  The origin of the proton-rich trans-iron isotopes in the solar system is
still uncertain. Single-degenerate thermonuclear supernovae (SNIa) with
n-capture nucleosynthesis seeds assembled in the external layers of the
progenitor's rapidly accreting white dwarf phase may produce these isotopes. We
calculate the stellar structure of the accretion phase of five white dwarf
models with initial masses >~ 0.85Msun using the stellar code MESA. The
near-surface layers of the 1, 1.26, 1.32 and 1.38Msun models are most
representative of the regions in which the bulk of the p nuclei are produced
during SNIa explosions, and for these models we also calculate the
neutron-capture nucleosynthesis in the external layers. Contrary to previous
rapidly-accreting white dwarf models at lower mass, we find that the H-shell
ashes are the main site of n-capture nucleosynthesis. We find high neutron
densities up to several 10^15 cm^-3 in the most massive WDs. Through the
recurrence of the H-shell ashes these intermediate neutron densities can be
sustained effectively for a long time leading to high neutron exposures with a
strong production up to Pb. Both the neutron density and the neutron exposure
increase with increasing the mass of the accreting WD. Finally, the SNIa
nucleosynthesis is calculated using the obtained abundances as seeds. We obtain
solar to super-solar abundances for p-nuclei with A>96. Our models show that
SNIa are a viable p-process production site.
