Quasifree ( p,pN) scattering of light neutron-rich nuclei near N = 14

PHYSICAL REVIEW C 97, 024311 (2018) Quasifree ( p,pN) scattering of light neutron-rich nuclei near N=14 P. Díaz Fernández,1,2,3H. Alvarez-Pol,2,3R. Crespo,4,5E. Cravo,6L. Atar,7A. Deltuva,8T. Aumann,7,9V. Avdeichikov,10 S. Beceiro-Novo,11 D. Bemmerer,12 J. Benlliure,2,3C. A. Bertulani,13 J. M. Boillos,2,3K. Boretzky,9M. J. G. Borge,14 M. Caamaño,2,3P. Cabanelas,2,3C. Caesar,7,9E. Casarejos,15 W. Catford,16 J. Cederkäll,10 M. Chartier,17 L. V. Chulkov,18 D. Cortina-Gil,2,3U. Datta Pramanik,19 I. Dillmann,20,9Z. Elekes,12 J. Enders,7O. Ershova,21 A. Estradé,9,22 F. Farinon,9 B. Fernández-Domínguez,2,3L. M. Fraile,23 M. Freer,24 D. Galaviz,25,26 H. Geissel,9R. Gernhäuser,27 P. Golubev,10 K. Göbel,21 J. Hagdahl,1T. Heftrich,21 M. Heil,9M. Heine,7A. Heinz,1A. Henriques,25 M. Holl,7A. Hufnagel,7A. Ignatov,7 H. T. Johansson,1B. Jonson,1D. Jurˇciukonis,8N. Kalantar-Nayestanaki,28 R. Kanungo,22 A. Kelic-Heil,9A. Knyazev,10 T. Kröll,7N. Kurz,9M. Labiche,29 C. Langer,21 T. Le Bleis,27 R. Lemmon,29 S. Lindberg,1J. Machado,30 J. Marganiec,7,31,9 A. M. Moro,32 A. Movsesyan,7E. Nacher,14 A. Najafi,28 E. Nikolskii,18 T. Nilsson,1C. Nociforo,9V. Panin,7S. Paschalis,7,33 A. Perea,14 M. Petri,7,33 B. Pietras,2,3S. Pietri,9R. Plag,21 R. Reifarth,21 G. Ribeiro,14 C. Rigollet,28 D. Rossi,9M. Röder,34,12 D. Savran,31,35 H. Scheit,7H. Simon,9O. Sorlin,36 I. Syndikus,7J. T. Taylor,17 O. Tengblad,14 R. Thies,1Y. Togano,31 M. Vandebrouck,37 P. Velho,25 V. Volkov,7A. Wagner,12 F. Wamers,7,9H. Weick,9C. Wheldon,24 G. Wilson,16 J. S. Winfield,9 P. Woods,38 D. Yakorev,12 M. Zhukov,1A. Zilges,39 and K. Zuber34 (R3B Collaboration) 1Institutionen för Fysik, Chalmers Tekniska Högskola, S-412 96 Göteborg, Sweden 2Departamento de Física de Partículas, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain 3IGFAE, Instituto Galego de Física de Altas Enerxías, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain 4Departamento de Física, Instituto Superior Técnico, Av Rovisco Pais 1, 1049-001 Lisboa, Portugal 5Centro de Ciências e Tecnologias Nucleares, Universidade de Lisboa, Estrada Nacional 10, 2695-066 Bobadela, Portugal 6Centro de Física Nuclear, Universidade de Lisboa, PT-1649-003 Lisboa, Portugal 7Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany 8Institute of Theoretical Physics and Astronomy, Vilnius University, LT-10222 Vilnius, Lithuania 9GSI Helmholtzzentrum für Schwerionenforschung, D-64291 Darmstadt, Germany 10Department of Physics, Lund University, S-22100 Lund, Sweden 11National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA 12Helmholtz-Zentrum Dresden-Rossendorf, D-01328 Dresden, Germany 13Department of Physics and Astronomy, Texas A&M University-Commerce, Commerce, Texas 75429, USA 14Instituto de Estructura de la Materia, CSIC, Serrano 113 bis, E-28006 Madrid, Spain 15University of Vigo, E-36310 Vigo, Spain 16Department of Physics, University of Surrey, Guildford GU2 5FH, United Kingdom 17Oliver Lodge Laboratory, University of Liverpool, L69 3BX, Liverpool, United Kingdom 18NRC Kurchatov Institute, pl. Akademika Kurchatova, Moscow, Russia 19Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata-700064, India 20Justus-Liebig-Universität Gießen, Gießen, Germany 21Goethe-Universität Frankfurt am Main, 60438 Frankfurt am Main, Germany 22Astronomy and Physics Department, Saint Marys University, Halifax, Nova Scotia, Canada B3H 3C3 23Grupo de Física Nuclear & IPARCOS, Universidad Complutense de Madrid, 28040 Madrid, Spain 24School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom 25Laboratório de Instrumentação e Física Experimental de Partículas - LIP, 1649-003 Lisbon, Portugal 26Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisbon, Portugal 27Physik Department E12, Technische Universität München, 85748 Garching, Germany 28KVI-CART, University of Groningen, Zernikelaan 25, NL-9747 AA Groningen, The Netherlands 29STFC Daresbury Laboratory, Daresbury, Warrington WA4 4AD, United Kingdom 30Laboratório de Instrumentação, Engenharia Biomédica e Física da Radiação (LIBPhys-UNL), Departamento de Física, Faculdade de Ciências e Tecnologias, Universidade Nova de Lisboa, 2829-516 Monte da Caparica, Portugal 31ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany 32Departamento de FAMN, Universidad de Sevilla, 1065, E-41080 Sevilla, Spain 33Department of Physics, University of York, Heslington YO10 5DD, United Kingdom 34Institut für Kern- und Teilchenphysik, Technische Universität, 01069 Dresden, Germany 35Frankfurt Institut for Advanced Studies FIAS, Frankfurt, Germany 36GANIL, CEA/DSM-CNRS/IN2P3, B. P. 55027, 14076 Caen Cedex 5, France 37GANIL, Bd Henri Becquerel, 14076, Caen, France 38School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom 2469-9985/2018/97(2)/024311(13) 024311-1 ©2018 American Physical Society P. DÍAZ FERNÁNDEZ et al. PHYSICAL REVIEW C 97, 024311 (2018) 39Institut für Kernphysik, Universität zu Köln, D-50937 Köln, Germany (Received 7 July 2017; revised manuscript received 14 December 2017; published 9 February 2018) Background: For many years, quasifree scattering reactions in direct kinematics have been extensively used to study the structure of stable nuclei, demonstrating the potential of this approach. The R3B collaboration has performed a pilot experiment to study quasifree scattering reactions in inverse kinematics for a stable 12C beam. Theresults fromthat experimentconstitutethefirstquasifreescatteringresultsininverseand completekinematics. This technique has lately been extended to exotic beams to investigate the evolution of shell structure, which has attracted much interest due to changes in shell structure if the number of protons or neutrons is varied. Purpose: In this work we investigate for the first time the quasifree scattering reactions (p,pn)and(p,2p) simultaneously for the same projectile in inverse and complete kinematics for radioactive beams with the aim to study the evolution of single-particle properties from N=14 to N=15. Method: The structure of the projectiles 23O, 22O, and 21N has been studied simultaneously via (p,pn)and(p,2p) quasifree knockout reactions in complete inverse kinematics, allowing the investigation of proton and neutron structure at the same time. The experimental data were collected at the R3B-LAND setup at GSI at beam energies of around 400 MeV/u. Two key observables have been studied to shed light on the structure of those nuclei: the inclusive cross sections and the corresponding momentum distributions. Conclusions: The knockout reactions (p,pn)and(p,2p) with radioactive beams in inverse kinematics have provided important and complementary information for the study of shell evolution and structure. For the (p,pn) channels, indications of a change in the structure of these nuclei moving from N=14 to N=15 have been observed, i.e., from the 0d5/2shell to the 1s1/2. This supports previous observations of a subshell closure at N=14 for neutron-rich oxygen isotopes and its weakening for the nitrogen isotopes. DOI: 10.1103/PhysRevC.97.024311 I. INTRODUCTION Quasifree scattering (QFS) in direct kinematics with stable beams has been demonstrated to be a powerful tool to study the single-particle properties of nuclei along the stability line. In direct kinematics, a proton beam removes a nucleon or a light particle from the target. At around 400 MeV incident energy the probability for nucleon-nucleon collisions within the projectile nucleus should be small [1] and it is generally assumed that the dominant mechanism is due to the quasifree collision between the proton and the knocked-out particle. This reaction mechanism alone offers the possibility to study not only the outer part but also allows the direct exploration of deeper regions inside the nucleus [1–3]. QFS experiments were first performed in 1952 at Berkeley [2,4] and showed that if light targets are bombarded with a proton beam with an energy of 340 MeV, proton pairs emerge from the collision with a polar angle of approximately 90◦. The opening angle of both particles is not exactly 90◦(free scattering) because the collision takes place in the presence of nuclear matter where the proton in the target is not at rest [1]. In 1957, an experiment performed by Tyren, Maris, and Hillman [5] not only proved the validity of the quasifree interpretation but also demonstrated that it is a fascinating tool to study nuclear shell structure. Recently, the R3B collaboration [6] undertook a pioneering experiment performing the first (p,2p) exclusive measurements with a stable beam of 12C in inverse and complete kinematics [7]. The experiment was performed at the GSI Helmholtzzentrum für Schwerionenforschung facility, in Darmstadt, Germany [8], using the R3B-LAND setup [6]. It is not possible to produce targets of short-lived isotopes, which limits direct reaction studies. This problem can be overcome by using radioactive beams in inverse kinematics. Here, most reaction products are focused in forward direction, which means that a detection system at forward angles, covers almost 4πin the center-of-mass frame. Moreover, fragments produced in the reaction escape from the rather thick target due to their high momentum, which allows the reconstruction of the four-vectors for all the outgoing particles by measuring their energies and angles. This can be used for a kinematically complete reconstruction of the reaction. Experimentally, the (p,pn) reaction channel is more challenging than (p,2p), due to the difficulty to detect neutrons with good efficiency. Thus, up to now, QFS studies have been mainly restricted to (p,2p) reactions. Using a similar setup as for 12C, the R3B collaboration has now performed an experiment where unstable light projectiles at relativistic energies have been investigated in this work via (p,pn) and (p,2p) QFS reactions in complete and inverse kinematics. The evolution of shell structure and its origin has been the subject of many studies. In the light neutron-rich region of the nuclear chart, some exotic nuclei that were expected to be magic are not (as it is the case for 12Be [9,10]); others, which were not expected to be magic, are (for instance 22O[11]). Recent studies have shown that the proton-neutron interaction plays a major role in magicity, in particular the tensor component [12]. In addition, it has also been shown that the neutron-neutron interaction is important [13]. In particular, experimental and theoretical studies have pursued the study of the shell evolution around N=14, for the oxygen isotopes and isotones. It has been demonstrated that the effective singleparticle energies (ESPE) are modified due to the removal of a proton or a neutron from an orbital. Therefore, it is crucial to analyze pknockout and nknockout under the same conditions. 024311-2 QUASIFREE (p,pN) SCATTERING OF LIGHT … PHYSICAL REVIEW C 97, 024311 (2018) FIG. 1. (Left) Zoom on the nuclear chart area studied in this paper. The projectiles studied simultaneously via (p,pn) (horizontal arrows) and (p,2p) (vertical arrows) are marked in dark shades (dark green shades in the color online version). The fragments produced in the reactions are indicated in a lighter shade (lighter shade of green in the color online version). (Right) Schematic evolution of the N=14 shell gap when protons are removed from the 0p1/2while the number of neutrons remains the same. The shaded grey circles represent the nucleons in their corresponding single-particle states that are involved in the (p,pn) reaction. It has been observed that the energy of the first 2+excited state of 22O (see Fig. 1 in Ref. [13]), is almost twice as high as that for 20O and 18O, indicating the appearance of a new shell closure. Based on previous observations on the magicity of N=14 for oxygen isotopes [11], it is interesting to investigate what happens if protons from the 0p1/2orbital are removed, producing nitrogen and carbon isotopes (see Fig. 1). For 21N, the 2+effective energy (see details in Ref. [13]) is larger than the one for 19N and 17N; but this increase is not as pronounced as that for the oxygen isotopes, indicating a weakening of the N=14 subshell for the nitrogen isotopes [14,15]. For carbon, itwasobservedthattheenergyof the2+stateisalmostconstant for A=16, 18, and 20, indicating the disappearance of the N=14subshellclosure.Summarizing,theremovalofprotons from the 0p1/2orbital weakens the N=14 shell closure until it disappears for carbon [16]. Calculations with standard effective interactions (details in Ref. [13]) to obtain the E(2+) energies show, irrespective of the interaction used, that the gap between the ν1s1/2and the ν0d5/2 orbitals decreases as the number of protons decreases. It is also observed that in this area the E(2+) experimental data are systematically overestimated by calculations for carbon and nitrogen isotopes (see Fig. 1 in Ref. [13]). A better agreement with the data requires a reduction of the neutron-neutron monopole interaction term (Vnn)inthesd shell. Moreover, that reduction was found to be different for C and N isotopes (0.75 and 0.875, respectively) [13]. The probabilities of the different configurations for the ground states of 20C, 21N, and 22O, calculated using the WBP [17] interaction, show that if the number of protons decreases, the probability of having six neutrons in the 0d5/2orbital decreases as well [18]. The mixing of configurations involving the ν0d5/2and the ν1s1/2orbitalsbecomesveryimportantforthecarbonisotopes. The explanation given is that removing protons from the π0p1/2causes a reduction in the attractive proton-neutron interaction term between the π0p1/2and the ν0d5/2[13]. Consequently, the ν0d5/2and the ν1s1/2orbitals are closer in energy, promoting mixed configurations and decreasing the Vnn term (see the right part of Fig. 1). Thestudypresentedinthisworkhasthreemainpurposes.(i) To assess the feasibility of studying quasifree proton-nucleon scattering of radioactive beams in inverse kinematics. This will be achieved by analyzing both (p,pn) and (p,2p) reactions simultaneously under identical experimental conditions, providing for the first time a comparison of the neutron and proton shells for the same projectile. (ii) The cross sections for both types of processes will be compared to shed light on the differences between the proton and neutron shells. (iii) Shell evolution and magic numbers will be investigated in the region of interest (around N=14). The theoretical analysis of (p,pN) reactions has been traditionally performed within the distorted-wave impulse approximation (DWIA) [3,19]. Nowadays, there are different models to study this type of reactions using DWIA [20], DWIA formalism within the eikonal model [21], transfer-to-the- continuum (TC) [22] and Faddeev–Alt-Grassberger-Sandhas (Faddeev/AGS) [23] approaches. In this work, we adopt the Faddeev/AGS formalism [24], which has been used recently in several exploratory studies of (p,pn) reactions [23,25] and reproduces the experimental transverse momentum distributions for pknockout from 12C at 400 MeV/u [26]. For an assumed three-body Hamiltonian (A+p+N), this reaction framework provides a formally exact solution of the scattering problem. The Faddeev/AGS formalism is able to provide the needed angular and energy distributions required to correct our data for the detector response to protons and neutrons. Up to now the structure of these nuclei has been studied mostly by high-energy heavy-ion induced knockout reactions [27,28], intermediate-energy one-neutron removal [29,30] and in-beam γ-ray spectroscopy [11,14]. In this work, our selected energy domain is expected to promote the QFS mechanism as dominant, probing single-particle orbits in a clean way, not limited to the valence nucleons. This is the first time these nuclei have been studied by this approach. It will be shown that the technique works, in a very interesting region of the chart of the nuclides, giving a glimpse of the possibilities that the new facility FAIR [31] will offer. 024311-3 P. DÍAZ FERNÁNDEZ et al. PHYSICAL REVIEW C 97, 024311 (2018) ! , FIG. 2. Schematic drawing of the experimental setup for the experiment (not to scale). Radioactive beams enter the cave from the left. The physical quantities measured by the different detectors are indicated in the figure (for more details see text). II. DESCRIPTION OF THE EXPERIMENTAL SETUP The primary beam, 40Ar+11, was provided by the linear accelerator UNILAC (UNIversal Linear ACcelerator). This 40Ar+11 beam was then injected into the SIS-18 (SchwerI- onenSynchrotron) where it was accelerated to an energy of 490MeV/uwithanintensityfluctuatingaround1010 ions/sand directed to the FRagment Separator (FRS), a high resolution forward-angle spectrometer [32]. At its entrance, a production target of Be, 4.011 g/cm2thick, was mounted. When the primary beam impinges on this target, a range of mostly unstable ions are produced by projectile fragmentation. The FRS separated the species of interest depending on their mass-to-charge ratio (A/Q), and those were transported to the experimental area where the R3B-LAND setup is located (see Fig. 2). Data for six different magnetic rigidity settings centered at different A/Q ratios were collected in the R3B-LAND experimental area. The velocity of the beam is measured by two positionsensitive plastic scintillators at the exit of the FRS and the entrance of the experimental setup (POS), respectively. An active collimator, ROLU, was used to ensure proper beam alignment. Behind this detector, for tracking and energy loss measurements (E), a position-sensitive silicon detector, PSP, is placed, which allows event-by-event identification of the incoming ions. Then, the beam enters a vacuum chamber where the targets (922 mg/cm2CH2and 935 mg/cm2C) weremountedon a remote-controlled targetwheel,surrounded by eight double-sided silicon-strip detectors (DSSSDs). The incoming ions of 23O, 22O, and 21N reached the target middepth with mean energies of 445, 414, and 417 MeV/u and average intensities of approximately 1, 30, and 5 ions/s, respectively. To extract the reactions of the protons in the CH2 targetwiththeprojectiles,thecontributionsfromCandfroman empty frame must be subtracted. The latter takes into account reactions in the target frame and in the in-beam detectors. The chamber is surrounded by Crystal Ball, a 4πcalorimeter which consists of 159 NaI(Tl) crystals, to measure deposited energy (E) and angular distributions (φ,θ)ofγrays and light particles (mainly neutrons and protons originating from the QFS reactions). After the reaction, the products traveling in a forward direction are deflected by the ALADIN dipole magnet and, according to their mass and charge, are deflected to one of three arms of the spectrometer. Neutrons are detected by LAND, a Large Area Neutron Detector, heavy fragments are tracked via two scintillating fiber detectors, GFIs, and a time-of-flight wall TFW, while protons are bent further and detected via two proton drift chambers, PDCs, and a second time-of-flightwall,DTF.Thereforeallfinalfragmentsandtheir four-momenta can be extracted. FIG. 3. Incoming identification plot, charge vs. mass-over-charge fraction, for the most exotic setting centered at 24O. 024311-4 QUASIFREE (p,pN) SCATTERING OF LIGHT … PHYSICAL REVIEW C 97, 024311 (2018) FIG. 4. EnergylossinthefirstDSSSDbehindthetargetvs.energy loss at the last detector in the setup, the TFW, for the incoming isotope 21N. III. ANALYSIS The incoming cocktail beam was identified by energy loss in the PSP detector and by ToF measurements between the final focal plane of the FRS and the POS detector. The selection of the desired incoming isotopes was performed by a two-dimensional elliptical cut using the “fragment trigger”, which requires a valid signal at POS and TFW. In Fig. 3an identification plot with Zvs. A/Z is presented for a setting centered on 24O.1 The outgoing fragments after the reaction target were identified according to their nuclear charge, determined from their energy losses measured in the first DSSSD detector after the target and in the TFW (see Fig. 4). For the outgoing fragments, the “Crystal-Ball reaction trigger” was used, which requires “fragment trigger” and an energy signal from the Crystal-Ball detector. The mass of the outgoing fragments was determined by reconstructing the trajectories of the particles through the ALADIN magnetic field and their paths until they reached the TFW detector, using the R3B-LAND tracker program2[33]. To do so, data from the two DSSSDs downstream from the target, as well as from the GFIs and the TFW were used. The tracker needs information about the laboratory positions of the detectors, the nuclear charge of the fragment, the magnetic field maps and the current applied to the magnet to be able to track the events. An example of the outgoing mass distributions in coincidence with the “Crystal-Ball reaction trigger”, obtained for the different targets used is shown in Fig. 5. A complete identification of the incoming and outgoing nuclei is available at this point of the analysis. The energies 1Reproducibility: for unpacking the data, the LAND02 software packagewiththe followinggit hasheswasused:8ff96c7and6d70331. The git hash for the experiment folder was 7e4d07a. 2Reproducibility: the R3B-LAND tracker software was used with the following git hash a7b74af. FIG. 5. Charge vs. outgoing mass of fragments after tracking with the “Crystal-Ball reaction trigger” for the plastic, carbon and empty targets, respectively (from top to bottom) when an incoming 21Nis used. and angular distributions of the two outgoing nucleons that do not enter ALADIN are measured by the Crystal Ball detector. To reconstruct the energy and angular distributions of the outgoing nucleons, an addback routine using the nearest neighboring crystals is used. The algorithm searches for the crystal with the highest energy deposition in an event and adds the energy of the nearest neighbor crystals, which constitute a cluster. For the reactions of interest, the condition of two high energy depositions, above 20 MeV, is required. Figure 6 showsthepolarangledistribution(left)andtheazimuthalangle distribution (right) for the representative case of 22O(p,pn)21O (top) and 22O(p,2p)21N (bottom). In this figure, data from the plastic target with proper subtraction of the contribution from carbon and empty frame measurements are plotted. The negative cross sections originate from statistical fluctuations in the histogram subtraction needed to obtain the hydrogen distributions. The opening angle peaks around 82◦. The azimuthal distribution peaks at 180◦. These results demonstrate that the 024311-5 P. DÍAZ FERNÁNDEZ et al. PHYSICAL REVIEW C 97, 024311 (2018) (deg) op θ 0 20 40 60 80 100 120 140 0 0.2 0.4 0.6 0.8 1 3− 10× (deg)φΔ 0 20 40 60 80 100 120 140 160 180 200 0 0.2 0.4 0.6 0.8 1 1.2 3− 10× (deg) o p θ 0 20 40 60 80 100 120 140 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 3− 10× (deg)φΔ 0 20 40 60 80 100 120 140 160 180 200 0 0.2 0.4 0.6 0.8 3− 10× arb. units) op σ) (arb. units) op θ /d( σd)(θ/d(d ) (arb. units) φ Δ/d(σd ) (arb. units) φ Δ /d(σd FIG. 6. Polar angle (left) and difference between the azimuthal angles (right) for one neutron and one proton 22O(p,pn)21O (top) and two protons 22O(p,2p)21N (bottom) in coincidence with the outgoing fragments. QFS mechanism is dominant in this energy regime. Note that the opening angle for (p,pn) has a contribution at lower angles whichisnotpresent(atleastwiththesamestrength)for(p,2p). Simulations performed show that for (p,pn), in 21% of the cases the neutron does not deposit the maximum energy in the first NaI crystal that is hit but in a subsequent one, resulting in a limited angular assignment. In most of these cases (61%), the first hit is in a direct neighbor of the crystal with the maximum energy deposition, which still allows for a reasonable angular distribution measurement. The situation is better for protons, where the maximum energy is deposited in the first hit in 93% of the cases. As no angular selection is considered, the results are not affected by the imperfect angular reconstruction of the neutrons. The cross sections are calculated from the number of reactions and the number of incoming nuclei. The number of incoming nuclei is approximated by the number of unreacted ions after the reaction target, which are counted at the end of the fragment arm in the TFW detector using the “fragment trigger”. As a consequence, the efficiencies of the different detectors, the acceptance, and other effects cancel out because the same detectors and similar conditions are used to perform both countings. This is expected to be a good approximation because the target is sufficiently thin and the energy is high, such that the probability to react in the target is relatively low (in the order of 10−2to 10−3). The number of reactions was counted using the “Crystal- Ball reaction trigger”, which had to be corrected for the response of the Crystal-Ball detector for events with two particlesdepositingatleast20MeVintheCrystal-Balldetector array, where response is defined as efficiency ×acceptance. To perform the response calculations, two different event generators were used: (i) A realistic Monte Carlo event generator, that creates a distribution of particles derived from calculated kinematically fully exclusive cross sections within the Faddeev/AGS reaction framework (F/A). This formalism has been applied to (p,pn) reactions with stable and exotic projectiles [26,34,35]. (ii) A pure kinematic event generator (Kin) that assumes isotropic center-of-mass collisions and employs the Goldhaber model to calculate the width of the momentum distributions [36]. 024311-6 QUASIFREE (p,pN) SCATTERING OF LIGHT … PHYSICAL REVIEW C 97, 024311 (2018) TABLE I. Detector responses calculated with the Faddeev/AGS (F/A) and the kinematical (Kin) event generators using the GEANT4 library INCLXX with the high-precision neutron library option and the condition of two particles depositing at least 20 MeV in the Crystal-Ball detector. Reaction Response F/A (%) Response Kin (%) INCLXX_HP INCLXX_HP 22O(p,pn)21O18 14 22O(p,2p)21N67 58 23O(p,pn)22O– 15 23O(p,2p)22N– 59 21N(p,pn)20N17 14 21N(p,2p)20C66 60 The simulations were performed using the R3BRoot framework3[37], which is being developed for simulations and data analysis for the new R3B setup currently under construction at FAIR/GSI [31]. To evaluate the response and its uncertainty, different GEANT4 (geant4-10-01-patch-02) physics lists [38] (BERT 3.0, INCLXX 1.0, BIC 2.0) suitable for the energy range of this work, neutrons and protons up to 700 MeV, were tested. To validate the simulation, two different studies were performed. In the first one, the same observables, namely, experimental data for energy and multiplicity detected by the Crystal Ball detector, were compared with simulated data. The results indicate that the INCLXX library performs slightly better than the BERT physics list. In order to choose the most suitable physics library, in the second study the experimental efficiency curve obtained in Ref. [39] for neutrons up to 700 MeV impinging on a NaI(Tl) crystal was compared with simulations using different libraries. Given that INCLXX reproduces the experimental efficiency better, all results in this work are based on simulations using INCLXX with the HP option, which uses the high precision library for neutrons. At present, all theoretical input files necessary for the F/A event generator are not available, making it impossible to obtain the response for all studied channels using the F/A event generator. For the cases where both event generators are available, two cross sections will be shown. Table Ilists the response values obtained with both generators. The transverse momentum distributions of the outgoing fragments were obtained from the time-of-flight between the target and the TFW to calculate the velocity and the angular distributions of the fragments measured by the two DSSSDs behind the target, using the tracker program. The impact point on the target is determined by the two upstream DSSSDs, and the angular distribution of the fragments by the two DSSSDs after the target. In addition to a proper calibration for these detectors, a good relative spatial alignment between them is also needed. This was achieved by performing a linear least squares fit to fragment trajectories in a run without target (unreacted ions), while optimizing the 3Reproducibility: for the simulations the R3BRoot software with the following git hash was used c8034f16ff. detector positions. Thereby the detectors were shifted virtually based on experimental data. Asthestatisticsavailableisverylow for most of thereaction channels under study, the root-mean-square (rms) is used instead of sigma values calculated from Gaussian fits which are commonly used in literature [27,28] to derive the width of the fragment momentum distributions. In order to extract the rms, a systematic study of differently binned histograms was performed. The rms has been observed to fluctuate for low bin number but stabilizes afterwards. The average of the rms values in the stable region is assigned to the width of the momentum distribution. The associated error takes the mean value of the errors and the largest deviation in the errors (for the stable area) into account, which are added quadratically. IV. RESULTS AND DISCUSSION The measured inclusive cross sections and widths of the momentum distributions for the one-neutron and one-proton knockout of the projectiles 23O, 22O and 21N are presented in the following (sub)sections, as well as the fragment momentum distributions. The experimental data will be compared with observables calculated using the Faddeev/AGS reaction framework. A. One-nucleon knockout inclusive cross sections The inclusive cross sections of the different n-knockout and p-knockout channels are determined from the number of reactions in a given target induced by a measured number of incoming ions. The resultant inclusive cross sections, uncorrected σraw as well as σF/Aand σKin corrected for the Crystal Ball detector response using the two different event generators F/A or Kin, respectively, are shown in Table II. The uncertainties in the table are statistic (first number) and systematic (second number). For the oxygen projectiles the results were obtained using two independent analyses performed within the collaboration with different cuts and statistical methods checking for consistency. Both methods return similar values. The values of the cross sections and the uncertainties in both methods have been combined to obtain the results presented in this paper. The systematic uncertainty given in Table II accounts for the small difference between the two procedures. The left part of Fig. 7presents the total inclusive cross sections for the one-neutron (top) and one-proton (bottom) knockout as a function of the neutron and proton number of the projectile, respectively. 1. ( p,pn) vs ( p,2p) Independently of the NaI response function considered, the cross sections of the one-neutron knockout channel are systematically larger than those for one-proton knockout for a given projectile as expected from the large neutron excess of the nuclei under study. The third column of Table II presents the measured cross sections for the investigated (p,2p) and (p,pn)reactionswithoutanycorrectionsfortheresponseofthe Crystal-Ball detector. Given that the probability for detecting a proton in NaI is larger than detecting a neutron at the given energies, taking any response function into account will just 024311-7 P. DÍAZ FERNÁNDEZ et al. PHYSICAL REVIEW C 97, 024311 (2018) TABLE II. Inclusive cross sections for the one-neutron and one-proton knock-out channels for the projectiles 23O, 22O, and 21N at 445, 414, and 417 MeV/u impinging on protons in the target, uncorrected and corrected for the Crystal Ball detector response. σraw,σF/A,andσKin stand for the inclusive cross sections without and with the Crystal-Ball detector response, while F/A and Kin indicate which generator was used for the correction. Uncertainties in the table are statistical (first number) and systematic (second number). Ebeam (MeV/u) Reaction σraw (mb) σF/A(mb) σKin (mb) 445 23O(p,pn)22O9.0±1.8±0.9–54.0±10.7±1.1 23O(p,2p)22N3.04 ±0.59 ±0.05 – 4.93 ±0.96 ±0.10 414 22O(p,pn)21O6.22 ±0.25 ±0.44 34.1±1.9±0.7 39.2 ±2.2±0.8 22O(p,2p)21N3.49 ±0.23 ±0.08 5.21 ±0.34 ±0.10 6.01 ±0.40 ±0.12 417 21N(p,pn)20N7.55 ±0.61 44.8±3.6±0.948.5±3.9±1.0 21N(p,2p)20C1.35 ±0.20 2.05 ±0.30 ±0.04 2.27 ±0.34 ±0.04 increase this trend in the data, as can be observed in the fourth and fifth columns of Table II. The difference between the (p,pn) and (p,2p) cross sections can be explained in a simplified mean field picture considering neutrons in the psd shell. All projectiles are neutron-rich nuclei and, therefore, there are more neutrons than protons available for reactions. Also, the neutron 0d5/2 orbital is almost full for the cases under study, giving rise to large spectroscopic factors for neutrons removed from this orbital (see shell model calculations in Sec. IVC). Moreover, the binding energy of the outermost neutrons is smaller than that of the protons. As a result, neutron-knockout is favored. Another difference between the (p,pn) and (p,2p) cases, that favors (p,pn) over (p,2p), stems from the difference between the p-nand p-pinteractions. Between 400 MeV and 500 MeV, the np scattering cross section is around 27% N 13 14 15 16 (mb)σ 0 10 20 30 40 50 60 70 80 90 100 N 21 O 22 O 23 N 21 N) = 4.6 MeV 21 ( n S O) = 6.8 MeV 22 ( n S O) = 2.7 MeV 23 ( n S n-knockout O 22 F/A F/A kin kin N 13 14 15 16 RMS (MeV/c) 40 60 80 100 120 140 160 N 21 O 22 O 23 N) = 4.6 MeV 21 ( n S O) = 6.8 MeV 22 ( n S O) = 2.7 MeV 23 ( n S n-knockout Z = 8 Z = 7 Z 6789 (mb)σ 0 1 2 3 4 5 6 7 8 9 10 N 21 N 21 O 22 O 22 O 23 N) = 19.6 MeV 21 ( p S O) = 23.3 MeV 22 ( p S O) = 24.7 MeV 23 ( p S p-knockout F/A kin kin Z 6789 RMS (MeV/c) 20 40 60 80 100 120 140 160 N 21 O 22 O 23 N) = 19.6 MeV 21 ( p S O) = 23.3 MeV 22 ( p S O) = 24.7 MeV 23 ( p S p-knockout N = 14 N = 15 FIG. 7. Top: cross sections (left) and rms (right) for the one-neutron knockout channel as a function of the neutron number for the projectiles 21Nand23,22O. Bottom: cross sections (left) and rms (right) for the one-proton knockout channel as a function of the proton number for the projectiles 21N, 23,22O. In both cases, the one neutron (proton) separation energy for each projectile is included in the plot, taken from [41]. The generator used for the response of the Crystal-Ball detector used in the cross section calculation is indicated in the legend. 024311-8 QUASIFREE (p,pN) SCATTERING OF LIGHT … PHYSICAL REVIEW C 97, 024311 (2018) (MeV/c) Y P 1000−500−0 500 1000 ) (arb. units) y /d(Pσd 1− 0 1 2 3 4 3− 10× O 22 O(p,pn) 23 (MeV/c) Y P 1000−500−0 500 1000 ) (arb. units) y /d(Pσd 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 3− 10× N 22 O(p,2p) 23 (MeV/c) Y P 1000−500−0 500 1000 ) (arb. units) y /d(Pσd 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 3− 10× O 21 O(p,pn) 22 (MeV/c) Y P 1000−500−0 500 1000 ) (arb. units) y /d(Pσd 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 3− 10× N 21 O(p,2p) 22 (MeV/c) Y P 1000−500−0 500 1000 ) (arb. units) y /d(Pσd 0 1 2 3 4 3− 10× N 20 N(p,pn) 21 (MeV/c) Y P 1000−500−0 500 1000 ) (arb. units) y /d(Pσd 0 0.2 0.4 0.6 0.8 1 1.2 1.4 3− 10× C 20 N(p,2p) 21 FIG. 8. Transverse momentum distributions for all (p,pN) channels. The (p,pn) channels are on the left, while (p,2p) channels are on the right. larger than that for pp scattering [40]. On the other hand, all kinematic contributions of the emitted light fragments have to be evaluated accurately. It was shown in Refs. [21,34] that the absorption part of the nucleon-nucleus potential produces a reduction of the (p,pn) inclusive cross section, compared to theplanewave impulseapproximation(PWIA).Thisreduction becomes increasingly important as a function of the binding energyoftheknocked-outnucleon[35],sothisisanotherfactor that needs to be taken into account when comparing the (p,pn) and (p,2p) cross sections. 2. ( p,pn) In the oxygen isotopic chain (Z=8), the (p,pn) cross section is larger for N=15 than for N=14, independent of 024311-9