Rigorous bounds on the energy-averaged effective Hamiltonian

Journal Article · Sun Nov 01 00:00:00 EST 1981 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.24.2267· OSTI ID:6167005

Chang, B D; Vincent, C M

Best possible bounds on expectation values of the energy-averaged Bloch-Horowitz effective Hamiltonian are derived, assuming knowledge of only moments m/sub 0/,...,m/sub n/ of the intermediate-state Hamiltonian. These bounds are independent of the presence of intruder states. The simplest case that leads to nontrivial bounds is n = 2. Explicit formulas are given for the n = 2 upper and lower bounds for the Lorentzian averaging width GAMMA. There exists an intermediate range of GAMMA values, within which the bounds depend weakly on GAMMA. For n = 2, the intermediate GAMMA values are of the order of the width of the strength function of the intermediate-state excitation. For larger n, the intermediate GAMMA values decrease, permitting finer resolution at the price of increased computation. A universal graph is given to aid in estimating the effect of Bloch-Horowitz self-consistency on the n = 2 bounds. For a low-lying state with moments typical of those suggested by statistical spectroscopic theory, the upper and lower bounds differ from their average by about 25% of the virtual excitation contribution. Finally, an iterative method for approximating the model-space wave function is described.

• Research Organization: Department of Physics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
• OSTI ID: 6167005
• Journal Information: Phys. Rev. C; (United States), Vol. 24:5
• Country of Publication: United States
• Language: English

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MATRIX ELEMENTS
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