Few-Body Systems

, Volume 57, Issue 9, pp 833–849

Calculation of Expectation Values of Operators in the Complex Scaling Method


DOI: 10.1007/s00601-016-1126-9

Cite this article as:
Papadimitriou, G. Few-Body Syst (2016) 57: 833. doi:10.1007/s00601-016-1126-9


The complex scaling method (CSM) provides with a way to obtain resonance parameters of particle unstable states by rotating the coordinates and momenta of the original Hamiltonian. It is convenient to use an \(\hbox {L}^2\) integrable basis to resolve the complex rotated or complex scaled Hamiltonian \(\hbox {H}_{\theta }\), with \(\theta \) being the angle of rotation in the complex energy plane. Within the CSM, resonance and scattering solutions have fall-off asymptotics. One of the consequences is that, expectation values of operators in a resonance or scattering complex scaled solution are calculated by complex rotating the operators. In this work we are exploring applications of the CSM on calculations of expectation values of quantum mechanical operators by using the regularized backrotation technique and calculating hence the expectation value using the unrotated operator. The test cases involve a schematic two-body Gaussian model and also applications using realistic interactions.

Funding information

Funder NameGrant NumberFunding Note
  • DE-AC52-07NA27344
  • SCW0498-59806

Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  1. 1.Nuclear and Chemical Science DivisionLawrence Livermore National LaboratoryLivermoreUSA

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