**1. Introduction**

The interacting shell model, which takes in account correlations beyond mean field in a valence space, is generally considered as the method of choice to describe medium-mass nuclei [1–3]. Such nuclei play crucial roles for the dynamics of astrophysical objects and their associated nucleosynthesis. Unfortunately, a direct experimental determination of the required input is often prohibited due to the extreme conditions of the astrophysical environment in terms of temperature, density and also proton-to-neutron ratio; hence, the information has to be modeled. Here, the shell model has led to decisive progress in many cases in recent years, mainly due to its ability to account for the relevant correlations among nucleons and to accurately reproduce low-energy spectra and electromagnetic transitions [2,4,5].

This paper summarizes some of the progress achieved on the basis of shell model studies. Here, two different versions of the interacting shell model have been exploited: the diagonalization shell model [2] and the Shell Model Monte Carlo (SMMC) approach [6,7]. Diagonalization shell model calculations, which in contrast to SMMC allow for detailed spectroscopy, have been performed to derive rates for weak interaction processes of nuclei up to the iron-nickel mass range [8–11]. In particular, the shell model rates for electron captures on nuclei have significant impact on the presupernova core evolution of massive stars [12,13], the core evolution at the end of the hydrostatic evolution of medium-mass stars [11,14,15] and on the nucleosynthesis in thermonuclear supernovae [16].

The SMMC approach is based on a statistical description of the nucleus at finite temperature. In contrast to diagonalization, the shell model allows the derivation of nuclear properties at finite temperatures in extremely large model spaces by taking the relevant nuclear correlations into account [6,7]. SMMC has been the basis for deriving

**Citation:** Martínez-Pinedo, G.; Langanke, K. Shell Model Applications in Nuclear Astrophysics. *Physics* **2022**, *4*, 677–689. https:// doi.org/10.3390/physics4020046

Received: 7 April 2022 Accepted: 17 May 2022 Published: 17 June 2022

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electron capture rates for heavier neutron-rich nuclei for which cross-shell correlations are essential in establishing the capture on nuclei as the main weak interaction process for the dynamics of the core collapse of a massive star [17–19].

Both varieties of the interacting shell model have improved the nuclear input required for simulations of rapid neutron-capture (r-process) nucleosynthesis. Diagonal shell model calculations have been used to derive half lives for neutron-rich nuclei with magic neutron numbers (called waiting points), which are crucial for the mass flow during the nucleosynthesis process [20–22]. Shell model calculations have also been used to study the general behavior of electromagnetic transitions, which are essential for modeling neutron capture rates, where an experimentally observed increase in the dipole's strength function at low energies has drawn attention recently [23,24]. The nuclear level density is another important ingredient in modeling neutron capture rates. Here, SMMC calculations have allowed a microscopic derivation of level densities, also allowing the exploration of parameter dependencies, used in phenomenological approachesl (see, e.g., [25,26]) .
