Perturbation theory and Padé approximants in realistic large-matrix models of the nuclear effective interaction

Aug 2, 1976
25 pages
Published in:
  • Nucl.Phys.A 266 (1976) 138-162
  • Published: Aug 2, 1976
    and
  • Published: 1976
DOI:

Citations per year

197619871998200920200123456
Abstract: (Elsevier B.V.)
Realistic extended shell-model calculations are used to construct exact effective Hamiltonians, the perturbation series for the effective Hamiltonian to any order, and the [N+1, N] Padé approximants to the series. It is found that the Padé approximants give reliable results even when the series diverge, but that for both convergent and divergent series reasonably accurate results can be obtained only in fifth, or even seventh order. In addition, the poles of the low-order Padé approximants are not always reliable indicators of singularities of the perturbation series. The perturbation series and Padé approximants for the Q-box (energy-dependent effective Hamiltonian) are no more accurate in low orders than those for the usual effective Hamiltonian. Explicit formulas for the matrix Padé approximants are given in an appendix.
  • PERTURBATION THEORY
  • APPROXIMATION: PADE
  • NUCLEAR REACTION
  • shell model
  • ENERGY DEPENDENCE
  • NUMERICAL CALCULATIONS
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