Resonance states in {sup 27}P using Coulomb dissociation and their effect on the stellar reaction {sup 26}Si(p,{gamma}) {sup 27}P

The stellar reaction ${}^{26}$Si($p,\\phantom{\\rule{-0.16em}{0ex}}\\ensuremath{\\gamma}$)${}^{27}$P was studied in the Coulomb dissociation of ${}^{27}$P. Two known resonance levels in ${}^{27}$P were excited and a candidate for the third excited state was found in the ${}^{26}$Si $p$ relative energy spectrum. The $E$2 resonance strengths $\\ensuremath{\\omega}\\ensuremath{\\gamma}$ were obtained to be $(6.5\\ifmmode\\pm\\else\\textpm\\fi{}1.3)\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}11}$, $(6.0\\ifmmode\\pm\\else\\textpm\\fi{}1.1)\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}10}$, and $(1.10\\ifmmode\\pm\\else\\textpm\\fi{}0.27)\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}10}$ MeV. The total ($E2+M$1) $\\ensuremath{\\omega}\\ensuremath{\\gamma}$ value for the first excited state was evaluated to be $1.{9}_{\\ensuremath{-}1.1}^{+1.9}\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}9}$ MeV with the help of the shell model. The error was estimated from the deviation of theoretical predictions with the same shell model from experimental strengths obtained in the present study for ${}^{27}$P and earlier ones for the mirror nucleus ${}^{27}$Mg. The astrophysical reaction rate for the ${}^{26}$Si($p,\\phantom{\\rule{-0.16em}{0ex}}\\ensuremath{\\gamma}$)${}^{27}$P reaction was also calculated and compared with previous estimations.