Structure of the essential spectrum and discrete spectrum of the energy operator of four-electron systems in the impurity Hubbard model. The third triplet state

The structure of the essential spectrum and the discrete spectrum of the energy operator of four-electron systems in the Hubbard impurity model for the third triplet state of the system are examined. The following statements are proved. (a) The essential spectrum of the third triplet is the union of three segments and the discrete spectrum of the third triplet is empty. (b) The essential spectrum of the third triplet is the union of eight segments and the discrete spectrum of the third triplet consists of three eigenvalues. (c) The essential spectrum of the third triplet is the union of sixteen segments and the discrete spectrum of the third triplet consists of eleven eigenvalues.