Gamow Peak Energy Research Articles

Reinvestigating the Gamow Factor of Reactions on Light Nuclei

We present a modified Gamow factor by reinvestigating the conventional assumptions used in its derivation. The conventional Gamow factor, factorized from the total cross section, effectively describes the penetration probabilities (PPs) in low-energy nuclear reactions under the assumption of particle energies significantly lower than the Coulomb barrier. However, we find that the assumption is invalid for light nuclei, resulting in PPs that depend on the nuclear potential depth for such nuclei. By adopting a potential depth fitted to experimental fusion cross sections, we demonstrate that PPs for light nuclei (D+D, D+T, D+3He, p+D, p+6Li, and p+7Li) become higher than those predicted by the conventional form near the Coulomb barrier. This reduces the Gamow peak energy by a factor of 5.3 maximally compared to the conventional form. Furthermore, we show that the enhancement factor due to the Debye screening effects in the solar core can be reduced by approximately 5%–10% due to the modified PP. Our findings hold implications for evaluating the available energy region in low-energy reaction experiments based on the Gamow peak energy region and for understanding electron screening effects in typical astrophysical environments.

Cluster effective field theory and nuclear reactions

An effective field theory (EFT) for a nuclear reaction at low energies is studied. The astrophysical $S$-factor of radiative $\alpha$ capture on $^{12}$C at the Gamow-peak energy, $T_G=0.3$ MeV, is a fundamental quantity in nuclear-astrophysics, and we construct an EFT for the reaction. To fix parameters appearing in the effective Lagrangian, the EFT is applied to the study for three reactions: elastic $\alpha$-$^{12}$C scattering at low energies, $E1$ transition of radiative $\alpha$ capture on $^{12}$C, and $\beta$ delayed $\alpha$ emission from $^{16}$N. We report an estimate of the $S_{E1}$-factor of the reaction through the $E1$ transition at $T_G$ by employing the EFT. We also discuss applications of EFTs to nuclear reactions at low energies.

SE1 factor of radiative α capture on C12 in cluster effective field theory

The $S_{E1}$-factor of radiative $\alpha$-capture on $^{12}$C is studied in effective field theory up to next-to-leading order. A modification of the counting rules for the radiative capture amplitudes is discussed. We find that only two unfixed parameters remain in the amplitudes, and those two parameters are fitted to the experimental $S_{E1}$ data. An $S_{E1}$ factor is calculated at the Gamow-peak energy as $S_{E1}=59\pm 3$ keV$\cdot$b, and the result is found to be about 30% smaller than the estimates reported recently. An uncertainty of the estimate in the present work is also discussed.

Measurement of fusion cross sections for 16O+16O

In earlier works, the fusion cross section for the 16O+16O reaction has been measured using different techniques. In the present work, we have obtained an experimental excitation function for 16O+16O using γ-ray spectroscopy. The measurements were performed at center-of-mass energies between 8.28 and 12.25 MeV. The theoretical predictions obtained with a coupled-channel model are consistent with the experimental data. From our analyses, the extrapolated S-factor value at 6.6 MeV, corresponding to the Gamow peak energy for core oxygen burning conditions, is about 3.6 × 1025 MeV barn.

Spectroscopy of high lying resonances in9Be produced with radioactive8Li beams

We present the results of the 8Li(p,α)5He and 8Li(p,p)8Li reactions measured at the RIBRAS (Radioactive Ion Beams in Brazil) system. The experiment was realized in inverse kinematics using a thick [CH2]n polyethylene target and an incident 8Li beam, produced by RIBRAS. Using the thick target method, the complete excitation function could be measured between Ecm = 0.2 - 2.1 MeV, which includes the Gamow peak energy region. The excitation function of the 8Li(p,α)5He reaction, populating resonances between 16.888 and 19.0 MeV in 9Be, was obtained[1] and the resonances were fitted using R-matrix calculations. This study shed light on spins, parities, partial widths and isospin values of high lying resonances in 9Be. The measurement of the resonant elastic scattering 8Li(p,p)8Li populating resonances in the same energy region can constrain the resonance parameters. Preliminary results of the elastic scattering are also presented. © Owned by the authors, published by EDP Sciences, 2014.

Gamow peak approximation near strong resonances

We discuss the most effective energy range for charged-particle-induced reactions in a plasma environment at a given plasma temperature. The correspondence between the plasma temperature and the most effective energy should be modified from the one given by the Gamow peak energy, in the presence of a significant incident-energy dependence in the astrophysical $S$ factor as in the case of resonant reactions. The suggested modification of the effective energy range is important not only in thermonuclear reactions at high temperature in the stellar environment, e.g., in advanced burning stages of massive stars and in explosive stellar environments, as has been already claimed, but also in the application of nuclear reactions driven by ultra-intense laser-pulse irradiation.

Revision of the15N(p,γ)16O reaction rate and oxygen abundance in H-burning zones

The NO cycle takes place in the deepest layer of a H-burning core or shell, when the temperature exceeds T {\simeq} 30 {\cdot} 106 K. The O depletion observed in some globular cluster giant stars, always associated with a Na enhancement, may be due to either a deep mixing during the RGB (red giant branch) phase of the star or to the pollution of the primordial gas by an early population of massive AGB (asymptotic giant branch) stars, whose chemical composition was modified by the hot bottom burning. In both cases, the NO cycle is responsible for the O depletion. The activation of this cycle depends on the rate of the 15N(p,{\gamma})16O reaction. A precise evaluation of this reaction rate at temperatures as low as experienced in H-burning zones in stellar interiors is mandatory to understand the observed O abundances. We present a new measurement of the 15N(p,{\gamma})16O reaction performed at LUNA covering for the first time the center of mass energy range 70-370 keV, which corresponds to stellar temperatures between 65 {\cdot} 106 K and 780 {\cdot}106 K. This range includes the 15N(p,{\gamma})16O Gamow-peak energy of explosive H-burning taking place in the external layer of a nova and the one of the hot bottom burning (HBB) nucleosynthesis occurring in massive AGB stars. With the present data, we are also able to confirm the result of the previous R-matrix extrapolation. In particular, in the temperature range of astrophysical interest, the new rate is about a factor of 2 smaller than reported in the widely adopted compilation of reaction rates (NACRE or CF88) and the uncertainty is now reduced down to the 10% level.

POSSIBLE RESONANCES IN THE12C +12C FUSION RATE AND SUPERBURST IGNITION

Observationally inferred superburst ignition depths are shallower than models predict. We address this discrepancy by reexamining the superburst trigger mechanism. We first explore the hypothesis of Kuulkers et al. that exothermic electron captures trigger superbursts. We find that all electron capture reactions are thermally stable in accreting neutron star oceans and thus are not a viable trigger mechanism. Fusion reactions other than {sup 12}C + {sup 12}C are infeasible as well since the possible reactants either deplete at much shallower depths or have prohibitively large Coulomb barriers. Thus, we confirm the proposal of Cumming and Bildsten and Strohmayer and Brown that {sup 12}C + {sup 12}C triggers superbursts. We then examine the {sup 12}C + {sup 12}C fusion rate. The reaction cross section is experimentally unknown at astrophysically relevant energies, but resonances exist in the {sup 12}C + {sup 12}C system throughout the entire measured energy range. Thus it is likely, and in fact has been predicted, that a resonance exists near the Gamow peak energy E {sup pk} {approx} 1.5 MeV. For such a hypothetical 1.5 MeV resonance, we derive both a fiducial value and upper limit to the resonance strength ({omega}{gamma}){sub R} and find that such a resonancemore » could decrease the theoretically predicted superburst ignition depth by up to a factor of 4; in this case, observationally inferred superburst ignition depths would accord with model predictions for a range of plausible neutron star parameters. Said differently, such a resonance would decrease the temperature required for unstable {sup 12}C ignition at a column depth 10{sup 12} g cm{sup -2} from 6 x 10{sup 8} K to 5 x 10{sup 8} K. A resonance at 1.5 MeV would not strongly affect the ignition density of Type Ia supernovae, but it would lower the temperature at which {sup 12}C ignites in massive post-main-sequence stars. Determining the existence of a strong resonance in the Gamow window requires measurements of the {sup 12}C + {sup 12}C cross section down to a center-of-mass energy near 1.5 MeV, which is within reach of the proposed DUSEL facility.« less

Measurement of the 16N(α, n) reaction cross section

In order to study the starting point of the r-process, the 16N(α, n) cross section has been measured directly at the energy region of E cm = 1.5 – 4.0 MeV, corresponding to the Gamow peak energy T 9 = 2 – 6.

Weak proton capture on3He

The astrophysical S factor for the proton weak capture on 3He is calculated with correlated-hyperspherical-harmonics bound and continuum wave functions corresponding to realistic Hamiltonians consisting of the Argonne v14 or Argonne v18 two-nucleon and Urbana-VIII or Urbana-IX three-nucleon interactions. The nuclear weak charge and current operators have vector and axial-vector components that include one- and many-body terms. All possible multipole transitions connecting any of the p-3He S- and P-wave channels to the 4He bound state are considered. The S factor at a p-3He center-of-mass energy of 10 keV, close to the Gamow-peak energy, is predicted to be 10.1×10-20 keV b with the AV18/UIX Hamiltonian, a factor of ≃4.5 larger than the value adopted in the standard solar model. The P-wave transitions are found to be important, contributing about 40% of the calculated S factor. The energy dependence is rather weak: the AV18/UIX zero-energy S factor is 9.64×10^-20 keV b, only 5% smaller than the 10 keV result quoted above. The model dependence is also found to be weak: the zero-energy S factor is calculated to be 10.2×10^-20 keV b with the older AV14/UVIII model, only 6% larger than the AV18/UIX result. Our best estimate for the S factor at 10 keV is therefore (10.1±0.6)×10^-20 keV b, when the theoretical uncertainty due to the model dependence is included. This value for the calculated S factor is not as large as determined in fits to the Super-Kamiokande data in which the hep flux normalization is free. However, the precise calculation of the S factor and the consequent absolute prediction for the hep neutrino flux will allow much greater discrimination among proposed solar neutrino oscillation solutions.