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Stellar evolution

Stellar evolution depends on nuclear, plasma and atomic physics and aspects related to theoretical modelling and hydrodynamics [5]. Investigations on important nuclear reactions in astrophysics were pioneered by Fowler and collaborators, with many open questions left until present [6]. A few are (a) pp-chain reactions in H-burning, which affect sub-solar and solar type stars and are directly connected to the solar neutrino emission, e.g. 3He( $\alpha, \gamma)^7$Be, 7Be( $ p,\gamma)^8$B 7Li( $p,\alpha)^4$He, CNO-cycle reactions like 14N( $p,\gamma)^{15}$O and 17,18O($p,\alpha$)14,15N, which directly relate to the surface abundances in intermediate mass stars, NeNa-cycle reactions in intermediate and massive stars, (b) the 12C( $\alpha,\gamma)^{16}$O reaction in He-burning, and (c) fusion reactions of late burning stages, e.g. 12C+12C, which are not well known at low energies.
 

    Massive stars, with initial masses beyond roughly 8 M$_\odot$, form an Fe-core after completing all nuclear burning stages. Its size is strongly dependent on the 12C( $\alpha,\gamma)^{16}$O rate in He-burning, the treatment of convection, and the electron captures on nuclei in O- and Si-burning. The evolution after the onset of C-burning takes only several hundred to a 1000 years, due to efficient energy loss via neutrinos, rather than radiation. Low and intermediate mass stars lose mass by efficient stellar winds which leads to remaining stable C/O-cores below the Chandrasekhar limit after H- and He-burning. At high densities/low temperatures Fermions form a degenerate gas and the pressure depends only on the stellar density. In the nonrelativistic limit of Fermi energies the pressure is proportional to $\rho^{5/3}$, in the relativistic limit towards higher densities the pressure scales as $\rho^{4/3}$. Powers less or equal to 4/3 cannot support a stable object, which is the reason for the Chandrasekhar mass limit of white dwarfs (degenerate electrons) and the maximum neutron star mass (degenerate nucleons), where the uncertainties due to nuclear interactions play a role as well. Their formation will be discussed in section 2.3. Based on stellar evolution models the energy generation in the Sun is provided to 98% by the nuclear fusion reactions of the pp-chains, while the CNO-cycle contributes 2%. Both hydrogen burning mechanisms are accompanied by the emission of neutrinos [7], which can provide immediate information on the details of the composition and the physical conditions at the solar centre. The detection of solar neutrinos is, therefore, a unique tool for the investigation of basic properties of the Sun, a typical star in the phase of core H-burning. Such information is complemented by helioseismology which can, due to the properties of the oscillation modes, deduce the radial dependence of composition as well as physical conditions. Discrepancies with model predictions give rise to the solar neutrino problem.

Figure: The neutrino spectrum of weak interactions in the pp-cycle (1H( $p,e^+\nu)^2$H, 1H( $e^-p,\nu)^2$H, 7Be( $e^-,\nu)^7$Li, 8B($e^+\nu)^8$Be) predicted by standard solar models [7], indicating also the different detector thresholds.
\begin{figure}\epsfig{file=astro/fig1.eps,width=\columnwidth}\end{figure}
 

The existing four solar neutrino experiments have different neutrino energy thresholds: (1) the HOMESTAKE gold-mine, using the inverse $\beta$-decay reaction 37Cl( $\nu_e,e^-)^{37}$Ar with a threshold energy of $814\,$keV, (2) the European GALLEX-experiment, based on the reaction 71Ga( $\nu_e,e^-)^{71}$Ge with a uniquely low detection threshold of $233\,$keV, and (3) the Soviet-American Gallium Experiment SAGE which uses the same detection reaction as GALLEX but a different chemical composition of the Ga target; (4) finally, there are the Japanese experiments KAMIOKANDE and SUPERKAMIOKANDE, which are based on the detection of $\nu$-e scattering via Cerenkov light in large volume underground water tanks with an energy threshold of $7.5\,$MeV due to the radioactive background. The Kamiokande experiments are only sensitive to the 8B-neutrinos, but have additional direction information and can observe day/night effects. They see about 50% of the expected neutrino flux. The Homestake results, which should be dominated to 80% by the 8B neutrinos and to 20% by the 7Be and CNO neutrinos, show only 30% of the expected neutrino flux. GALLEX and SAGE, the only experiments detecting the high flux of pp-neutrinos, see about 50% of the expected total flux. Given these significantly suppressed neutrino rates, the standard model - being supported by helioseismology - leaves not much room for conventional solutions. Numerous studies indicate that neutrino oscillations appear to be the most likely explanation for the solar neutrino problem. This could be vacuum neutrino oscillations in space or the Mikheyev, Smirnov, Wolfenstein effect (MSW), inverting the neutrino mass hierarchy in (solar) matter. This would be a spectacular first indication for "new physics" beyond the standard model of electroweak interaction. For an unambiguous proof of these possible solutions and/or potential conclusions about neutrino properties, the input parameters, like nuclear reaction rates at solar energies and the solar neutrino energy spectrum, must be placed on a substantially improved basis. This can be achieved by ultra-low energy cross section measurements and a series of second-generation solar neutrino experiments. He-burning can provide neutrons in a stellar environment, produced e.g. by the sources 13$(\alpha,n)^{16}$O or 22Ne $(\alpha,n)^{25}$Mg. The sequence 14N( $\alpha,\gamma)^{18}$F( $\beta^+\nu)^{18}$O( $\alpha,\gamma)^{22}$Ne($\alpha,n$) produces 22Ne, with 14N being the main product of the CNO-cycle in the preceeding H-burning. 13C can only be existent in sufficient amounts in He-burning environments, when some mixed in hydrogen acts on the abundant 12C nucleus via 12C( $p,\gamma)^{13}$N( $\beta^+)^{13}$C. Both neutron sources lead to the s-process, being characterised by neutron captures which are slow in comparison to beta-decay rates and produce about one half of the observed abundances of the nuclides above $A\sim$ 60. It is recognised to occur in at least two different astrophysical sites, the weak component accounting for most of the s-nuclei below the Kr-Rb-Sr abundance peak, and the main component accounting for heavier nuclei up to Pb. A third site (strong component) might be required to account for about 50% of the double magic nucleus 208Pb [8]. The main s-process component is due to the thermally-pulsing phase of shell He- and H-burning in low mass stars ($M \le$ 3 M$_\odot$) and primarily driven by 13C( $\alpha,n)^{16}$O rather than 22Ne( $\alpha,n)^{25}$Mg . Its composition can condensate into dust when expelled in form of stellar winds. Such dust grains are actually found in the form of incorporated pre-solar grain inclusions in solar system meteorites which show the expected isotopic anomalies [9]. Recent research indicates that 13$(\alpha,n)^{16}$O burns in the interpulse phases at lower temperatures, i.e. lower neutron energies ($\sim$ 8 keV), where cross sections are often badly known. Core He-burning with the 22Ne source contributes to the weak s-component which is a complex combination of core He-, and shell C-, and Ne-burning in massive stars. The latter two also involve neutron captures on a number of unstable nuclei, traditionally ascribed to the rapid neutron capture process (r-process).
Over the past 10 years impressive improvements have been achieved in the nuclear input data, mainly the stellar neutron capture cross sections for stable nuclei above Fe [8], while for light and intermediate mass nuclei, including C, O, Ne, Mg, Si, Ar, Ca, and Ti isotopes, which play a role as neutron poisons and in the composition of wind ejecta and dust grains, mostly old cross sections are available with generally large uncertainties. Experimental cross sections are also required for long-lived unstable nuclides involved in branchings due to comparable beta-decay and neutron capture rates [8]. Improved measurements of the small cross sections at neutron shell closures are necessary for a better description of the s-process and for discriminating among different stellar environments. Among the most important and difficult examples is the branching occurring at 85Kr, which involves Kr, the Rb and Sr isotopes. Decay properties of fully ionized atoms, as occurring in stellar environments, differ from atomic decays and can be investigated at radioactive ion beam facilities. Important for the study of the weak s-process neutron source is the direct measurement of low energy resonances in 18O($\alpha$,$\gamma$)22Ne and 22Ne($\alpha$,n)25Mg. 


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