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

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