Efficient method for evaluating energydependent sum rules
Abstract
Energydependent sum rules are useful tools in many fields of physics. In nuclear physics, they typically involve an integration of the response function over the nuclear spectrum with a weight function composed of integer powers of the energy. More complicated weight functions are also encountered, e.g., in nuclear polarization corrections of atomic spectra. Using the Lorentz integral transform method and the Lanczos algorithm, we derive a computationally efficient technique for evaluating such sum rules that avoids the explicit calculation of both the continuum states and the response function itself. Our numerical results for electric dipole sum rules of the He4 nucleus with various energydependent weights show rapid convergence with respect to the number of Lanczos steps. This demonstrates the usefulness of the method in a variety of electroweak reactions.
 Publication:

Physical Review C
 Pub Date:
 June 2014
 DOI:
 10.1103/PhysRevC.89.064317
 arXiv:
 arXiv:1403.7651
 Bibcode:
 2014PhRvC..89f4317N
 Keywords:

 36.10.Ee;
 21.60.De;
 25.30.c;
 Muonium muonic atoms and molecules;
 Ab initio methods;
 Leptoninduced reactions;
 Nuclear Theory;
 Nuclear Experiment;
 Physics  Atomic Physics
 EPrint:
 7 pages, 2 figures, 1 table