Cluster correlation effects in 12C+12C and 14N+10B fusion-evaporation reactions

The decay of highly excited states of Mg is studied in fusion evaporation events completely detected in charge in the reactions C+C and N+B at 95 and 80 MeV incident energy respectively. The comparison of light charged particles measured spectra with statistical model predictions suggests that the dominant reaction mechanism is compound nucleus (CN) formation and decay. However, in both reactions, a discrepancy with statistical expectations is found for α particles detected in coincidence with Carbon, Oxigen and Neon residues. The comparison between the two reactions shows that this discrepancy is only partly explained by an entrance channel effect. Evidence for cluster correlations in excited Mg CN is suggested by the comparison between the measured and calculated branching ratios for the channels involving α particles. DOI: 10.1051/ C © Owned by the authors, published by EDP Sciences / 0002 2015) 201 epjconf EPJ Web of Conferences 0002 5 88, 88


Introduction
The statistical decay of hot nuclei and nuclear clustering are very active research topics in nuclear physics [1].The accurate study of the fusionevaporation channel in light nuclei (A∼30,Z∼15) reactions allows to strongly constrain the level density in a mass and excitation energy region where few data exist, altogether coming from rather inclusive measurements.In addition, nuclear structure signatures are especially evident in light nuclei, even at high excitation energy.By carefully selecting the various decay channels and using a highly constrained statistical code, it is possible to put in evidence deviations from a statistical behaviour in the decay of the hot CN.Indeed there exist evidences in this mass region for some excited states with pronounced cluster features.These correlations may persist in the ground state along some selected isotopic chains, as shown by sophisticated ab-initio calculations [2]; according to the Ikeda diagrams [3] α-clustered excited states are expected at high excitation energies close to the multialpha decay threshold in all even-even N = Z nuclei.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.
In this respect, the NUCL-EX collaboration carried on several exclusive measurements of fusion-evaporation reactions with light nuclei as interacting partners.We report here on the two system 12 C+ 12 C and 14 N + 10 B which were measured in order to study the decay of the 24 Mg compound nucleus, populated at the same excitation energy ε * = 2.6 A.MeV but through different entrance channels.

The experiments
The experiments were performed at the LNL (Laboratori Nazionali di Legnaro), with 12 C and 14 N beams provided by the XTU TANDEM accelerator.The experimental setup [4] is composed of the GARFIELD apparatus and the Ring-Counter (RCo) annular detector, now fully equipped with digital electronics [5].The combination of the two devices allows a nearly-4π coverage, which, combined with a high granularity, allows 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.The set-up also provides information on the mass of the charged products in a wide range of energy and type.The GARFIELD detector, efficiently covering the polar range from 30 • to 150 • , is a two detection stage device, made by a microstrip gaseous drift chamber (μSGC), filled with CF 4 gas at low pressure (about 50 mbar), and CsI(Tl) scintillation detectors lodged in the same gas volume.The RCo detector is a forward-angle array of threestage telescopes with truncated cone shape.The first stage is an ionization chamber (IC), the second a 300 μm reverse-mounted Si(nTD) strip detector, and the last a set of CsI(Tl) scintillators.It has azimuthal symmetry, with 8 sectors, and covers, with eight strips, the polar region from 6 • ≤ θ ≤ 18 • , with an angular resolution Δθ ≈ 0.7 • and an energy resolution of 0.3% (silicon strips) and 2-3% (CsI (Tl)).

Results
The fusion-evaporation events are selected setting conditions on the total detected charge and on the coincidence between a residue at forward angles (when Z res <12) (RCo) and light charged particles (LCP) detected in GARFIELD.Only complete events where the total charge of the entrance channel (Z det = 12) is detected are retained for this analysis.Experimental data are compared to the predictions of a Monte Carlo Hauser-Feshbach code (HF ) [6,7] for the evaporation of the compound nucleus 24 Mg, at ε * = 2.6 A.MeV, corresponding to a complete fusion source, and filtered through a software replica of the experimental set-up.For both reactions the best reproduction of the systematics of the fusion cross sections is obtained assuming two different maximum value (J 0max ) for the angular momentum distribution of the hot fused source [8].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 diffusiveness parameter ΔJ = 2 for both reactions.Moreover, only even values of J 0 are allowed for the 12 C+ 12 C case, respecting parity conservation.The difference between theoretical predictions of the HF code for the two reactions are therefore only due to the different angular momentum distribution of the decaying CN.As expected, this difference affects in a minor way observables as multiplicity distributions and energy spectra summed over different channels, while shows up more clearly in correlations and single channel observables.Therefore, for the observables presented hereafter in Fig. 1 and 2 we only show for simplicity filtered HF calculations for the 12 C+ 12 C reaction.The inclusive charge and α multiplicity distributions are reported for both reactions, in Fig. 1.
The two experimental charge distributions are globally well-reproduced by the theoretical calculation and their overall shape is typical of fusionevaporation reactions.A detailed quantitative comparison of the single element cross section reveals discrepancies between data and calculation.First, light residue (Z=3,4) yield is systematically underestimated.This is an expected result, because of the absence of the break-up channel in the model.Second, Z=6 and Z=12 are also underestimated.The Z=12 yield strongly depends on the trigger condition.Concerning Z=6, the experimental excess could be attributed to the entrance channel of the reaction.A partial confirmation of this hypothesis comes from the reduced Carbon yield measured in the 14 N reaction, although the Carbon yield is in any case underpredicted by the HF model.Concerning the α-multiplicity distribution, reported in the right part of Fig. 1, the model reproduces the data quite well.The largest observed deviation is the underestimation of 3-α coincidences in both reactions: this is cleary linked to the underproduction of the Carbon residue.The good reproduction achieved for several global observables suggests anyway that the dominant reaction mechanism is the compound nucleus formation and decay.
This can be concluded also from Fig. 2, in which the energy spectra for protons and α particles detected at GARFIELD angles are plotted, for residues of different charge, for the 14 N reaction, and compared to HF [6] 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 except in events with an Oxygen residue, where the energy tails for α particles are not reproduced by the model.
For the 12 C+ 12 C reaction it has been already shown in [7,9] that this discrepancy is mostly due to the an extra experimental cross section for channels of the type (2α, 16 O gs/ * ).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.However, 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 for the 14 N reaction.Thanks to the completeness of event reconstruction, a Q-value distribution [10] can be built to further investigate the (2α, A O) channel in both reactions: , where E α i and E O are, respectively, the laboratory energy of α particles and Oxygen, and E beam is the energy of the incident projectile.Fig. 3 displays the obtained Q kin distributions for 12 C+ 12 C (left panel) and 14 N+ 10 B (right panel) reactions.We can see that the two spectra show a common structure, with two narrow peaks and a broader region.In the statistical model interpretation, the two peaks correspond to α-decay chains, starting from the 24 Mg * compound nucleus and leaving a 16 O residue either in its ground state or in one of its excited bound states.The Q-values Q kin = −15.78MeV for 12 C and Q kin = −0.8MeV for 14 N reactions correspond to the opening of the 4-body channel 15 O+n + α + α.We will therefore call less (more) dissipative the events characterized by a Q kin value greater (smaller) than such threshold values.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, and their kinetic energy has not been collected.A difference in the relative population of less dissipative events is evident between the 12 C+ 12 C (left panel) and 14 N+ 10 B (right panel) reactions in Fig. 3.In particular, a much higher percentage of (2α, 16 O) events populates the less dissipative Q-value region in the 12 C experimental sample.This difference between the two data-sets confirms the possible contribution of direct reactions for the 12 C+ 12 C experiment.Since a residual deviation is observed in Fig. 2 for α's 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.This can be achieved through the definition of a new variable R clust , obtained for each residue as a difference between experimental and expected probability for the maximum α multiplicity channel: Where Y (Z; n Z α) (Y (Z)) indicates coincident (inclusive) yields; n Z α = (12−Z)/2 is the maximum α multiplicity associated to the residue of charge Z and the subscripts "exp" and "HF " refer to experimental and theoretical yields, respectively.The extra probability of α emission defined by ( 1) is plotted in Fig. 4.
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.

Conclusions
In this work we discussed preliminary results for the 14 N+ 10 B reaction at 80 MeV beam energy, measured at LNL-INFN with the GARFIELD+RCo experimental set-up.Using the same selection described in Ref. [7,9] we have compared experimental data to the 12 C+ 12 C reaction and to HF statistical model calculations for the decay of the 24 Mg * source.The selected sample is compatible with the expected behavior of a complete fusion-evaporation reaction, with some exception of specific channels corresponding to the emission of two or three α particles in coincidence with a Oxygen or Carbon residue.The experimental branching ratio excess for α particle emission has been quantified for both reactions, putting in 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.

Figure 4 :
Figure 4: Branching ratio excess (Eq.3.1 in the text) for α decay as a function of the charge of the final residue.Dots: 12 C+ 12 C. Square: 14 N+ 10 B.
Figure 1: Inclusive charge distribution (left part) and alpha particle multiplicity (right part) of events completely detected in charge.Experimental data (dots and square for 12 C+ 12 C and 14 N+ 10 B respectively) are compared to filtered HF calculations (line) for 12 C+ 12 C (see text for details).
Figure 2: Proton (upper part) and α (lower part) energy spectra in complete Z det =12 events detected in coincidence with a residue of charge Z res , indicated in each figure column.Data (dots and square for 12 C+ 12 C and 14 N+ 10 B respectively) are compared to model calculations (lines) for 12 C+ 12 C (see text for details).All distributions are normalized to unitary area.