Response functions are at the heart of any comparison of theory with experiment in studies of the nuclear dynamics with electroweak probes. Calculations performed in the laboratory frame often suffer from center of mass contaminations that need to be removed. By confining the system in a harmonic oscillator, we derive a set of analytical formulas to subtract the center of mass effects from calculations of response functions and associated sum rules. After a general analytical derivation, we first deal specifically with the longitudinal response function appearing in electron scattering and provide expressions for the center of mass correcting functions. Next, we present a proof of principle study for the case of the electric dipole sum rules in a two-body problem with a numerical implementation of our formalism. These steps pave the way to applying the proposed method to heavier nuclei in the future.
Bibliographical noteFunding Information:
S.B. would like to thank Matteo Vorabbi for useful discussions. This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through the Cluster of Excellence “Precision Physics, Fundamental Interactions, and Structure of Matter” ( EXC 2118/1) funded by the DFG within the German Excellence Strategy (Project ID 39083149), and by the Israel Science Foundation, Grant No. 1086/21.
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