Evaluation of Effective Astrophysical S factor for Non-Resonant   Reactions
  We derived analytic formulas of the effective S astrophysical S factor,S^eff for a non-resonant reaction of charged particles using a Taylor expension of the astrophysical S factor and a uniform approximation.The formulas will be able to generate generate more accurate approximation to S^eff than previous ones. 
M.Ueda, A.J.Sargeant, M.P.Pato and M.S.Hussein