Crossover region between nodal and anti-nodal states at the Fermi level of optimally and overdoped Bi$_{2}$Sr$_{1.6}$Nd$_{0.4}$CuO$_{6+\delta}$

We have studied Bi$_{2}$Sr$_{1.6}$Nd$_{0.4}$CuO$_{6+\delta}$ using Angle Resolved Photoemission Spectroscopy in the optimal and overdoped regions of the phase diagram. We identify a narrow crossover region in the electronic structure between the nodal and antinodal regions associated with the deviation from a pure d-wave gap function, an abrupt increase of the quasiparticle lifetime, the formation of Fermi arcs above T$_c$, and a sudden shift of the bosonic mode energy from higher energy, $\sim${60meV}, near the nodal direction, to lower energy, $\sim${20meV}, near the antinodal direction. Our work underscores the importance of a unique crossover region in the momentum space near E$_F$ for the single layered cuprates, between the nodal and antinodal points, that is independent of the antiferromagnetic zone boundary.