
Complexenergy approach to sum rules within nuclear density functional theoryComplexenergy approach to sum rules within nuclear density functional theoryAA00773613 
"/Hinohara, Nobuo/"Hinohara, Nobuo ,
"/Kortelainen, Markus/"Kortelainen, Markus ,
"/Nazarewicz, Witold/"Nazarewicz, Witold ,
"/Olsen, Erik/"Olsen, Erik
91
(
4
)
, p.044323 , 201504 , the American Physical Society
ISSN:05562813
NCID:AA00773613
Description
Background: The linear response of the nucleus to an external field contains unique information about the effective interaction, the correlations governing the behavior of the manybody system, and the properties of its excited states. To characterize the response, it is useful to use its energyweighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or the nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding.Purpose: To establish an efficient framework to compute energyweighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and largescale surveys of collective strength, we have developed a new technique within the complexenergy finiteamplitude method (FAM) based on the quasiparticle randomphase approximation (QRPA).Methods: To compute sum rules, we carry out contour integration of the response function in the complexenergy plane. We benchmark our results against the conventional matrix formulation of the QRPA theory, the Thouless theorem for the energyweighted sum rule, and the dielectric theorem for the inverseenergyweighted sum rule.Results: We derive the sumrule expressions from the contour integration of the complexenergy FAM. We demonstrate that calculated sumrule values agree with those obtained from the matrix formulation of the QRPA. We also discuss the applicability of both the Thouless theorem about the energyweighted sum rule and the dielectric theorem for the inverseenergyweighted sum rule to nuclear density functional theory in cases when the EDF is not based on a Hamiltonian.Conclusions: The proposed sumrule technique based on the complexenergy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and welladaptable to parallel computing. The FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and the external field cannot be used.
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