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The effects of Umklapp scattering on electronic states are studied in onespatial dimension at absolute zero. The model is basically the Hubbard model,where parameters characterizing the normal ($U$) and Umklapp ($V$) scatteringare treated independently. The density of states is calculated in the t-matrixapproximation by taking only the forward and Umklapp scattering into account.It is found that the Umklapp scattering causes the global splitting of thedensity of states. In the presence of sufficiently strong Umklapp scattering, apole in the t-matrix appears in the upper half plane, signalling an instabilitytowards the '$G/2-$pairing' ordered state ($G$ is the reciprocal latticevector), whose consequences are studied in the mean field approximation. Itturns out that this ordered state coexists with spin-density-wave state andalso brings about Cooper-pairs. A phase diagram is determined in the plane of$V$ and electron filling $n$.Comment: 22 pages, LaTeX, 17 figures included, uses jpsj.st

Effects of Umklapp Scattering on Electronic States in One Dimension