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The location of electron capture heat sources in the crust of accreting neutron stars depends on the masses of extremely neutron-rich nuclei. We present first results from a new implementation of the time-of-flight technique to measure nuclear masses of rare isotopes at the National Superconducting Cyclotron Laboratory. The masses of 16 neutron-rich nuclei in the scandium -- nickel range were determined simultaneously, improving the accuracy compared to previous data in 12 cases. The masses of $^{61}${V}, $^{63}${Cr}, $^{66}${Mn}, and $^{74}${Ni} were measured for the first time with mass excesses of $-30.510(890)$ MeV, $-35.280(650)$ MeV, $-36.900(790)$ MeV, and $-49.210(990)$ MeV, respectively. With the measurement of the $^{66}$Mn mass, the locations of the two dominant electron capture heat sources in the outer crust of accreting neutron stars that exhibit superbursts are now experimentally constrained. We find that the location of the $^{66}$Fe$\rightarrow^{66}$Mn electron capture transition occurs significantly closer to the surface than previously assumed because our new experimental Q-value is 2.1 MeV (2.6$\sigma$) smaller than predicted by the FRDM mass model., Comment: 4 pages, 3 figures

The reaction 17O({\alpha},{\gamma})21Ne has been measured by in-beam gamma spectroscopy for the first time in the energy range E{\alpha} = 750 keV to 1650 keV using highly enriched anodized Ta2(17O)5 targets. Resonances were found at E({\alpha}) = 1002 keV, 1386 keV and 1619 keV. Their strengths and primary gamma-ray branchings are given. The new results exclude the low reaction rate of Descouvemont and support the rate of Caughlan and Fowler. Implications for the neutron poisoning efficiency of 16O in the weak s process are discussed., Comment: 5 pages, 5 figures, 2 tables, Accepted for publication in Phys. Rev. C

The 15N(p,g)16O reaction represents a break out reaction linking the first and second cycle of the CNO cycles redistributing the carbon and nitrogen abundances into the oxygen range. The reaction is dominated by two broad resonances at Ep = 338 keV and 1028 keV and a Direct Capture contribution to the ground state of 16O. Interference effects between these contributions in both the low energy region (Ep < 338 keV) and in between the two resonances (338

Nuclear reaction rates determine the abundances of isotopes in stellar burning processes. A multitude of reactions determine the reaction flow pattern which is described in terms of reaction network simulations. The reaction rates are determined by laboratory experiments supplemented by nuclear reaction and structure theory. We will discuss the experimental approach as well as the theoretical tools for obtaining the stellar reaction rates. A detailed analysis of a reaction is only possible for a few selected cases which will be highlighted in this section. The bulk of nuclear reaction processes is however described in terms of a statistical model approach, which relies on global nuclear structure and reaction parameters such as level density and mass and barrier penetration, respectively. We will discuss a variety of experimental facilities and techniques used in the field, this includes low energy stable beam experiments, measurements at radioactive beam accelerators, and neutron beam facilities., Comment: 28 pages, 2 figures; appeared in "Astronomy with Radioactivities", as Chapter 9, Eds. Roland Diehl, Dieter H. Hartmann, and Nikos Prantzos, Springer Lect. Notes in Physics, Vol. 812, 2010; differences to published version: corrected Eqs. 9.6, 9.8, 9.10; updated or replaced references; modified layout

We propose a physically transparent analytic model of astrophysical S-factors as a function of a center-of-mass energy E of colliding nuclei (below and above the Coulomb barrier) for non-resonant fusion reactions. For any given reaction, the S(E)-model contains four parameters [two of which approximate the barrier potential, U(r)]. They are easily interpolated along many reactions involving isotopes of the same elements; they give accurate practical expressions for S(E) with only several input parameters for many reactions. The model reproduces the suppression of S(E) at low energies (of astrophysical importance) due to the shape of the low-r wing of U(r). The model can be used to reconstruct U(r) from computed or measured S(E). For illustration, we parameterize our recent calculations of S(E) (using the Sao Paulo potential and the barrier penetration formalism) for 946 reactions involving stable and unstable isotopes of C, O, Ne, and Mg (with 9 parameters for all reactions involving many isotopes of the same elements, e.g., C+O). In addition, we analyze astrophysically important 12C+12C reaction, compare theoretical models with experimental data, and discuss the problem of interpolating reliably known S(E) values to low energies (E <= 2-3 MeV)., Comment: 13 pages, 5 figures, Phys. Rev. C, accepted

The neutron long counter NERO was built at the National Superconducting Cyclotron Laboratory (NSCL), Michigan State University, for measuring beta-delayed neutron-emission probabilities. The detector was designed to work in conjunction with a beta-decay implantation station, so that beta decays and beta-delayed neutrons emitted from implanted nuclei can be measured simultaneously. The high efficiency of about 40%, for the range of energies of interest, along with the small background, are crucial for measuring beta-delayed neutron emission branchings for neutron-rich r-process nuclei produced as low intensity fragmentation beams in in-flight separator facilities.

We summarize and critically evaluate the available data on nuclear fusion cross sections important to energy generation in the Sun and other hydrogen-burning stars and to solar neutrino production. Recommended values and uncertainties are provided for key cross sections, and a recommended spectrum is given for 8B solar neutrinos. We also discuss opportunities for further increasing the precision of key rates, including new facilities, new experimental techniques, and improvements in theory. This review, which summarizes the conclusions of a workshop held at the Institute for Nuclear Theory, Seattle, in January 2009, is intended as a 10-year update and supplement to Reviews of Modern Physics 70 (1998) 1265., Comment: 54 pages, 20 figures, version to be published in Reviews of Modern Physics; various typos corrected and several updates made

The slow neutron capture process in massive stars (the weak s-process) produces most of the s-only isotopes in the mass region 60 < A < 90. The nuclear reaction rates used in simulations of this process have a profound effect on the final s-process yields. We generated 1D stellar models of a 25 solar mass star varying the 12C + 12C rate by a factor of 10 and calculated full nucleosynthesis using the post-processing code PPN. Increasing or decreasing the rate by a factor of 10 affects the convective history and nucleosynthesis, and consequently the final yields., Comment: Conference proceedings for the Nuclear Physics in Astrophysics IV conference, 8-12 June 2009. 4 pages, 3 figures. Accepted for publication to the Journal of Physics: Conference Series

Using the Sao Paulo potential and the barrier penetration formalism we have calculated the astrophysical factor S(E) for 946 fusion reactions involving stable and neutron-rich isotopes of C, O, Ne, and Mg for center-of-mass energies E varying from 2 MeV to 18-30 MeV (covering the range below and above the Coulomb barrier). We have parameterized the energy dependence S(E) by an accurate universal 9-parameter analytic expression and present tables of fit parameters for all the reactions. We also discuss the reduced 3-parameter version of our fit which is highly accurate at energies below the Coulomb barrier, and outline the procedure for calculating the reaction rates. The results can be easily converted to thermonuclear or pycnonuclear reaction rates to simulate various nuclear burning phenomena, in particular, stellar burning at high temperatures and nucleosynthesis in high density environments., Comment: 30 pages including 11 tables, 4 figures, ADNDT, accepted

The neutron capture cross section of 14C is of relevance for several nucleosynthesis scenarios such as inhomogeneous Big Bang models, neutron induced CNO cycles, and neutrino driven wind models for the r process. The 14C(n,g) reaction is also important for the validation of the Coulomb dissociation method, where the (n,g) cross section can be indirectly obtained via the time-reversed process. So far, the example of 14C is the only case with neutrons where both, direct measurement and indirect Coulomb dissociation, have been applied. Unfortunately, the interpretation is obscured by discrepancies between several experiments and theory. Therefore, we report on new direct measurements of the 14C(n,g) reaction with neutron energies ranging from 20 to 800 keV.

The total cross sections for the 120Te(p,gamma)121I and 120Te(p,n)120I reactions have been measured by the activation method in the effective center-of-mass energies between 2.47 MeV and 7.93 MeV. The targets were prepared by evaporation of 99.4 % isotopically enriched 120Te on Aluminum and Carbon backing foils, and bombarded with proton beams provided by the FN tandem accelerator at the University of Notre Dame. The cross sections and $S$ factors were deduced from the observed gamma ray activity, which was detected off-line by two Clover HPGe detectors mounted in close geometry. The results are presented and compared with the predictions of statistical model calculations using the codes NON-SMOKER and TALYS., Comment: 17 pages, 5 figures, 5 tables, regular article

The goal of this paper is to analyze the impact of a primary neutron source on the s-process nucleosynthesis in massive stars at halo metallicity. Recent stellar models including rotation at very low metallicity predict a strong production of primary N14. Part of the nitrogen produced in the H-burning shell diffuses by rotational mixing into the He core where it is converted to Ne22 providing additional neutrons for the s process. We present nucleosynthesis calculations for a 25 Msun star at [Fe/H] = -3, -4, where in the convective core He-burning about 0.8 % in mass is made of primary Ne22. The usual weak s-process shape is changed by the additional neutron source with a peak between Sr and Ba, where the s-process yields increase by orders of magnitude with respect to the yields obtained without rotation. Iron seeds are fully consumed and the maximum production of Sr, Y and Zr is reached. On the other hand, the s-process efficiency beyond Sr and the ratio Sr/Ba are strongly affected by the amount of Ne22 and by nuclear uncertainties, first of all by the Ne22(alpha,n)Mg25 reaction. Finally, assuming that Ne22 is primary in the considered metallicity range, the s-process efficiency decreases with metallicity due to the effect of the major neutron poisons Mg25 and Ne22. This work represents a first step towards the study of primary neutron source effect in fast rotating massive stars, and its implications are discussed in the light of spectroscopic observations of heavy elements at halo metallicity., Comment: Accepted for publication in ApJ Letters, 11 pages, 2 figures, 1 table

The cross sections of the 70Ge(p,gamma)71As and 76Ge(p,n)76As reactions have been measured with the activation method in the Gamow window for the astrophysical p process. The experiments were carried out at the Van de Graaff and cyclotron accelerators of ATOMKI. The cross sections have been derived by measuring the decay gamma-radiation of the reaction products. The results are compared to the predictions of Hauser-Feshbach statistical model calculations using the code NON-SMOKER. Good agreement between theoretical and experimental S factors is found. Based on the new data, modifications of the optical potential used for low-energy protons are discussed., Comment: Accepted for publication in Phys. Rev. C

The impact of nuclear molecular configurations on the astrophysical S-factor for $^{16}$O + $^{16}$O is investigated within the realistic two-center shell model based on Woods-Saxon potentials. These molecular effects refer to the formation of a neck between the interacting nuclei and the radial dependent collective mass parameter. It is demonstrated that the former is crucial to explain the current experimental data with high accuracy and without any free parameter, whilst in addition the latter predicts a pronounced maximum in the S-factor. In contrast to very recent results by Jiang et al., the S-factor does not decline towards extremely low values as energy decreases., Comment: In press in Physics Letters B

The breakout reaction $^{15}$O($\alpha,\gamma$)$^{19}$Ne, which regulates the flow between the hot CNO cycle and the rp-process, is critical for the explanation of the burst amplitude and periodicity of X-ray bursters. We report on the first successful measurement of the critical $\alpha$-decay branching ratios of relevant states in $^{19}$Ne populated via $^{19}$F($^3$He,t)$^{19}$Ne. Based on the experimental results and our previous lifetime measurements of these states, we derive the first experimental rate of $^{15}$O($\alpha,\gamma$)$^{19}$Ne. The impact of our experimental results on the burst pattern and periodicity for a range of accretion rates is analyzed., Comment: 4 pages with 5 figures

We analyze thermonuclear and pycnonuclear fusion reactions in dense matter containing atomic nuclei of different types. We extend a phenomenological expression for the reaction rate, proposed recently by Gasques et al. (2005) for the one-component plasma of nuclei, to the multi-component plasma. The expression contains several fit parameters which we adjust to reproduce the best microscopic calculations available in the literature. Furthermore, we show that pycnonuclear burning is drastically affected by an (unknown) structure of the multi-component matter (a regular lattice, a uniform mix, etc.). We apply the results to study nuclear burning in a carbon_12-oxygen_16 mixture. In this context we present new calculations of the astrophysical S-factors for carbon-oxygen and oxygen-oxygen fusion reactions. We show that the presence of a CO lattice can strongly suppress carbon ignition in white dwarf cores and neutron star crusts at densities > 3e9 g cm^{-3} and temperatures T<1e8 K., Comment: 16 pages, 5 figures, to appear in Phys. Rev. C

The astrophysical p process, which is responsible for the origin of the proton rich stable nuclei heavier than iron, was investigated using a full nuclear reaction network for a type II supernova explosion when the shock front passes through the O/Ne layer. Calculations were performed with a multi-layer model adopting the seed of a pre-explosion evolution of a 25 solar mass star. The reaction flux was calculated to determine the main reaction path and branching points responsible for synthesizing the proton rich nuclei. In order to investigate the impact of nuclear reaction rates on the predicted p-process abundances, extensive simulations with different sets of collectively and individually modified neutron-, proton-, alpha-capture and photodisintegration rates have been performed. These results are not only relevant to explore the nuclear physics related uncertainties in p-process calculations but are also important for identifying the strategy and planning of future experiments., Comment: 27 pages, 24 figures, accepted for publication in ApJS

The 106Cd(alpha,gamma)110Sn reaction cross section has been measured in the energy range of the Gamow window for the astrophysical p-process scenario. The cross sections for 106Cd(alpha,n)109Sn and for 106Cd(alpha,p)109In below the (alpha,n) threshold have also been determined. The results are compared with predictions of the statistical model code NON-SMOKER using different input parameters. The comparison shows that a discrepancy for 106Cd(alpha,gamma)110Sn when using the standard optical potentials can be removed with a different alpha+106Cd potential. Some astrophysical implications are discussed., Comment: 10 pages, 9 figures, accepted for publication in Phys. Rev C

We present new rates for the 22Ne(alpha, n)25Mg and 22Ne(alpha,gamma)26Mg reactions, with uncertainties that have been considerably reduced compared to previous estimates, and we study how these new rates affect the production of the heavy magnesium isotopes in models of intermediate mass Asymptotic Giant Branch (AGB) stars of different initial compositions. All the models have deep third dredge-up, hot bottom burning and mass loss. Calculations have been performed using the two most commonly used estimates of the 22Ne + alpha rates as well as the new recommended rates, and with combinations of their upper and lower limits. The main result of the present study is that with the new rates, uncertainties on the production of isotopes from Mg to P coming from the 22Ne + alpha-capture rates have been considerably reduced. We have therefore removed one of the important sources of uncertainty to effect models of AGB stars. We have studied the effects of varying the mass-loss rate on nucleosynthesis and discuss other uncertainties related to the physics employed in the computation of stellar structure, such as the modeling of convection, the inclusion of a partial mixing zone and the definition of convective borders. These uncertainties are found to be much larger than those coming from 22Ne + alpha-capture rates, when using our new estimates. Much effort is needed to improve the situation for AGB models., Comment: 38 pages, 10 figures, 6 tables, Accepted to ApJ

In this paper we analyze the nuclear fusion rate between equal nuclei for all five different nuclear burning regimes in dense matter (two thermonuclear regimes, two pycnonuclear ones, and the intermediate regime). The rate is determined by Coulomb barrier penetration in dense environments and by the astrophysical S-factor at low energies. We evaluate previous studies of the Coulomb barrier problem and propose a simple phenomenological formula for the reaction rate which covers all cases. The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate. The results are illustrated for the example of the ^{12}C+^{12}C fusion reaction. This reaction is very important for the understanding of nuclear burning in evolved stars, in exploding white dwarfs producing type Ia supernovae, and in accreting neutron stars. The S-factor at stellar energies depends on a reliable fit and extrapolation of the experimental data. We calculate the energy dependence of the S-factor using a recently developed parameter-free model for the nuclear interaction, taking into account the effects of the Pauli nonlocality. For illustration, we analyze the efficiency of carbon burning in a wide range of densities and temperatures of stellar matter with the emphasis on carbon ignition at densities rho > 10^9 g/cc., Comment: 22 pages, 6 figures, accepted for publication in PRC

In the light of recent recalculations of the \el{19}{F}(alpha,p)\el{22}{Ne} reaction rate we present results of the expected yield of \el{19}{F} from Wolf-Rayet (WR) stars. We have computed models using the upper and lower limits for the rate in addition to the recommended rate and hence we constrain the uncertainty in the yield with respect to this reaction. We find a yield of 3.1x10^{-4}M_sol of \el{19}{F} with our recommended rate and a difference of a factor of two between the yields computed with the upper and lower limits. In comparison with previous work we find a difference in the yield of approximately a factor of 4, connected to a different choice of mass loss. Model uncertainties must be carefully evaluated in order to obtain a reliable estimate of the yield of fluorine from WR stars together with its uncertainties., Comment: 6 pages, 3 figures. Accepted for publication in MNRAS

The half-lives of 110Sn and 109In isotopes have been measured with high precision. The results are T1/2 =4.173 +- 0.023 h for 110Sn and T1/2 = 4.167 +-0.018 h for 109In. The precision of the half-lives has been increased by a factor of 5 with respect to the literature values which makes results of the recently measured 106Cd(alpha,gamma)110Sn and 106Cd(alpha,p)109In cross sections more reliable., Comment: 3 pages, 2 figures, accepted for publication in Phys. Rev C as brief report

This paper reports on the detailed rp-process reaction flow on an accreting neutron star and the resulting ashes of a type I X-ray burst. It is obtained by coupling a 298 isotope reaction network to a self-consistent one-dimensional model calculation with a constant accretion rate of dM/dt=1.0e17g/s (0.09 Eddington)., Comment: 4 pages, 2 figures, submitted to the INPC2004 proceedings

The astrophysical p-process is responsible for the origin of the proton rich nuclei,which are heavier than iron. A huge network involving thousands of reaction rates is necessary to calculate the final p-abundances. But not all rates included in the network have a strong influence on the p-nuclei abundances. The p-process was investigated using a full nuclear reaction network for a type II supernovae explosion when the shock front passes through the O/Ne layer. Calculations were done with a multi-layer model adopting the seed of a pre-explosion evolution of a 25 mass star. In extensive simulations we investigated the impact of single reaction rates on the final p-abundances. The results are important for the strategy of future experiments in this field., Comment: 4 pages

Multi-zone models of Type I X-ray bursts are presented that use an adaptive nuclear reaction network of unprecedented size, up to 1300 isotopes. Sequences of up to 15 bursts are followed for two choices of accretion rate and metallicity. At 0.1 Eddington (and 0.02 Eddington for low metallicity), combined hydrogen-helium flashes occur. The rise times, shapes, and tails of these light curves are sensitive to the efficiency of nuclear burning at various waiting points along the rp-process path and these sensitivities are explored. The bursts show "compositional inertia", in that their properties depend on the fact that accretion occurs onto the ashes of previous bursts which contain left-over hydrogen, helium and CNO nuclei. This acts to reduce the sensitivity of burst properties to metallicity. For the accretion rates studied, only the first anomalous burst in one model produces nuclei as heavy as A=100, other bursts make chiefly nuclei with A~64. The amount of carbon remaining after hydrogen-helium bursts is typically <1% by mass, and decreases further as the ashes are periodically heated by subsequent bursts. At the lower accretion rate of 0.02 Eddington and solar metallicity, the bursts ignite in a hydrogen-free helium layer. At the base of this layer, up to 90% of the helium has already burned to carbon prior to the unstable ignition. These helium-ignited bursts have briefer, brighter light curves with shorter tails, very rapid rise times (<0.1 s), and ashes lighter than the iron group., Comment: Submitted to the Astrophysical Journal (42 pages; 27 figures)

With the exception of the Big Bang, responsible for 1,2H, 3,4He, and 7Li, stars act as sources for the composition of the interstellar medium. Cosmic rays are related to the latter and very probably due to acceleration of the mixed interstellar medium by shock waves from supernova remnants. Thus, the understanding of the abundance evolution in the interstellar medium and especially the enrichment of heavy elements, as a function of space and time, is essential. It reflects the history of star formation and the lifetimes of the diverse contributing stellar objects. Therefore, the understanding of the endpoints of stellar evolution is essential as well. These are mainly planetary nebulae and type II/Ib/Ic supernovae as evolutionary endpoints of single stars, but also events in binary systems can contribute, like e.g. supernovae of type Ia, novae and possibly X-ray bursts and neutron star or neutron star - black hole mergers. Despite many efforts, a full and self-consistent understanding of supernovae (the main contributors to nucleosynthesis in galaxies) is not existing, yet. Their fingerprints, however, seen either in spectra, lightcurves, radioactivities/decay gamma-rays or in galactic evolution, can help to constrain the composition of their ejecta and related model uncertainties., Comment: Review, 20 pages, uses style icrc.sty, to be published in Proc. ICRC 2001

We calculate the rapid proton (rp) capture process of hydrogen burning on the surface of an accreting neutron star with an updated reaction network that extends up to Xe, far beyond previous work. In both steady-state nuclear burning appropriate for rapidly accreting neutron stars (such as the magnetic polar caps of accreting X-ray pulsars) and unstable burning of Type I X-ray bursts, we find that the rp process ends in a closed SnSbTe cycle. This prevents the synthesis of elements heavier than Te and has important consequences for X-ray burst profiles, the composition of accreting neutron stars, and potentially galactic nucleosynthesis of light p nuclei., Comment: 6 pages, including 4 figures, accepted for publication in Phys. Rev. Lett

Except for 1H, 2H, 3He, 4He, and 7Li, originating from the Big Bang, all heavier elements are made in stellar evolution and stellar explosions. Nuclear physics, and in many cases nuclear structure far from stability, enters in a crucial way. Therefore, we examine in this review the role of nuclear physics in astrophysics in general and in particular how it affects stellar events and the resulting nucleosynthesis. Stellar modeling addresses four major aspects: 1. energy generation and nucleosynthesis, 2. energy transport via conduction, radiation or possibly convection, 3. hydrodynamics/hydrostatics, and finally 4. thermodynamic properties of the matter involved. Nuclear Physics enters via nuclear reaction cross sections and nuclear structure (affecting the composition changes and nuclear energy generation), neutrino-nucleon and neutrino-nucleus cross sections (affecting neutrino opacities and transport), and e.g. the equation of state at and beyond nuclear densities which creates a relation between the nuclear many-body problem and the hydrodynamic response like pressure and entropy. In the following we review these four topics by highlighting the role and impact of nuclear physics in each of these aspects of stellar modeling. The main emphasis is put on the connection to element synthesis., Comment: 32 pages, 8 figures, review, to appear in Prog. Nuc. Part. Phys.; layout changed (v2), journal reference corrected (v3)

The hydrogen-rich accreted envelopes of neutron stars in binary systems are the site for the rapid proton capture nucleosynthethic process (rp-process), which involves nuclei close to the proton dripline. An overview of the relevant reactions and nuclear properties for rp-process studies is given, along with motivations for further experimental nuclear physics studies., Comment: 6 pages, 4 figures; Proc. Workshop "The beta Decay, from Weak Interaction to Nuclear Structure", eds. P. Dessagne, A. Michalon, C. Miehe (IRes, Strasbourg 1999), p. 51

The reaction rates for alpha capture processes on self-conjugate nuclei in the mass range A=20-40 have been investigated. The rates were calculated using the statistical model code NON-SMOKER taking into account isospin suppression rules. These theoretical predictions are compared with rates derived from the available experimental data about the alpha capture reactions taking also into account additional experimental information from different reaction channels populating the alpha unbound states of the self-conjugate compound nuclei., Comment: 29 pages including 7 figures; figures are revised in the new version; accepted for publication in Nuclear Physics A

The reaction rates of neutron capture reactions on light nuclei are important for reliably simulating nucleosynthesis in a variety of stellar scenarios. Neutron capture reaction rates on neutron-rich C-, N-, and O-isotopes are calculated in the framework of a hybrid compound and direct capture model. The results are tabulated and compared with the results of previous calculations as well as with experimental results., Comment: 33 pages (uses revtex) and 9 postscript figures, accepted for publication in Phys. Rev. C

Hot (explosive) hydrogen burning or the Rapid Proton Capture Process (rp-process) occurs in a number of astrophysical environments. Novae and X-ray bursts are the most prominent ones, but accretion disks around black holes and other sites are candidates as well. The expensive and often multidimensional hydro calculations for such events require an accurate prediction of the thermonuclear energy generation, while avoiding full nucleosynthesis network calculations. In the present investigation we present an approximation scheme applicable in a temperature range which covers the whole range of all presently known astrophysical sites. It is based on the concept of slowly varying hydrogen and helium abundances and assumes a kind of local steady flow by requiring that all reactions entering and leaving a nucleus add up to a zero flux. This scheme can adapt itself automatically and covers situations at low temperatures, characterized by a steady flow of reactions, as well as high temperature regimes where a $(p,\gamma)-(\gamma,p)$-equilibrium is established. In addition to a gain of a factor of 15 in computational speed over a full network calculation, and an energy generation accurate to more than 15 %, this scheme also allows to predict correctly individual isotopic abundances. Thus, it delivers all features of a full network at a highly reduced cost and can easily be implemented in hydro calculations., Comment: 18 pages, LaTeX using astrobib and aas2pp4, includes PostScript figures; Astrophysical Journal, in press. PostScript source also available at http://quasar.physik.unibas.ch/preps.html