Carbon Burning: Theory, Astrophysics and Experiments

30 Jun 2026, 08:30 → 2 Jul 2026, 16:30 Europe/Rome

Sala Conferenze di Palazzo del Monte di Pietà

Jakub Skowronski (UNIPD and INFN PD)

The workshop aims to merge and deeply discuss recent results from the main experimental groups, active in the measurement of the cross section of the ¹²C+¹²C reactions. The workshop is going to be organized to have a session for the detailed description of the data and their uncertainty. One of the main session of the workshop will be dedicated to the discussion and comperison between the different datasets. The astrophysical impact of the data, as well as the open questions will be investigated and evaluated thanks to the expertise of theoretical groups, focused on stellar models. 

Ultimately the workshop aims to define a shared roadmap with the  goals for the future measurements, opening the path to collaborations among the groups.

1st_Circular_Carbon.pdf

2nd_Circular_Carbon-2.pdf

Carbon Burning, Theory,Astrophysics and Experiments.-6.png

Tuesday 30 June

Welcome

Astrophysics I

1 The role of the 12C+12C on the stellar evolution"

Speaker: Dr Alessandro Chieffi (INAF - Rome)

2 Carbon burning and Type I a Supernova

In spite of their pivotal role in observational cosmology and and in the determination of the chemical composition of matter in the Universe, Type Ia SNe Ia still represent an intriguing mystery. In fact, up to now no clear consensus there exists concerning their progenitor systems and the explosion mechanism.
In this talk I review the uncertainties in our current understanding of these explosive phenomena and I will discuss how a more precise determination of the C12+C12 cross section could help in solving the "SNe Ia problem".

Speaker: Luciano Piersanti (INAF - Rome)

3 12C+12C and 12C+160 reaction rates and stellar evolution

Speaker: Dr Thibaut Dumont (IPHC Strasbourg)

10:30 Cofee Break

Astrophysics II

4 Impact of 12C+12C on massive stars nucleosynthesis in general

Speaker: Dr Lorenzo Roberti (INFN - LNS)

5 The impact of the carbon fusion rate for superbursts

Superbursts are very energetic explosions occurring at the outer crusts of neutron stars, as a consequence of unstable carbon burning . They release up to $10^{40}$ erg in a span of hours/days and have recurrence times in the order of years. In contrast to the standard, less-energetic bursts due to H/He burning, only a few multi-zone simulations have been reported. While these pioneering works are successful in explaining the observational characteristics of the superbursts, from the point of view of nuclear physics many questions are still open. For instance, the impact changing the carbon fusion rate has over all the observable properties of the superbursts, as well as those not directly observable, such as the distribution of ashes from carbon burning. In recent years the carbon fusion rate has been reviewed, and although at high temperatures there is agreement with the old CF88 rate, at temperatures between $10^8$ and $10^9$ K  - typical of superburst ignition - it has been claimed the rate can be either 1000 times larger or smaller than CF88. The purpose of my talk is to present my results from recent multi-zone simulations of superbursts carried with the public stellar code MESA, in which we consider four different versions of the carbon fusion rate. We find that enhancing the carbon fusion rate leads to a reduction in the recurrence time and exponential decay of luminosity, while reducing the carbon fusion rate leads to the reverse effect. We find changing the carbon fusion rate has comparable effects as to change the base luminosity of the crust.

Speaker: Dr MARTIN JAVIER NAVA CALLEJAS (Université Libre de Bruxelles)

6 Low mass density deflagration burning led to premature type Iax supernovae

The progenitor systems of normal type Ia supernovae (SNe Ia) remain a central puzzle. The long-debated single-degenerate (SD) channel, where a white dwarf (WD) accretes mass from a companion, faces major observational conflicts. The unknown rising form the carbon ignition and detonation mechanism in sub-Chandrasekhar mass led us to run 3D hydrodynamic simulations that address these tensions by showing a fundamental dichotomy: accreting WDs predominantly ignite prematurely at sub-Chandrasekhar masses, producing low-energy, incomplete explosions consistent with Type Iax supernovae. Only WDs reaching a narrow mass threshold of 1.37 M⊙ undergo complete destruction, characteristic of normal SNe Ia. This ”safety valve” mechanism effectively recasts the SD channel as the main pathway to SNe Iax, not normal SNe Ia, providing a unified explanation for the observed scarcity of progenitor signatures in the latter and suggesting alternative channels dominate normal SNe Ia production.

Speaker: Dr Amir Michaelis (Technion – Israel Institute of Technology)

12:30 Lunch Break

Direct Measurements I

7 Experimental Techniques for 12C + 12C Reaction

Speaker: Prof. Micheal Wiescher (University of notre Dame, USA)

8 Status of the 12C + 12C at LUNA

Speaker: Dr Alba Formicola (INFN Rome)

9 Status of the 12C + 12C at ERNA-CIRCE

Speaker: Prof. Antonino Di Leva (University and INFN of Naples)

16:00 Coffee Break

Direct Measurements II

10 Status of the STELLA measurements

In this contribution, we present an overview of the measurements of the $^{12}$C+$^{12}$C fusion reaction conducted with the mobile measurement station STELLA (STELlar LAboratory). This apparatus is designed for fusion studies involving light heavy ions and has been employed for carbon fusion measurements at Andromède, IJCLab (Orsay) and at the Felsenkeller shallow underground laboratory (Dresden).

STELLA enables high-duty-cycle experiments using intense beams on thin targets over extended periods. It is optimized for reliable and precise measurements of cross-sections below the nanobarn level. The main components include a rotating target mechanism for large, thin, self-supporting foils; high-granularity charged-particle detectors with wide angular coverage; and a triggerless data acquisition system providing nanosecond gamma-particle timing coincidences through an extended array of LaBr₃(Ce) crystals, in collaboration with UK-FATIMA.

The measurement technique and its impact on particle and timing spectra will be presented. We will demonstrate the refinement of cross-section measurements using timing coincidences and the estimation of residual random background. Statistical analyses at the lowest cross sections will be discussed, along with our results interpreted in terms of $S$-factors and reaction rates relevant to astrophysical applications.

Speaker: Dr Marcel Heine (IPHC Strasbourg)

11 Status of the 12C + 12C at LEAF-TDL

Speaker: Prof. Xiaodong Tang (Institute of Modern Physics Chinese Academy of Sciences)

12 Direct Carbon Fusion Measurements with STELLA for Nuclear Astrophysics

The oscillations in the excitation function of $^{12}$C+$^{12}$C, from energies above the Coulomb barrier down to the astrophysical region, is believed to be associated to molecular states in the compound nucleus [1], or linked to the fusion dynamics. Cluster states has been identified for example in $^{24}$Mg near subsystems breakup threshold, as $^{12}$C+$^{12}$C and $^{16}$O+$2\alpha$/$^{8}$Be with substantial $\alpha$ decay as 0$^{+}$ states [2], and the impact on carbon fusion needs to be evaluated.
The STELLA apparatus is designed to identify the evaporated charged particles of the $^{12}$C($^{12}$C,$\alpha$)$^{20}$Ne$^{(*)}$ and $^{12}$C($^{12}$C,p)$^{23}$Na$^{(*)}$ reactions. It combines a array of high granularity silicon detectors for charged particle detection in coincidence with the corresponding recoils' de-sexcitations $\gamma$ rays with LaBr$_{3}$ scintillators [3]. This technique enables a clear identification of populated excitation channels over a wide angular coverage.
New measurements of the excitation function arround the barrier have recently been performed at the Felsenkeller Underground Laboratory in Dresden, Germany, with fine energy steps. These new measurements allow for investigating the angular distributions of p and $\alpha$, associated to ground and excited states of the respective evaporation residues. This allows J$^{\pi}$ assignments and to calculate the respective exclusive cross sections. This upgraded STELLA configuration will be presented.

[1] David Jenkins and Sandrine Courtin. Weighing the evidence for clustering in nuclei. Journal of Physics G: Nuclear and Particle Physics, 42(3):034010, feb 2015.
[2] P. Adsley, et al. Extending the hoyle-state paradigm to $^{12}$C+$^{12}$C fusion. Phys. Rev. Lett., 129:102701, Sep 2022.
[3] M. Heine et al. The STELLA apparatus for particle-gamma coincidence fusion measurements with nanosecond timing. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 903:1–7, 2018.

Speaker: Guillaume Harmant (IPHC-CNRS)

13 The challenging direct measurement of the 12C+12C reaction rate at LUNA

Carbon burning is a crucial stage of stellar evolution, determining whether stars evolve
toward neutron stars, black holes, or CO white dwarfs. These outcomes depend strongly on
the (^{12})C+(^{12})C reaction rate, which is still uncertain at astrophysical energies.
This reaction mainly proceeds through the (^{12})C((^{12})C,(\alpha))(^{20})Ne and
(^{12})C((^{12})C,p)(^{23})Na channels. While it has been studied over a wide energy range,
direct measurements only reach 2.1 MeV, above the astrophysical region. Indirect methods
extend to lower energies, but with significant normalization uncertainties, making new
direct measurements essential.
A direct study is now being carried out by the LUNA collaboration at LNGS using high-
intensity carbon beams and a low-background (\gamma)-detection setup based on a 150% HPGe
detector surrounded by NaI scintillators. This configuration combines high efficiency,
excellent resolution, and strong background suppression, providing a sensitivity much
higher than previous direct experiments.
Besides improving the measurement of the (^{12})C+(^{12})C cross section, this setup will
also allow the study of the level density and possible cluster structure of (^{24})Mg in
the (E_{cm}=1.5)–(3.5) MeV region, which may play an important role in the astrophysical
reaction rate.
In this contribution, I will present the recent progress in setup development and
installation, Geant4 simulations, HPGe detector characterization, and the first beam-on-
target results for the direct study of the (^{12})C+(^{12})C reaction.

Speaker: Riccardo Maria Gesue (GSSI, INFN LNGS)

20:00 Social Dinner

Wednesday 1 July

Indirect Measurements I

14 Trojan Horse Method for the 12C + 12C Reaction: An Update

Trojan Horse Method for the 12C + 12C Reaction: An Update

M. La Cognata, A. Tumino, A.A. Oliva, A. Nurmukhanbetova, G. L. Guardo, L. Lamia, D. Lattuada, R. G. Pizzone, G. G. Rapisarda, S. Romano, M. L. Sergi, R. Spartá

Carbon burning plays a key role in astrophysical environments that determine the fate of stars, including late-stage massive stars and superbursts in accreting neutron stars. However, the relevant 12C + 12C fusion reactions at astrophysical energies remain poorly constrained from direct measurements, as they are hindered by the strong Coulomb barrier and significant uncertainties in low-energy data. We present results obtained via the Trojan Horse Method (THM), using 14N as a Trojan Horse nucleus to access the 12C + 12C interaction at sub-Coulomb energy. The measurements of the 12C(12C,α)20Ne and 12C(12C, p)23Na channels reveal a rich resonance structure in the astrophysical S-factor. We discuss how a multiresonance approach challenges scenarios invoking fusion hindrance, and that the three-body cross sections are well reproduced by preliminary DWBA calculations. The experimental results are also supported by recent theoretical models, including those based on molecular resonance frameworks.

Speaker: marco la cognata (infn-lns)

15 Extending the Hoyle-state paradigm to 12C + 12C fusion

Speaker: Prof. David Jenkins (University of York)

16 THM measurement of ¹²C+¹²C

Speaker: Prof. Qun-Gang Wen (Anhui University, China)

10:30 Coffee Break

Indirect Measurements II

17 Fusion hindrance in medium-light systems as a path toward the lighter cases of astrophysical interest

The physics underlying the fusion hindrance phenomenon [a] and, consequently, its features
in the various systems, as well as their link to different nuclear structure situations, may be related to the Pauli exclusion principle [b], but it has not yet been fully clarified. Furthermore, we know that its existence in the fusion of light systems may have significant consequences in astrophysics [c], since it impacts the stellar evolution and nucleosynthesis of heavier elements. The experimental study of fusion in light systems (Q$_{fus}$ > 0) is particularly challenging, especially when trying to identify the hindrance phenomenon, given the S-factor oscillations observed in some cases.
The behaviour of slightly heavier cases may allow a reliable extrapolation towards $^{12}$C+$^{12}$C and nearby systems. In recent years, we investigated the cases of $^{12}$C + $^{28-30}$Si,$^{24-26}$Mg, and for all of them, the hindrance phenomenon has been observed. In particular, the fusion excitation function of $^{12}$C + $^{28}$Si has been measured down to ~40 nb [d], using the $^{28}$Si beams from the XTU Tandem accelerator of LNL, and by detecting the evaporated charged particles with two DSSD in coincidence with the prompt $\gamma$-rays identified by the spectrometer AGATA. The figure on the left shows the excitation function, where the red dots were obtained by the electrostatic deflector PISOLO, allowing a useful normalisation of the AGATA data (blue dots). Very recently, the fusion of the lighter system $^{12}$C + $^{19}$F has been studied. The hindrance effect also shows up in this case, as reported in the centre figure, where the logarithmic derivative of the energy-weighted cross sections vs the energy reaches the LCS limit.

https://drive.google.com/file/d/15EvGpA3mjeEfJwnC7iGhNH-ACb6vHJyG/view?usp=sharing
Left: Fusion excitation function of $^{12}$C + $^{28}$Si; Centre: Logarithmic derivative of $^{12}$C + $^{19}$F fusion; Right: Hindrance systematics of medium-light systems

$^{12}$C + $^{19}$F has a very large positive Q-value (~23MeV), and no sub-barrier fusion data were available before the recent experiment. The threshold energy for the onset of hindrance has been obtained and included in the systematics shown in the figure on the right [e], which reports the threshold (E$_s$) for several medium-light systems with Q$_{fus}$>0. The abscissa is the parameter $\zeta$ characterising the system [c] ($\mu$ is the reduced mass). The magenta line is a phenomenological fit of the experimental systematics using the function shown. The thresholds for several light systems going from $^{10}$B + $^{10}$B to $^{16}$O+$^{16}$O (open dots, plotted with increasing $\zeta$) are extrapolations from higher energies using the hindrance model [a,c]. They were not included in the fit to the measured data for the heavier systems, which leads to an extrapolation to the lighter ones, very close to the hindrance model results. In the talk, the experimental evidence will be examined in depth, offering a basis for discussing the conclusions that can be drawn from these measurements.

[a] C. L. Jiang, et al., Phys. Rev. Lett. 89, 052701 (2002)
[b] C. Simenel et al., Phys. Rev. C 95, 032601(R) (2015)
[c] C. L. Jiang, et al., Phys. Rev. C 75, 015803 (2007); Phys. Rev. C 79, 044601 (2009)
[d] A. M. Stefanini et al., Phys. Lett. B 872, 140084 (2026)
[e] A. M. Stefanini et al., Phys. Rev. C 111, 064620 (2025), and to be published

Speaker: Prof. Giovanna Montagnoli (UNIPD)

18 Bayesian Analysis of the 12C + 12C Astrophysical S Factor and Reaction Rate with Modern Inverse-Kinematics Constraints

A Bayesian analysis of the modified astrophysical factor S∗(E) for the 12C + 12C fusion reaction is presented using available data at carbon–carbon energies Ecm < 3.5 MeV, including direct measurements, Coulomb-renormalized Trojan Horse Method results, and recent inverse-kinematics data.
The inference is performed for y(E) = log10 S∗(E), represented by a quadratic polynomial in energy with global coefficients determined by Monte Carlo sampling of the weighted χ2 likelihood. All quoted experimental uncertainties are included in the likelihood. To obtain a stable weighted-χ2 analysis of about 600 heterogeneous data points with different normalizations and systematic effects, I added an additional conservative 25% systematic uncertainty. The posterior for y(E) is then propagated to obtain the median smooth S∗(E) curve and its 68% credible band.
Except at the lowest extrapolated energies, the resulting S*(E) is below the estimate of Fowler, Caughlan, and Zimmerman [W. A. Fowler, G. R. Caughlan, and B. A. Zimmerman, Annu. Rev. Astron. Astrophys. 13, 69 (1975)] over most of the considered energy interval. The astrophysical impact is evaluated through the thermonuclear reaction rate NA⟨σv⟩, retaining the measured low-energy resonance structure through the direct inverse-kinematics input. The resulting rate band is noticeably lower than the CF88 analytic rate [G. R. Caughlan and W. A. Fowler, At. Data Nucl. Data Tables 40, 283 (1988)].

Speaker: Prof. Akram Mukhamedzhanov (Texas A&M University)

19 Investigation of $^{24}$Mg nuclear structure in the energy range relevant to carbon-burning in stars

The nuclear structure of $^{24}$Mg in the excitation energy region relevant to the $^{12}$C+$^{12}$C fusion reaction is crucial for constraining carbon-burning processes in massive stars. Although this reaction has been extensively studied over the past decades, significant uncertainties persist, particularly at center of mass energies below 2.5 MeV, where direct measurements are hindered by extremely low cross sections. In this context, indirect approaches providing detailed spectroscopic information on the compound nucleus $^{24}$Mg are essential.

In this contribution, we present a new dedicated experiment to be performed at the Oslo Cyclotron Laboratory (OCL) to investigate the excited states of $^{24}$Mg in the energy range 14-17 MeV via $\alpha$ inelastic scattering. Reaction products will be detected in coincidence using the Oslo Scintillator Array (OSCAR), the SiRi particle telescope, and the INFN OSCAR silicon hodoscope. The combined use of charged-particle and $\gamma$-ray spectroscopy will enable a reliable determination of the spin and parity of the populated states in $^{24}$Mg, as well as an estimate of the branching ratios of its decay channels.

Speaker: Federica Ercolano (Università degli studi di Napoli "Federico II", INFN Sezione di Napoli)

20 Fusion of $^{12}$C + $^{16}$O at extreme sub-barrier energies

The $^{12}$C + $^{16}$O reaction plays a particularly important role in both the carbon and oxygen-burning phases of stars. Fang et al. measured this reaction in a thick-target experiment a few years ago, with both singles and particle-γ coincidence techniques down to a few nanobarns. However, the lowest energy points suffer from large experimental uncertainties which prevent discriminating between the Fowler model and the hindrance approach. Further measurements at low energies with smaller errors are therefore needed to clarify the underlying physics, in order to determine the reaction rate at astrophysical energies.
An experiment on $^{12}$C + $^{16}$O aiming at the measurement of fusion cross sections below the μb range with the combined set-up of AGATA and silicon detectors was performed at LNL. The fusion events were identified by coincidences between the prompt $\gamma$-rays and the light charged particles (p,$\alpha$) evaporated from the compound nucleus $^{28}$Si.

Speaker: Julgen Pellumaj (University of Padova, INFN-Padova)

12:30 Lunch Break

Theory I

21 Impact of the molecular resonances on the 12C + 12C reaction

Speaker: Dr M. Kimura

16:00 Coffee Break

Theroy II

22 R-matrix for nuclear reactions

Speaker: Prof. Edward Simpson (Australian National University)

23 Channel-Coupling Effects in Low-Energy 12C+12C Fusion Reactions

Low-energy $^{12}\mathrm{C}+^{12}\mathrm{C}$ fusion reactions play a crucial role in astrophysical phenomena such as X-ray superbursts (XRSBs), the evolution of massive stars, and Type Ia supernovae. In this reaction, resonance contributions dominate the fusion cross section, and channel-coupling effects are expected to be essential.

We theoretically investigate the $^{12}\mathrm{C}+^{12}\mathrm{C}$ fusion reaction rate within a microscopic framework that explicitly incorporates channel coupling among the $^{12}\mathrm{C}+^{12}\mathrm{C}$, $\alpha+^{20}\mathrm{Ne}$, $p+^{23}\mathrm{Na}$, and related channels. Coupling to these channels leads to fragmentation of $^{12}\mathrm{C}+^{12}\mathrm{C}$ molecular resonances, resulting in the appearance of resonance states just above the $^{12}\mathrm{C}+^{12}\mathrm{C}$ threshold.

These near-threshold resonances can significantly enhance the reaction rate at low temperatures relevant to X-ray superbursts. Experimental confirmation of such resonances is therefore of great importance. In particular, isoscalar monopole (IS0) and quadrupole (IS2) transitions via inelastic scattering provide promising probes to selectively populate these states.

We also discuss ongoing upgrades of the theoretical framework and potential directions for future collaboration.

Speaker: Yasutaka TANIGUCHI (Fukuyama University)

Thursday 2 July

Miscellaneous I

24 Impact of 12C+12C on massive stars nucleosynthesis of the elements heavier than iron

Speaker: Dr Marco Pignatari (Konkoly Observatory, Budapest, Hungary)

25 Screening effect in stellar environments

Speaker: Prof. Yuanbin Wu (East China Normal University)

26 R-matrix Study for the 12C + 12C Reaction

Speaker: Dr Aliya Nurmukhanbetova (INFN LNS)

10:30 Coffee Break

Round Table

12:30 Lunch Break

Outreach Seminar

16:00 Coffee Break