Proton-Capture Rates on Carbon Isotopes and Their Impact on the Astrophysical

The ^{12}C/^{13}C ratio is a significant indicator of nucleosynthesis and mixing processes during hydrogen burning in stars. Its value mainly depends on the relative rates of the ^{12}C(p,γ)^{13}N and ^{13}C(p,γ)^{14}N reactions. Both reactions have been studied at the Laboratory for Underground Nuclear Astrophysics (LUNA) in Italy down to the lowest energies to date (E_{c.m.}=60 keV) reaching for the first time the high energy tail of hydrogen burning in the shell of giant stars. Our cross sections, obtained with both prompt γ-ray detection and activation measurements, are the most precise to date with overall systematic uncertainties of 7%-8%. Compared with most of the literature, our results are systematically lower, by 25% for the ^{12}C(p,γ)^{13}N reaction and by 30% for ^{13}C(p,γ)^{14}N. We provide the most precise value up to now of 3.6±0.4 in the 20-140 MK range for the lowest possible ^{12}C/^{13}C ratio that can be produced during H burning in giant stars.

Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems.

High-temperature series are computed for a generalized three-dimensional Ising model with arbitrary potential. Three specific "improved" potentials (suppressing leading scaling corrections) are selected by Monte Carlo computation. Critical exponents are extracted from high-temperature series specialized to improved potentials, achieving high accuracy; our best estimates are gamma=1.2371(4), nu=0.630 02(23), alpha=0.1099(7), eta=0.0364(4), beta=0.326 48(18). By the same technique, the coefficients of the small-field expansion for the effective potential (Helmholtz free energy) are computed. These results are applied to the construction of parametric representations of the critical equation of state. A systematic approximation scheme, based on a global stationarity condition, is introduced (the lowest-order approximation reproduces the linear parametric model). This scheme is used for an accurate determination of universal ratios of amplitudes. A comparison with other theoretical and experimental determinations of universal quantities is presented.