**3. r-Process Nucleosynthesis**

The r-process is the astrophysical origin of about half of the elements heavier than iron [78]. It occurs in an astrophysical environment with extreme neutron densities [79,80]. The r-process site has been a mystery for a long time until the observation of the neutron star merger event GW170817 by gravitational waves and its associated electromagnetic signal proved that heavy elements are produced by neutron star mergers [81,82]. The observed electromagnetic transient, called "kilonova," agreed well with prior predictions [83].

r-process simulations show that the reaction path in the nuclear chart runs through nuclei with such large neutron excesses that most of them have yet not been made in the laboratory and their properties have to be modeled. The relevant nuclear properties are masses, half lives, fission rates and yields and neutron capture rates [80]. Shell model calculations improved the determination of half lives for the nuclei with magic neutron numbers, which with their relatively long half-lives, act as obstacles in the r-process flow. They have also demonstrated new methods to calculate electromagnetic strength functions and nuclear level densities, which are both required to calculate neutron capture rates within the framework of the statistical model. For a very recent review of the various astronomical, astrophysical, nuclear, and atomic aspects of r-process nucleosynthesis; see Ref. [84].

r-Process nucleosynthesis proceeds by successive neutron captures and beta decays, which increase the mass and charge numbers, respectively. Nuclear half lives decide the time required to produce the heaviest elements, beginning from free protons and neutrons

that exist in the hot environment of merging neutron stars before matter is ejected and cooled allowing nuclei to form. Hence, nuclear beta decays compete with the time scales of the dynamical evolution of the ejected matter. There has been important progress made by measuring the half lives of some intermediate-mass nuclei on the r-process path [85,86]. However, most half lives still have to be modeled. Global sets of r-process half lives have been determined by QRPA calculations on the basis of phenomenological parametrizations [87,88] and more recently of microscopic Hartree-Fock-Bogoliubov (HFB) or density functional approaches [89–93].

Particularly important for the r-process mass flow are the waiting point nuclei at the magic neutron numbers *N* = 50, 82 and 126, which have rather long half lives due to their closed-shell configurations. For these nuclei, large-scale shell model calculations exist. Importantly, a few of these half lives could also been measured, showing good agreement with the shell model results: for 78Ni, an experiment done at the National Superconducting Cyclotron Laboratory (NSCL) experiment found a half life of 110 ± 40 ms [94], while the shell model predicted 127 ms [4]. Data and shell model results for the *N* = 82 waiting points are compared in Figure 3. Unfortunately, no data exist yet for *N* = 126 waiting points. For these nuclei, two independent shell model calculations have pointed to the importance of forbidden transitions induced by intruder states [21,22]. These forbidden transitions are predicted to shorten the half lives of the *N* = 126 waiting points noticeably and enhanced the mass flow through these waiting points [95]. This implies more r-process material available for fission, thus affecting the abundances of the second r-process peak around atomic mass number, *A* = 130, which for very neutron-rich ejecta is built up by fission yields [95,96]. The enhanced mass flow also increase late-time *α*-decays from the decaying r-process matter, which influence the kilonova signal [97].

**Figure 3.** Comparison of shell model half lives for neutron number *N* = 82 r-process (rapid neutroncapture process) waiting point nuclei with data [86,98–100]. The GT strengths underlying the shell model results have been quenched with the standard factor of (0.74)<sup>2</sup> [30]. Taken from [84].

Neutron capture rates become relevant for r-process nucleosynthesis once the process drops out of (*n*, *γ*) (*γ*, *n*) equilibrium at temperatures below about 1 GK. Neutron capture rates are traditionally derived within the statistical Hauser–Feshbach model, although this approach might not always be justified for r-process nuclei; see discussion and references in [84]. Important ingredients in the Hauser–Feshbach approach are the nuclear level densities and the *γ*-strength functions [80]. Shell model calculations have provided a better understanding of both quantities.

A method has been presented to derive level densities within the SMMC approach by exploiting its ability to describe nuclei in extremely large model spaces and to account for the correlations among nucleons [25,26]. The method has been used to explore the effects of parity, angular-momentum and pairing on the level density [101–103]. Based on SMMC studies, Alhassid et al. [104] presented an approach in which a microscopically derived parity-dependence is incorporated into phenomenological level density formulas. This approach has been used to derive a large set of r-process nuclei by also employing a temperature-dependent parametrization of the pairing parameter modeled after SMMC calculations [105]. These improved level densities are now part of statistical model packages NON-SMOKER and SMARAGD, developed by Rauscher [106–108]. An alternative microscopic approach to level densities, built on the HFB model, has been derived by Goriely and collaborators [109–111].

Experimentally determined dipole *γ*-strength functions show an upbend of the strength towards low gamma energies [112,113], which can have important impacts on neutron capture rates [23,24,113–116]. The upbend in the M1 strength has been studied and reproduced in shell model calculations for *p f*-shell and heavier nuclei [117,118]. Similar studies have been used to calculate the M1 contribution to the neutron capture rate in a consistent state-by-state approach [119]. This study found that the rate will be dominated by a single resonance if this state happens to fall into the Gamow window of the reaction. Such a situation is difficult to describe within a statistical approach. The calculation also shows that the M1 scissors mode observed in deformed nuclei [120] can lead to a significant enhancement of the capture rate.
