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Disintegration of 12C nuclei by 700–1500 MeV photons
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ScienceDirect Nuclear Physics A 940 (2015) 264–278 www.elsevier.com/locate/nuclphysa
Disintegration of 12 C nuclei by 700–1500 MeV photons V. Nedorezov a , A. D’Angelo b,c , O. Bartalini b,c , V. Bellini d,e , M. Capogni b,c , L.E. Casano c , M. Castoldi f , F. Curciarello g,e , V. De Leo g,e , J.-P. Didelez h , R. Di Salvo c , A. Fantini b,c , D. Franco b,c , G. Gervino i,j , F. Ghio k,l , G. Giardina g,e , B. Girolami k,l , A. Giusa d,e , A. Lapik a , P. Levi Sandri m , F. Mammoliti d,e , G. Mandaglio g,e , M. Manganaro g,e , D. Moricciani c , A. Mushkarenkov a , I. Pshenichnov a,∗ , C. Randieri d,e , N. Rudnev a , G. Russo d,e , C. Schaerf b,c , M.-L. Sperduto d,e , M.-C. Sutera e , A. Turinge a , V. Vegna b,c , I. Zonta b,c a Institute for Nuclear Research, Russian Academy of Sciences, Prospekt 60-letiya Oktyabrya 7a, 117312 Moscow,
Russia b Dipartimento di Fisica – Università degli Studi di Roma “Tor Vergata”, via della Ricerca Scientifica 1,
I-00133 Roma, Italy c INFN – Sezione di Roma “Tor Vergata”, via della Ricerca Scientifica 1, I-00133 Roma, Italy d Dipartimento di Fisica – Università degli Studi di Catania, via Santa Sofia 64, I-95123 Catania, Italy e INFN – Sezione di Catania, via Santa Sofia 64, I-95123 Catania, Italy f Dipartimento di Fisica – Università degli Studi di Genova, via Dodecaneso 33, I-16146 Genova, Italy g Dipartimento di Fisica e di Scienze della Terra, Università di Messina, salita Sperone 31, I-98166 Messina, Italy h IN2P3, Institut de Physique Nucléaire, Rue Georges Clemenceau, F-91406 Orsay, France i Dipartimento di Fisica Sperimentale – Università degli Studi di Torino, via Pietro Giuria 1, I-10125 Torino, Italy j INFN – Sezione di Torino, via Pietro Giuria 1, I-10125 Torino, Italy k Istituto Superiore di Sanità, viale Regina Elena 299, I-00161 Roma, Italy l INFN – Sezione di Roma, piazzale Aldo Moro 2, I-00185 Roma, Italy m INFN – Laboratori Nazionali di Frascati, via E. Fermi 40, I-00044 Frascati, Italy
Received 22 January 2015; received in revised form 3 May 2015; accepted 5 May 2015 Available online 8 May 2015
* Corresponding author.
E-mail address: [email protected] (I. Pshenichnov). http://dx.doi.org/10.1016/j.nuclphysa.2015.05.001 0375-9474/© 2015 Elsevier B.V. All rights reserved.
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Abstract Disintegration of 12 C nuclei by tagged photons of 700–1500 MeV energy at the GRAAL facility has been studied by means of the LAGRANγ E detector with a wide angular acceptance. The energy and momentum distributions of produced neutrons and protons as well as their multiplicity distributions were measured and compared with corresponding distributions calculated with the RELDIS model based on the intranuclear cascade and Fermi break-up models. It was found that eight fragments are created on average once per about 100 disintegration events, while a complete fragmentation of 12 C into 12 nucleons is observed typically only once per 2000 events. Measured multiplicity distributions of produced fragments are well described by the model. The measured total photoabsorption cross section on 12 C in the same energy range is also reported. © 2015 Elsevier B.V. All rights reserved.
Keywords: Photonuclear reactions; Fragmentation of light nuclei; Tagged photons; Total photoabsorption cross section
1. Introduction It is commonly accepted that nuclei can be effectively heated in proton-nucleus [1] or nucleus– nucleus collisions [2]. In collisions of intermediate mass or heavy nuclei many nucleons of a projectile nucleus deliver their kinetic energy to a target nucleus simultaneously in a single collision event. They also essentially change the mass, charge and nuclear structure of the target nucleus. Therefore, hot nuclear systems created in such collisions are characterized by a wide range of their mass and excitation energy and thus keep only a weak resemblance to the initial target nucleus. As proven by calculations [3–6], a simultaneous explosive decay of an excited nucleus into three and more nuclear fragments is observed when the excitation energy of the nucleus E is comparable to its total binding energy. This is considered as a phase transition between nuclear matter and gas of nucleons. The onset of this phenomenon, which is widely known under the name of multifragmentation, is found already at E ∼ 3 MeV per nucleon where it competes with sequential evaporation of nucleons. The multifragment break-up dominates at higher E [4]. The decays of medium-weight or heavy nuclei were mostly studied in the above-mentioned papers [1–5]. It is expected that a nuclear system created after the absorption of a photon by a nucleus is typically closer to the target nucleus compared to nucleus–nucleus collisions. Indeed, the photoabsorption delivers pure energy, rather than energy and additional nucleons to the target nucleus and, as a rule, involves less participant nucleons. This generally leads to mass and charge distributions of excited residual nuclei which are more narrow compared to the respective distributions in nucleus–nucleus collisions. In contrast to nucleus–nucleus collisions, in photonuclear reactions there are no uncertainties related to the identification of nuclear fragments as target or projectile fragments. The nuclear excitation and decay resulting from photoabsorption can be studied in experiments with beams of tagged photons [7,8] or by detecting ultraperipheral collisions of nuclei resulting in their electromagnetic dissociation due to the impact of virtual photons emitted by collision partners [9–14]. As demonstrated by modeling photoabsorption on lead, thorium and neptunium nuclei [15], the average E calculated per nucleon of residual nucleus is below 0.5 MeV. This leads to nuclear fission rather than to multifragmentation of heavy residual nuclei.
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Much less attention of experimentalists has been devoted so far to photodisintegration of light nuclei. This equally concerns the experiments with real photons and fixed targets and the experimental studies of nuclear fragmentation in ultraperipheral collisions induced by virtual photons. In the latter case this is explained by a low value of the electromagnetic fragmentation cross section for light projectile nuclei. It is much lower compared to the total hadronic reaction cross section and usually neglected. Nevertheless, valuable information on the clustering in light nuclei was obtained in experiments on fragmentation of light nuclei in nuclear emulsion [16,17]. Events of nuclear disintegration in ultraperipheral collisions were identified and thoroughly studied in these experiments. The first papers devoted to the disintegration of light nuclei by photons were published more than 40 years ago, see e.g. [18–20]. Electromagnetic dissociation of ultrarelativistic 16 O, 28 Si and 32 S nuclei in collisions with Ag nuclei in nuclear emulsion was identified in several experiments [21,22] and later successfully described by modeling photonuclear reactions on these nuclei induced by virtual photons in the giant resonance region [11]. The disintegration of 12 C into four particles by photons with energy of about 40 MeV was also investigated recently in another experiment [23]. However, to the best of our knowledge, no processes of multifragmentation of light nuclei induced by energetic photons (∼1 GeV) were detected so far. Since the time of first experiments [18–20] several detectors with a wide angular acceptance were developed, in particular, the LAGRANγ E detector [24–27]. This detector is capable to register all particles produced in a photonuclear reaction thus providing a possibility to evaluate the mass and charge of the excited nuclear residue as well as its excitation energy. In the present work the decay of 12 C into several fragments following the absorption of 700–1500 MeV photons at the GRAAL facility is investigated with the LAGRANγ E detector. Special attention is paid to decays of the target nucleus into several light fragments, in particular, into 12 nucleons. The total photoabsorption cross section on 12 C measured in the range of 700–1500 MeV is also presented. In contrast to the numerous studies devoted to the meson photoproduction off nuclei [28], photo-excitation of quasi-free intranuclear nucleons and final-state interaction of produced mesons, the present study is focused on the decays of the nuclear residue created after the first stage of the nuclear photoabsorption. It is expected that multifragment decays of light nuclei take place during carbon-ion therapy of cancer among other fragmentation reactions of therapeutic 12 C nuclei in human tissues [29]. One can also note that since light nuclei are present in cosmic rays, the present study also helps to understand the photodisintegration mechanisms of cosmic ray nuclei under the impact of solar photons known as the Gerasimova– Zatsepin effect, see Ref. [30] and the references therein. 2. Experiment The measurements were performed with the Large Acceptance GRaal-beam Apparatus (for) Nuclear Gamma Experiments (LAGRANγ E) detector system installed at the Grenoble Anneau Accelerateur Laser (GRAAL) beam line facility [31] which provided beams of tagged photons with energy from 700 to 1500 MeV. Such photons were obtained by the Compton scattering of laser photons off 6.03 GeV electrons circulating in the storage ring of the European Synchrotron Radiation Facility (ESFR) in Grenoble, France. The energy resolution of the tagged photon system was approximately 16 MeV. A general layout of the GRAAL experimental setup is shown in Fig. 1. The LAGRANγ E detector [24–26] has been designed to detect both neutral and charged particles produced by photons off protons and light nuclei in a wide range of angle θ with respect
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Fig. 1. General layout of the GRAAL setup, not in scale.
to the beam direction. The detector consists of two major parts: a central BGO calorimeter ball (25◦ ≤ θ ≤ 155◦ ) and forward detectors (θ ≤ 25◦ ). The calorimeter ball is the main component of the LAGRANγ E detector. It is assembled from 480 BGO crystals, each of them is 21 radiation length long. This calorimeter provides the energy resolution of 0.0244 × E 0.47 GeV, where E is the energy of a detected particle expressed in GeV. In order to disentangle neutral and charged particles a E detector made of 32 plastic plates, each 5 mm thick, as well as two cylindrical proportional chambers were placed between the target and BGO. These chambers make possible to identify the interaction point of a photon with the target material with a 1 mm accuracy. These detectors have provided the time-of-flight resolution at the level of 0.5 ns (FWHM). A 25◦ forward cone is not covered by the BGO calorimeter, but additional forward detectors are placed there. Forward-emitted particles are detected by planar proportional chambers, double plastic scintillator walls of 9 m2 area and an electromagnetic calorimeter, which is assembled from plastic and lead layers of the same area (placed at 3.3 meters from the target and consisting of 16 vertical modules). Both scintillator walls consist of 26 horizontal and 26 vertical stripes, each of them is 3 cm thick. Particles emitted in the backward direction (at θ > 155◦ ) are intercepted by a sandwich detector made of one plastic and one lead layer. Such a sophisticated geometry of the LAGRANγ E detector ensures its 4π -coverage. The carbon target used in the present measurements was placed in the centre of the BGO ball. It was prepared as a graphite disk with a thickness of 5 mm and of 30 mm in diameter and replaced liquid hydrogen or deuterium targets used in previous experiments with the LAGRANγ E detector. The LAGRANγ E detector has several features, which make it very advantageous for detecting multifragment decays of 12 C. Nucleons can be disentangled from pions and photons emitted at various angles with respect to the photon beam. Charged particles at forward angles can be identified by an angular and time coincidence between the planar MWPC, scintillator and calorimeter walls. Neutral particles in the same angular range activate only the calorimeter wall. We discriminate charged and neutral particles by the time-of-flight method, see Fig. 2. The velocity of protons created in meson photoproduction on 12C was less than 82% of the speed of light. This makes possible to disentangle them from pions and photons. Particles emitted at larger angles (25◦ ≤ θ ≤ 155◦ ) are successfully identified by taking into account the relation between
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Fig. 2. Distinguishing protons from pions and photons in the forward shower detector (a, b) and BGO calorimeter (c, d). Simulated (a, c) and detected (b, d) events are shown for both cases. Solid lines circumscribe the events selected for the analysis with separated protons and pions as denoted in the figure.
the energy loss E in the barrel and BGO calorimeter, see Fig. 2. Because of the thickness of the carbon target and the detector support materials, heavier nuclear fragments like 3H, 3 He, 4 He and others, cannot reach the BGO calorimeter or forward walls. According to our estimations only 15% of deuterons can be detected due to the same reasons. This makes it difficult to identify composite nuclear fragments in the present experiment. Therefore, some admixture of deuterons to proton data cannot be excluded. In the considered energy range of 700–1500 MeV the photon wavelength becomes too small to induce a knock-out of composite nuclear fragments. Therefore, the main contribution to the yields of fast nucleons comes from recoil nucleons involved into meson photoproduction processes. In the region of the angle θ between 25◦ and 155◦ with respect to the beam direction we identify neutral particles (neutrons and photons) by applying the condition to have signal only in the BGO calorimeter, and charged particles (protons and pions) by the constraint to have signals in the angle and time coincidence of the cylindrical MWPC, barrel and BGO ball detectors. Therefore, the MWPC and barrel detectors provide a veto for the identification of neutral particles. The BGO ball was divided into compartments of a smaller size, which are fired while
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Fig. 3. Probability to have a given number of fired crystals (cluster size) mclus for neutrons, photons and low-energy photons with Eγ ≤ 50 MeV which hit the BGO ball.
particles cross them. It was possible to exploit the dependence of the cluster size mclus (i.e. the number of close-fired compartments) on the particle type. In this way we can distinguish photons with energy higher than 50 MeV and neutrons by looking at the number of mclus , see Fig. 3. About 50% of neutron events are characterized by mclus = 1, while 70% of neutron events have 1 ≤ mclus ≤ 2. This is illustrated by Fig. 3, where the probability to have a given mclus is shown for neutrons, photons and specifically for photons with Eγ ≤ 50 MeV. In our central detector we cannot disentangle low energy photons from neutrons because their cluster multiplicities are similar, typically one or two crystals per cluster. However, our simulation results suggest that in the present data on photoproduction on 12 C the contribution of low-energy (<50 MeV) photon background to the neutron yield does not exceed 2%. In order to select meson photoproduction events with high efficiency (86–90%) and minimal background, the experimental trigger requests a photon tagged in coincidence with the total energy released in the BGO calorimeter higher than 160 MeV, as explained in Ref. [27]. It was important to set a proper threshold for particle detection in each BGO crystal. As proven by simulations, the efficiency of neutron detection approaches 60% when a 2 MeV threshold is set. A detailed description of the neutron detection technique and estimations of detection efficiency are given elsewhere [26]. One can note that the developed discrimination method is applicable only to energetic neutrons and photons. As seen in Fig. 3, the cluster size for photons of energy less than 50 MeV is very small. As a rule, it consists of one or two crystals, and such photons are not easily distinguished from neutrons. At the same time neutrons with energy below 50 MeV can be distinguished from more energetic neutrons as the number of fired crystals is small (mclus ∼ 1) for such low-energy neutrons. 3. Measurement results 3.1. Total photoabsorption cross section The total photoabsorption cross section measured for the 12 C nucleus at GRAAL is shown in Fig. 4. In order to evaluate the total carbon photoabsorption cross section, complementary expositions were performed when the carbon target was removed from the beam, according to the background subtraction method described in Ref. [27]. It was shown that the background comes
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Fig. 4. Total photoabsorption cross section on 12 C calculated per target nucleon. The GRAAL data are presented by points with error bars together with the respective cross section data obtained in Frascati [32] (full circles) and Bonn [33] (open circles). The so-called universal curve [34] is presented by a solid line. Table 1 Average numbers of protons and neutrons registered by the forward detectors and BGO ball, respectively.
Forward detectors BGO ball
Protons
Neutrons
0.35 ± 0.01 2.08 ± 0.03
0.04 ± 0.01 0.53 ± 0.01
mostly outside of the target, whereas the background contribution from the target itself is negligible. Our results agree well with the results of previous measurements performed in Frascati [32] and Bonn [33] for the same target nucleus, as well as with the so-called universal curve [34] which presents the total photoabsorption cross section divided by the number of nucleons in the target. This universal curve, which is valid for various nuclei from beryllium to uranium, reflects a gross property of nuclear forces which bind nucleons into stable nuclei. 3.2. Average numbers of fragments The average numbers of protons and neutrons detected, respectively, in the forward direction and in the BGO ball are listed in Table 1. These numbers are given without accounting for detection efficiency which is close to 100% for protons, but much smaller (about 50%) for neutrons. The event selection was based on the criteria described above and presented in Fig. 2. As follows from Table 1, the number of particles detected in the forward direction is essentially smaller compared to the number of particles detected in the BGO ball. In particular, the efficiency of neutron detection in the shower wall is only about 22%. Nevertheless, the contributions from both detectors were taken into account in the data analysis. 3.3. Energy and angular distributions of secondary nucleons At the first step of the data analysis the differences between the products of photonuclear reactions on proton, deuteron and 12 C targets were investigated. The data for protons and deuterons obtained with the LAGRANγ E detector in previous runs with a liquid hydrogen target were used for this purpose. In particular, it was found that the probability of two neutral clusters, e.g., due
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Fig. 5. Energy distributions of protons produced in photodisintegration of 12 C. Measured (solid line) and calculated (dash-dotted line) distributions in the laboratory system are shown together with the calculated distribution (dashed line) for the centre-of-mass system. The distributions are normalized to the average total photoabsorption cross section on nuclei at 700–1500 MeV calculated per target nucleon. Only statistical errors are shown by error bars.
to a photon and a neutron in the BGO ball was 1.5 times higher for 12C target than for a hydrogen one. The distribution of energy loss of protons in the BGO ball is shown in Fig. 5. For protons with kinetic energy less than 250 MeV this distribution is equivalent to the energy distribution of such protons because their range in BGO is less than the thickness of the wall of this detector. The energy of more energetic protons is measured less accurately as they traverse the wall and escape it. The detection of slow protons is also suppressed due to the trigger condition that the total energy released in the BGO should exceed 160 MeV. The same condition was applied in the total photoabsorption measurements and provided the results consistent with the results obtained in Frascati and Bonn, see Section 3.1. Therefore, one can conclude that the distribution shown in Fig. 5 includes most of the protons emitted in the photoabsorption on 12C and accepted in the analysis. The distributions calculated by means of the RELDIS model, see Section 4, are also presented in Fig. 5. These two distributions are given separately for the laboratory and centre-of-mass systems. They were obtained by calculating the convolution of simulated energy distributions with a Gaussian-shaped function with a width of 18 MeV which is related to the resolution of the tagged photon system. Due to a low velocity of the nuclear system after the absorption of a photon, typically about 0.1 of the light speed, these two simulated distributions are close to each other. Fast protons with energy higher than 250 MeV do not stop in the BGO material, but rather pass through the BGO wall. This explains the overestimation of the calculated yields over the measured ones at higher nucleon energies which is seen in Fig. 5. As follows from our data analysis, the measured energy distributions weakly depend on the photon energy between 700 and 1500 MeV. Therefore, the data for the entire photon energy range of 700–1500 MeV are presented in Fig. 5. The angular distributions of nucleons emitted in the photoabsorption on 12C provide valuable information on the reaction mechanism. Such distributions measured, respectively, for three distinct nucleon multiplicity groups with two, three and 7–12 nucleons are shown in Fig. 6. The distributions are given for the entire photon energy range of 700–1500 MeV considered in the present work. In this analysis the most energetic (leading) proton was firstly identified in each event and angular distributions of such nucleons were obtained for the respective multiplicity
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Fig. 6. Angular distributions of nucleons produced in photodisintegration of 12 C in the laboratory system in events with two (top panel), three (middle panel), seven or more fragments (bottom panel). The measured and calculated angular distributions for the leading most energetic proton in each event are presented by open circles and solid-line histograms, respectively. The measured and calculated distributions for all other nucleons in the same event are presented by solid circles and dashed-line histograms, respectively.
group. Such a fast proton was selected on the basis of the maximum energy loss in the BGO calorimeter. Secondly, the angular distributions for other less energetic nucleons were obtained. As seen in Fig. 6, the angular distributions of leading protons are forward-peaked in all three multiplicity groups and have very similar shapes. Almost all such protons are emitted in the forward hemisphere. This is explained by a high fraction of the beam photon momentum taken away by the leading proton as a product of a primary γ N reaction on a nucleon of 12 C. It is very probable that the leading proton is represented by a recoil nucleon, which escape from the nuclear residue without any secondary interactions. As seen in Fig. 6, the second and third nucleons in two- and three-nucleon events are emitted in the forward and backward directions with comparable rates. They are represented by products of secondary interactions at the cascade stage of the photonuclear reaction and also by nucleons emitted during de-excitation of a nuclear residue, see Section 4. Finally, in Fig. 6 one can see a remarkably isotropic distribution of nucleons in multifragment events with 7–12 nucleons following the subtraction of the contribution of the most energetic nucleon. Such an isotropic distribution suggests that these nucleons are emitted at the last stage of the reaction in explosive decays of highly excited residual nuclei, see Section 4, rather than in
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Fig. 7. Measured and calculated probabilities of 12 C photodisintegration events with a given number of fragments. Results for absorption of photons with energy of 0.7–1. GeV (left), 1–1.25 GeV (middle) and 1.25–1.5 GeV (right) are shown separately in each panel.
the initial interaction of beam photons with intranuclear nucleons. This means that all correlations of nucleons with beam photons are lost in multifragment events. The main results of our study are presented in Fig. 7. They are related to high-multiplicity events of photodisintegration of 12 C. Measured and calculated probabilities of events with a given number of fragments (from 5 to 12) are plotted in this figure. As seen, in all three intervals of photon energy, 0.7–1. GeV, 1–1.25 GeV and 1.25–1.5 GeV, approximately 1% of all photoabsorption events lead to the production of eight fragments. This probability drops down for events with nine and, especially, with 10, 11 and 12 fragments. The probability of a full disintegration of 12 C into 12 nucleons is very small, about 0.05%, i.e. ones per 2000 events on average. As explained in Section 4, the multifragment breakup of the target nucleus is a rare event because of a low probability to deliver high excitation energy to the nuclear residue created after the cascade stage of the photonuclear reaction. Probability distributions of events with a given number of protons and with a given number of neutrons are shown, respectively in two panels of Fig. 8. As seen from these plots, the most probable photoabsorption events, some 20% of all events, are characterized by the production of a single proton, possibly accompanied by neutron emission. High multiplicity fragmentation events, e.g. with seven and eight protons, are detected only in 1% and 0.01% cases, respectively. One or two additional protons with respect to six protons contained in the 12 C target are produced in γ n → π − p and secondary charge-exchange interactions of photoproduced mesons on intranuclear neutrons. As seen from Figs. 7 and 8, the probabilities calculated with the RELDIS model agree well with the measured values. In particular, a good agreement is obtained between calculated and measured distributions of events according to the numbers of produced neutrons, see Fig. 8. It is remarkable that some events with seven neutrons are observed despite the fact that the target nucleus contains only six neutrons. This is explained by γp → π + n and other reactions of meson production which lead to a recoil neutron rather than to a proton. A very low probability of these events calculated with the RELDIS model agrees well with the measured value. The GRAAL setup makes it possible to measure not only the emission of protons and neutrons, but also the probabilities for nucleon emission in coincidence with meson production. Experimental data for π + n and π ◦ p photoproduction on 12 C are presented in Fig. 9. In order to demonstrate the validity of particle identification procedure adopted in the present work for
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Fig. 8. Measured (points) and calculated (histograms) probabilities of photodisintegration events of 12 C with a given number of protons (top) and neutrons (bottom). Events with at least one proton are selected. Only statistical uncertainties of measurements are shown.
nucleons and mesons, the respective probabilities for photoabsorption on a hydrogen target are also shown in Fig. 9. These distributions were obtained with the LAGRANγ E detector in previous experiments at the GRAAL setup following the same particle identification procedure. In photoabsorption on hydrogen there are no protons in the final state of γp → π + n reaction, and there is only a single proton in γp → π ◦ p reaction. Any deviation from this rule indicates a deficiency of proton identification by the LAGRANγ E detector. Indeed, as seen from Fig. 9, in the photoabsorption on proton about 10% of γp → π + n events are misidentified as events of proton emission. However, the main goal of the present study consists in the identification of multi-proton events. In view of this one can also conclude from Fig. 9 that there are no γp events identified as events with more than two protons. This demonstrates that low- and highmultiplicity events are disentangled with confidence in the photoproduction on 12C. 4. Modeling of nuclear fragmentation induced by photoabsorption on 12 C In the region of photon energies relevant to the present study the RELDIS model [35] can be employed to simulate photonuclear reactions by means of the Monte Carlo technique. It takes into account quasideuteron absorption of photons as well as the meson production on intranuclear nucleons. The two-body channel γ N → πN dominates up to Eγ ∼ 0.5 GeV, while at 0.5 ≤ Eγ ≤ 2 GeV the channels γ N → 2πN and γ N → 3πN play the main role. An excited
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Fig. 9. Measured probabilities of proton emission together with π + n (a) and π ◦ p (b) in the photodisintegration of 12 C (dashed-line histograms). The measured probabilities to detect protons in γp → π + n and γp → π ◦ p reactions on the hydrogen target are also shown by solid-line histograms to demonstrate the accuracy of particle identification procedure.
residual nucleus is formed after the completion of the intranuclear cascade which involves the production and secondary interactions of mesons as well as recoil nucleons. The decays of this nuclear residue are also simulated by the Monte Carlo method implemented in the Statistical Multifragmentation Model (SMM) [6]. Depending on the mass A and excitation energy E of the residual nucleus various de-excitation models are activated in the SMM code. For mediumweight and heavy nuclei (A > 16) the code employs the statistical multifragmentation model, nucleon evaporation or simulate evaporation-fission competition. However, decays of light nuclei (A ≤ 16) are simulated exclusively on the basis of the Fermi break-up model [6]. Similar multistage approaches to simulate photonuclear reactions up to 1.5 GeV are implemented in CEM2k+GEM and LAQGSM models [36], as well as up to tens of GeV in LAQGSM03.01 models [37]. In the papers [36,37] the history of development of these models is described in detail, and their relations to the Moscow intranuclear cascade model, on which RELDIS is based, are explained. In contrast to photonuclear reactions on medium-weight and heavy nuclei, it is more probable that a light target nucleus (A ≤ 16) obtains excitation energy E which is comparable to its total binding energy [38]. In this case an explosive decay of such an excited nucleus into several smaller nuclear fragments can be considered as a dominant de-excitation mode. In order to describe such decays a model similar to the Fermi break-up model for multiple particle production
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Fig. 10. Probability distribution to create a residual nucleus with a given excitation energy per nucleon, E /A, in the absorption of 1 GeV photons by 12 C, as calculated by the RELDIS model.
in proton–proton collisions [39] is employed [40–43]. This model is a component of the SMM code [6] and it is applied specifically to light (A ≤ 16) nuclei with any E . It is assumed that during the decay time of about 100 fm/c the excited nucleus disintegrates simultaneously into cold or slightly excited fragments. The masses of fragments in their ground and lowest excited states were taken from nuclear data tables [44]. All possible break-up channels, which satisfy the mass number, charge, energy and momenta conservations are considered. For example, an excited 12 C nucleus can decay into more than 200 channels containing various combinations of protons, neutrons and light nuclei. It is assumed that the probability of an individual break-up channel containing n particles with masses mi (i = 1, · · · , n) is proportional to its phase space volume [39–43]. The momentum distributions of final products were obtained by the random generation over the accessible phase space which is defined by the total energy taking into account the energy and momentum conservation. According to the RELDIS model most of events of photoabsorption on 12 C do not lead to multiple production of fragments as the main part of the photon energy is taken away by fast nucleons and mesons. However, the presence of highly excited nuclear residues created following the intranuclear cascade in the target nucleus is also predicted by the RELDIS model [12,13]. The probability distribution to obtain a given E /A value for a residual nucleus with mass number A created in the photoabsorption of 1 GeV photons by 12 C is shown in Fig. 10. As seen, the main part of events is characterized by E /A < 2 MeV. According to the Fermi break-up model this typically implies [6] the emission of individual nucleons by the excited nuclear residue. However, there is a low probability to create nuclei with E /A > 5 MeV which undergo multifragment break-up [6]. The calculated distribution of residual nuclei resulting from intranuclear cascades initiated by 1 GeV photons in 12 C is shown in Fig. 11. This distribution is given in the form of the probability to produce a residual nucleus with a given mass number A and a charge Z. As one can see from this plot, the most frequent residual nuclei are 11 C and 11 B, which are produced, respectively, by knock-out of a neutron or a proton from the target nucleus. However, this distribution is quite broad and extends to highly excited residual nuclei with large excess of protons or neutrons which are very far from the stability line. As explained above, the Fermi break-up model is used to simulate decays of the residual nuclei shown in Fig. 11.
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Fig. 11. Calculated probability to create a residual nucleus with a mass number A and a charge Z after intranuclear cascades initiated by the absorption of 1 GeV photons by 12 C.
5. Conclusions As follows from our measurements and simulations, the disintegration of 12 C nuclei which results from the absorption of 700–1500 MeV photons can be reasonably well described as a two-stage process. At the first stage of the photonuclear reaction the photon interacts with an intranuclear nucleon and initiates a cascade of particles which develops inside the target nucleus. Since a large part of the photon momenta is typically taken away by such fast particles, they are emitted mostly in the forward direction. This is confirmed by the angular distributions of most energetic protons which were measured in the present work for events with various numbers of nucleons in the final state. At the second stage of the photonuclear reaction a nuclear residue is formed after all fast particles produced in γ N reactions on intranuclear nucleons escape from this nucleus. As follows from the simulations performed with the RELDIS model, the distribution of the excitation energy of nuclear residues is very broad. Despite of the low probability of high excitations, such events were successfully detected by the LAGRANγ E detector in the present work. They are characterized by several specific signatures of multifragment decays with multiple nucleon emission. Nucleons produced in multifragment decays of highly-excited nuclear residues are distributed isotropically in the laboratory system and their correlation with beam photons and cascade nucleons is lost. As shown, important information on the break-up mechanism of 12 C can be extracted by measuring angular distributions of produced fragments. After the subtraction of the contribution of the fast cascade protons such a distribution measured for events with 7–12 nucleons becomes isotropic. The probability distributions of multifragment events with production of 5–12 fragments agree well with the corresponding distributions calculated with the RELDIS model based on the intranuclear cascade and Fermi break-up models. The yields of more heavy nuclear fragments, e.g., 2 H, 3 H, 4 He, 11 C, produced in the photoabsorption on 12 C cannot be measured in the present experiment and will be a subject of future studies. Acknowledgements The authors are grateful to the European Synchrotron Radiation Facility accelerator group for the stable and reliable operation of the ring. I.P. is indebted to Dr. A.S. Botvina for providing the SMM code for simulations of multifragment decays.
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ScienceDirect Nuclear Physics A 940 (2015) 264–278 www.elsevier.com/locate/nuclphysa
Disintegration of 12 C nuclei by 700–1500 MeV photons V. Nedorezov a , A. D’Angelo b,c , O. Bartalini b,c , V. Bellini d,e , M. Capogni b,c , L.E. Casano c , M. Castoldi f , F. Curciarello g,e , V. De Leo g,e , J.-P. Didelez h , R. Di Salvo c , A. Fantini b,c , D. Franco b,c , G. Gervino i,j , F. Ghio k,l , G. Giardina g,e , B. Girolami k,l , A. Giusa d,e , A. Lapik a , P. Levi Sandri m , F. Mammoliti d,e , G. Mandaglio g,e , M. Manganaro g,e , D. Moricciani c , A. Mushkarenkov a , I. Pshenichnov a,∗ , C. Randieri d,e , N. Rudnev a , G. Russo d,e , C. Schaerf b,c , M.-L. Sperduto d,e , M.-C. Sutera e , A. Turinge a , V. Vegna b,c , I. Zonta b,c a Institute for Nuclear Research, Russian Academy of Sciences, Prospekt 60-letiya Oktyabrya 7a, 117312 Moscow,
Russia b Dipartimento di Fisica – Università degli Studi di Roma “Tor Vergata”, via della Ricerca Scientifica 1,
I-00133 Roma, Italy c INFN – Sezione di Roma “Tor Vergata”, via della Ricerca Scientifica 1, I-00133 Roma, Italy d Dipartimento di Fisica – Università degli Studi di Catania, via Santa Sofia 64, I-95123 Catania, Italy e INFN – Sezione di Catania, via Santa Sofia 64, I-95123 Catania, Italy f Dipartimento di Fisica – Università degli Studi di Genova, via Dodecaneso 33, I-16146 Genova, Italy g Dipartimento di Fisica e di Scienze della Terra, Università di Messina, salita Sperone 31, I-98166 Messina, Italy h IN2P3, Institut de Physique Nucléaire, Rue Georges Clemenceau, F-91406 Orsay, France i Dipartimento di Fisica Sperimentale – Università degli Studi di Torino, via Pietro Giuria 1, I-10125 Torino, Italy j INFN – Sezione di Torino, via Pietro Giuria 1, I-10125 Torino, Italy k Istituto Superiore di Sanità, viale Regina Elena 299, I-00161 Roma, Italy l INFN – Sezione di Roma, piazzale Aldo Moro 2, I-00185 Roma, Italy m INFN – Laboratori Nazionali di Frascati, via E. Fermi 40, I-00044 Frascati, Italy
Received 22 January 2015; received in revised form 3 May 2015; accepted 5 May 2015 Available online 8 May 2015
* Corresponding author.
E-mail address: [email protected] (I. Pshenichnov). http://dx.doi.org/10.1016/j.nuclphysa.2015.05.001 0375-9474/© 2015 Elsevier B.V. All rights reserved.
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Abstract Disintegration of 12 C nuclei by tagged photons of 700–1500 MeV energy at the GRAAL facility has been studied by means of the LAGRANγ E detector with a wide angular acceptance. The energy and momentum distributions of produced neutrons and protons as well as their multiplicity distributions were measured and compared with corresponding distributions calculated with the RELDIS model based on the intranuclear cascade and Fermi break-up models. It was found that eight fragments are created on average once per about 100 disintegration events, while a complete fragmentation of 12 C into 12 nucleons is observed typically only once per 2000 events. Measured multiplicity distributions of produced fragments are well described by the model. The measured total photoabsorption cross section on 12 C in the same energy range is also reported. © 2015 Elsevier B.V. All rights reserved.
Keywords: Photonuclear reactions; Fragmentation of light nuclei; Tagged photons; Total photoabsorption cross section
1. Introduction It is commonly accepted that nuclei can be effectively heated in proton-nucleus [1] or nucleus– nucleus collisions [2]. In collisions of intermediate mass or heavy nuclei many nucleons of a projectile nucleus deliver their kinetic energy to a target nucleus simultaneously in a single collision event. They also essentially change the mass, charge and nuclear structure of the target nucleus. Therefore, hot nuclear systems created in such collisions are characterized by a wide range of their mass and excitation energy and thus keep only a weak resemblance to the initial target nucleus. As proven by calculations [3–6], a simultaneous explosive decay of an excited nucleus into three and more nuclear fragments is observed when the excitation energy of the nucleus E is comparable to its total binding energy. This is considered as a phase transition between nuclear matter and gas of nucleons. The onset of this phenomenon, which is widely known under the name of multifragmentation, is found already at E ∼ 3 MeV per nucleon where it competes with sequential evaporation of nucleons. The multifragment break-up dominates at higher E [4]. The decays of medium-weight or heavy nuclei were mostly studied in the above-mentioned papers [1–5]. It is expected that a nuclear system created after the absorption of a photon by a nucleus is typically closer to the target nucleus compared to nucleus–nucleus collisions. Indeed, the photoabsorption delivers pure energy, rather than energy and additional nucleons to the target nucleus and, as a rule, involves less participant nucleons. This generally leads to mass and charge distributions of excited residual nuclei which are more narrow compared to the respective distributions in nucleus–nucleus collisions. In contrast to nucleus–nucleus collisions, in photonuclear reactions there are no uncertainties related to the identification of nuclear fragments as target or projectile fragments. The nuclear excitation and decay resulting from photoabsorption can be studied in experiments with beams of tagged photons [7,8] or by detecting ultraperipheral collisions of nuclei resulting in their electromagnetic dissociation due to the impact of virtual photons emitted by collision partners [9–14]. As demonstrated by modeling photoabsorption on lead, thorium and neptunium nuclei [15], the average E calculated per nucleon of residual nucleus is below 0.5 MeV. This leads to nuclear fission rather than to multifragmentation of heavy residual nuclei.
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Much less attention of experimentalists has been devoted so far to photodisintegration of light nuclei. This equally concerns the experiments with real photons and fixed targets and the experimental studies of nuclear fragmentation in ultraperipheral collisions induced by virtual photons. In the latter case this is explained by a low value of the electromagnetic fragmentation cross section for light projectile nuclei. It is much lower compared to the total hadronic reaction cross section and usually neglected. Nevertheless, valuable information on the clustering in light nuclei was obtained in experiments on fragmentation of light nuclei in nuclear emulsion [16,17]. Events of nuclear disintegration in ultraperipheral collisions were identified and thoroughly studied in these experiments. The first papers devoted to the disintegration of light nuclei by photons were published more than 40 years ago, see e.g. [18–20]. Electromagnetic dissociation of ultrarelativistic 16 O, 28 Si and 32 S nuclei in collisions with Ag nuclei in nuclear emulsion was identified in several experiments [21,22] and later successfully described by modeling photonuclear reactions on these nuclei induced by virtual photons in the giant resonance region [11]. The disintegration of 12 C into four particles by photons with energy of about 40 MeV was also investigated recently in another experiment [23]. However, to the best of our knowledge, no processes of multifragmentation of light nuclei induced by energetic photons (∼1 GeV) were detected so far. Since the time of first experiments [18–20] several detectors with a wide angular acceptance were developed, in particular, the LAGRANγ E detector [24–27]. This detector is capable to register all particles produced in a photonuclear reaction thus providing a possibility to evaluate the mass and charge of the excited nuclear residue as well as its excitation energy. In the present work the decay of 12 C into several fragments following the absorption of 700–1500 MeV photons at the GRAAL facility is investigated with the LAGRANγ E detector. Special attention is paid to decays of the target nucleus into several light fragments, in particular, into 12 nucleons. The total photoabsorption cross section on 12 C measured in the range of 700–1500 MeV is also presented. In contrast to the numerous studies devoted to the meson photoproduction off nuclei [28], photo-excitation of quasi-free intranuclear nucleons and final-state interaction of produced mesons, the present study is focused on the decays of the nuclear residue created after the first stage of the nuclear photoabsorption. It is expected that multifragment decays of light nuclei take place during carbon-ion therapy of cancer among other fragmentation reactions of therapeutic 12 C nuclei in human tissues [29]. One can also note that since light nuclei are present in cosmic rays, the present study also helps to understand the photodisintegration mechanisms of cosmic ray nuclei under the impact of solar photons known as the Gerasimova– Zatsepin effect, see Ref. [30] and the references therein. 2. Experiment The measurements were performed with the Large Acceptance GRaal-beam Apparatus (for) Nuclear Gamma Experiments (LAGRANγ E) detector system installed at the Grenoble Anneau Accelerateur Laser (GRAAL) beam line facility [31] which provided beams of tagged photons with energy from 700 to 1500 MeV. Such photons were obtained by the Compton scattering of laser photons off 6.03 GeV electrons circulating in the storage ring of the European Synchrotron Radiation Facility (ESFR) in Grenoble, France. The energy resolution of the tagged photon system was approximately 16 MeV. A general layout of the GRAAL experimental setup is shown in Fig. 1. The LAGRANγ E detector [24–26] has been designed to detect both neutral and charged particles produced by photons off protons and light nuclei in a wide range of angle θ with respect
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Fig. 1. General layout of the GRAAL setup, not in scale.
to the beam direction. The detector consists of two major parts: a central BGO calorimeter ball (25◦ ≤ θ ≤ 155◦ ) and forward detectors (θ ≤ 25◦ ). The calorimeter ball is the main component of the LAGRANγ E detector. It is assembled from 480 BGO crystals, each of them is 21 radiation length long. This calorimeter provides the energy resolution of 0.0244 × E 0.47 GeV, where E is the energy of a detected particle expressed in GeV. In order to disentangle neutral and charged particles a E detector made of 32 plastic plates, each 5 mm thick, as well as two cylindrical proportional chambers were placed between the target and BGO. These chambers make possible to identify the interaction point of a photon with the target material with a 1 mm accuracy. These detectors have provided the time-of-flight resolution at the level of 0.5 ns (FWHM). A 25◦ forward cone is not covered by the BGO calorimeter, but additional forward detectors are placed there. Forward-emitted particles are detected by planar proportional chambers, double plastic scintillator walls of 9 m2 area and an electromagnetic calorimeter, which is assembled from plastic and lead layers of the same area (placed at 3.3 meters from the target and consisting of 16 vertical modules). Both scintillator walls consist of 26 horizontal and 26 vertical stripes, each of them is 3 cm thick. Particles emitted in the backward direction (at θ > 155◦ ) are intercepted by a sandwich detector made of one plastic and one lead layer. Such a sophisticated geometry of the LAGRANγ E detector ensures its 4π -coverage. The carbon target used in the present measurements was placed in the centre of the BGO ball. It was prepared as a graphite disk with a thickness of 5 mm and of 30 mm in diameter and replaced liquid hydrogen or deuterium targets used in previous experiments with the LAGRANγ E detector. The LAGRANγ E detector has several features, which make it very advantageous for detecting multifragment decays of 12 C. Nucleons can be disentangled from pions and photons emitted at various angles with respect to the photon beam. Charged particles at forward angles can be identified by an angular and time coincidence between the planar MWPC, scintillator and calorimeter walls. Neutral particles in the same angular range activate only the calorimeter wall. We discriminate charged and neutral particles by the time-of-flight method, see Fig. 2. The velocity of protons created in meson photoproduction on 12C was less than 82% of the speed of light. This makes possible to disentangle them from pions and photons. Particles emitted at larger angles (25◦ ≤ θ ≤ 155◦ ) are successfully identified by taking into account the relation between
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Fig. 2. Distinguishing protons from pions and photons in the forward shower detector (a, b) and BGO calorimeter (c, d). Simulated (a, c) and detected (b, d) events are shown for both cases. Solid lines circumscribe the events selected for the analysis with separated protons and pions as denoted in the figure.
the energy loss E in the barrel and BGO calorimeter, see Fig. 2. Because of the thickness of the carbon target and the detector support materials, heavier nuclear fragments like 3H, 3 He, 4 He and others, cannot reach the BGO calorimeter or forward walls. According to our estimations only 15% of deuterons can be detected due to the same reasons. This makes it difficult to identify composite nuclear fragments in the present experiment. Therefore, some admixture of deuterons to proton data cannot be excluded. In the considered energy range of 700–1500 MeV the photon wavelength becomes too small to induce a knock-out of composite nuclear fragments. Therefore, the main contribution to the yields of fast nucleons comes from recoil nucleons involved into meson photoproduction processes. In the region of the angle θ between 25◦ and 155◦ with respect to the beam direction we identify neutral particles (neutrons and photons) by applying the condition to have signal only in the BGO calorimeter, and charged particles (protons and pions) by the constraint to have signals in the angle and time coincidence of the cylindrical MWPC, barrel and BGO ball detectors. Therefore, the MWPC and barrel detectors provide a veto for the identification of neutral particles. The BGO ball was divided into compartments of a smaller size, which are fired while
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Fig. 3. Probability to have a given number of fired crystals (cluster size) mclus for neutrons, photons and low-energy photons with Eγ ≤ 50 MeV which hit the BGO ball.
particles cross them. It was possible to exploit the dependence of the cluster size mclus (i.e. the number of close-fired compartments) on the particle type. In this way we can distinguish photons with energy higher than 50 MeV and neutrons by looking at the number of mclus , see Fig. 3. About 50% of neutron events are characterized by mclus = 1, while 70% of neutron events have 1 ≤ mclus ≤ 2. This is illustrated by Fig. 3, where the probability to have a given mclus is shown for neutrons, photons and specifically for photons with Eγ ≤ 50 MeV. In our central detector we cannot disentangle low energy photons from neutrons because their cluster multiplicities are similar, typically one or two crystals per cluster. However, our simulation results suggest that in the present data on photoproduction on 12 C the contribution of low-energy (<50 MeV) photon background to the neutron yield does not exceed 2%. In order to select meson photoproduction events with high efficiency (86–90%) and minimal background, the experimental trigger requests a photon tagged in coincidence with the total energy released in the BGO calorimeter higher than 160 MeV, as explained in Ref. [27]. It was important to set a proper threshold for particle detection in each BGO crystal. As proven by simulations, the efficiency of neutron detection approaches 60% when a 2 MeV threshold is set. A detailed description of the neutron detection technique and estimations of detection efficiency are given elsewhere [26]. One can note that the developed discrimination method is applicable only to energetic neutrons and photons. As seen in Fig. 3, the cluster size for photons of energy less than 50 MeV is very small. As a rule, it consists of one or two crystals, and such photons are not easily distinguished from neutrons. At the same time neutrons with energy below 50 MeV can be distinguished from more energetic neutrons as the number of fired crystals is small (mclus ∼ 1) for such low-energy neutrons. 3. Measurement results 3.1. Total photoabsorption cross section The total photoabsorption cross section measured for the 12 C nucleus at GRAAL is shown in Fig. 4. In order to evaluate the total carbon photoabsorption cross section, complementary expositions were performed when the carbon target was removed from the beam, according to the background subtraction method described in Ref. [27]. It was shown that the background comes
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Fig. 4. Total photoabsorption cross section on 12 C calculated per target nucleon. The GRAAL data are presented by points with error bars together with the respective cross section data obtained in Frascati [32] (full circles) and Bonn [33] (open circles). The so-called universal curve [34] is presented by a solid line. Table 1 Average numbers of protons and neutrons registered by the forward detectors and BGO ball, respectively.
Forward detectors BGO ball
Protons
Neutrons
0.35 ± 0.01 2.08 ± 0.03
0.04 ± 0.01 0.53 ± 0.01
mostly outside of the target, whereas the background contribution from the target itself is negligible. Our results agree well with the results of previous measurements performed in Frascati [32] and Bonn [33] for the same target nucleus, as well as with the so-called universal curve [34] which presents the total photoabsorption cross section divided by the number of nucleons in the target. This universal curve, which is valid for various nuclei from beryllium to uranium, reflects a gross property of nuclear forces which bind nucleons into stable nuclei. 3.2. Average numbers of fragments The average numbers of protons and neutrons detected, respectively, in the forward direction and in the BGO ball are listed in Table 1. These numbers are given without accounting for detection efficiency which is close to 100% for protons, but much smaller (about 50%) for neutrons. The event selection was based on the criteria described above and presented in Fig. 2. As follows from Table 1, the number of particles detected in the forward direction is essentially smaller compared to the number of particles detected in the BGO ball. In particular, the efficiency of neutron detection in the shower wall is only about 22%. Nevertheless, the contributions from both detectors were taken into account in the data analysis. 3.3. Energy and angular distributions of secondary nucleons At the first step of the data analysis the differences between the products of photonuclear reactions on proton, deuteron and 12 C targets were investigated. The data for protons and deuterons obtained with the LAGRANγ E detector in previous runs with a liquid hydrogen target were used for this purpose. In particular, it was found that the probability of two neutral clusters, e.g., due
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Fig. 5. Energy distributions of protons produced in photodisintegration of 12 C. Measured (solid line) and calculated (dash-dotted line) distributions in the laboratory system are shown together with the calculated distribution (dashed line) for the centre-of-mass system. The distributions are normalized to the average total photoabsorption cross section on nuclei at 700–1500 MeV calculated per target nucleon. Only statistical errors are shown by error bars.
to a photon and a neutron in the BGO ball was 1.5 times higher for 12C target than for a hydrogen one. The distribution of energy loss of protons in the BGO ball is shown in Fig. 5. For protons with kinetic energy less than 250 MeV this distribution is equivalent to the energy distribution of such protons because their range in BGO is less than the thickness of the wall of this detector. The energy of more energetic protons is measured less accurately as they traverse the wall and escape it. The detection of slow protons is also suppressed due to the trigger condition that the total energy released in the BGO should exceed 160 MeV. The same condition was applied in the total photoabsorption measurements and provided the results consistent with the results obtained in Frascati and Bonn, see Section 3.1. Therefore, one can conclude that the distribution shown in Fig. 5 includes most of the protons emitted in the photoabsorption on 12C and accepted in the analysis. The distributions calculated by means of the RELDIS model, see Section 4, are also presented in Fig. 5. These two distributions are given separately for the laboratory and centre-of-mass systems. They were obtained by calculating the convolution of simulated energy distributions with a Gaussian-shaped function with a width of 18 MeV which is related to the resolution of the tagged photon system. Due to a low velocity of the nuclear system after the absorption of a photon, typically about 0.1 of the light speed, these two simulated distributions are close to each other. Fast protons with energy higher than 250 MeV do not stop in the BGO material, but rather pass through the BGO wall. This explains the overestimation of the calculated yields over the measured ones at higher nucleon energies which is seen in Fig. 5. As follows from our data analysis, the measured energy distributions weakly depend on the photon energy between 700 and 1500 MeV. Therefore, the data for the entire photon energy range of 700–1500 MeV are presented in Fig. 5. The angular distributions of nucleons emitted in the photoabsorption on 12C provide valuable information on the reaction mechanism. Such distributions measured, respectively, for three distinct nucleon multiplicity groups with two, three and 7–12 nucleons are shown in Fig. 6. The distributions are given for the entire photon energy range of 700–1500 MeV considered in the present work. In this analysis the most energetic (leading) proton was firstly identified in each event and angular distributions of such nucleons were obtained for the respective multiplicity
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Fig. 6. Angular distributions of nucleons produced in photodisintegration of 12 C in the laboratory system in events with two (top panel), three (middle panel), seven or more fragments (bottom panel). The measured and calculated angular distributions for the leading most energetic proton in each event are presented by open circles and solid-line histograms, respectively. The measured and calculated distributions for all other nucleons in the same event are presented by solid circles and dashed-line histograms, respectively.
group. Such a fast proton was selected on the basis of the maximum energy loss in the BGO calorimeter. Secondly, the angular distributions for other less energetic nucleons were obtained. As seen in Fig. 6, the angular distributions of leading protons are forward-peaked in all three multiplicity groups and have very similar shapes. Almost all such protons are emitted in the forward hemisphere. This is explained by a high fraction of the beam photon momentum taken away by the leading proton as a product of a primary γ N reaction on a nucleon of 12 C. It is very probable that the leading proton is represented by a recoil nucleon, which escape from the nuclear residue without any secondary interactions. As seen in Fig. 6, the second and third nucleons in two- and three-nucleon events are emitted in the forward and backward directions with comparable rates. They are represented by products of secondary interactions at the cascade stage of the photonuclear reaction and also by nucleons emitted during de-excitation of a nuclear residue, see Section 4. Finally, in Fig. 6 one can see a remarkably isotropic distribution of nucleons in multifragment events with 7–12 nucleons following the subtraction of the contribution of the most energetic nucleon. Such an isotropic distribution suggests that these nucleons are emitted at the last stage of the reaction in explosive decays of highly excited residual nuclei, see Section 4, rather than in
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Fig. 7. Measured and calculated probabilities of 12 C photodisintegration events with a given number of fragments. Results for absorption of photons with energy of 0.7–1. GeV (left), 1–1.25 GeV (middle) and 1.25–1.5 GeV (right) are shown separately in each panel.
the initial interaction of beam photons with intranuclear nucleons. This means that all correlations of nucleons with beam photons are lost in multifragment events. The main results of our study are presented in Fig. 7. They are related to high-multiplicity events of photodisintegration of 12 C. Measured and calculated probabilities of events with a given number of fragments (from 5 to 12) are plotted in this figure. As seen, in all three intervals of photon energy, 0.7–1. GeV, 1–1.25 GeV and 1.25–1.5 GeV, approximately 1% of all photoabsorption events lead to the production of eight fragments. This probability drops down for events with nine and, especially, with 10, 11 and 12 fragments. The probability of a full disintegration of 12 C into 12 nucleons is very small, about 0.05%, i.e. ones per 2000 events on average. As explained in Section 4, the multifragment breakup of the target nucleus is a rare event because of a low probability to deliver high excitation energy to the nuclear residue created after the cascade stage of the photonuclear reaction. Probability distributions of events with a given number of protons and with a given number of neutrons are shown, respectively in two panels of Fig. 8. As seen from these plots, the most probable photoabsorption events, some 20% of all events, are characterized by the production of a single proton, possibly accompanied by neutron emission. High multiplicity fragmentation events, e.g. with seven and eight protons, are detected only in 1% and 0.01% cases, respectively. One or two additional protons with respect to six protons contained in the 12 C target are produced in γ n → π − p and secondary charge-exchange interactions of photoproduced mesons on intranuclear neutrons. As seen from Figs. 7 and 8, the probabilities calculated with the RELDIS model agree well with the measured values. In particular, a good agreement is obtained between calculated and measured distributions of events according to the numbers of produced neutrons, see Fig. 8. It is remarkable that some events with seven neutrons are observed despite the fact that the target nucleus contains only six neutrons. This is explained by γp → π + n and other reactions of meson production which lead to a recoil neutron rather than to a proton. A very low probability of these events calculated with the RELDIS model agrees well with the measured value. The GRAAL setup makes it possible to measure not only the emission of protons and neutrons, but also the probabilities for nucleon emission in coincidence with meson production. Experimental data for π + n and π ◦ p photoproduction on 12 C are presented in Fig. 9. In order to demonstrate the validity of particle identification procedure adopted in the present work for
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Fig. 8. Measured (points) and calculated (histograms) probabilities of photodisintegration events of 12 C with a given number of protons (top) and neutrons (bottom). Events with at least one proton are selected. Only statistical uncertainties of measurements are shown.
nucleons and mesons, the respective probabilities for photoabsorption on a hydrogen target are also shown in Fig. 9. These distributions were obtained with the LAGRANγ E detector in previous experiments at the GRAAL setup following the same particle identification procedure. In photoabsorption on hydrogen there are no protons in the final state of γp → π + n reaction, and there is only a single proton in γp → π ◦ p reaction. Any deviation from this rule indicates a deficiency of proton identification by the LAGRANγ E detector. Indeed, as seen from Fig. 9, in the photoabsorption on proton about 10% of γp → π + n events are misidentified as events of proton emission. However, the main goal of the present study consists in the identification of multi-proton events. In view of this one can also conclude from Fig. 9 that there are no γp events identified as events with more than two protons. This demonstrates that low- and highmultiplicity events are disentangled with confidence in the photoproduction on 12C. 4. Modeling of nuclear fragmentation induced by photoabsorption on 12 C In the region of photon energies relevant to the present study the RELDIS model [35] can be employed to simulate photonuclear reactions by means of the Monte Carlo technique. It takes into account quasideuteron absorption of photons as well as the meson production on intranuclear nucleons. The two-body channel γ N → πN dominates up to Eγ ∼ 0.5 GeV, while at 0.5 ≤ Eγ ≤ 2 GeV the channels γ N → 2πN and γ N → 3πN play the main role. An excited
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Fig. 9. Measured probabilities of proton emission together with π + n (a) and π ◦ p (b) in the photodisintegration of 12 C (dashed-line histograms). The measured probabilities to detect protons in γp → π + n and γp → π ◦ p reactions on the hydrogen target are also shown by solid-line histograms to demonstrate the accuracy of particle identification procedure.
residual nucleus is formed after the completion of the intranuclear cascade which involves the production and secondary interactions of mesons as well as recoil nucleons. The decays of this nuclear residue are also simulated by the Monte Carlo method implemented in the Statistical Multifragmentation Model (SMM) [6]. Depending on the mass A and excitation energy E of the residual nucleus various de-excitation models are activated in the SMM code. For mediumweight and heavy nuclei (A > 16) the code employs the statistical multifragmentation model, nucleon evaporation or simulate evaporation-fission competition. However, decays of light nuclei (A ≤ 16) are simulated exclusively on the basis of the Fermi break-up model [6]. Similar multistage approaches to simulate photonuclear reactions up to 1.5 GeV are implemented in CEM2k+GEM and LAQGSM models [36], as well as up to tens of GeV in LAQGSM03.01 models [37]. In the papers [36,37] the history of development of these models is described in detail, and their relations to the Moscow intranuclear cascade model, on which RELDIS is based, are explained. In contrast to photonuclear reactions on medium-weight and heavy nuclei, it is more probable that a light target nucleus (A ≤ 16) obtains excitation energy E which is comparable to its total binding energy [38]. In this case an explosive decay of such an excited nucleus into several smaller nuclear fragments can be considered as a dominant de-excitation mode. In order to describe such decays a model similar to the Fermi break-up model for multiple particle production
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Fig. 10. Probability distribution to create a residual nucleus with a given excitation energy per nucleon, E /A, in the absorption of 1 GeV photons by 12 C, as calculated by the RELDIS model.
in proton–proton collisions [39] is employed [40–43]. This model is a component of the SMM code [6] and it is applied specifically to light (A ≤ 16) nuclei with any E . It is assumed that during the decay time of about 100 fm/c the excited nucleus disintegrates simultaneously into cold or slightly excited fragments. The masses of fragments in their ground and lowest excited states were taken from nuclear data tables [44]. All possible break-up channels, which satisfy the mass number, charge, energy and momenta conservations are considered. For example, an excited 12 C nucleus can decay into more than 200 channels containing various combinations of protons, neutrons and light nuclei. It is assumed that the probability of an individual break-up channel containing n particles with masses mi (i = 1, · · · , n) is proportional to its phase space volume [39–43]. The momentum distributions of final products were obtained by the random generation over the accessible phase space which is defined by the total energy taking into account the energy and momentum conservation. According to the RELDIS model most of events of photoabsorption on 12 C do not lead to multiple production of fragments as the main part of the photon energy is taken away by fast nucleons and mesons. However, the presence of highly excited nuclear residues created following the intranuclear cascade in the target nucleus is also predicted by the RELDIS model [12,13]. The probability distribution to obtain a given E /A value for a residual nucleus with mass number A created in the photoabsorption of 1 GeV photons by 12 C is shown in Fig. 10. As seen, the main part of events is characterized by E /A < 2 MeV. According to the Fermi break-up model this typically implies [6] the emission of individual nucleons by the excited nuclear residue. However, there is a low probability to create nuclei with E /A > 5 MeV which undergo multifragment break-up [6]. The calculated distribution of residual nuclei resulting from intranuclear cascades initiated by 1 GeV photons in 12 C is shown in Fig. 11. This distribution is given in the form of the probability to produce a residual nucleus with a given mass number A and a charge Z. As one can see from this plot, the most frequent residual nuclei are 11 C and 11 B, which are produced, respectively, by knock-out of a neutron or a proton from the target nucleus. However, this distribution is quite broad and extends to highly excited residual nuclei with large excess of protons or neutrons which are very far from the stability line. As explained above, the Fermi break-up model is used to simulate decays of the residual nuclei shown in Fig. 11.
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Fig. 11. Calculated probability to create a residual nucleus with a mass number A and a charge Z after intranuclear cascades initiated by the absorption of 1 GeV photons by 12 C.
5. Conclusions As follows from our measurements and simulations, the disintegration of 12 C nuclei which results from the absorption of 700–1500 MeV photons can be reasonably well described as a two-stage process. At the first stage of the photonuclear reaction the photon interacts with an intranuclear nucleon and initiates a cascade of particles which develops inside the target nucleus. Since a large part of the photon momenta is typically taken away by such fast particles, they are emitted mostly in the forward direction. This is confirmed by the angular distributions of most energetic protons which were measured in the present work for events with various numbers of nucleons in the final state. At the second stage of the photonuclear reaction a nuclear residue is formed after all fast particles produced in γ N reactions on intranuclear nucleons escape from this nucleus. As follows from the simulations performed with the RELDIS model, the distribution of the excitation energy of nuclear residues is very broad. Despite of the low probability of high excitations, such events were successfully detected by the LAGRANγ E detector in the present work. They are characterized by several specific signatures of multifragment decays with multiple nucleon emission. Nucleons produced in multifragment decays of highly-excited nuclear residues are distributed isotropically in the laboratory system and their correlation with beam photons and cascade nucleons is lost. As shown, important information on the break-up mechanism of 12 C can be extracted by measuring angular distributions of produced fragments. After the subtraction of the contribution of the fast cascade protons such a distribution measured for events with 7–12 nucleons becomes isotropic. The probability distributions of multifragment events with production of 5–12 fragments agree well with the corresponding distributions calculated with the RELDIS model based on the intranuclear cascade and Fermi break-up models. The yields of more heavy nuclear fragments, e.g., 2 H, 3 H, 4 He, 11 C, produced in the photoabsorption on 12 C cannot be measured in the present experiment and will be a subject of future studies. Acknowledgements The authors are grateful to the European Synchrotron Radiation Facility accelerator group for the stable and reliable operation of the ring. I.P. is indebted to Dr. A.S. Botvina for providing the SMM code for simulations of multifragment decays.
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