## Gamow-Jordan vectors and non-reducible density operators from higher-order S-matrix poles

In analogy to Gamow vectors that are obtained from first-order resonance poles of the S-matrix, one can also define higher-order Gamow vectors which are derived from higher-order poles of the S-matrix. An S-matrix pole of r-th order at z{sub R}=E{sub R}{minus}i{Gamma}/2 leads to r generalized eigenvectors of order k=0,1,{hor_ellipsis},r{minus}1, which are also Jordan vectors of degree (k+1) with generalized eigenvalue (E{sub R}{minus}i{Gamma}/2). The Gamow-Jordan vectors are elements of a generalized complex eigenvector expansion, whose form suggests the definition of a state operator (density matrix) for the microphysical decaying state of this higher-order pole. This microphysical state is a mixture ofmore »