Nuclear excitations as coupled one and two random--phase--approximation modes

TL;DR

This paper introduces the double RPA (DRPA), an extension of the random-phase approximation that includes up to two RPA phonons, providing a simplified alternative to SRPA for modeling nuclear excitations and improving agreement with experimental data.

Contribution

The paper develops the DRPA model, which extends RPA by including two phonons, avoiding some SRPA limitations and offering a computationally simpler approach.

Findings

DRPA shifts energies downward compared to RPA.

DRPA reduces the energy shift compared to SRPA.

DRPA results agree well with experimental data except for certain low-lying states.

Abstract

We present an extension of the random--phase approximation (RPA) where the RPA phonons are used as building blocks to construct the excited states. In our model, that we call double RPA (DRPA), we include up to two RPA phonons. This is an approximate and simplified way, with respect to the full second random--phase approximation (SRPA), to extend the RPA by including two particle--two hole configurations. Some limitations of the standard SRPA model, related to the violation of the stability condition, are not encountered in the DRPA. We also verify in this work that the energy--weighted sum rules are satisfied. The DRPA is applied to low--energy modes and giant resonances in the nucleus $^{16}$O. We show that the model (i) produces a global downwards shift of the energies with respect to the RPA spectra; (ii) provides a shift that is however strongly reduced compared to that generated by the standard SRPA. This model represents an alternative way of correcting for the SRPA anomalous energy shift, compared to a recently developed extension of the SRPA, where a subtraction procedure is applied. The DRPA provides results in good agreeement with the experimental energies, with the exception of those low--lying states that have a dominant two particle--two hole nature. For describing such states, higher--order calculations are needed.