The reactions 12 C( 12 C,a) 20 Ne, 12 C( 12 C,^) 23 Na, and 12 C( 12 C,w) 23 Mg have been studied to provide reliable predictions of their cross-sections in the energy region of interest in stellar carbon burning. Many excited-state transitions have been observed for the a-particles and protons. Measurements for these particles have been made in the center-of-mass energy range 3.23-8.75 MeV. The relatively small yield of the 12 C( 12 C,w) 23 Mg reaction has been investigated from 4.25 to 6.25 MeV. The new results for these reactions lead to lower cross-sections than previously estimated for the region of astrophysical interest.The 12 C + 12 C reaction in stars has aroused new interest recently, owing to strong evidence that in many cases a substantial fraction of 12 C produced in the helium-burning process is not converted to 16 0 (Stephenson 1966;Loebenstein et al. 1967). The carbon burning is expected to occur at temperatures near 10 9 ° K, which corresponds to an effective thermal energy Eq of approximately 2 MeV. At such a temperature, energy losses due to the proposed neutrino process e + + p + P may dominate the radiation loss and considerably reduce the lifetime of the carbon-burning stage. This problem has been discussed in detail by Hayashi, Höshi, and Sugimoto (1962).The experimental study of the reaction 12 C + 12 C is quite complicated because of the large number of final states, as shown in the energy-level diagram of Figure 1. The possible end products are: 23 Na + p, 23 Mg + n, 20 Ne + a, 16 0 + 2a, and 24 Mg + 7. The Coulomb barrier for 12 C + 12 C is about 7 MeV in the center-of-mass system. For convenience, all energies in the 12 C + 12 C system will be given in the center-of-mass system. Previous experimental investigations by Almqvist, Bromley, and Kuehner (1960) and by Almqvist et al. (1964) have shown that the a-particle and proton channels produce the major yield while the neutron channel makes only a small contribution. In their experiment, the a-particle-plus-proton cross-section was measured between 5.0 and 12.5 MeV. All charged particles were counted in a solid-state detector at several angles, and the angular distributions were integrated to obtain the total cross-section. The number of excited states detected, however, was limited by the fairly high detector-cutoff energies of 7.5 and 6 MeV (laboratory) for a-particles and protons, respectively. Reeves (1966) has used these data for an extrapolation of the cross-section down to astrophysical energies. His results will be discussed later. Arnett and Truran (1969) have reexamined the process of carbon burning with regard to nucleosynthesis and energy generation. They have set up a nuclear-reaction network among the elements between carbon and sulfur and have solved the coupled non-linear equations numerically under a variety of conditions. Models for carbon-burning stars including evolutionary effects have also been studied recently by Rakavy, Shaviv, and Zinamon (1967), Murai et al. (1968), Vila (1966), and Beaudet and Salpeter ...

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The most recent observations of the abundances of oxygen, sodium, magnesium, and aluminum provide strong support for the idea that "deep mixing" occurs within Ml3 giants. In deep-mixing scenerios, material from the envelopes of globular-cluster giants is assumed to be mixed well into the hydrogen-burning shells of some (but not all) stars. There the abundances of a number of light elements are reshuffled by proton capture before the material is returned to the envelope above. The recent observations also put strong constraints on the conditions under which the reshuffling occurs. Shetrone's (BAAS, 27, 1432(BAAS, 27, 1995 AJ, 112, 2639 AJ, 112, , 1996 estimates of magnesium isotope ratios provide especially powerful constraints on the reshuffling temperature for the brightest aluminum-rich Ml3 giants. We find that proton-capture nucleosynthesis can give an excellent account of the abundances of aluminum and the isotopes of magnesium in the brightest aluminum-rich giants in Ml3-and of the abundances of oxygen and sodium as well. In order to match the observations, the abundances in about ninety percent of the material that makes up the envelopes of these stars would have to have been reshuffled by proton capture at a temperature near 70 million kelvins (MK). The maximum temperatures in the hydrogen shells of canonical models for bright M13 giants is only ~55 MK. We briefly discuss ways in which the observations and the models might be reconciled. Our "best bet" is that hydrogen burning occurs intermittently (at higher temperatures) in some Ml3 giants rather than steadily (at lower temperatures) as it does in canonical models. We also find that recent rates for the Ne-Na cycle reactions (El Eid and Champagne, ApJ, 451, 298, 1995) suggest solutions to two earlier puzzles: the shape of the Na-0 abundance anticorrelation observed in globular-cluster giants and the Na-N correlation observed in field halo giants.

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The question of how long it takes an inverted point-mass pendulum to fall according to classical, semiclassical, and quantum theories is examined. The semiclassical analysis is based on the uncertainty introduced by measurement.