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Two astrophysically important reactions, 22Mg(p,γ)23Al and 26Si(p,γ)27P, were studied experimentally by using the Coulomb dissociation of proton-rich nuclei 23Al and 27P. The radiative widths determined from the cross sections suggest that the β+ decay of 22Mg is favored over the 22Mg(p,γ)23Al reaction while 26Si(p,γ)27P reaction is faster than the β+ decay of 26Si around the peak temperature of heavy novae. The measured radiative widths are consistent with the theoretical values used in the network calculations of nucleosynthesis, therefore providing confirmation that the theoretical stories of nucleosynthesis do not require any change in these sites of the reaction chains. [ABSTRACT FROM AUTHOR]