Far-infrared {ital c}-axis response of La{sub 1.87}Sr{sub 0.13}CuO{sub 4} determined by ellipsometry

We have measured the {ital c}-axis optical response of a large, high-quality single crystal of La{sub 1.87}Sr{sub 0.13}CuO{sub 4} between 30 and 700 cm{sup {minus}1} in the 10{endash}300 K temperature range with a far-infrared Fourier ellipsometer. Since ellipsometry provides both amplitude and phase information, we directly obtain the complex dielectric function, thereby avoiding the errors introduced by the Kramers-Kronig transformation or the reference determination. A purely algebraic treatment of our data within the two-fluid Gorter-Casimir model reveals no indication of a reduction of the normal carrier scattering rate {Gamma} below {ital T}{sub {ital c}}. We obtain {Gamma}{approx_equal}130{plus_minus}70 cm{sup {minus}1} and a plasma frequency for the superconducting carriers of {omega}{sub {ital ps}}{approx_equal}260{plus_minus}40 cm{sup {minus}1}. Thus, assuming a weak-coupling BCS gap (3.5{ital k}{sub {ital BT}}{sub {ital c}}{approx_equal}77 cm{sup {minus}1}, with {ital T}{sub {ital c}}=31.5 K) we conclude that the {ital c}-axis optical response of La{sub 1.87}Sr{sub 0.13}CuO{sub 4} can neither be modeled within the clean nor with the dirty limit. {copyright} {ital 1996 The American Physical Society.}