We report on the electrical conductivity s of a series of nominally uncompensated neutrontransmutation-doped isotopically enriched 70 Ge:Ga samples with the Ga concentration [Ga] near N c for the metal-insulator transition. s of all insulating samples obeys ln s~2͑T 0 ͞T͒ 1͞2 with T 0~͑ N c -͓Ga͔͒͞N c while the zero temperature conductivity s͑0͒ of the metallic samples is s͑0͕͒ ͓͑Ga͔-N c ͒͞N c ͖ n with the critical exponent n ഠ 0.5. The values of N c obtained from the two independent scalings of T 0 and s͑0͒ are identical, i.e., n ഠ 0.5 is established unambiguously for uncompensated Ge:Ga. [S0031-9007(96)01533-5] PACS numbers: 71.30.+h, 72.80.Cw In experimental studies of the metal-insulator (MI) transition one measures the critical behavior of physical quantities such as conductivity, dielectric constant, heat capacity, etc. The doping induced MI transition in semiconductors is considered to be a model case for the general theory of the critical behaviors of solids. In particular the conductivity extrapolated to zero temperature ͓s͑0͔͒ is evaluated routinely as a function of doping concentration (N) immediately above the MI transition critical concentration ͑N c ͒;where s 0 is the prefactor and n is the critical exponent. The value of n, determined experimentally, is compared with theoretical predictions. Up to now n ഠ 0.5 has been obtained with nominally uncompensated semiconductors (Si:P [1], Si:As [2,3], Ge:As [4], Si:B [5]) while n ഠ 1 has been found with compensated semiconductors (Ge:Sb [6], Si:P,B [7], Ge:Ga,As [8]) and amorphous alloys [9-12]. Exceptions are uncompensated Ge:Sb with n ഠ 1 [13] and Ga x Ar 12x amorphous alloys with n ഠ 0.5 [14]. As we explain below, the value of n ഠ 0.5 obtained with simple systems like uncompensated semiconductors turns out to be inconsistent with theoretical predictions [15]. In his original theory Mott considered only the electron-electron ͑e 2 -e 2 ͒ interaction (Mott transition) and predicted a discontinuous transition of s͑0͒ at N c [16]. Although there is much evidence for the importance of e 2 -e 2 interactions, no experimental observation of such an abrupt transition has been reported. Anderson's idea of MI transitions is based solely on the disordered potential arising from randomly distributed dopants (Anderson transition) [17]. This lead to the development of the well-known "scaling theory" which predicted n ഠ 1 for three dimensional systems [18]. More recently, higher order calculations of the scaling theory (exclusively with disorder and no interactions) predict n ഠ 1.3 [19], and, more importantly, this value is shown to be independent of time reversal invariance [20] and of the strength of spin-orbit interactions [21]. It is therefore clear that the effect of disorder alone cannot explain the experimental results of n ഠ 0.5 or 1. Chayes et al. combined the theories of Mott and Anderson and successfully set the lowest limit n . 2͞3 [22]. This result permits n ഠ 1 obtained with compensated semiconductors and amorphous alloys. However, there still is no th...

Publication costs assisted by Keio University Absorption spectra of rhodamine B are examined in solutions of glycerol, ethylene glycol, and acetic acid. Particular attention is given to the absorption spectra of monomers and dimers of rhodamine B in these solutions. Furthermore, dimeric structures of rhodamine B in these solutions are also investigated.

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