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- W2000189980 abstract "The energy-independent effective Hamiltonian $mathcal{H}(z)$ is considered as an analytic function of the coupling parameter $z$. It is shown that a point ${z}_{b}$ is not a singularity of $mathcal{H}(z)$ unless the energy of some state that is selected for representation in the model space (${L}_{P}$) coincides, at $z={z}_{b}$, with the energy of a state that is excluded from representation in ${L}_{P}$. This result establishes the correctness of previous conjectures by Schucan and Weidenmuller, and implies that perturbation theory for $mathcal{H}(z)$ will generally have a larger radius of convergence than perturbation theory for the individual energies. For the case of a cut (intruder-state cut) joining an isolated pair of branch points close to the real axis, the singular behavior of $mathcal{H}(z)$ is examined in detail. The residue of the cut is expressed in terms of quantities that can be calculated by diagonalization of a real, symmetric modification (minimal smoothing) of the Hamiltonian matrix. A formula is given for the contribution of an intruder-state cut to the error incurred by $nmathrm{th}$ order perturbation theory for the physical quantity $mathcal{H}(1)$. Consideration of a numerical example shows that if the values of sufficiently high orders of perturbation theory are known, the residues of intruder-state cuts may be evaluated. This allows estimation of the errors that intruder-state cuts produce in perturbation theory summed to finite order, and yields a criterion for the optimal truncation of divergent perturbation series.NUCLEAR STRUCTURE Effective Hamiltonian for $^{18}O{J}^{ensuremath{pi}}={0}^{+}$; estimated errors of perturbation theory produced by intruder state." @default.
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- W2000189980 date "1976-08-01" @default.
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- W2000189980 title "Influence of singularities on perturbation theory for the effective Hamiltonian" @default.
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- W2000189980 doi "https://doi.org/10.1103/physrevc.14.660" @default.
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