Thermal properties of light nuclei from ¹²C + ¹²C fusion–evaporation reactions

The backshifted Fermi gas model (BSFG), with the LD parameter and the pairing backshift left as free fit parameters, is known to be a phenomenological approach well suited to reproduce the many-body correlated nuclear LD: pairing effects are included through the backshift Δ_p, and all correlations are taken into account in the renormalization of the LD parameter a(E*).

In [12] LD parameters for the BSFG model have been determined for a large set of nuclei (310 nuclei between ¹⁸F and ²⁵¹Cf), by the fit of complete level schemes at low excitation energy and s-wave neutron resonance spacings at the neutron binding energy.

In [12], the adopted expression for ρ(E*) (after integration on angular momentum J and parity π) reads:

$$\begin{equation} \rho (E^*)=\frac{\exp [2\sqrt{a(E^*-E_2)}]}{12\sqrt{2}\sigma a^{1/4}(E^*-E_2)^{5/4}} \end{equation} \tag{ 3 }$$

where σ is the spin cut-off parameter:

$$\begin{equation} \sigma ^2 =0.0146A^{5/3}\frac{1+\sqrt{1+4a(E^*-E_2)}}{2a}. \end{equation} \tag{ 4 }$$

The energy backshift Δ_p = E₂ is left as the first free parameter in the data fitting. The second fit parameter is the asymptotic value $\tilde{a}$ of the following functional form for a(E*, Z, N) [28]:

$$\begin{equation} a=\tilde{a}\left[1+\frac{S(Z,N)-\delta E_p}{E^*-E_2}\left(1-{\rm e}^{-0.06(E^*-E_2)}\right)\right] \end{equation} \tag{ 5 }$$

where S(Z, N) = M_exp(Z, N) − M_LD(Z, N) is a shell correction term, M_exp and M_LD being respectively the experimental mass and the mass calculated with a macroscopic liquid drop formula for the binding energy not including any pairing or shell corrections. δE_p is a pairing term expressed in terms of the deuteron separation energy. Full details on the parameter definition and fit procedure can be found in [12]. As a final result, analytic formulas for E₂ and $\tilde{a}$ as a function of tabulated nuclear properties are given. With such formulas for the calculation of LD parameters, the model of (3) allows for a very good reproduction of experimental distributions of measured levels in the mass region of interest for the present work. Two selected examples are given in figure 1. The isotope ²⁰Ne belongs to the fitted data set, and the good agreement between the line and the histogram shows the quality of the fit procedure of [12]. Concerning ¹⁶O, the values of the parameters are an extrapolation of the formulas proposed in [12] out of the fitted data set; from the figure it is also clear that (3) can be considered reliable also for nuclei whose LD has not been directly optimized. A similar agreement is observed for all the other particle-stable isotopes in the mass region of interest for the present study.

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Still, numerical values for the pairing backshift and for the asymptotic limit of a(E*) with increasing excitation energy obtained through this approach are to be considered reliable only up to E*/A ≈ 1 MeV for A ≈ 20 nuclei.

In particular, it is found that the values of the LD parameter needed to reproduce the information on discrete levels are usually lower than the ones coming from higher-energy constraints, through the reproduction of data for fusion–evaporation or evaporation-after fragmentation studies (E*/A ≈ 2–3 MeV). A functional form giving a good reproduction of evaporation spectra at very high excitation energy was proposed in [29]:

$$\begin{equation} a_{\infty }=\frac{A}{14.6}\left(1+\frac{3.114}{A^{1/3}}+\frac{5.626}{A^{2/3}}\right). \end{equation} \tag{ 6 }$$

To correctly reproduce at the same time the low- and high-energy experimental constraints, we have adopted a functional form for the LD parameter that gives a continuous interpolation between (5) and (6).

We have adopted the following expression:

$$\begin{equation} a(E^*,A)=\left\lbrace \begin{array}{@{}lll@{}}a_D = (5) & & \quad {\rm if} \quad E^*\le E_{m}+E_2\\ a_C = \alpha \exp [-\beta (E^{*}-E_2)^2]+ a_{\infty } & & \ \ \ \ {\rm if} \quad E^* > E_{m}+E_2 .\\ \end{array} \right. \end{equation} \tag{ 7 }$$

The choice of a rapid (exponential) increase is imposed by the fact that the asymptotic value (6) is connected to the opening of the break-up or multifragmentation channels, which is a sharp threshold phenomenon. The α and β parameters are fully determined by the matching conditions between the low-energy and high-energy regime: a_D(E_m, A) = a_C(E_m, A) and a_C(E_l, A) = a_∞ ± 10%.

Here, E_l represents the limiting energy at which the break-up or fragmentation regime is attained, while E_m is the excitation energy marking the transition between the discrete and the continuum part of the spectrum. This latter quantity is of the order of E_m ≈ 10 MeV, coherently with the value of the critical energy for the damping of pairing effects in [30]. In the case of light nuclei for which a large set of measured levels is available, this value well corresponds to the excitation energy maximizing the number of levels in bins of E*. Above E_m the experimental information is too poor to consider the set of resolved levels exhaustive of the nuclear LD, due to the physical emergence of the continuum.

The limiting energy E_l is then left as the only free parameter of the calculation, governing the rapidity of the variation of a(E*) above E_m. As an example of the overall functional form resulting for the LD parameter, in figure 2 we plot a(E*, A) for ²⁰Ne, for two different choices of E_l.

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In the statistical code, starting from a given CN (A, Z, J, E*), the decay pattern is calculated with the Monte Carlo technique as a sequence of two-body decays governed by the emission probability given by (1). When the emitted particle leaves the daughter nucleus at an excitation energy $E^*_d<E_m$, the excitation energy is considered as a discrete variable, and one of the tabulated levels [27] of the daughter discrete spectrum is populated. The level is chosen according to the Breit–Wigner distribution of the discrete levels considering their respective widths, including the full spectroscopic information of [27], and the particle kinetic energy is adjusted if necessary to ensure energy conservation. When a particle bound level is populated, the subsequent decay is assumed to be due to a single γ emission to the corresponding ground state. If the daughter excitation energy $E^*_d$ is greater than E_m, the spectroscopic information is not sufficient to fully constrain the spin and energy of the daughter nucleus. If measured excited states exist, they are populated with a probability given by the ratio between the measured LD from discrete states and the total LD including the continuum states and given by (3) with a given by (7). If no levels are known, the emission is assumed to take place in the continuum.

The experimental setup is composed by the GARFIELD detector, covering almost completely the angular range of polar angles from 30° to 150°, and the ring-counter (RCo) annular detector [31], centred at 0° with respect to the beam direction and covering forward laboratory angles in the range 5° ⩽ θ ⩽ 17°.

The combination of the two devices allows for a nearly-4π coverage of the solid angle, which, combined with a high granularity, permits to measure the charge, the energy and the emission angles of nearly all charged reaction products. The setup also provides information on the mass of the emitted charged products in a wide range of particle energy [32].

The GARFIELD apparatus is a two-detection stage device, consisting of two microstrip gaseous drift chambers (μSGC), filled with CF₄ gas at low pressure (50 mbar) and placed back to back, with CsI(Tl) scintillation detectors lodged in the same gas volume.

Due to the small size of the studied system, mainly light particles are emitted in the reaction which are efficiently detected and identified through the use of the fast–slow shape method for the 180 CsI(Tl) scintillators [33].

The energy identification thresholds are, on average, 3, 6, 9, 20, 7 MeV for p, d, t, ³He, and α particles, respectively. As for other experimental devices using the fast–slow technique [34], ³He can be discriminated from αs starting from ≈20 MeV. This increase of the ³He threshold does not affect too much the α yield in our reaction, since ³He is estimated to represent less than 2%–3% of Z = 2 particles [22]. In all the experimental percentages, the associated error takes into account both the statistical error and the possible ³He − α contamination. In the present analysis, the information coming from the μSGC has been used to validate the particle identification, especially in the lower part of the range, where the fast–slow curves tend to merge.

The RCo detector is an array of three-stage telescopes realized in a truncated cone shape. The first stage is an ionization chamber, the second a 300 μm reverse mounted Si(nTD) strip detector, and the last a CsI(Tl) scintillator.

The angular resolution is Δθ ≈ ±0.7° and the energy resolution of silicon strips and CsI(Tl) detectors resulted 0.3% and 2%–3%, respectively. In the present experiment, reaction products with Z ⩾ 3 have relatively low energies and are stopped in the Si detectors. Therefore, they can be identified only in charge thanks to the ΔE − E correlation between the energy loss in the gas and the residual energy in the silicon detectors, with 1 A MeV energy threshold. Only for the high energy tails of 3 ⩽ Z ⩽ 5 fragments mass identification has been possible, thanks to the application of a pulse shape technique to signals coming from the Si detectors [35]. Light charged particles (LCP, Z = 1, 2) flying at the RCo angles and punching through the 300 μm Si pads (E/A ⩾ about 6 MeV) are identified in charge and mass by the conventional Si–CsI ΔE − E method. LCP stopped in the silicon stage are identified only in charge.

More details on this setup can be found in [32].

The analysis considers only events with a coincidence between at least one LCP, detected and identified in GARFIELD, and a particle or fragment (Z ⩾ 3) detected at forward angles in the RCo and identified in charge. In the case of a fusion–evaporation reaction, this latter is the residue Z_res of the CN decay chain, and it is expected to have a velocity close to the centre-of-mass velocity of the reaction, v_CM ≈ 2 cm ns⁻¹. Due to the lack of isotopic resolution for such low energy fragments, a hypothesis on their mass has to be done. Our initial hypothesis (to be further discussed in section 4.2) is A_res = 2 · Z_res.

A first selection within the measured events is based on figure 3, where we show the total detected charge as a function of the total longitudinal momentum. Requiring that at least 60% of the total incoming parallel momentum is collected, we obtain a total charge distribution centred at Z_tot = 10, corresponding to the 80% of the total charge. A yield peak around Z_tot/Z_{p + t} = 0.5 is evident in the picture, corresponding to (quasi)-elastic events with only the carbon ejectile detected. Since we would like to concentrate on specific decay channels, we would keep a complete detection (Z_tot = 12). We have therefore checked that this stringent requirement does not bias the characteristics of the events, comparing the distribution of representative observables with a less stringent selection Z_tot ⩾ 10. Very similar distributions are obtained with the two 'minimum bias' selections which henceforth we name 'quasi-complete' (Z_tot ⩾ 10) and 'complete' (Z_tot = 12) (see section 4.1). Complete events are ≈ 20% of quasi-complete ones.

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The inclusive charge and multiplicity distribution of events completely and quasi-completely detected in charge are presented in figure 4 in comparison with the filtered HFℓ calculation. In this figure and in the following ones experimental data are always shown with statistical error bars, when visible.

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The charge distribution is globally well-reproduced by the theoretical calculation and its overall shape is typical of fusion–evaporation reactions.

However, a few discrepancies can be observed. Notably, Z = 4 fragments are absent in the HF prediction while they are not negligible in the experimental sample. This could be interpreted as the presence of a break-up contribution in the data which is not properly treated by the sequential calculation. To confirm this statement, we show in the same figure the result from a GEMINI++ calculation [25] subject to the same filtering procedure. This model, which has also been largely and successfully used by the nuclear physics community since more than 20 years, includes the emission of intermediate mass fragments within the transition state formalism. We can see that GEMINI++ predicts sizeable yields of the lightest fragments, which in the HF formalism have a negligible probability to be emitted and are only obtained as evaporation residues. In particular, the transition state formalism succeeds in explaining the missing Be cross section.

Concerning the multiplicity distribution, presented in the right part of figure 4, we can see that both the HFℓ and the GEMINI++ calculations reproduce the data satisfactorily. We can however remark that GEMINI++ overpredicts events of high multiplicity. This means that the transition state formalism is not entirely satisfactory in describing the production of light fragments, which could also be due to a breakup mechanism. Such a mechanism is not accounted for in the presented models.

Apart from the missing Z = 4 channel, another discrepancy between the HFℓ calculation and the data concerns the Z = 6 yield which is underestimated by the model. This extra yield could in principle be explained by the transition state model, as shown by the fact that data are well reproduced in this channel by GEMINI++. As an alternative explanation, the carbon excess with respect to HFℓ predictions could be due to the entrance channel of the reaction. Indeed, many other experiments [39] where reactions with carbon projectile and/or target were studied, showed an extra-production of carbon residues with respect to statistical models expectations. At low bombarding energy, C–C quasi-molecular states [39] can be invoked. In our experiment, as it will be discussed in the following, this anomaly is essentially associated with the specific C − 3α channel.

Because of the great similarity between the HFℓ and GEMINI++ calculations, and the fact that the HFℓ code was optimized on light systems (see section 2), in the following we exclusively use the HFℓ code as a reference statistical model calculation.

Due to the low statistics of the experiment for Z = 3, 4 residues, we will not study these residue channels any further.

The dominant fusion–evaporation character of the reaction is further demonstrated in figure 5, which shows the velocity distributions in the laboratory frame of the different fragments with Z ⩾ 5. The good reproduction by the statistical model allows interpreting these fragments mainly as evaporation residues left over by the decay of ²⁴Mg CN originated from complete fusion.

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Complementary information is shown in figure 6, which displays the laboratory energy spectra of protons and α particles detected in GARFIELD. Experimental data (dots) are compared to model calculations (lines). From now on we will concentrate on events with a residue detected in the RCo (5°–17°) and LCP in GARFIELD (30°–150°) as in the previous experiment [22]. This choice is essentially due to the different thresholds on LCP identification in RCo and GARFIELD, as pointed out in section 3.1. To facilitate the comparison of the spectral shapes, distributions are always normalized to the same area.

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We can see that the choice of the set of events (complete and quasi-complete) does not deform the shape of the spectra. A satisfactory reproduction of the proton energy spectrum is achieved, while a large discrepancy in the shape of the distributions appears for α particles for both completeness requirements.

Another piece of information can be obtained from the angular distribution of protons and α-particles (see figure 7). The proton distribution is in agreement with the model, while the excess of α particles at backward laboratory angles could suggest a preferential alpha emission from the quasi-target. Alternatively, it could indicate an alpha transfer mechanism from an excited ¹²C nucleus with strong alpha correlations.

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As it is commonly known, the shape of LCP energy spectra is determined by the interplay of all physical ingredients entering in the evaporation process, notably including transmission coefficients, angular momentum and deformation effects, as well as LD [9]. Nevertheless, when comparing data to statistical model calculations, it is possible to try to disentangle the effects of single ingredients [9]. In particular, while transmission coefficients define the shape of evaporated spectra in the Coulomb barrier region, the LD mostly affects the slope of the exponential tail. Concerning angular momentum, the inclusion of deformation has a stronger influence on heavier fragment emission, as it is the case for α particles, and, as a consequence, the tail of the energy distribution for such fragments becomes steeper. Different works on fusion observables with light systems [40, 41] have shown the importance of accounting for the deformation of the CN source in the statistical model. To this purpose, an empirical modification of the CN momentum of inertia has been proposed [40, 41]. This modification has the effect of lowering the yrast line at high angular momentum. As a consequence, the number of phase space states at higher angular momentum is increased, which decreases the emission of high-energy α particles. Such an effect would be at variance with the observed behaviour. For this reason we have neglected possible deformation effects in the present work and kept the standard rigid body momentum of inertia for the calculation of the rotational energy in the statistical code.

Thus the two theoretical uncertainties which could be responsible of the observed deviations are the estimated maximum angular momentum leading to CN formation, and the level density parameter. As we have discussed in section 2, a very different angular momentum distribution was used in [22] to describe the same system. Concerning our LD model, the only unknown is the asymptotic value of the a parameter at very high excitation energy. The effects of a very wide variation of these parameters are shown in figure 8. This figure shows that no common choice of the LD parameters can be done in the present model in order to reproduce at the same time proton and α energy spectra. For this reason we keep in the rest of the analysis the fiducial value for the angular momentum and level density (red lines). The comparison made so far on many inclusive observables suggests that the dominant reaction mechanism is CN formation and the discrepancy found for α particles reflects an out-of-equilibrium emission.

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A first confirmation of this hypothesis comes from the finding that the largest source of disagreement between data and calculations is for decay channels with α particles detected in coincidence with an oxygen fragment. This is shown in figure 9, which presents energy spectra of protons and α particles detected in coincidence with a residue of a given atomic number. The discrepancy, larger at the most forward angles [21], is mainly due to the 2 α-channel, as we will discuss in section 4.3. A similar, though much less important, non-statistical component in the alpha particle energy spectra was observed in the ²⁸Si+¹²C reaction[41] and attributed to non-statistical ⁸Be cluster emission from the compound. For our experiment, the contribution of ⁸Be will be quantified by α–α correlations in the second paper of the series, and shown to be very small.

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With the exception of the α–O coincidence, particle energy spectra are very well reproduced by the statistical model. This gives strong confidence to our level density model of (3) and (7) with E_l = 3A MeV (corresponding to a ≈ 3.5 MeV⁻¹ for E*/A = 3 MeV) for the light A ≈ 20 CN decay.

A small difference of the experimental and calculated energy spectra is also observed for α-particles in coincidence with a carbon residue. This does not seem to be related to the presence of peripheral events with a carbon quasi-projectiles, since the velocity distribution of carbon residues (shown in figure 5) displays a good agreement with statistical calculations.

The angular distributions of protons and α particles in coincidence with each residue are shown in figure 10. The good agreement among data and model predictions as far as proton distributions are concerned is confirmed. A large discrepancy is evident for α particles at backward laboratory angles detected in coincidence with an oxygen fragment.

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To understand the origin of the deviations from a statistical behaviour, the BRs to α decay and α kinematics in the different channels involving α emission will be studied in greater detail in section 4.3.

A deeper understanding of the reaction mechanism and a complementary test of the statistical behaviour can be obtained by studying the mass distribution of the different residues. Unfortunately we do not have isotopic resolution for fragments with atomic number Z ⩾ 5. However, if we consider in the analysis events completely detected in charge, the residue mass can be evaluated from the energy balance of the reaction, as we now explain.

Let us consider a well defined channel, characterized by a given residue charge Z_res, LCP charge Z_lcp = 12 − Z_res and mass A_lcp. We define $\bar{Q}=m_{{\rm lcp}}c^2-m(^{24}{\rm Mg})c^2$ the partial Q-value associated with that channel, where m_lcp is the total mass of the channel particles and m(²⁴Mg) is the mass of the composite nucleus. The unknown residue mass number $A_{{\rm res}}^k$ and unknown neutron number $N_n^k$ in each event k belonging to the considered channel are defined as a function of an integer isotopic variable x as A_res(x) = 2Z_res + x and N_n(x) = 24 − A_lcp − A_res(x) = 24 − A_lcp − 2Z_res − x. The residue mass and total neutron energy are thus defined as a function of x: m_res(x) = m(A_res(x), Z_res), E_n(x) = (〈e_n〉 + m_nc²)N_n(x), where 〈e_n〉 is the estimate of the average neutron kinetic energy from the average measured proton one, with the subtraction of an average 2.9 MeV Coulomb barrier.

The excitation energy of the event k reads:

$$\begin{equation} E^*_{{\rm theo}}=\bar{Q}+m_{{\rm res}}(x)+E_{{\rm kin}}^k+E_n(x)+E_\gamma ^k \end{equation} \tag{ 8 }$$

where $E_{{\rm kin}}^k$ is the total measured kinetic energy, $E^*_{{\rm theo}}=62.4$ MeV the total available energy, and $E_\gamma ^k$ the unmeasured γ energy, in the centre of mass system. The excitation energy which would be associated with this event assuming that the residue has A_res = 2Z_res and is produced in its ground state is:

$$\begin{equation} E_{{\rm cal}} (k)=\bar{Q}+m_{{\rm res}}(x=0)+E_{{\rm kin}}^k+E_n(x=0). \end{equation} \tag{ 9 }$$

The example of oxygen is reported in figure 11. The calorimetric excitation energy distribution E_cal(k) divided by the total mass of the system is displayed for the different measured channels associated with the production of Z = 8 fragments in complete events, together with the filtered model calculations. In all cases we can observe a wide distribution corresponding to different, often unresolved states of different isotopes. The qualitative agreement with the model calculations confirms once again that the selected events largely correspond to complete fusion.

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In the hypothesis that the kinetic energies of LCP and neutrons depend on average on the channel, but not on the average value of the residue mass (through 〈x〉), (8) and (9) can be averaged over the events of the channel giving:

$$\begin{eqnarray} &&E^*_{{\rm theo}}=\bar{Q}+m_{{\rm res}}(x)+\langle E_{{\rm kin}}\rangle +E_n(x)+\langle E_\gamma \rangle \end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray} &&\langle E_{{\rm cal}}\rangle =\bar{Q}+m_{{\rm res}}(x=0)+\langle E_{{\rm kin}}\rangle +E_n(x=0). \end{eqnarray} \tag{ 11 }$$

Equations (10) and (11) allow deducing the unmeasured neutron excess, and therefore the residue mass, from the average measured calorimetric energy. Indeed, subtracting the two equations we get:

$$\begin{equation} \langle E_{{\rm cal}}\rangle (x,I) = E^*_{{\rm theo}}-(m_{{\rm res}}(x)-m_{{\rm res}}(x=0))-(E_n(x)-E_n(x=0))-E^*_I. \end{equation} \tag{ 12 }$$

This equation gives the calorimetric energy which is expected on average for a residue of mass number A_res = 2Z_res + x produced in its excited state I, if we have assumed via (9) that its mass number is 2Z_res, as shown for various cases by the blue vertical lines in figure 11.

Our energy resolution is not sufficient to determine the detailed spectroscopy of each residue, but the comparison of the measured calorimetric energy in each event given by (9) with the expected value from (12) allows for a reasonably good isotopic identification.

To attribute a definite isotope to each residue, we have minimized in each event k the distance in energy between the calorimetric result and the theoretical value associated with the resolved states of the associated channel

$$\begin{equation} |E_{{\rm cal}}(k)-\langle E_{{\rm cal}}\rangle (x,I)|={\rm min}. \end{equation} \tag{ 13 }$$

We have repeated the same procedure for all the residues. The resulting isotopic distributions are presented in figure 12, again compared to the model calculations. Errors on experimental results have been obtained combining the statistical error with the one coming from the reconstruction procedure. This has been estimated by comparing, within the model, the values obtained by the reconstruction procedure with the original predictions. The global agreement is good, particularly for odd charge residues. Both the average and the width of the distributions are reproduced by the model. The distributions are generally bell-shaped and structureless, with the exception of carbon, which shows an important depletion for ¹³C similarly to the model calculation.

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The case of oxygen is particularly interesting. The experimental and theoretical widths are comparable, but while the experimental distribution has a negative skewness and is centred on the neutron poor ¹⁵O, the opposite is seen in the calculation which favours neutron rich isotopes and presents a positive skewness [22]. As we can see in figure 11, this is largely due to the specific O + 2α channel. Indeed this channel is the only one which leads to a non-negligible production of ¹⁵O.

The information from the isotopic distribution and the energy spectra coherently points towards an increased probability for the O + 2α channel with respect to the statistical model. We therefore turn to see if the experimental sample contains, together with a dominant contribution of standard compound reactions, other reaction mechanisms which could selectively populate a few specific channels, possibly associated with α emission.

In table 1 we report for each residue the most populated channel in the experimental sample, as well as the associated BR. The results are compared to the prediction of the statistical model for the same channel, filtered through the characteristics of the experimental apparatus. We can see that the BR 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.

For oxygen, the predicted most probable channel is ^AO + α + 2H (here 2H stands for two Z = 1 products) with a BR BR_HFℓ = 84%, while this channel is experimentally populated with BR_EXP = 37%.

For carbon, ¹²C+3α is the most probable theoretical channel consistent with the data, but an important contribution of the channel ¹²C+2α + 2H is also predicted (BR_HFℓ = 21%), while this contribution is negligible in the experimental sample. Also for neon a disagreement is present, but the theoretical calculation well reproduces the shape of the α spectrum, as shown in figure 9. This is not the case for oxygen and, to a lesser extent, carbon. For these residues the discrepancy in the BRs affects the shape of the α particle spectra. This is shown in figure 13, where, for the carbon case (upper panels), the measured inclusive α spectrum is dominated by the multiple α channel, while in the statistical model the channel containing only two α particles (and hence two hydrogen isotopes) is very important for low α energies, thus modifying the slope of the inclusive spectrum with respect to the data.

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A similar analysis for oxygen is presented in figure 13 (lower panels). The same considerations as for carbon apply in this case. Again, the extra yield associated with multiple α events with respect to the statistical model leads to a broader spectrum extending towards higher α energies.

If we now compare experimental data with model predictions in specific channels, we obtain, for the carbon case (see figure 14, upper panels), that the shape of the spectra of the different channels are very well reproduced by the statistical model calculations. The same holds true for the angular distributions, well reproduced by calculations. This shows that the kinematics of the decay is well described by a sequential evaporation mechanism. However these shapes depend on the channel, multiple αs leading to spectra which are less steep and extend further in energy, with respect to channels where hydrogens are also present. Because of that, the disagreement in BRs between model and data shown in table 1 affects the global shape of the α spectrum, where the different channels are summed up.

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Taking now into account the oxygen residue, in figure 15 we show the comparison of the energy spectra (upper panels) and angular distributions. At variance with the carbon case, the shape of the α spectrum in the O + 2α channel is not well reproduced by the statistical model. This indicates that the kinematics in this channel is not fully compatible with CN decay, and suggests a contamination from direct reactions.

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The anomalously high probability of multiple α emission in coincidence with oxygen and carbon residues, with respect to the expectation from a statistical behaviour, can explain the deviations observed in the inclusive α observables (see figures 6 and 7). This suggests that non-statistical processes are at play in the experimental sample concerning the two specific multiple α channels that show anomalously high BRs.

Alpha production is known to be an important outcome of direct ¹²C+¹²C reactions [42, 43]. In these studies, though at lower bombarding energy than the present experiment, the α dominance has been associated with quasi-molecular two-carbon excited states with a pronounced α structure.

In order to see if similar effects still persist at higher bombarding energies, in the second paper of the series we will focus on a detailed analysis of the multiple α channels.