Clustering effects in fusion evaporation reactions with light even-even N=Z nuclei. The 24 Mg and 28 Si cases

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INTRODUCTION
The NUCL-EX collaboration has recently started an experimental campaign of exclusive measurements of fusion-evaporation reactions with light nuclei as interacting partners. The aim is to progress in the understanding of statistical properties of the decay of light nuclei at excitation energies above particle emission thresholds and to measure observables linked to the presence of cluster structures in nuclear excited levels.
The statistical decay of hot nuclei and nuclear clustering are very active research topics in nuclear physics [1]. Using the statistical theory of Compound Nucleus (CN) decay, the detailed output of a fusion-evaporation reaction is uniquely predicted under the knowledge of nuclear ground state properties and level densities. The knowledge of level densities is not only important for the understanding of nuclear structure [5], but it is also required for different applications of nuclear physics, from nucleosynthesis calculations to reactor science.
Despite the interest of this issue, few studies, mainly based on inclusive experiments, exist on the evaporation of very light nuclei (A ∼ 20 region) at relatively high excitation energy (ε * ≈ 3 A.MeV). The interest on this mass -excitation energy region is easily justified: from the experimental point of view, measuring light nuclei means low multiplicity events, which, together with a high detection coverage and high energy and angular resolution, leads to the possibility of achieving a complete event reconstruction, thus having a full control on the reaction mechanism.
In addition, the knowledge of the decay mechanism could help in the backtracing procedure in multifragmentation events. Indeed in the statistical framework fragments formed in the freeze-out volume are mainly in this energy and mass region.
Nuclear structure signatures are especially evident in light nuclei, even at high excitation energy. By using an exclusive channel selection and a highly constrained statistical code, it is possible to put into evidence deviations from a statistical behavior in the decay of the hot sources formed in the collision. Indeed some excited states of different nuclei in this mass region are known to present pronounced cluster structures. These correlations may persist in the ground state along some selected isotopic chains [6] and, according to the Ikeda diagrams [2], α-clustered excited states are sizeably expected at high excitation energies close to the multi-alpha decay threshold in all even-even N = Z nuclei.
The subject of α-clustering has been a central issue in nuclear physics and has witnessed a gain of interest in recent years. On the theoretical side, highly sophisticated ab-initio calculations have shown pronounced cluster features in the ground state of a large number of light nuclei [6]. Concerning experimental research, rotational bands consistent with α-cluster structures have been identified in different even-even light nuclei and shown to persist even along their isotopic chains. Such effects can be experimentally seen as an excess of cluster production with respect to the prediction of the statistical model, provided that the ingredients of the latter are sufficiently constrained via experimental data. A campaign of exclusive measurements of fusion-evaporation reactions with light nuclei as interacting partners is currently carried on by our collaboration. In the framework of this campaign, the 12 C+ 12 C and 14 N + 10 B reactions have been measured in order to study the decay of the same 24 Mg compound nucleus, populated at the same excitation energy but through different entrance channels. The results obtained in our first measurements are briefly reported in the following sections.
A very interesting clustering effect is for instance that of the so-called Hoyle state, i.e. the excited state 0 + at 7.65 MeV of 12 C, which plays a decisive role in stellar nucleosynthesis of 12 C.
In several cases experimental results have interpreted the Hoyle state as mainly sequential through an intermediate 8 Be gs decay [8][9][10][11][12]; other experimental data show sizeable amount of instantaneous three α-particle decay [13,14] where the three α particles are characterized by low kinetic energies and low kinetic energy dispersion. Most of the results indicate a nearly complete agreement with a sequential decay with a very small amount (0.2 % [12]) of the instantaneous one.
In this work we show some preliminary results from the analysis of semiperipheral 12 C + 12 C reactions where the projectile decays in three α-particles passing through the Hoyle state.
The results compatible with indications for non-sequential decay have been obtained in reactions involving heavy ions [13,14]. We have therefore investigated the Hoyle state when obtained in the decay chain of 24 Mg* formed in central collisions and in particular we have analyzed six α-particles in the final stage of the 24 Mg* decay. We will compare the experimental results both for central and peripheral collisions with the prediction of a model based on Hauser-Feshbach formalism which includes light nuclei ecxcited states. The main features of this model have been extensively described in [4]. The predictions have been filtered in order to be compared to experimental data, taking into account detector characteristics such as thresholds, energy and angular resolutions. Data have been also compared to filtered simple model calculations for simultaneous decay (DDE), i.e. three α-particles simultaneously emitted from the excited Carbon and for a linear chain (DDL), i.e. two α-particles emitted back to back with the third α-particle at rest in the 12 C frame.
Similary to the 24 Mg*, the compound nucleus 28 Si* can be formed through fusion of α-cluster stable nuclei in the entrance channel and in the future of light radioactive beams provided by SPES. It is interesting for such systems that they can be studied at different beam energies, thus extracting information on how (and to what extent) structure effects are still at play in the decay of hot nuclei at different excitation regimes.

THE EXPERIMENTS
The experiments were performed at the LNL (Laboratori Nazionali di Legnaro), with 12 C, 14 N and 16 O beams provided by the XTU TANDEM accelerator. We have studied the two systems 12 C + 12 C and 14 N + 10 B, leading to the same compound nucleus 24 Mg* at the same excitation energy. The decay of the 28 Si* compound nucleus has been investigated using 16 O + 12 C reaction at three different energies. For these last reactions the analysis has been focused up to now on the necessary preliminary checks on the quality of collected data. Charge (and mass, where the information is available) identification and energy calibration are in progress.
The apparatus has been described in [15]. Here we recall the main features. The experimental setup is composed of the GARFIELD apparatus and the Ring-Counter (RCo) annular detector, fully equipped with digital electronics [16]. The forward polar angles (7 o ÷17 o ) are covered by a three stage apparatus (RCo), ionization chamber (IC), silicon strip s (Si) and CsI(Tl) scintillators. The angular resolution is ∼ ± 0.7 o for the polar angle and ∼ ± 11 o for the azimuthal one for particles detected in the scintillators. The performances of the RCo allow to reach energy determination with the accuracy of percent, charge identification of particles and fragment with threshold as low as 0.8 ÷ 1 AMeV and mass identification of light isotopes with ∼ 6 AMeV threshold through ΔE -E technique in Si-CsI(Tl) and/or pulse shape analysis (PSA)in the CsI [15]. The remaning polar angles (θ = 30 o ÷ 170 o ) are covered by a two stage, drift ionization chamber -CsI(Tl) scintillator apparatus (GARFIELD). Energy is determined with accuracy of the order of few percent and reaction products are identified in charge and mass (for light products) with a threshold around 1 AMeV [15]. The combination of the two devices allows a nearly-4π coverage, which, combined with a high granularity, permits to measure the charge, the energy and the emission angles of nearly all the charged reaction products, with an excellent discrimination of the different reaction mechanisms.

Central 12 C + 12 C and 14 N + 10 B reaction
The selection of the fusion-evaporation mechanism is based on the coincidence between LCP's and a fragment detected at forward angles (RCo). At the same time we ask the complete charge detection and longitudinal momentum conservation. We compare experimental data to the predictions of a dedicated Monte Carlo Hauser-Feshbach (HF ) code for the decay of the compound nucleus [3,4], explicitly including all the experimentally measured particle unstable levels from the archive NUDAT2(http://www.nndc.bnl.gov/nudat2/). For both reactions the best reproduction of the systematics of the fusion cross sections is obtained assuming two different maximum values (J 0max ) for the angular momentum distribution of the hot fused source [17]. In particular we use J 0max =18 for 12 C+ 12 C reaction and J 0max =15 for 14 N + 10 B reaction and we adopt the same diffusness parameter ΔJ = 2 for both reactions. Energy spectra for protons and α particles detected at GARFIELD angles are plotted in figure 1, for residues of different charge, for the 14 N reaction, and compared to HF [4] calculations and to data for the 12 C+ 12 C reaction. For both reactions, a good reproduction of proton and α energy spectra is achieved in all channels. Some discrepancies are present in events with an Oxygen residue, where the energy tails for α particles are not reproduced by the model, especially for the 12 C+ 12 C case. It has been already shown in [18] that this discrepancy is mostly due to the an extra experimental cross section for channels of the type (2α, 16 O gs/ * ) 1 . Such outgoing channels populated in the 12 C+ 12 C collisions can be attributed to an entrance channel effect, given the α-like structure of reaction partners and produced fragments. Indeed, for the 14 N + 10 B case inclusive distributions are better reproduced by calculations. This seems not to exhaust the total discrepancy with HF calculations, as we infer from the energy spectrum of α particles in coincidence with Oxygen and with 20 Ne for the 14 N reaction.
Thanks to the completeness of event reconstruction, an estimate of the dissipated energy [18] can be extracted to further investigate all the channels involving alpha particles in both reactions: where E α i and E Z Res are, respectively, the laboratory energy of α particles and residues, and E beam is the energy of the incident projectile. Figure 2 displays the obtained Q kin distributions for 12 C+ 12 C (black dots) and 14 N+ 10 B (blue dots) reactions, taking into account the different initial Q-value for the two reactions. In particular we plot only the channels with the maximum α multiplicity associated to the residue of charge Z. In the Q kin distribution for the channel (2α, 16 O gs/ * figure 2d), the two peaks correspond to α-decay chains, starting from the 24 Mg * compound nucleus and leaving a 16 15 O+n + α + α. Neutrons are not detected in the experiments, and the broader distribution observed for lower Q kin values is due to events in which neutron(s) emission has taken place. A difference in the relative population of less dissipative events is evident between the 12 C+ 12 C (black dots) and 14 N+ 10 B (blue dots) reactions in figure 2 2 . In particular, a much higher percentage of (2α, 16 O) events populates the less dissipative Q-value region in the 12 C sample. This larger deviations are evident in the relative population of the different regions for all the even-Z residues, while we observe a very good agreement in Q kin distributions for the odd-Z residue. This difference between the two data-sets confirms a possible larger contribution of direct reactions for the 12 C+ 12 C experiment. Since a residual deviation is observed in figure 2 for α particles emitted in coincidence with an Oxygen in the 14 N reaction, we turn now to an estimation of the possible α clustering effects for both reactions, both in the entrance channel and in the excited 24 Mg. In order to put into evidence the differences in terms of branching ratio, not only between data samples, but also considering the HF predictions for both reactions we present, in Table 1, the most populated channel in the experimental sample for each residue. We can see that the BR (branching ratio) of the dominant decay channels is reasonably well reproduced by the statistical model for odd Z residues, while discrepancies can be seen for even-Z ones.
The evaporation chains leading to a final Carbon or Oxygen or Neon residue show a preferential α decay in both reactions. A possible interpretation of this α excess could be the presence of residual α correlations in the excited 24 Mg or in its daughter nucleus 20 Ne, populated irrespective of the entrance channel of the reaction.

12 C* Hoyle state in 24 Mg* decay: the 6-α channel
We now turn to examine events where the whole available mass and charge is found as α particles. This selection has been performed in [4] and the inclusive results show compatibility with a sequential α-particle emission. To improve the statistics we have analyzed here also events where only five αparticles have been detected and extracted the properties of the sixth α-particle from momentum and energy conservation. We have reconstructed the energy dissipated by the quantity Q kin previously defined (Q kin = 6 i=1 E i − E beam ). In figure 3 (left panel) the Q kin distribution is shown, together with the cut used for the analysis.
In order to reconstruct the intermediate 12  The lowest energy peak in the lower panel of figure 3 corresponds to the very well known Hoyle state, which has been studied in past years by several authors [8-11, 13, 14]. The main debate consists in the interpretation of the decay of this state as sequential, via the 8 Be gs formation, or if there is a contribution of instantaneous breakup. Different observables have been proposed to clarify this point and we will show our results for some of these observables.
The first observable is the minimum relative energy (see figure 4) of two out of the three α-particles assigned to an excited 12 C* produced along the 24 Mg* decay chain. Despite of the low statistics, the results are compatible with the ones obtained for HF , indicating that the decay mainly proceeds through the intermediate formation of a 8 Be gs . The same is true for the Dalitz plot where data and HF predictions show the same configuration (see figure 5). As usual one defines the two coordinates of the Dalitz plot as x d = √ 3(e 1 − e 2 ) and y d = 2e 3 − e 1 − e 2 , where e i, j,k = E i, j,k /(E i + E j + E k ) are the α-particle energies in the 12 C frame, normalized to the total energy.  All the results for central collisions are compared to HF predictions, showing a very good agreement. All the results obtained in inelastic channels in 12 C+ 12 C reaction [19] and in various reactions at different energies [8][9][10][11][12] indicate a very low limit of this contribution of the order of permil. On the other side reactions with heavier ions at higher energies, involving more complex systems, seem to be compatible with a simultaneous decay of some percent [13,14]. Our results for central reactions with the formation of 12 C* Hoyle state in the decay chain of 24 Mg*, give no indications of deviations from the sequential decay mechanisms.

The Hoyle state in peripheral collisions
With a different selection we repeated the same analysis performed for central collisions, with the aim of investigating the decay mechanism of the Hoyle state in different conditions. We have selected events where three α-particles are detected in the forward cone (RCo) and nothing is detected in the rest of the solid angle. If we want to unambiguously identify "true" α-particles we have to exploit the ΔE-E Si-CsI or the pulse shape analysis in CsI(Tl) scintillators [16]. This implies that the threshold for the identification is about 24 MeV and consequently that the kinetic energy of 12 C nucleus emitting three α-particles is relatively high. The recoil nucleus 12 C is therefore very slow and its energy not sufficient to reach the detector, even with a very thin target. In figure 6(left panel) the energy spectrum of the reconstructed 12 C quasi-projectile is shown, as calculated from the sum of the energy of the three α-particles: where E rec is the recoil energy of the 12 C quasi-target. As it can be easily seen most of the kinetic energy is peaked at ≈88 MeV and a small peak is present at about 84 MeV, corresponding to the 12 C quasi-target at about 4.4 MeV excitation energy, the first 12 C excited level. The excitation energy of the 12 C quasi-projectile can be calculated as: Figure 6 (right panel) (E th = -Q) where Q =-7.272 MeV is the Q-value for the decay of 12 C in three α-particles. Three excited 12 C quasi-projectile levels are present for "true" αparticles (≈ 7.7, 9.6 and 10.8 MeV). We have analyzed data corresponding to the first 7.65 MeV 12 C* excited state, the first observable is the minimum relative energy of two out of the three α-particles The other observable proposed in the previous section is the Dalitz-plot calculated for the αparticle energies in the 12 C frame, normalized to the total energy. The results from data and HF calculations are shown in figure 8. We would expect that the simultaneous decay should result in three equal kinetic energies, i.e. in an enhancement of the central part of the plot which is not the case of our data. On the contrary, it shows enhancements in regions where the energy of two α-particles are very close one to the other and the third α-energy is far from the two others. This can be considered as a signal of the predominance of the sequential decay, as confirmed by HF predictions (see figure 8 right panel). Other observables, proposed in [12] have been analyzed such as the mean energy < E α >, the max- imum energy normalized to the total energy max and the deviation from the average center-of-mass energy, defined as E rms = < E 2 α > − < E α > 2 . The results show a good agreement with HF predictions, i.e. with a sequential decay [20].

The 16 O+ 12 C reaction
For the new performed experiment 16 O+ 12 C at three different beam energies, namely E beam = 90, 110 and 130 MeV, the analysis has been focused up to now on the preliminary checks of collected data. . Preliminary results of inclusive charge distribution (left part) and alpha particle multiplicity (right part) of events selected for the reaction 16 O + 12 C at three different beam energies.
In the case of complete fusion, such reactions lead to a fused 28 Si* system respectively at 55, 62 and 74 MeV excitation energy. From our previous results on the decay of excited 24 Mg we expect cluster correlations to possibly persist in the 28 Si* system, even at such high excitation energies. Extrapolating the information from Ikeda diagrams, we also expect the cluster degree of freedom be differently expressed varying the E* of the system, thus leading to different decay patterns deviating from statistical expectations. For the three different beam energies, the charge distributions corresponding to the preliminary selection of the fusion-evaporation channel out of the entire dataset is shown in figure 9, together with the α multiplicity spectra detected at GARFIELD angles in coincidence with an evaporation residue in the RCo. As expected, we note a quick increase of the alpha multiplicity when the beam energy goes up.

Conclusions and perspectives
In this work we have discussed the clustering effects in nuclear reactions involving N=Z nuclei. In particular results from the measurements with a 12 C beam on a 12 C target at 95 MeV and the 14 N+ 10 B reaction at 80 MeV beam energy are presented.
We have compared experimental data for the two reactions among them and, moreover, each experiment with the results of HF statistical calculations for the decay of the 24 Mg * source. The measured data are compatible with the expected behavior of a complete fusion-evaporation reaction, with some exception of specific channels corresponding to the emission α particles in coincidence with DOI: 10.1051/ , 2 epjconf/2016 EPJ Web of Conferences 12 122 a Oxygen, Carbon or Neon residue. The experimental branching ratio excess for α particle emission has been quantified for both reactions, putting into evidence an effect due to the cluster nature of projectile and target in 12 C+ 12 C reaction but, at the same time, an indication of the persistence of cluster correlations also in the hot fused 24 Mg, as suggested by data from 14 N+ 10 B collisions.
To investigate the importance of discrete levels and the clustering effects in the CN decay, we have studied the decay of the well known Hoyle state in three α-particles. We have isolated this level in the 6-alpha decay channel in central collisions and, for the first time, we have compared its features with those of the same Hoyle level populated for the 12 C* quasi-projectile. It has been debated if the decay mechanism is sequential, through a 8 Be g.s. formation, or if a simultaneous decay in three α-particles could be contribute. Our results obtained comparing peripheral and central reactions with the formation of 12 C* Hoyle state in the decay chain of 24 Mg*, give no indications of deviations from the sequential decay mechanisms. Further measurements are needed, increasing the energy and the number of nucleons involved, in order to investigate if in medium effects may distort the decay of the Hoyle state. A natural extension of the same experimental scheme will be to compare the decay of a compound system formed in collisions between stable α-clustered reaction partners, or induced by an unstable light projectile on a chosen target in the future SPES facility at Legnaro National Laboratory. Together with the previously studied 24 Mg, the compound nucleus 28 Si can be formed with light radioactive beams provided by SPES.