Gap anisotropy in the angle-resolved photoemission spectroscopy of Bi_2Sr_2CaCu_2O_{8+\delta}

The gap anisotropy in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ is revisited in the framework of a d-wave scenario in view of the recent angle-resolved photoemission experiment. Based on a tight-binding fit to the normal state dispersion, a detail analysis on the effects of the inclusion of the next harmonic in the d-wave has been presented. Significant effect has been observed in the superconducting T$_c$. The density of states is linear at the nodes with enhanced weight, caused by a marked increase in the low energy excitaions which affect the thermodynamics considerably. The slope of the $\rho_s - T$ curve in the low temperature regime increases and the specific heat reflects the enhanced entropy at low temperatures. The leading edge of the ARPES energy distribution curves have been calculated and found to shift towards higher energy. The effect of scattering by non-magnetic impurities in this context is also outlined.