12C + + Reaction

L. Morelli1, M. Bruno1, M.DAgostino1, S Barlini2, M. Bini2, G Casini2, M. Cinausero3, M. Degerlier4, D. Fabris5, N.Gelli2, F Gramegna3, T. Marchi3, A. Olmi2 , G. Pasquali2, S. Piantelli2, S. Valdr2

1 Istituto Nazionale di Fisica Nucleare, Sezione di Bologna and Dipartimento di Fisica e Astronomia dellUniversit, Bologna, Italy. 2 Istituto Nazionale di Fisica Nucleare, Sezione di Firenze and Dipartimento di Fisica dellUniversit, Firenze, Italy

3 INFN, Laboratori Nazionali di Legnaro, Legnaro (Padova), Italy. 4 Physics Department, University of Nevsehir, Science and Art Faculty, Nevsehir, Turkey

5 INFN, Sezione di Padova, Padova, Italy.

INTRODUCTION

The low-lying 12C excited states have been recently studied through different experiments [1, 2, 3] which have pointed out the features of these states. In particular the Hoyle state at 7.65 MeV excitation energy [4] has been interpreted as mainly instantaneous [3] or sequential through an intermediate 8Begs decay [2]. Many efforts have been dedicated to model comparisons and most of the results indicate a nearly complete agreement with a sequential decay with a very small (around 0.3%) contamination by the instantaneous one. A very recent review of the Hoyle state, together with implication on nuclear forces, structure and astrophysics, has been recently published [5].

We have studied the reaction 12C + 12C with a 95 MeV Carbon beam delivered by the Tandem accelerator of INFN Laboratori Nazionali di Legnaro (LNL) with the [GARFIELD + RCo] apparatus covering approximately 4 [6]. The collected data have been analyzed with the aim of selecting compound nucleus reactions and compared to a dedicated Hauser-Feshbach calculation [HF], which includes excited states of light nuclei. The results, published in [7], show a substantial good agreement with theoretical predictions except some discrepancies for even residues, showing contamination from clustering effects. In this report we will concentrate on the analysis of semiperipheral 12C + 12C reactions and in particular reactions where the projectile interacts with the target, leaves the target in the ground or in a slightly excited state and decays in three -particles.

THE EXPERIMENT AND THE ANALYSIS

The forward polar angles (7o17o) are covered by the three stage apparatus (RCo), ionization chamber (IC), silicon strip detector (Si) and CsI(Tl) scintillator. The performance of the RCo allows to reach energy determination with the accuracy of percent, charge identification of particles and fragment with threshold as low as 0.81 AMeV and mass identification of light isotopes with 6 AMeV threshold through E-E plots for Si-CsI(Tl) and scintillator pulse shape analysis (PSA).

We have selected events where three -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 -particles we have to exploit the E-E Si- CsI or the pulse shape analysis in CsI(Tl) scintillators [8]. This implies that the threshold for the identification is about 24 MeV and consequently that the kinetic energy of 12C nucleus emitting three -particles is relatively high. The recoil 12C nucleus is therefore very slow and its energy not sufficient to reach the detector, even with a very thin target.

RESULTS

In Fig. 1 the energy spectrum of the reconstructed 12C quasi-projectile is shown, as calculated from the sum of the energy of the three -particles:

3

1ibeamrecitot QEEEE

where Q = -7.272 MeV is the Q-value for the decay of 12C in three -particles and Erec is the recoil of the 12C quasi-target. As it can be easily seen most of the energy corresponds to a negligible recoil energy and therefore a 12C quasi-target nearly at rest in the laboratory frame.

Fig. 1 Total energy spectrum for -particles products. From right to left the peaks correspond to the ground and the first excited states of the recoil 12C nucleus.

Most of the kinetic energy is peaked at 88 MeV and a small peak is present at about 84 MeV, corresponding to the 12C quasi-target at about 4.4 MeV excitation energy, the first 12C excited level.

Etot MeV75 80 85 90

Yie

ld (

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.)

2000

4000

The excitation energy of the 12C quasi-projectile can be calculated as:

3

1

2*

2ith

C

Ci Em

pEE

and is presented in Fig. 2 (Eth = |Q| = 7.272 MeV). Three excited 12C quasi-projectile levels are present for true -particles (7.7, 9.6 and 10.8 MeV).

Fig. 2. Excitation energy spectrum for the breakup of 12C into three -particles.

The lower peak in Fig. 2 corresponds to the well-known Hoyle state. Different observables have been proposed to determine if the decay of this state is instantaneous or sequential through the formation of 8Begs. The first is the minimum relative energy between a pair of the three . The presence of a peak at about 92 KeV is the first observable compatible with a prevalent sequential decay and it has been presented in the 2013 LNL Annual report [9].

A second observable which can contribute to the discussion is the deviation from the average center-of-mass energy:

22 EEErms

here E represents the energy of the -particles in the 12C

rest frame and the average is over the three -particles in each event. E corresponds to 1/3 of the Q-value for the Hoyle-state decay into three -particles (127 KeV).

The results are shown in Fig, 3 where the plot of Erms vs. the mean -particle energy is shown. As it can be easily inferred for Fig. 3 the simultaneous decay, corresponding to three -particles at nearly the same kinetic energy, i.e. at very low Erms values, is absent in our analysis, contrary to the bump at Erms < 25 KeV obtained in Ref. [3].

Finally if we analyze the Dalitz plot (see Fig. 4) of the energies of the three -particles normalized to the total energy. We would expect that the simultaneous decay should result in 3 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 the region where the energy of two -particles are very close one to the other and the third -energy is far from the two others.

This can be considered as a signal of the importance of the sequential decay.

[1] O. S. Kirsebom - Few Body Sist. 54 (2013) 755; J. Manfredi

et al. Phys. Rev. C 85 (2012) 037603 [2] T. K. Rana et al. Phys. Rev. C 88 (2013) 021601 [3] Ad. R. Raduta et al. Phys.Lett. B705 (2011) 65 [4] F. Hoyle The Astrophysical Journal, Suppl. Series 1 (1954) 12 [5] M. Freer and H.O.U. Fynbo Prog. Part.Nucl. Phys 78 (2014) 1 [6] M. Bruno et al. Eur. Phys. J. A 49 (2013) 128 [7] L. Morelli et al. J. Phys. G: Nucl. Part. Phys. 41 (2014)

075107; J. Phys. G: Nucl. Part. Phys. 41 (2014) 075108. [8] L. Morelli et al. Nucl. Instr. ad Meth. A620 (2010) 305. [9] L. Morelli et al. 2013 LNL Annual Report, page 50.

E* 12C MeV8 9 10 11 12 13

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0.06

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0.1

0.12

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X-1 -0.5 0 0.5 1

Y

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Fig. 3. Erms vs: the mean -particle energy.

1Fig. 4. Energy Dalitz-plot normalized to the total energy.