Triple-alpha Reaction Research Articles

3D hydrodynamic simulations of white dwarf–main-sequence star collisions – I. Head-on collisions

ABSTRACT Recently inaugurated telescopes, such as the MeerKAT radio telescope and the upcoming Rubin Observatory Legacy Survey of Space and Time, will be able to detect millions of transient events in the night sky. Stellar collisions between white dwarfs (WDs) and main-sequence (MS) stars may be detectable among such transients. Simulations will play a key role in characterizing these events and selecting targets for follow-up. We present 3D smoothed particle hydrodynamics models of dynamical interactions between a $0.6\ {\rm M}_{\odot }$ WD and 0.3, 0.6, and $1.2\ {\rm M}_{\odot }$ MS stars within globular cluster environments. Utilizing a 34-isotope nuclear network, we investigate the energetics, gas morphologies, and mass-loss properties of these collisions for different stellar mass ratios. Our models predict an overabundance of $^{13}$C, $^{15}$N, and $^{17}$O isotopes relative to solar abundances. Moreover, we find that the time-scale of the collisions is too short and maximum temperatures too low for any significant hydrogen burning or triple-alpha reactions to occur. This combined with a negligible production of elements heavier than neon may be key signatures in distinguishing these events from other transient events with similar peak bolometric luminosities ($\sim\!\! 10^{38}\!\!-\!\!10^{41}$ erg s$^{-1}$).

Effects of triple alpha and CNO reaction rates on the evolution of low- mass stars

In this study, the effects of the energy generation rates of Triple Alpha and CNO nuclear reactions on the evolution of Main sequence star models with masses in the range of 0.65-1.2 Mʘ are investigated. Paczynski's GOB, SCH and HB7 star model programs are used for each model. The ages of stars are calculated using the original NACRE (Nuclear Astrophysics Compilation of Reactions) energy generation rates and NACRE rates reduced by ten percent. The ages of the current IT Cas and V636 Cen stars are calculated and compared with the results in the literature. Since Triple Alpha reactions are very difficult to perform in terrestrial laboratories, this theoretical model study will shed light on observational studies of low-mass and even massive stars.

Effects of Hoyle state de-excitation on νp–process nucleosynthesis and Galactic chemical evolution

The particle-induced hadronic de-excitation of the Hoyle state in 12C induced by inelastic scattering in a hot and dense plasma can enhance the triple-alpha reaction rate. This prevents the production of heavy nuclei within the neutrino-driven winds of core-collapse supernovae and raises a question as to the contribution of proton-rich neutrino-driven winds as the origin of p–nuclei in the solar-system abundances. Here we study νp-process nucleosynthesis in proton-rich neutrino-driven winds relevant to the production of Mo92,94 and Ru96,98 by considering such particle-induced de-excitation. We find that the enhanced triple-alpha reaction rate induced by proton inelastic scattering can increase the production of Mo92,94 and Ru96,98 in an energetic hypernova wind model with a massive proto-neutron star although the abundances of these p–nuclei decrease in a wind model of ordinary core-collapse supernovae. The enhancement of the triple-alpha reaction rate induced by the neutron scattering hardly affects the νp-process at low temperature. We show the new result that, contrary to the results for ordinary core-collapse supernovae, the hypernova νp-process can contribute to the Galactic chemical evolution of p–nuclei regardless of the particle-induced Hoyle state de-excitation and even enhance the solar isotopic fractions of Mo92,94 and Ru96,98.

Neutron-upscattering enhancement of the triple-alpha process

The neutron inelastic scattering of carbon-12, populating the Hoyle state, is a reaction of interest for the triple-alpha process. The inverse process (neutron upscattering) can enhance the Hoyle state’s decay rate to the bound states of 12C, effectively increasing the overall triple-alpha reaction rate. The cross section of this reaction is impossible to measure experimentally but has been determined here at astrophysically-relevant energies using detailed balance. Using a highly-collimated monoenergetic beam, here we measure neutrons incident on the Texas Active Target Time Projection Chamber (TexAT TPC) filled with CO2 gas, we measure the 3α-particles (arising from the decay of the Hoyle state following inelastic scattering) and a cross section is extracted. Here we show the neutron-upscattering enhancement is observed to be much smaller than previously expected. The importance of the neutron-upscattering enhancement may therefore not be significant aside from in very particular astrophysical sites (e.g. neutron star mergers).

Measurement of 12C(n,n’) reaction cross section to determine triple-alpha reaction rate in high-density environments

The reaction rate of the triple-alpha reaction can be enhanced in hot and dense environments due to the deexcitation of the Hoyle state in 12C by neutrons. The cross section of the deexcitation should be determined for the enhanced reaction rate. We plan to obtain the cross section by measuring the inverse reaction using a neutron beam around 10 MeV and an active target system. In the present paper, we report a proof-of-principle experiment using a neutron beam at 14 MeV. The obtained cross section is consistent with a previous result, demonstrating the validity of our method.

Evidence against the Efimov effect in C12 from spectroscopy and astrophysics

Background: The Efimov effect is a universal phenomenon in physics whereby three-body systems are stabilized via the interaction of an unbound two-body sub-systems. A hypothetical state in $^{12}\mathrm{C}$ at 7.458 MeV excitation energy, comprising of a loose structure of three $\alpha$-particles in mutual two-body resonance, has been suggested in the literature to correspond to an Efimov state in nuclear physics. The existence of such a state has not been demonstrated experimentally. Method: Using the combined data sets from two recent experiments, one with the TexAT TPC to measure $\alpha$-decay and the other with Gammasphere to measure $\gamma$-decay of states in $^{12}\mathrm{C}$ populated by $^{12}\mathrm{N}$ and $^{12}\mathrm{B}$ $\beta$-decay respectively, we achieve high sensitivity to states in close-proximity to the $\alpha$-threshold in $^{12}\mathrm{C}$. Results: No evidence of a state at 7.458 MeV is seen in either data set. Using a likelihood method, the 95\% C.L. $\gamma$-decay branching ratio is determined as a function of the $\beta$-decay feeding strength relative to the Hoyle state. In parallel, calculations of the triple-alpha reaction rate show the inclusion of the Efimov corresponds to a large increase in the reaction rate around $5 \times 10^{7}$ K. Conclusion: From decay spectroscopy - at the 95\% C.L., the Efimov state cannot exist at 7.458 MeV with any $\gamma$-decay branching ratio unless the $\beta$-strength is less than 0.7\% of the Hoyle state. This limit is evaluated for a range of different excitation energies and the results are not favorable for existence of the hypothetical Efimov state in $^{12}\mathrm{C}$. Furthermore, the triple-alpha reaction rate with the inclusion of a state between 7.43 and 7.53 MeV exceeds the rate required for stars to undergo the red giant phase.

First experimental determination of the radiative-decay probability of the [formula omitted] state in 12C for estimating the triple alpha reaction rate in high temperature environments

The triple alpha reaction is one of the most important reactions in the nuclear astrophysics. However, its reaction rate in high temperature environments at T9> 2 was still uncertain. One of the major origins of the uncertainty was that the radiative-decay probability of the 31− state in 12C was unknown. In the present work, we have determined the radiative-decay probability of the 31− state to be 1.3−1.1+1.2×10−6 by measuring the 1H(12C,12Cp) reaction for the first time, and derived the triple alpha reaction rate in high temperature environments from the measured radiative-decay probability. The present result suggests that the 31− state noticeably enhances the triple alpha reaction rate although the contribution from the 31− state had been assumed to be small.

Coulomb screening correction to the Q value of the triple-alpha process in thermal plasmas

Abstract The triple-alpha reaction is key to $^{12}$C production and is expected to occur in weakly coupled thermal plasmas as encountered in normal stars. We investigate how Coulomb screening affects the structure of a system of three alpha particles in such a plasma environment by precise three-body calculations within the Debye–Hückel approximation. A three-alpha model that has the Coulomb interaction modified in the Yukawa form is employed. Precise three-body wave functions are obtained by a superposition of correlated Gaussian basis with the aid of the stochastic variational method. The energy shifts of the Hoyle state due to the Coulomb screening are obtained as a function of the Debye screening length. The results, which automatically incorporate the finite-size effect of the Hoyle state, are consistent with the conventional result based on the Coulomb correction to the chemical potentials of ions that are regarded as point charges in a weakly coupled thermal plasma. We have given a theoretical basis to the conventional point-charge approach to the Coulomb screening problem relevant for nuclear reactions in normal stars by providing the first evaluation of the Coulomb corrections to the $Q$ value of the triple-alpha process that produces a finite-size Hoyle state.

An update on fine-tunings in the triple-alpha process

The triple-alpha process, whereby evolved stars create carbon and oxygen, is believed to be fine-tuned to a high degree. Such fine-tuning is suggested by the unusually strong temperature dependence of the triple-alpha reaction rate at stellar temperatures. This sensitivity is due to the resonant character of the triple-alpha process, which proceeds through the so-called “Hoyle state” of {}^{12}mathrm{C} with spin-parity 0^+. The question of fine-tuning can be studied within the ab initio framework of nuclear lattice effective field theory, which makes it possible to relate ad hoc changes in the energy of the Hoyle state to changes in the fundamental parameters of the nuclear Hamiltonian, which are the light quark mass m_q and the electromagnetic fine-structure constant alpha _mathrm{em}. Here, we update the effective field theory calculation of the sensitivity of the triple-alpha process to small changes in the fundamental parameters. In particular, we consider recent high-precision lattice QCD calculations of the nucleon axial coupling g_A, as well as new and more comprehensive results from stellar simulations of the production of carbon and oxygen. While the updated stellar simulations allow for much larger ad hoc shifts in the Hoyle state energy than previously thought, recent lattice QCD results for the nucleon S-wave singlet and triplet scattering lengths now disfavor the “no fine-tuning scenario” for the light quark mass m_q.

Enhancement of the Triple Alpha Rate in a Hot Dense Medium.

In a sufficiently hot and dense astrophysical environment the rate of the triple-alpha (3α) reaction can increase greatly over the value appropriate for helium burning stars owing to hadronically induced deexcitation of the Hoyle state. In this Letter we use a statistical model to evaluate the enhancement as a function of temperature and density. For a density of 10^{6} g cm^{-3} enhancements can exceed a factor of 100. In high temperature or density situations, the enhanced 3α rate is a better estimate of this rate and should be used in these circumstances. We then examine the effect of these enhancements on production of ^{12}C in the neutrino wind following a supernova explosion and in an x-ray burster.

On the habitability of universes without stable deuterium

In both stars and in the early universe, the production of deuterium is the first step on the way to producing heavier nuclei. If the strong force were slightly weaker, then deuterium would not be stable, and many authors have noted that nuclesynthesis would be compromised so that helium production could not proceed through standard reaction chains. Motivated by the possibility that other regions of space-time could have different values for the fundamental constants, this paper considers stellar evolution in universes without stable deuterium and argues that such universes can remain habitable. Even in universes with no stellar nucleosynthesis, stars can form and will generate energy through gravitational contraction. Using both analytic estimates and a state-of-the-art stellar evolution code, we show that such stars can be sufficiently luminous and long-lived to support life. Stars with initial masses that exceed the Chandrasekhar mass cannot be supported by degeneracy pressure and will explode at the end of their contraction phase. The resulting explosive nucleosynthesis can thus provide the universe with some heavy elements. We also explore the possibility that helium can be produced in stellar cores through a triple-nucleon reaction that is roughly analogous to the triple-alpha reaction that operates in our universe. Stars burning hydrogen through this process are somewhat hotter than those in our universe, but otherwise play the same role. Next we show that with even trace amounts (metallicity Z∼10−10) of heavy elements — produced through the triple-nucleon process or by explosive nucleosynthesis — the CNO cycle can operate and allow stars to function. Finally, we consider Big Bang Nucleosynthesis without stable deuterium and find that only trace amounts of helium are produced, with even smaller abundances of other nuclei. With stars evolving through gravitational contraction, explosive nucleosynthesis, the triple-nucleon reaction, and the CNO cycle, universes with no stable deuterium are thus potentially habitable, contrary to many previous claims.

Stellar helium burning in other universes: A solution to the triple alpha fine-tuning problem

Motivated by the possible existence of other universes, with different values for the fundamental constants, this paper considers stellar models in universes where 8Be is stable. Many previous authors have noted that stars in our universe would have difficulty producing carbon and other heavy elements in the absence of the well-known 12C resonance at 7.6 MeV. This resonance is necessary because 8Be is unstable in our universe, so that carbon must be produced via the triple alpha reaction to achieve the requisite abundance. Although a moderate change in the energy of the resonance (200–300 keV) will indeed affect carbon production, an even smaller change in the binding energy of beryllium (∼100 keV) would allow 8Be to be stable. A stable isotope with A=8 would obviate the need for the triple alpha process in general, and the 12C resonance in particular, for carbon production. This paper explores the possibility that 8Be can be stable in other universes. Simple nuclear considerations indicate that bound states can be realized, with binding energy ∼0.1−1 MeV, if the fundamental constants vary by a ∼few−10%. In such cases, 8Be can be synthesized through helium burning, and 12C can be produced later through nuclear burning of beryllium. This paper focuses on stellar models that burn helium into beryllium; once the universe in question has a supply of stable beryllium, carbon production can take place during subsequent evolution in the same star or in later stellar generations. Using both a semi-analytic stellar structure model as well as a state-of-the-art stellar evolution code, we find that viable stellar configurations that produce beryllium exist over a wide range of parameter space. Finally, we demonstrate that carbon can be produced during later evolutionary stages.

Ab initio alpha-alpha scattering.

Processes such as the scattering of alpha particles ((4)He), the triple-alpha reaction, and alpha capture play a major role in stellar nucleosynthesis. In particular, alpha capture on carbon determines the ratio of carbon to oxygen during helium burning, and affects subsequent carbon, neon, oxygen, and silicon burning stages. It also substantially affects models of thermonuclear type Ia supernovae, owing to carbon detonation in accreting carbon-oxygen white-dwarf stars. In these reactions, the accurate calculation of the elastic scattering of alpha particles and alpha-like nuclei--nuclei with even and equal numbers of protons and neutrons--is important for understanding background and resonant scattering contributions. First-principles calculations of processes involving alpha particles and alpha-like nuclei have so far been impractical, owing to the exponential growth of the number of computational operations with the number of particles. Here we describe an ab initio calculation of alpha-alpha scattering that uses lattice Monte Carlo simulations. We use lattice effective field theory to describe the low-energy interactions of protons and neutrons, and apply a technique called the 'adiabatic projection method' to reduce the eight-body system to a two-cluster system. We take advantage of the computational efficiency and the more favourable scaling with system size of auxiliary-field Monte Carlo simulations to compute an ab initio effective Hamiltonian for the two clusters. We find promising agreement between lattice results and experimental phase shifts for s-wave and d-wave scattering. The approximately quadratic scaling of computational operations with particle number suggests that it should be possible to compute alpha scattering and capture on carbon and oxygen in the near future. The methods described here can be applied to ultracold atomic few-body systems as well as to hadronic systems using lattice quantum chromodynamics to describe the interactions of quarks and gluons.

Three-Body Calculation of 4He(αα,γ)12C Reaction at Stellar Energies**Supported by the University of Birjand.

The triple-alpha reaction is the key to our understanding about the nucleosynthesis and the observed abundance of 12C in stars. On the basis of our model, the triple-alpha radiative capture process is studied by using the three-body Faddeev approach as well as two- and three-body electromagnetic currents. The bound and resonance states of 12C are calculated via an inverse process: three-α photodisintegration of a 12C nucleus.

Cluster states and container picture in light nuclei, and triple-alpha reaction rate

The excited states in 12C are investigated by using an extended version of the so- called Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function, where both the 3α condensate and 8Be + α cluster asymptotic configurations are included. We focus on the structures of the “Hoyle band” states, 2+2, and 4+2 states, which are recently observed above the Hoyle state, and of the 0+3 and 0+4 states, which are also quite recently identified in experiment. We show that the Hoyle band is not simply considered to be the 8Be(0+) + α rotation as suggested by previous cluster model calculations, nor to be a rotation of a rigid-body triangle-shaped object composed of the 3α particles. We also discuss the rate of the triple-alpha radiative capture reaction, applyng the imaginary-time method. Results of the triple-alpha reaction rate are consistent with NACRE rate for both high (≈ 109K) and low (≈ 107 K) temperatures. We show that the rate of the imaginary-time calculation in coupled-channels approach has a large enhancement for low temperatures if we truncate the number of channels.

Three-α model calculations of low-lying 12C states and the triple-α reaction

Properties of some 12C resonant states at low energies are studied in three-α- particle model. Calculations for breakup reactions of 12 C bound state leading to three-body continuum states are performed at energies up to a few MeV above the breakup threshold by applying the Faddeev three-body formalism in coordinate space. Calculated cross sections reveal some resonant peaks. Decay modes and the structure at interior region of these resonant states as well as their effects on the triple-alpha reaction rate will be reported.

Low-Energy 12C States in Three-α Model

Cross sections for three-α photodisintegration process of the12C nucleus are calculated by a Faddeev formalism, from which 0+- and 2+ low-lying resonant 12C states are studied. The triple-alpha reaction rate is evaluated from the calculated cross sections of the disintegration process.

Cumulative physical uncertainty in modern stellar models

Using our updated stellar evolutionary code, we quantitatively evaluate the effects of the uncertainties in the main physical inputs on the evolutionary characteristics of low mass stars from the main sequence to the zero age horizontal branch (ZAHB). We calculated more than 3000 stellar tracks and isochrones, with updated solar mixture, by changing the following physical inputs within their current range of uncertainty: 1H(p,nu e+)2H, 14N(p,gamma)15O, and triple-alpha reaction rates, radiative and conductive opacities, neutrino energy losses, and microscopic diffusion velocities. We performed a systematic variation on a fixed grid, in a way to obtain a full crossing of the perturbed input values. The effect of the variations of the chosen physical inputs on relevant stellar evolutionary features, such as the turn-off luminosity, the central hydrogen exhaustion time, the red-giant branch (RGB) tip luminosity, the helium core mass, and the ZAHB luminosity in the RR Lyrae region are statistically analyzed. For a 0.9 Msun model, the cumulative uncertainty on the turn-off, the RGB tip, and the ZAHB luminosities accounts for $\pm$ 0.02 dex, $\pm$ 0.03 dex, and $\pm$ 0.045 dex respectively, while the central hydrogen exhaustion time varies of about $\pm$ 0.7 Gyr. The most relevant effect is due to the radiative opacities uncertainty; for the later evolutionary stages the second most important effect is due to the triple-alpha reaction rate uncertainty. For an isochrone of 12 Gyr, we find that the isochrone turn-off log luminosity varies of $\pm$ 0.013 dex, the mass at the isochrone turn-off varies of $\pm$ 0.015 Msun, and the difference between ZAHB and turn-off log-luminosity varies of $\pm$ 0.05 dex. The effect of the physical uncertainty affecting the age inferred from turn-off luminosity and from the vertical method are of $\pm$ 0.375 Gyr and $\pm$ 1.25 Gyr respectively.

Variation of fundamental constants and the role ofA=5andA=8nuclei on primordial nucleosynthesis

We investigate the effect of a variation of fundamental constants on primordial element production in big bang nucleosynthesis (BBN). We focus on the effect of a possible change in the nucleon-nucleon interaction on nuclear reaction rates involving the A=5 (Li-5 and He-5) and A=8 (Be-8) unstable nuclei and complement earlier work on its effect on the binding energy of deuterium. The reaction rates for He3(d,p)He4 and H3(d,n)He4 are dominated by the properties of broad analog resonances in He-5 and Li-5 compound nuclei respectively. While the triple alpha process is normally not effective in BBN, its rate is very sensitive to the position of the "Hoyle state" and could in principle be drastically affected if Be-8 were stable during BBN. The nuclear properties (resonance energies in He-5 and Li-5 nuclei, and the binding energies of Be-8 and D) are all computed in a consistent way using a microscopic cluster model. The n(p,gamma)d, He3(d,p)He4 and H3(d,n)He4 and triple-alpha reaction rates are subsequently calculated as a function of the nucleon-nucleon interaction that can be related to the fundamental constants. We found that the effect of the variation of constants on the He3(d,p)He4 and H3(d,n)He4 and triple-alpha reaction rates is not sufficient to induce a significant effect on BBN, even if Be-8 was stable. In particular, no significant production of carbon by the triple alpha reaction is found when compared to standard BBN. We also update our previous analysis on the effect of a variation of constants on the n(p,gamma)d reaction rate.

Faddeev Three-body Calculation of Triple-Alpha Reaction

The triple-alpha (3α) process, in which three 4He nuclei are transformed into a 12C nucleus, is studied in terms of a three-alpha (3-α) model. The reaction rate of the process is calculated via an inverse process, 3-α photodisintegration of a 12C nucleus. Both of 3-α bound and -continuum states are calculated by a Faddeev method with accommodating the long range Coulomb interaction. Results of the 3α reaction rate are about 103 times larger than a standard rate from the Nuclear Astrophysics Compilation of Reaction Rates (NACRE) at a low temperature (T = 107 K), which means our results are remarkably smaller than recent three-body calculations by the method of continuum-discretized coupled-channel.