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We investigate the effect of k-space broadening of the interlayer pairingkernel on the critical temperature T_c and the k-dependence of the gap functionin a one-dimensional version of the interlayer pair-tunneling model of high-T_csuperconductivity. We consider constant as well as k-dependent intralayerpairing kernels. We find that the sensitivity to k-space broadening is largerthe smaller the width of the peak of the Fermi-level gap calculated for zerobroadening. This width increases with the overall magnitude of the interlayertunneling matrix element, and decreases with the bandwidth of thesingle-electron intralayer excitation spectrum. The width also increases as theFermi level is moved towards regions where the excitation spectrum flattensout. We argue that our qualitative conclusions are valid also for atwo-dimensional model. This indicates that at or close to half-filling in twodimensions, when the Fermi-surface gap for zero broadening attains its peaks at$(\pm \pi/a,0)$ and $(0,\pm\pi/a)$ where the excitation spectrum is flat, thesepeaks should be fairly robust to moderate momentum broadening.Comment: 10 pages including 4 figures, to be published in Journal of Low  Temperature Physic

Non-k-Diagonality in the Interlayer Pair-Tunneling Model of High-Temperature Superconductivity