there are indeed a few paper with the incorrect spelling Casmir, but the Gorter-Casimir effect actually refers to Hendrik Casimir. Did you try with the right spelling ? You should be more successful. Best regards
The now historically dated Gorter-Casimir factor [1-(T/T_c)^4}^(1/2) was in fact an empirical expression, that matches experimental data for selected materials. in some temperature range. For some materials other fits, e.g. a (T/Tc)^2 fit, work better. See a discussion e.g in Ginsberg's book "Physical properties of high temperature semiconductors II" pp.660-666 (World Scientfic), that derives some clue on the type of coupling depending on the temperature dependence lambda(T). For more recent litterature, Tinkham's "Introduction to superconductivity" relativizes the importance of the G-C relation, and describes why one shouldn't put too much emphasis on it.