Solar Fusion Cross Sections for the pp chain and CNO cycles
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1 Solar Fusion Cross Sections for the pp chain and CNO cycles Working Group 10: Theoretical Issues (Wick Haxton, Stefan Typel) status of theory at 1997 meeting (Rev. Mod. Phys. 70 (1998) 1265) progress during the last 12 years major issues to discuss Institute for Nuclear Theory, Seattle January 2008
2 Status of Theory at 1997 Meeting - I theory in RMP paper general issues extrapolation of cross sections definition of S-factor, power series in energy laboratory screening parametrization with electron screening energy U e comparison theory (e.g. adiabatic appproximation) vs. experiment (agreement?) stellar screening Salpeter/Debye-Hückel model, corrections application to specific reactions extrapolation of experimental data guided by theoretical models calculation of cross sections where no experimental information available no explicit section on theory
3 Status of Theory at 1997 Meeting - II weak interaction rates: no direct experimental data pp, pep, hep reactions wave functions (from Schrödinger equation, potentials constrained by experimental data) weak-interaction matrix elements various corrections 7 Be electron capture continuum-state and bound-state electrons density-matrix formulation conditions inside stellar plasma
4 Status of Theory at 1997 Meeting - III radiative capture/rearrangement reactions: extrapolation of measured cross sections simple functional parametrizations little physical justification R-matrix parametrizations fitted parameters: formal level widths and energies two-body potential models (e.g. direct-capture model) simple potentials (e.g. Woods-Saxon) fitted to to certain properties of the system microscopic (many-body) cluster models (e.g. resonating group method) more systematic potentials, few free parameters
5 Progress and Major Issues - I use of realistic interactions fitted to two-nucleon bound/scattering data many-body ab-initio calculations No-Core Shell Model (NCSM) Green s Function Monte-Carlo (GFMC) Fermionic Molecular Dynamics (FMD) Correlated Hyperspherical Harmonics (CHH) description of bound states (main application) scattering calculations radiative/rearrangement reactions (small number of cases so far, problem of asymptotics of wave functions) effective field theory (EFT) independent systematic approach
6 Progress and Major Issues - II extrapolation of cross sections low-energy expansion of energy-dependence analytical forms, effects of bound states R-matrix parametrization standard form: non-physical parameters alternative form: physical level energies and widths small effects monopole (E0) contribution, vacuum polarization, bremsstrahlung,... electron screening dynamical calculations, adiabatic approximation,...
7 Progress and Major Issues - III Indirect Methods: reaction theory needed for conversion of measured to astrophysical cross sections radiative capture reactions (a + b c + γ) Coulomb dissociation semiclassical/quantal/hybrid calculations higher-order effects/multi-photon exchange, dynamical description various monopole contributions, Coulomb-nuclear interference relativistic effects asymptotic normalization coefficients (ANC) coupled-channel calculations, continuum effects, optical potentials relation ANC spectroscopic factors conversion ANC capture cross section
8 Progress and Major Issues - IV Indirect Methods: reaction theory needed for conversion of measured to astrophysical cross sections rearrangement reactions (a + b c + d) Trojan-horse method non-resonant vs. resonant reactions (validity of surface approximation) different approximations for quasi-free scattering conditions (PWIA, PWBA, DWBA,... ) parametrization using R-matrix theory factorization of cross section off-shell effects
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