 r HF at the HF-predicted binding energy, where r HF is the HF rms radius of each orbit. The spin-orbit potential had the same a 0 and r 0 as the central one with a strength of −12 MeV in the notation of Ref. [52]. The HF radius for the p 1/2 (p 3/2 ) orbit of 17 C, for example, is 2.966 (2.779) fm; this translates into r sp = 3.057 (2.865) fm, which is reproduced by taking r 0 = 1.263 (1.234) fm. The C 2 S values were obtained by the shell-model code nushell [53] using the WBT interaction [46] in the spsdp f model space. The calculated results for relevant states are given in Table 1. σ th −1n includes contributions from both stripping (σ str ) and diffractive (σ diff ) mechanisms. Due to inert nature of the proton, the latter dominates the knockout processes.
The state observed at E x = 5.45 MeV was found to be well ex-  The migration of energies of (known) lowest-lying states in C isotopes, whose parities are opposite to those of their respective ground states, in comparison to shell-model values obtained by using the WBT interaction [46]. Data for 11−15 C (filled circles) are from Refs. [30,55]. The data point for 16 C (red filled square) is from the present study, while that for 17 C (open diamond) is from Ref. [29]. The shell-model calculations were performed within the 2hω and 0hω bases (for both positive and negative parity states) for 11−15 C and 16,17 C, respectively. Fig. 2 shows the laboratory parallel momentum (p ) distribution leading to the 5.45-MeV state. This was obtained by subdividing, in terms of p , the inclusive spectrum and repeating the fitting procedure described above. The errors are statistical ones. Also plotted in Fig. 2 are the p distributions calculated with csc_gm for varying l values. An experimental resolution of 43(1) MeV/c in rms is convoluted. Factors relevant to stripping mechanisms are dropped, and the curves represent the Fourier transform of the single-particle wave functions. The full width at half maximum (FWHM) of the experimental distribution for the 5.45-MeV state was determined by a fit using a Gaussian to be 210(11) MeV/c after unfolding the resolution. In the fit, a lowenergy tail (p < 5.72 GeV/c), which often suffers from higherorder effects [54], was eliminated. The fit curve (not shown) is similar to the l = 1 curve (solid line). The width agrees well with 233 MeV/c FWHM calculated for p-wave knockout, whereas for s-(dotted line) and d-wave (dashed line) knockout, widths of 121 and 377 MeV/c FWHM were respectively predicted, incompatible with the measurement. This observation agrees to the expected character of the 5.45-MeV, 2 − state as having a neutron hole in the p orbit, illustrating the robust feature of the p distribution as an l identifier.
The large populating cross sections observed for the 6.11-MeV state in the 14 C(t, p) 16 C reactions [33,36] have suggested that this state is either of the natural parity 2 + , 3 − , or 4 + states. The knockout cross sections calculated for the relevant 2 + 3 , 3 − 1 , and 4 + 2 shell-model states, together with their shell-model energies, are compared to the data in Table 1. The present data turned out not to provide a strong constraint on the J π values for this state, although in terms of comparisons in both E x and σ −1n they seem to prefer the assignment of 2 + or 3 − . The 6.28-MeV state exhibited the same decay pattern as the strongest 5.45-MeV 2 − state with a sizable cross section. The 1 − 2 and 2 − 2 states predicted at 6.55 and 6.63 MeV, respectively, had large populating cross sections and are candidates for this state.
The presently observed 2 − , 5.45-MeV state in 16 C belongs to a member of the lowest-lying states having an opposite parity to the ground state. The location of such states provides a measure of the p-sd shell gap and it is well explained by the shell model using the WBT interaction across the C isotopes, 11−15 C. To illustrate the latter, their energies are compared to the shell-model values in Fig. 3. In a recent study of β-delayed neutron emission of 17 B [29], three low-lying negative parity states were newly identified in just one-neutron heavier nucleus 17 C. The WBT interaction turned out to fail in predicting their location by about 1 MeV (theory predicts lower values, see also Fig. 3), and several possible mechanisms, such as reduction in pairing energy for neutrons in the sd orbits, were discussed. The present study adds a case in which the shell model with the WBT interaction predicts the location of the lowest-lying cross shell transition properly (see also Fig. 3), showing that this interaction describes the p-sd shell gap in 16 C adequately. To pin down the source of the discrepancy between theory and experiment on the position of the cross shell transition in 17 C, as discussed in Ref. [29], and to better understand the dynamical evolution of single-particle orbits and relevant residual interactions away from stability, further spectroscopic studies on such states in heavier C as well as neighboring isotopes are of help.
In summary, one-neutron knockout from 17 C on a proton target was exploited in populating two new states at 5.45(1) and 6.28(2) MeV, and a previously known state at 6.11 MeV in 16 C. The energy spectrum was constructed utilizing the invariant mass method involving a decay neutron and a 15 C fragment. Deexcitation γ rays from the latter were measured to correctly locate the resonances. For the 5.45-MeV state, an attempt was made to deduce the orbital angular momentum of the knocked-out neutron from the parallel momentum distribution associated with the unbound knockout residue. This, together with a comparison in terms of the measured and calculated knockout cross sections, has led to a spin-parity assignment of 2 − for this state. Possible spins and parities have been suggested for the other states, bringing about an advanced understanding of the level scheme of 16 C. The energy of the first 2 − state was adequately reproduced by the standard shell-model calculation using the WBT interaction without invoking modifications to the residual interaction.