Bounding methods in nuclear physics

✍ Scribed by M. Barnsley; G. Turchetti

• Publisher: Elsevier Science
• Year: 1981
• Tongue: English
• Weight: 1018 KB
• Volume: 22
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(81)90068-0

✦ Synopsis

Bounding methods for nuclear energy levels from the general area of variational inequalities, moment theory and Pads approximant theory are considered. It is shown that rigorous bounds can be obtained both from Brillouin-Wigner and from Rayleigh-Schrodinger perturbation series.

For many-body Hamiltonians of structure H 0 + XV it is shown that the matrix Padé approximants to the Brillouin-Wigner effective Hamiltonian provide monotonic sequences of upper bounds to any finite set of levels. Lower bounds are also

Again, starting from Rayleigh-Schr~dinger perturbation series for low-lying levels, a procedure is presented for the construction of effective Hamiltonians whose eigenvalues are upper bounds to the exact levels. New explicit bounds, extending the well known convexity bound for the ground state, are derived.