Clustering in Oxygen Nuclei and Spectator Fragments in 16 O– 16 O Collisions at the LHC

: A new version of the Abrasion–Ablation Monte Carlo for Colliders model with the Minimum Spanning Tree clusterization algorithm (AAMCC-MST) is used to simulate 16 O– 16 O collisions at the LHC, accounting for the presence of alpha-clustered states in 16 O. The yields of He, Li, Be, B, C and N spectator nuclei are calculated taking into account the pre-equilibrium clusterization of spectator matter and short-range correlations (SRC) between nucleons in 16 O. The impact of α -clustering and SRC on the production of spectator neutrons and deuterons is investigated. The results on the production of spectator nucleons and fragments can help in evaluating the performance of Zero Degree Calorimeters in future studies of 16 O– 16 O collisions at the LHC.


Introduction
Proton-proton and nucleus-nucleus collisions are the main subjects of the research program at the Large Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN) in Geneva, Switzerland. Over the years pp, p-208 Pb, 129 Xe-129 Xe and 208 Pb-208 Pb interactions were studied in A Large Ion Collider Experiment (ALICE) [1] at the LHC. The ALICE measurements covered a broad set of observables related to Quantum Chromodynamics (QCD), the theory of strong interactions, to understand, in particular, the dependence of the observables on the masses of colliding species. As discussed [2,3], in future LHC runs ALICE and other experiments may benefit from studies of smaller volumes of hot and dense nuclear matter created in 16 O- 16 O collisions to understand the emerging collectivity in interactions of light nuclei in comparison to the already studied interactions of heavy species.
An interesting feature of 16 O consists of a possible presence of intranuclear 4 He clusters, as suggested by the numbers of neutrons and protons contained in 16 O. The nucleons can be arranged to form four intranuclear α-clusters in 16 O. Tetrahedral configurations of α-clusters were considered for 16 O [4,5] to match the spherical symmetry of the ground states of this nucleus. The coexistence of the clustered states with non-clustered ones is expected. The contribution of the clustered states to the 16 O ground state was evaluated to be below 30% [6].
As reported recently for calculations with a multi-phase transport model (AMPT) [7], the global properties of 16 O- 16 O collisions, such as initial energy density and final chargedparticle multiplicity, remain similar in modelling with α-clustered structure of 16 O and the harmonic oscillator non-clustered density profile of 16 O. However, as shown in Refs. [8][9][10], a kind of snapshot of the overlap zone of colliding nuclei can be made by exploring the relativistic 16 O- 16 O collisions to reveal the intranuclear clustering in 16 O despite the global spherical symmetry of the tetrahedral state. The cluster structure of initial 16 O may impact the eccentricity of the overlap zone [11], the triangular flow of π ± , K ± , p and p [8,9], and the nuclear modification factor R AA for D-mesons [12].
As known, nuclear matter outside the interaction zone of colliding nuclei remains relatively cold and forms spectator matter. Much less attention has been paid so far to a possible impact of the presence of α-clustered states in 16 O on the production of spectator fragments in 16 O- 16 O collisions. One can expect that a part of α-clusters from 16 O survive in collisions and thus form 4 He spectators. The data on fragmentation of 2-200A GeV 16 O in nuclear emulsion [13] confirm such expectations. In these measurements the events of 16 O fragmentation in collisions with light (CNO: carbon, nitrogen, oxygen) and heavy nuclei (AgBr: silver, bromine) were distinguished, but in both cases the events containing He as spectator nuclear fragments were the most frequent ones [13]. This was understood as the experimental evidence for the formation of α-clusters as building blocks of initial 16 It is important to find out whether the tetrahedral geometry of α-clustered states in 16 O [4,5] is consistent with enhanced production of 4 He as spectators. The first comparison of the measurements [13] with results of an early version of our Abrasion-Ablation Monte Carlo for Colliders model with the Minimum Spanning Tree clusterization algorithm (AAMCC-MST), which took into account the pre-equilibrium clusterization of spectator matter [14], but neglected the α-clustering in initial 16 O, was presented in Ref. [15]. As found [15], the yields of He nuclei were underestimated by the model. Therefore, in our next study [16], the tetrahedral configuration of α-clustering in 16 O was introduced and various parameters of AAMCC-MST were tuned to describe the data [13] on the probabilities to produce specific elements (H, He, Li, Be, B, C and N) as spectator nuclei and also on the multiplicity distributions of He spectator fragments. In particular, on the basis of comparison with the data [13], the contribution of the clustered states to the ground state of 16 O was estimated at the level of 30% [16].
The α-clustering in nuclei is not the only phenomenon responsible for the correlations between intranuclear nucleons. The impact of short-range nucleon-nucleon correlations (SRC) [17] on the momentum distributions of spectator nucleons in fragmentation of 16 O, 40 Ca and 208 Pb nuclei was investigated in detail in Ref. [18]. As shown by modelling ultracentral 208 Pb-208 Pb collisions, the average numbers of spectator deuterons calculated for such collisions are affected by including SRC in AAMCC-MST [19]. Therefore, it is also necessary to evaluate the influence of SRC on the production of spectator nucleons and fragments in 16 O- 16 O collisions in AAMCC-MST modelling taking into account the presence of the tetrahedral α-clustered states in 16 O.
In the present paper, a new version of the AAMCC-MST model is used to simulate 16 O- 16 O collisions at the LHC. As described in Section 2, the model takes into account the admixture of α-clustered states and SRC in 16 O [16] and also pre-equilibrium clusterization of spectator matter [14,19]. Multiplicity distributions of spectator neutrons and deuterons as well as yields of secondary nuclei calculated for 16 O-16 O collisions at the nucleon-nucleon center-of-mass energy, √ s NN = 6.37 TeV are presented in Section 3. General features of 16 O- 16 O fragmentation at the LHC and the sensitivity of results to the choice of various calculation options are discussed in Conclusions, Section 4.

Modelling 16 O-16 O Collisions in AAMCC-MST
A new version of AAMCC-MST model (for the source code see [20]) is used in the present study to model the production and decay of spectator matter in collisions of relativistic 16 O nuclei. Each collision event is simulated with AAMCC-MST in several stages.
The modelling of an 16 O- 16 O collision starts with sampling positions of nucleons in both colliding nuclei. Three options were used for this procedure. The first option denoted hereafter as "no clustering, SRC" represents non-clustered 16 O with the positions of nucleons taken from pre-sampled nucleon configurations provided in Ref. [17] where the short-range nucleon-nucleon correlations were taken into account.
The second option denoted as "clustered, step-like SRC" represents the clustered state of 16 O. The centres of four α-clusters are arranged first in the vertices of a tetrahedron [4,5,7] assuming its random orientation. In its turn, two parametrizations of the radial nucleon density distribution inside the α-clusters, ρ(r), are used with r defined as the radial distance from the cluster center. The first one is the harmonic oscillator (HO) parametrization based on the HO intranuclear potential in 4 H: ρ HO (r) ∝ (1 + R · (r/a HO ) 2 ) exp (−r 2 /a 2 HO ) with R = 1.68, and a HO = 0.544 fm, defining, respectively, the periphery-to-center ratio of ρ HO (r) and its periphery diffuseness. The second one is the Woods-Saxon (WS) parametrization ρ(r) ∝ 1/(1 + exp((r − r 0 )/a)), with r 0 = 1.68 fm as the cluster radius, and a = 0.544 fm as the skin depth. The parameters of both distributions are taken to fit the radial density distribution of 4 He [6,21]. The length of the edges of the tetrahedron with the centres of α-clusters in its vertices was taken as 4.18 fm and 4 fm for HO and WS distributions, respectively. In both cases with 30% of the clustered configurations mixed with 70% of non-clustered ones, the RMS (root mean square) charge radius of 2.6991 ± 0.0052 fm [22] for 16 O is reproduced. The mixed radial distributions of protons and neutrons were assumed to be the same, and the resulting nucleon density distributions are shown in Figure 1 with the RMS radius for nucleons r RMS = 2.69 fm calculated as the average from 5000 nucleon configurations generated for 16 O. The assumption of the equality of neutron and proton distributions can be questioned even in 16 O with the same numbers of protons and neutrons, Z = N = 8; see Ref. [23] for details. However, r RMS = 2.54 ± 0.02 fm and 2.631 ± 0.061 fm were extracted, respectively, in Refs. [24,25] from nucleus-nucleus reaction cross sections at low and intermediate collision energies. Comparing these values with the measured RMS charge radius 2.6991 ± 0.0052 fm [22], one can conclude that the difference between the RMS radii for protons and neutrons is actually quite small (<0.2 fm).
The short-range nucleon-nucleon correlations in the second option are modelled by a step-like function differently with respect to SRC introduced in the first option following Ref. [17]. Here the minimum separation distance between nucleons (∼0.8 fm) is implemented in the Gibbs sampling algorithm [26] to sample the positions of nucleons in 16 O.
The third option to sample the positions of nucleons in the clustered 16 O is based on the same algorithm as the second option, but without accounting for SRC. It is denoted as "clustered, no SRC". Since the probability of the clustered states in 16 O is estimated below 30% [6], the non-clustered states were also sampled according to the HO parametrization of the 16 O density following Ref. [27] with R = 1.833 and a HO = 1.544 fm. The outputs of the Monte Carlo modelling with the second or third options and without clustering were combined in the certain proportions (30% and 70%, respectively) to obtain final results.
Participant nucleons are removed from the initial nuclei at the abrasion stage modelled with the Glauber Monte Carlo (GlauberMC) model [28]. The sizes and shapes of spectator prefragments representing the remnants of both colliding nuclei are defined at the end of the abrasion stage.
The total excitation energy for each of the prefragments is calculated at the next stage of modelling with AAMCC-MST. Following the study of ALADIN Collaboration [29], a phenomenological parabolic dependence of the average excitation energy ε, per prefragment nucleon on the relative prefragment mass is used: ε = ε 0 1 − A p f /A. Here A p f is the prefragment mass and A is the mass of the initial nucleus. The parameter values, ε 0 = 4 MeV and 8 MeV, were used in our previous calculations [16], and the results were compared to the data [13]. It was found [16] that the results were less sensitive to ε 0 than to the contribution of the clustered states. The calculations with ε 0 = 4 MeV and the contribution of the clustered states of 30% demonstrated better agreement with the measured multiplicity distribution of He fragments. Therefore, this set of parameters is used also in the present study. Following the calculation of ε for each prefragment, the pre-equilibrium clusterization of the prefragments is modelled by means of the MST-clustering algorithm described in Refs. [14,19].
Finally, the decays of multiple excited nuclear fragments resulting from pre-equilibrium

Results
In Ref. [3] 16 O- 16 O collisions were modelled at √ s NN = 6.37 TeV. So, the same collision energy for future oxygen runs at the LHC is assumed in the present study. Three options for the nuclear density distribution of 16 O (see Section 2) are used in calculations.

Production of Spectator Neutrons at the LHC
Some of the experiments at the LHC are capable of detecting spectator neutrons by forward hadronic calorimeters. In particular, the ALICE experiment is equipped with Zero Degree Calorimeters [31] to detect spectator neutrons for the measurements of collision centrality [32] and collider luminosity [33] in 208 Pb-208 Pb collisions because at least one neutron is emitted in each event. It is interesting to investigate whether these methods can be applied also to 16 Figure 2, the multiplicity distributions, P(N neutr. ), of spectator neutrons calculated with three different options for nuclear density in 16 O are generally consistent with each other and the distributions obtained with different parameterizations of the nuclear density of α-clusters (HO and WS) are also in agreement regarding shape. However, the events with large numbers of spectator neutrons N neutr. > 3 are essentially suppressed with accounting for SRC, because more neutrons remain bound in spectator nuclear fragments.
Spectator neutrons are absent in a large fraction of the simulated events: in ∼33% of events modelled without SRC and in ∼43% with SRC. This means that in contrast to 208 Pb-208 Pb collisions, where spectator neutrons are emitted in ∼100% of events, less than 70% of 16 O- 16 O events will be triggered by the forward neutron calorimeters at the LHC.

Production of Spectator Deuterons at the LHC
As shown in Ref. [19], the production of deuterons in ultracentral 208 Pb-208 Pb collisions at the Super Proton Synchrotron (SPS) at CERN was enhanced in calculations with accounting for SRC. A similar effect can be expected in modelling 16 O-16 O collisions at the LHC. The multiplicity distributions of spectator deuterons calculated with three nuclear density options for 16 O are presented in Figure 3.  As shown in Figure 3, in ∼85% of 16 O fragmentation events spectator deuterons are absent, while in the rest of events (∼14%) a single spectator deuteron is produced in calculations with all considered density parametrizations. The calculated P(N d ) obtained with different nuclear density parametrizations in 16 O diverge noticeably only for much less frequent (∼1%) multiple deuteron production, for N d = 2 and 3 for both density parametrizations (HO and WS) implemented for α-clusters in 16 O. In the absence of clustering in 16

Production of Spectator Nuclei at the LHC
In Figure 4, the probabilities to produce specific spectator nuclei in 16 O- 16 O collisions at the LHC are presented. The probabilities were calculated with accounting for SRC for HO and WS parametrizations of the nucleon density inside α-clusters in 16 O, and they are ordered according to charge-to-mass Z/M F ratios of the respective nuclei. The masses M F were taken from the nuclear data tables [34]. The 30% contribution of the clustered states in 16 O is assumed in all calculations.  As seen in Figure 4, all possible elements (H, He, Li, Be, B, N and C) are produced as spectator nuclei after removing participant nucleons from initial 16 O. Spectator nuclei are produced with similar probabilities in calculations with HO and WS parametrizations of the nucleon density inside α-clusters. One can note that the production of spectator nuclei with enhanced neutron ( 6 He and 12 B) or proton ( 10 C) content is also possible. Such nuclei are produced in events with the dominant abrasion of protons with respect to neutrons and vice versa.
In contrast to the calculations with the previous version of the AAMCC-MST model [15], which predicted 2 H as the most frequent spectator fragment, the production of 4 He dominates according to the present version of AAMCC-MST, see Figure 4. This is explained by accounting for α-clustered states in initial 16 O in the present calculations. At the same time, the present calculations demonstrate the absence of 13,14,15 O and 15 N spectator nuclei seen with the previous AAMCC-MST version [15]. The production of these nuclei is suppressed since the ALADIN parameterization [29] used in the present study delivers higher prefragment excitation energy in comparison to the hybrid parameterization used in the previous calculations [15]. As shown [16], the description of experimental data [13] on fragmentation of 16 is improved with the ALADIN parameterization also used in the present work.
Finally, one can note that the yields of stable Z = N spectator nuclei such as 2 H, 4 He, 6 Li, 10 B, 12 C and 14 N are of special interest because their Z/M F ratios are close to the ratio for 16 O nuclei accelerated at the LHC. As seen from Figure 4, the probability to produce at least one of these nuclei approaches 1, and the respective cross section is close to the total hadronic cross section σ h = 1.34 b. These Z = N nuclei can propagate in the vicinity of 16 O beam nuclei in the magnetic field of the LHC, pass through the collimators of the collider and stay in the beam. According to Ref. [35], the integrated luminosity of L ≈ 4 nb −1 is expected in a 40 hour run in total for all four experiments at the LHC. Therefore, about N = L × σ h = 4 nb −1 × 1.34 · 10 9 nb= 5.36 · 10 9 of Z = N spectator nuclei will be produced and can potentially circulate in the LHC along with initially injected 6 bunches of 4.6 · 10 9 ions each with 2.76 · 10 10 of 16 O in total. Therefore, some 4 He- 16 O, 6 Li-16 O, ... 14 N- 16 O events could potentially contaminate at the level of 1-10% the data on 16 O- 16 O collisions to be collected in future LHC runs. As pointed out in Ref. [35], this transmutation effect needs further investigations.

Conclusions
In the present paper, the new version of Abrasion-Ablation Monte Carlo for Colliders (AAMCC-MST) model tuned [16] to describe the data [13] on the fragmentation of 2-200A GeV 16 O has been employed to model the production of spectator nucleons and nuclear fragments in 16 O- 16 O collisions at the LHC. In total, three options for 16 O nuclear density distribution were used in calculations: (1) without considering α-clustering but with accounting for SRC; (2) with accounting for α-clustering and SRC; and (3) with accounting for α-clustering but without considering SRC. In addition, with options (2) and (3) two distributions of the nuclear density in α-clusters were used: the harmonic oscillator and Woods-Saxon distributions.
The multiplicity distributions of spectator neutrons and deuterons calculated for 16 O-16 O collisions at the LHC with different options generally consistent with each other. In all cases, the fraction of events without spectator neutrons turned out to be significant (33-43%). Therefore, forward neutron calorimeters presently installed at the LHC are expected to be less effective in the measurements of collision centrality in 16 O- 16 O collisions. As follows from the calculations, the probabilities of events with two or three spectator deuterons are sensitive to accounting for the short-range nucleon-nucleon correlations in 16 O.
The inclusion of α-clustering in 16 O enhances the production of 4 He and makes it the most frequent spectator fragment in 16 O- 16 O collisions. The calculated yields of spectator fragments with equal numbers of protons and neutrons ( 2 H, 4 He, 6 Li, 10 B, 12 C and 14 N) as in 16 O, may help to evaluate their impact on LHC components. These secondary nuclei could propagate close to the beam nuclei, hit superconducting magnets or contaminate 16  Acknowledgments: The authors are grateful to Yury Tchuvil'sky and Dmitry Rodkin for discussions of α-clustering effects in light nuclei.

Conflicts of Interest:
The authors declare no conflict of interest.