Theoretical Methods for Giant Resonances

TL;DR

This paper reviews the theoretical methods, especially RPA and its extensions, used to describe Giant Resonances, highlighting recent developments, alternative approaches, and the importance of continuum effects and observables.

Contribution

It provides a comprehensive overview of recent advances in RPA-based methods, including Finite Amplitude Method and ab initio calculations, for modeling Giant Resonances.

Findings

RPA naturally emerges for harmonic time dependence in particle-hole space.

Extensions of RPA improve the description of Giant Resonances.

Recent methods incorporate continuum effects and ab initio approaches.

Abstract

The Random Phase Approximation (RPA) and its variations and extensions are, without any doubt, the most widely used tools to describe Giant Resonances within a microscopic theory. In this chapter, we will start by discussing how RPA comes out naturally if one seeks a state with a harmonic time dependence in the space of one particle-one hole excitations on top of the ground state. It will be also shown that RPA is the simplest approach in which a ``collective'' state emerges. These are basic arguments that appear in other textbooks but are also unavoidable as a starting point for further discussions. In the rest of the chapter, we will give emphasis to developments that have taken place in the last decades: alternatives to RPA like the Finite Amplitude Method (FAM), state-of-the-art calculations with well-established Energy Density Functionals (EDFs), and progress in {\em ab initio} calculations. We will discuss extensions of RPA using as a red thread the various enlargements of the one particle-one hole model space. The importance of the continuum, and the exclusive observables like the decay products of Giant Resonances, will be also touched upon.