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As it is well known there may arise situations when an interaction betweenelectrons is attractive. A weak attraction should manifest itself strongly in1D systems, since it can create two-electron bound states. This paperinterprets the 0.7 $(2e^2/h)$ conductance structure, observed recently in aone-dimensional constriction, as a manifestation of two-electron bound statesformed in a barrier saddle-point. The value 0.75 $(2e^2/h)$ follows naturallyfrom the 3:1 triplet-singlet statistical weight ratio for the two-electronbound states, if the triplet energy is lower. Furthermore, the value 0.75 hasto be multiplied by the probability T of the bound state formation duringadiabatic transmission of two electrons into 1D channel ($T\simeq 1$). If thebinding energy is larger than the sub-band energy spacing the 0.7 structure canbe seen even when the integer steps are smeared away by the temperature. Boundstates of several electrons, if they exist, may give different steps at 1/2,5/16, 3/16 etc in the conductance. The latter results are sensitive to thelength of 1D system and the electron density at the barrier. It is not excludedthat the fractional conductance quantization may also appear for a repulsiveinteraction between electrons. In this case the electron level splitting is dueto the exchange interaction with two nearest neighbors in a 1D Wigner crystal.Comment: 8 pages, Revte

Possible mechanism of the fractional-conductance quantization in a one-dimensional constriction