Changes in the self-energy and d-wave pairing strength with doping in overdoped La(2-x)Sr(x)CuO4

Angle resolved photoemission spectroscopy (ARPES) studies of the overdoped cuprate superconductor La$_{2-x}$Sr$_x$CuO$_4$ find only small changes in the near nodal electron self energy over a spectral range of several hundred meV as the doping increases from x=0.2 to x=0.3 and the superconducting transition temperature T_c decreases from 32K to 0K. These measurements put constraints on the structure of the electron-electron interaction. Here we show that a spin-fluctuation interaction leads to behavior which is consistent with these experimental results.