Neutron occupancy of the 0d5/2 orbital and the N=16 shell closure in 24O

One-neutron knockout from 24O leading to the first excited state in 23O has been measured for a proton target at a beam energy of 62 MeV/nucleon. The decay energy spectrum of the neutron unbound state of 23O was reconstructed from the measured four momenta of the 22O fragment and emitted neutron. A sharp peak was found at Edecay=50$\pm$3 keV, corresponding to an excited state in 23O at 2.78$\pm$0.11 MeV, as observed in previous measurements. The longitudinal momentum distribution for this state was consistent with d -wave neutron knockout, providing support for a J{\pi} assignment of 5/2+. The associated spectroscopic factor was deduced to be C2S(0d5/2)=4.1$\pm$0.4 by comparing the measured cross section (View the MathML source) with a distorted wave impulse approximation calculation. Such a large occupancy for the neutron 0d5/2 orbital is in line with the N=16 shell closure in 24O.

One-neutron knockout from 24 O leading to the first excited state in 23 O has been measured for a proton target at a beam energy of 62 MeV/nucleon. The decay energy spectrum of the neutron unbound state of 23 O was reconstructed from the measured four momenta of the 22 O fragment and emitted neutron. A sharp peak was found at E decay = 50 ± 3 keV, corresponding to an excited state in 23 O at 2.78 ± 0.11 MeV, as observed in previous measurements. The longitudinal momentum distribution for this state was consistent with d-wave neutron knockout, providing support for a J π assignment of 5/2 + .
In this Letter we report on the spectroscopic factor for d 5/2 neutron removal from 24 O. The first excited state of 23 O, which is neutron unbound [15,13,16], was populated by one-neutron knockout from 24 O with a proton target. The excitation energy, cross section, and longitudinal momentum distribution were determined and allowed the 0d 5/2 neutron-hole nature of this state to be identified. The large spectroscopic factor deduced for this state is in line with the N = 16 shell closure in 24   The experiment was performed at the RIPS facility [17] at RIKEN. The experimental setup has been described in Refs. [14,18], and is depicted in Fig. 1. The secondary 24 O beam was produced using a 1.5 mm-thick Be production target and a 95 MeV/nucleon 40 Ar primary beam of ∼40 pnA. The average intensity of the 24 O beam was ∼4 particles/sec. The momentum of the secondary beam was determined particle-by-particle by measuring the position at the dispersive focus F1 of RIPS with a parallel plate avalanche counter. The energy loss ( E) and time-of-flight (TOF) were measured using 350 μm-thick silicon and 500 μm-thick plastic scintillator detectors, respectively, at the achromatic focus F2. The liquid-hydrogen (LH 2 ) target [19] was installed at the achromatic focus F3. The effective target thickness and the mid-target energy of 24 O were 159 ± 3 mg/cm 2 and 62 MeV/nucleon, respectively. The 24 O beam incident on the target was tracked particleby-particle by using two multi-wire drift chambers installed just upstream of the target. The target was surrounded by an array consisting of 48 NaI(Tl) crystals (DALI) to detect γ rays from deexcitation of the fragments.
The Bρ-TOF-E method was employed to determine mass and charge of the fragment following reactions of the 24 O beam with the LH 2 target. The magnetic rigidity (Bρ) was determined from the position and angle information measured with two multi-wire drift chambers placed at the entrance and exit of the dipole magnet. The TOF of the fragment was measured with the plastic scintillator charged particle hodoscope which also gave energy loss information. The beam velocity decay neutron was detected using a plastic scintillator counter array placed some 4.7 m downstream of the target, equipped with a charged particle veto counter. A neutron detection efficiency of 25 ± 1% at 64 MeV was measured for a 2 MeVee threshold in a separate 7 Li(p, n) measurement performed during the experiment.
The decay energy spectrum of 23 O * was reconstructed from the measured four momenta of 22 O and the emitted neutron. The decay energy E decay is expressed as: , and M f (M n ) are the total energy, momentum, and mass of 22 O (neutron), respectively. Fig. 2 shows the decay energy spectrum in terms of cross section (dσ /dE decay ) after correcting for the detection efficiencies and acceptances. The background contribution was subtracted here by using data taken with an empty target. The error bars are statistical only. The geometrical acceptance was estimated using a Monte Carlo simulation taking into account the beam profile, geometry of the setup, experimental resolutions, and multiple scattering of the charged particles. The experimental energy resolution was estimated to be The decay energy spectrum was described using one resonance for the peak at E decay = 50 ± 3 keV and a Maxwellian distribution for the non-resonant continuum [20]. The peak observed has an  asymmetric lineshape owing to its proximity to threshold, and its width is fully dominated by the experimental resolution. The corresponding excitation energy is E x = 2.78 ± 0.11 MeV, given the separation energy of S n ( 23 O) = 2.73 ± 0.11 MeV [21][22][23]. Since no γ -ray lines were observed for the 22 O−n channel, we assumed that 22 O is in the ground state. As such, the location of the resonance is in good agreement with previous experiments [15,16]. The one-neutron knockout cross section to the resonance at E decay = 50 keV was determined to be σ exp −1n = 61 ±6 mb, after subtracting the non-resonant continuum. The quoted error arises from the uncertainty in the choice of the functional form describing the non-resonant continuum (8%), statistical uncertainty (4%), neutron detection efficiency (3%), and the target thickness (2%). The single-particle configurations for the ground states of 23,24 O are expected to be ν(0d 5/2 ) 6 ν(1s 1/2 ) 1 and ν(0d 5/2 ) 6 ν(1s 1/2 ) 2 , respectively, in the shell-model picture (see, e.g., Refs. [8,24]), and suggest that the first excited state of 23 O presented here (neutron hole state) is very likely to be populated by the 0d 5/2 neutron knockout. Calculations using the USDB interaction [25] in the sd model space, as well as WBT [26] interaction in the spsdp f model space, predict that the spin-parity of this state is J π = 5/2 + (Table 1). The one-neutron knockout cross section, above a few tens MeV/nucleon energy, can be decomposed into the single-particle cross section (σ sp ) related to the reaction and the spectroscopic factor (C 2 S) reflecting the nucleon occupancy [27], as follows: where J π is the spin-parity of the final state of the residue (core); nls denote the quantum numbers of the knocked-out neutron; S eff n is the effective separation energy which corresponds the sum of the neutron separation energy of the projectile and the excitation energy of the core; A is the mass number of the projectile; (A/(A − 1)) Λ is the center-of-mass correction factor [28] where A is the mass number of the projectile and Λ is the major oscillator quantum number given by the relation of Λ = 2n + l. The single-particle cross section assuming a spectroscopic factor of unity was calculated using the distorted wave impulse approximation (DWIA) calculation for the quasifree (p, pn) reaction as described in Ref. [29]. The calculation employed the eikonal approximation for the distorted wave functions of incoming and outgoing reaction channels. The effective nucleon-nucleon interaction M3Y [30] along with the Coulomb potential was adopted for the real part of the optical potential. The nucleon-nucleus cross section in nuclear matter developed in Refs. [31][32][33] and the densities of the projectile, or core, folded with the matter density of proton were employed to introduce the imaginary part of the optical potential.
The wave functions of single-particle neutron orbits around the core were calculated using the Woods-Saxon potential in the manner as described in Ref. [34]. The Skyrme (SkX) Hartree-Fock (HF) calculation [35] was employed to deduce the root-mean-squared (rms) radius r HF of each single-particle orbit in the projectile. The code nushell [36] was used for this calculation. The HF rms radius of 24 O was r HF = 3.434 fm for the 0d 5/2 orbital. The reduced radius r 0 was determined so that the calculated single-particle wave function within the potential well adopting a diffuseness of a 0 = 0.7 fm satisfies r sp = √ A/( A − 1)r HF at the HF predicted binding energy.
The reduced radius was calculated to be 1.171 fm for the 0d 5/2 orbital. With this r 0 , the depth of the potential well was further adjusted to reproduce S eff n . The S eff n was calculated for the 2.78-MeV state to be 6.97 MeV by adopting S n ( 24 O) = 4.19 ± 0.14 MeV [21].
The single-particle cross section was calculated to be σ sp = 13.5 mb, from which we deduced the spectroscopic factor C 2 S exp (0d 5/2 ) = 4.1 ± 0.4 by using Eq. (2). The one-neutron knockout cross section was calculated to be σ th −1n (0d 5/2 ) = 83.1 mb by employing the shell-model spectroscopic factor of C 2 S th = 5.67 obtained using the USDB interaction. The reduction factor defined as R s = σ exp −1n /σ th −1n was derived to be R s = 0.73 ± 0.07 which is consistent with the systematics in Refs. [37,34]. Moreover, a reduction factor of R s = 0.84 ± 0.10 may be deduced for inclusive one-neutron knockout at 51 MeV/nucleon from the neighboring N = 14 closed sub-shell nucleus 22 O [38].
In the core ( 23 O) +n system description, the width of the longitudinal momentum (p ) distribution of the core is directly linked to the single-particle wave function of the knocked-out neutron, and can be utilized to identify its orbital angular momentum (l). We have reconstructed here the longitudinal momentum distribution of 23 O * from the measured momenta of the 22 O fragment and neutron. The p distribution for the first excited state of 23 O in the laboratory frame is displayed in Fig. 3. The error bars are statistical only. The width of the distribution was determined to be 356 ± 28 MeV/c (FWHM) by a Gaussian fit. The experimental dis- tribution is compared in Fig. 3 with the DWIA calculations. The results of the calculation for the removal of 0d 5/2 (solid line) and 1s 1/2 (dashed line) neutrons are shown in Fig. 3, where the calculated distributions were convoluted with the momentum resolution. The momentum resolution was determined to be 195 MeV/c (FWHM) using the Monte Carlo simulation taking into account the momentum spread of the 24 O beam, range difference of incoming and outgoing particles inside the LH 2 target, Coulomb multiple scattering effects, and the detector resolutions. The widths of the calculated distributions for the 0d 5/2 and 1s 1/2 knocked-out neutrons were to be 334 and 270 MeV/c (FWHM), respectively. The result for 0d 5/2 neutron knockout reproduces well the momentum distribution, supporting the spin-parity assignment of J π = 5/2 + .
It should be noted that this state has also been measured via twoproton and one-neutron removal [15] and proton inelastic scattering [16].
The excitation energy and the spectroscopic factor for neutron removal from 24 O are compared with the results of the shell-model calculations using the USDB and WBT interactions in Table 1. Both calculations reproduce the energy and also the spectroscopic factor assuming a reduction factor of R s ≈ 0.7-0.9 suggested by Gade et al. [37,34]. We note that the USDB interaction successfully describes the energies of the first excited states and the quadrupole transition parameters of 22,24 O reported in Refs. [14,39]. Fig. 4 shows the proton number dependency of the experimentally determined and calculated (dashed lines) spectroscopic factors for the even-even N = 16 isotones. While the spectroscopic factor for the ν1s 1/2 orbital gradually increases in moving from Z = 12 to 8, that for the ν0d 5/2 orbital dramatically rises at Z = 8.
This trend is reasonably well reproduced by the USDB shell model calculations. Significantly, the C 2 S(0d 5/2 ) for 24 O is much larger than those of other isotones, indicating a large neutron occupancy of the 0d 5/2 orbital. These results are in line with an N = 16 subshell closure in 24 O.
The gray bands in Fig. 4 represent the results of the USDB shellmodel calculations including a reduction factor of R s = 0.7-0.9. As such, the experimentally determined spectroscopic factors for the ν0d 5/2 orbit are in agreement with the calculations. While the reduction factor is close to unity for the 1s 1/2 neutron (for Z < 14), it is smaller than unity for the 0d 5/2 neutron (R s ≈ 0.7-0.8). This behaviour may provide a benchmark to test more sophisticated nuclear structure models, as well as reaction mechanisms. Recently, for example, Grinyer et al. [42] have investigated the quenching of the spectroscopic factors in 10 Be and 10 C for one-neutron knockout and found that an ab initio structure calculation, taking both 3-body forces and continuum effects into account, well describes the reduction.
In summary, we have investigated the occupancy of the neutron 0d 5/2 orbital in 24 O via one-neutron knockout from 24 O with a proton target. The excitation energy of the first excited state of 23 O was measured to be 2.78 ± 0.11 MeV and the spin-parity was assigned, based on the longitudinal momentum distribution, to be J π = 5/2 + . The large corresponding spectroscopic factor of C 2 S exp (0d 5/2 ) = 4.1 ± 0.4 supports the picture of an N = 16 spherical shell closure in 24 O.