Group-theoretical deduction of a dyadic Tamm–Dancoff equation by using a matrix-valued generator coordinate

Abstract

The traditional Tamm–Dancoff (TD) method is one of the standard procedures for solving the Schrodinger equation of fermion many-body systems. However, it meets a serious difficulty when an instability occurs in the symmetry-adapted ground state of the independent particle approximation (IPA) and when the stable IPA ground state becomes of broken symmetry. If one uses the stable but broken symmetry IPA ground state as the starting approximation, TD wave functions also become of broken symmetry. On the contrary, if we start from a symmetry-adapted but unstable wave function, the convergence of the TD expansion becomes bad. Thus, the requirements of symmetry and rapid convergence are not in general compatible in the conventional TD expansion of the systems with strong collective correlations. Along the same line as Fukutome's, we give a group-theoretical deduction of a U(n) dyadic TD equation by using a matrix-valued generator coordinate.