# Four $\alpha$-particles as a final state of $^{16}$O* Quasi Projectile decay

Maria Vittoria Managlia, Mauro Bruno, Michela d'Agostino, Luca Morelli, Giorgio Baiocco, Francesca Gulminelli, Catalin Frosin, Sandro Barlini, Antonio Buccola, Alberto Camaiani, et al.

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Maria Vittoria Managlia, Mauro Bruno, Michela d'Agostino, Luca Morelli, Giorgio Baiocco, et al. Four $\alpha$-particles as a final state of $^{16}$O* Quasi Projectile decay. 4th International Conference on Nuclear Structure and Dynamics, May 2019, Venice, Italy. pp.01036, 10.1051/epjconf/201922301036 hal-02423716

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Submitted on 29 May 2024

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<figure><img src="image_2.png" /></figure>

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# Four $\alpha$-particles as a final state of $^{16}$O* Quasi Projectile decay

Maria Vittoria Managlia, Mauro Bruno, Michela d'Agostino, Luca Morelli, Giorgio Baiocco, Francesca Gulminelli, Catalin Frosin, Sandro Barlini, Antonio Buccola, Alberto Camaiani, et al.

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Maria Vittoria Managlia, Mauro Bruno, Michela d'Agostino, Luca Morelli, Giorgio Baiocco, et al. Four $\alpha$-particles as a final state of $^{16}$O* Quasi Projectile decay. 4th International Conference on Nuclear Structure and Dynamics, May 2019, Venice, Italy. pp.01036, 10.1051/epjconf/201922301036. [hal-02423716](https://hal.science/hal-02423716v1)

HAL Id: hal-02423716

https://hal.science/hal-02423716v1

Submitted on 29 May 2024

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Four α-particles as a final state of $^{16}$O* Quasi Projectile decay

Maria Vittoria Managlia¹, Mauro Bruno¹,², Michela D'Agostino¹,², Luca Morelli¹,², Giorgio Baiocco³, Francesca Gulminelli⁴, Catalin Frosin⁵,⁶, Sandro Barlini⁵,⁶, Antonio Buccola⁵,⁶, Alberto Camaiani⁵,⁶, Giovanni Casini⁶, Magda Cicerchia⁷, Marco Cinausero⁷, Daniela Fabris⁸, Fabiana Gramegna⁷, Giorgia Mantovani⁷, Tommaso Marchi⁷, Pietro Ottanelli⁵,⁶, Gabriele Pasquali⁵,⁶, Silvia Piantelli⁶, and Simone Valdré⁶

¹Dipartimento di Fisica e Astronomia dell'Università di Bologna, Italy.

²INFN Sezione di Bologna, Bologna, Italy.

³Dipartimento di Fisica dell'Università, Pavia, Italy.

⁴Normandie Univ. ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, 14000 Caen, France.

⁵Dipartimento di Fisica e Astronomia dell'Università di Firenze, Italy.

⁶INFN Sezione di Firenze, Firenze, Italy.

⁷INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy.

⁸INFN Sezione di Padova, Padova, Italy.

**Abstract.** Four α-particles as a final state of $^{16}$O* quasi-projectile decay produced in peripheral $^{16}$O+$^{12}$C reactions at 130 MeV is thoroughly studied. The different decay channels leading to the four α-particles final state are reconstructed by carrying out an event-by-event analysis of α correlations in the population of intermediate $^{8}$Be and $^{12}$C. Although small, a non negligible contribution due to $^{8}$Be$_{gs}$ evaporation is found. A comparison between predictions of an accurate Hauser-Feshbach decay code and branching ratios of the different decay channels is performed. Significant deviations are observed, among these the Hoyle state population which is considerably lower than the one predicted according to the statistical model, thus suggesting possible structure effects in the Coulomb barrier and/or in the transmission coefficients.

## 1 Introduction

The aim of this experimental campaign carried out by the NUCL-EX collaboration is investigating the properties of light nuclei [1]. In this contribution we will present results of peripheral $^{16}$O+$^{12}$C collisions with the decay of the excited $^{16}$O* Quasi Projectile (QP) in a final state of four α-particles. A comparison with the predictions of a statistical decay code (HFℓ) based on Hauser-Feshbach formalism and including all the discrete levels of light nuclei, taken from the NUDAT2 database [2], was made. Agreement or disagreement with statistical decay code could be a hint of the importance of non statistical effects. The analysis explores the two channels of the decay [3]: the first foresees the formation of two $^{8}$Be$_{gs}$ which both decay in two α particles

$$^{16}\text{O}^* \rightarrow {}^{8}\text{Be}_{\text{gs}} + {}^{8}\text{Be}_{\text{gs}} \rightarrow \alpha + \alpha + \alpha + \alpha, \quad (1)$$

the second consists in the emission of an α-particle leaving a $^{12}$C* as a residue, which in turn decays in three α-particles, through a $^{8}$Be intermediate state.

$$^{16}\text{O}^* \rightarrow {}^{12}\text{C}^* + \alpha \rightarrow {}^{8}\text{Be}_{\text{gs}} + \alpha + \alpha \rightarrow \alpha + \alpha + \alpha + \alpha \quad (2)$$

where $^{12}$C* can be in the Hoyle state ($0_2^+$, 7.65 MeV) [4] or in a $3^-$ excited state at 9.64 MeV.

## 2 The experiment and the event selection

Measurements were carried out at the INFN laboratories in Legnaro using a pulsed beam of $^{16}$O at 130 MeV [5]. The apparatus consists of GARFIELD, a multi-detector located inside a large scattering chamber, coupled with the Ring Counter (RCo), a three-stage annular detector with a truncated cone geometry aimed for the detection at forward angles [6]. ΔE-E correlation and fast-slow PSA techniques were used for particle identification. The selection of events of interest has been performed by considering only events which feature four α-particles, in the final state, detected at forward angles (by the RCo in 5° ÷ 17° angular range) and no product detected by GARFIELD (30° ÷ 150°).

## 3 Analysis

From energy and momentum conservation one obtains the target and projectile excitation energy:

$$E_{tot_i} = E_{beam} = E_{tot_f} = \sum_{i=1}^{4} E_{\alpha_i} + E_{rec} + E_{exc_i} - Q \quad (3)$$

where $E_{α_i}$ is kinetic energy of the i-th α-particle, $E_{rec}$ the QT excitation energy, Q is the reaction Q-value and $E_{rec}$ is the QT recoil energy.
# Four $\alpha$-particles as a final state of $^{16}\text{O}^*$ Quasi Projectile decay

Maria Vittoria Managlia¹, Mauro Bruno¹,², Michela D'Agostino¹,², Luca Morelli¹,², Giorgio Baiocco³, Francesca Gulminelli⁴, Catalin Frosin⁵,⁶, Sandro Barlini⁵,⁶, Antonio Buccola⁵,⁶, Alberto Camaiani⁵,⁶, Giovanni Casini⁶, Magda Cicerchia⁷, Marco Cinausero⁷, Daniela Fabris⁸, Fabiana Gramegna⁷, Giorgia Mantovani⁷, Tommaso Marchi⁷, Pietro Ottanelli⁵,⁶, Gabriele Pasquali⁵,⁶, Silvia Piantelli⁶, and Simone Valdré⁶

¹Dipartimento di Fisica e Astronomia dell'Università di Bologna, Italy.

²INFN Sezione di Bologna, Bologna, Italy.

³Dipartimento di Fisica dell'Università, Pavia, Italy.

⁴Normandie Univ. ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, 14000 Caen, France.

⁵Dipartimento di Fisica e Astronomia dell'Università di Firenze, Italy.

⁶INFN Sezione di Firenze, Firenze, Italy.

⁷INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy.

⁸INFN Sezione di Padova, Padova, Italy.

**Abstract.** Four $\alpha$-particles as a final state of $^{16}\text{O}^*$ quasi-projectile decay produced in peripheral $^{16}\text{O}+^{12}\text{C}$ reactions at 130 MeV is thoroughly studied. The different decay channels leading to the four $\alpha$-particles final state are reconstructed by carrying out an event-by-event analysis of $\alpha$ correlations in the population of intermediate $^{8}\text{Be}$ and $^{12}\text{C}$. Although small, a non negligible contribution due to $^{8}\text{Be}_{\text{gs}}$ evaporation is found. A comparison between predictions of an accurate Hauser-Feshbach decay code and branching ratios of the different decay channels is performed. Significant deviations are observed, among these the Hoyle state population which is considerably lower than the one predicted according to the statistical model, thus suggesting possible structure effects in the Coulomb barrier and/or in the transmission coefficients.

## 1 Introduction

The aim of this experimental campaign carried out by the NUCL-EX collaboration is investigating the properties of light nuclei [1]. In this contribution we will present results of peripheral $^{16}\text{O}+^{12}\text{C}$ collisions with the decay of the excited $^{16}\text{O}^*$ Quasi Projectile (QP) in a final state of four $\alpha$-particles. A comparison with the predictions of a statistical decay code (HFℓ) based on Hauser-Feshbach formalism and including all the discrete levels of light nuclei, taken from the NUDAT2 database [2], was made. Agreement or disagreement with statistical decay code could be a hint of the importance of non statistical effects. The analysis explores the two channels of the decay [3]: the first foresees the formation of two $^{8}\text{Be}_{\text{gs}}$ which both decay in two $\alpha$ particles

$$^{16}\text{O}^* \rightarrow {}^{8}\text{Be}_{\text{gs}} + {}^{8}\text{Be}_{\text{gs}} \rightarrow \alpha + \alpha + \alpha + \alpha, \quad (1)$$

the second consists in the emission of an $\alpha$-particle leaving a $^{12}\text{C}^*$ as a residue, which in turn decays in three $\alpha$-particles, through a $^{8}\text{Be}$ intermediate state.

$$^{16}\text{O}^* \rightarrow {}^{12}\text{C}^* + \alpha \rightarrow {}^{8}\text{Be}_{\text{gs}} + \alpha + \alpha \rightarrow \alpha + \alpha + \alpha + \alpha \quad (2)$$

where $^{12}\text{C}^*$ can be in the Hoyle state ($0_2^+$, 7.65 MeV) [4] or in a $3^-$ excited state at 9.64 MeV.

## 2 The experiment and the event selection

Measurements were carried out at the INFN laboratories in Legnaro using a pulsed beam of $^{16}\text{O}$ at 130 MeV [5]. The apparatus consists of GARFIELD, a multi-detector located inside a large scattering chamber, coupled with the Ring Counter (RCo), a three-stage annular detector with a truncated cone geometry aimed for the detection at forward angles [6]. ΔE-E correlation and fast-slow PSA techniques were used for particle identification. The selection of events of interest has been performed by considering only events which feature four $\alpha$-particles, in the final state, detected at forward angles (by the RCo in 5° ÷ 17° angular range) and no product detected by GARFIELD (30° ÷ 150°).

## 3 Analysis

From energy and momentum conservation one obtains the target and projectile excitation energy:

$$E_{tot_i} = E_{beam} = E_{tot_f} = \sum_{i=1}^{4} E_{\alpha_i} + E_{rec} + E_{exc_i} - Q \quad (3)$$

where $E_{\alpha_i}$ is kinetic energy of the $i^{th}$ $\alpha$-particle, $E_{exc_i}$ the QT excitation energy, Q is the reaction Q-value and $E_{rec}$ is the QT recoil energy.
Taking into account also the energy loss in the target, $E_{rec}$ turns out to be always lower than the threshold for $^{12}$C detection.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** QT excitation energy as calculated in eq. (3).</figcaption></figure>

In the energy spectrum of the QT, shown in Fig. 1, it is possible to observe the corresponding peaks at the ground state and first $\gamma$ excited state at 4.4 MeV of the QT ($^{12}$C) nucleus. A tail to higher excitation energies can be seen as well. The analysis presented here includes only the events in which the QT remains in its ground state. However, other analyses that consider the other QT excitation energies have been carried out [7]. In order to determine the decay channel in two $^{8}$Be$_{gs}$, the relative energy of the pair of $\alpha$-particles providing the lowest value out of the four is considered together with the relative energy of the two complementary $\alpha$-particles. The vertical red lines in Fig. 2

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Left panel: minimum relative energy of couples of $\alpha$-particles. Right panel: relative energy of the complementary couple.</figcaption></figure>

represent the selection performed in order to consider the two relative energies corresponding to the ground state of the $^{8}$Be. In this way, only events with the production of two contemporary $^{8}$Be$_{gs}$ are taken into account. This accounts for 7.5 % of the total number of events with the QT in the ground state.

To consider the events corresponding to the second decay channel, from the excitation energy of three $\alpha$-particles out of the four, the excitation energy of carbon is calculated as the minimum energy of the four combinations. This amount is added to the energy of the fourth $\alpha$ particle to obtain the excitation energy of the $^{16}$O.

In Fig. 3 we show the excitation energy of the $^{12}$C*. The two excited carbon states (Hoyle $0_2^+$ and $3^-$ state, labelled as $C_1^*$ and $C_2^*$) can be distinguished. The selection of the data that fall within the 7.65 MeV or 9.64 MeV peaks enables a separate analysis of the two decay

channels in which an excited carbon nucleus is formed.

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Excitation energy spectrum of $^{12}$C* in which $^{16}$O* decays with the emission of an $\alpha$ particle.</figcaption></figure>

The decay process with the formation of $^{12}$C in the Hoyle state accounts for 32 % of the occurrences, whereas the one with carbon in $3^-$ state represents 49 %. This results in the preferential decay of $^{16}$O* through these decay channels.

Finally, we have performed the comparison with the $HF\ell$ predictions where we considered the decay of a mixing of excited levels with characteristics extracted from experimental data. Table 1 shows the results of this comparison: the observed branching ratios differ significantly

<table><caption>**Table 1.** Experimental branching ratios of different reactions compared to $HF\ell$ predictions. $C_1^*$ corresponds to the Hoyle state, $C_2^*$ to 9.64 MeV.</caption><thead><tr><th>reaction</th><th>EXP.(%)</th><th>HFℓ (%)</th></tr></thead><tbody><tr><td><sup>12</sup>C(<sup>16</sup>O, <sup>8</sup>Be<sub>gs</sub> + <sup>8</sup>Be<sub>gs</sub>)<sup>12</sup>C<sub>gs</sub></td><td>7.5</td><td>20.8</td></tr><tr><td><sup>12</sup>C(<sup>16</sup>O, <sup>12</sup>C<sub>1</sub><sup>*</sup> + <sup>α</sup>)<sup>12</sup>C<sub>gs</sub></td><td>32.0</td><td>53.0</td></tr><tr><td><sup>12</sup>C(<sup>16</sup>O, <sup>12</sup>C<sub>2</sub><sup>*</sup> + <sup>α</sup>)<sup>12</sup>C<sub>gs</sub></td><td>49.0</td><td>19.3</td></tr><tr><td>background</td><td>11.5</td><td>6.8</td></tr></tbody></table>

from the theoretical ones, especially as far as Hoyle state is concerned. A possible explanation might be the influence of the well-known $\alpha$-cluster structure of the Hoyle state on the Coulomb barrier and the associated transmission coefficients of the corresponding evaporation channel.

## References

[1] L. Morelli et al., J. Phys. G 41, 075107 (2014). L. Morelli et al., J. Phys. G 41, 075108 (2014). L. Morelli et al., J. Phys. G 43, 045110 (2016), F. Gulminelli et al. in Nuclear Particle Correlations and Cluster Physics ed. U. Schroeder, p 257, L. Morelli et al. ibid p.283.

[2] www.nndc.bnl.gov/nudat2/.

[3] M. Freer et al. Phys. Rev C 51, 1682 (1995).

[4] F. Hoyle *The Astrophysical Journal, Supplement Series* 1, 12 (1954).

[5] C. Frosin, Thesis: The $^{16}$O+$^{12}$C reaction at 90.5, 110 and 130 MeV beam energy, University of Bologna, 2016.

[6] M. Bruno et al., Eur. J. Phys. A 49, 128 (2013).

[7] M. Bruno et al. submitted to J. Physics G.
Taking into account also the energy loss in the target, $E_{rec}$ turns out to be always lower than the threshold for $^{12}$C detection.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** QT excitation energy as calculated in eq. (3).</figcaption></figure>

In the energy spectrum of the QT, shown in Fig. 1, it is possible to observe the corresponding peaks at the ground state and first $\gamma$ excited state at 4.4 MeV of the QT ($^{12}$C) nucleus. A tail to higher excitation energies can be seen as well. The analysis presented here includes only the events in which the QT remains in its ground state. However, other analyses that consider the other QT excitation energies have been carried out [7]. In order to determine the decay channel in two $^{8}$Be$_{gs}$, the relative energy of the pair of $\alpha$-particles providing the lowest value out of the four is considered together with the relative energy of the two complementary $\alpha$-particles. The vertical red lines in Fig. 2

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Left panel: minimum relative energy of couples of $\alpha$-particles. Right panel: relative energy of the complementary couple.</figcaption></figure>

represent the selection performed in order to consider the two relative energies corresponding to the ground state of the $^{8}$Be. In this way, only events with the production of two contemporary $^{8}$Be$_{gs}$ are taken into account. This accounts for 7.5 % of the total number of events with the QT in the ground state.

To consider the events corresponding to the second decay channel, from the excitation energy of three $\alpha$-particles out of the four, the excitation energy of carbon is calculated as the minimum energy of the four combinations. This amount is added to the energy of the fourth $\alpha$ particle to obtain the excitation energy of the $^{16}$O.

In Fig. 3 we show the excitation energy of the $^{12}$C*. The two excited carbon states (Hoyle $0_2^+$ and $3^-$ state, labelled as $C_1^*$ and $C_2^*$) can be distinguished. The selection of the data that fall within the 7.65 MeV or 9.64 MeV peaks enables a separate analysis of the two decay

channels in which an excited carbon nucleus is formed.

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Excitation energy spectrum of $^{12}$C* in which $^{16}$O* decays with the emission of an $\alpha$ particle.</figcaption></figure>

The decay process with the formation of $^{12}$C in the Hoyle state accounts for 32 % of the occurrences, whereas the one with carbon in $3^-$ state represents 49 %. This results in the preferential decay of $^{16}$O* through these decay channels.

Finally, we have performed the comparison with the $HF\ell$ predictions where we considered the decay of a mixing of excited levels with characteristics extracted from experimental data. Table 1 shows the results of this comparison: the observed branching ratios differ significantly

<table><caption>**Table 1.** Experimental branching ratios of different reactions compared to $HF\ell$ predictions. $C_1^*$ corresponds to the Hoyle state, $C_2^*$ to 9.64 MeV.</caption><thead><tr><td>reaction</td><td>EXP.(%)</td><td>HF<sub>ℓ</sub> (%)</td></tr></thead><tbody><tr><td><sup>12</sup>C(<sup>16</sup>O,+<sup>8</sup>Be<sub>gs</sub>+<sup>8</sup>Be<sub>gs</sub>)<sup>12</sup>C<sub>gs</sub></td><td>7.5</td><td>20.8</td></tr><tr><td><sup>12</sup>C(<sup>16</sup>O,<sup>12</sup>C<sub>1</sub><sup>*</sup> + α)<sup>12</sup>C<sub>gs</sub></td><td>32.0</td><td>53.0</td></tr><tr><td><sup>12</sup>C(<sup>16</sup>O,<sup>12</sup>C<sub>2</sub><sup>*</sup> + α)<sup>12</sup>C<sub>gs</sub></td><td>49.0</td><td>19.3</td></tr><tr><td>background</td><td>11.5</td><td>6.8</td></tr></tbody></table>

from the theoretical ones, especially as far as Hoyle state is concerned. A possible explanation might be the influence of the well-known $\alpha$-cluster structure of the Hoyle state on the Coulomb barrier and the associated transmission coefficients of the corresponding evaporation channel.

## References

[1] L. Morelli et al., J. Phys. G 41, 075107 (2014). L. Morelli et al., J. Phys. G 41, 075108 (2014). L. Morelli et al., J. Phys. G 43, 045110 (2016), F. Gulminelli et al. in Nuclear Particle Correlations and Cluster Physics ed. U. Schroeder, p 257, L. Morelli et al. ibid p.283.

[2] www.nndc.bnl.gov/nudat2/.

[3] M. Freer et al. Phys. Rev C 51, 1682 (1995).

[4] F. Hoyle The Astrophysical Journal, Supplement Series 1, 12 (1954).

[5] C. Frosin, Thesis: The $^{16}$O+$^{12}$C reaction at 90.5, 110 and 130 MeV beam energy, University of Bologna, 2016.

[6] M. Bruno et al., Eur. J. Phys. A 49, 128 (2013).

[7] M. Bruno et al. submitted to J. Physics G.