A Bird’s Eye View on the Concept of Multichannel Scattering with Applications to Materials Science, Condensed Matter, and Nuclear Astrophysics
The last few years have witnessed remarkable advances in two branches of condensed matter physics. The first deals with the experimental investigation by electron spectroscopy techniques of the laws governing the behavior of strongly correlated systems. This flourishing experimental area has been fueled most notably by potential applications of high-Tc superconductors (Kordyuk, 2012), graphene (Dresselhaus, 2014), graphenelike structures (Butler et al., 2013), and layered heterostructures (Novoselov et al., 2005) to device engineering. The most remarkable outcome of this analysis is the realization that electronic states other than simple Fermi liquids occur in several materials families. Consequently, a wealth of theoretical and computational methods have been developed to describe accurately the electronic correlation in these low-dimensional many-fermion systems and to investigate unusual physical phenomena that appear in the presence of charge confinement or strong interaction. These methodological developments can be branched in two categories: selfconsistent mean-field approaches, such as Hartree-Fock (HF) and density functional, and approaches beyond mean-field, such as multi-configurational methods and manybody perturbation theory (MBPT) (Szabo and Ostlund, 1996; Onida et al., 2002). In this regard, the new “Fermi-Dirac” physics of graphene and its derivatives represents one of the most significant case studies of interlacing novel theories and experiments so far (Taioli et al., 2009a; Haberer et al., 2010, 2011; Umari et al., 2012; Taioli, 2014). However, while these methods found extensive use in the specific research field for which they were tailored, mainly related to materials science, it is rather unusual to observe applications crossing the borders between different areas. At variance, the goal of this opinion article is to provide a “bird’s eye view” on a recently developed ab initio method (Taioli et al., 2009b,c, 2010), firstly implemented to perform spectral analysis of solids at drastically reduced computational cost. This method has been further extended, as well as successfully used, in apparently distant applications, ranging from materials science to astrophysics. Hereby, after a description of the conceptual framework behind this approach we will prove its ability to span different research fields by interpreting a specific set of physical problems in the meV to MeV range. In particular, we will discuss the Auger effect in SiO2 (Taioli et al., 2009b), the BEC-BCS crossover in ultracold Fermi gases (UFG) (Simonucci et al., 2011, 2012; Garberoglio et al., 2013), and finally the electron capture in stellar plasma (Simonucci et al., 2013). The physical picture, under which all the previous phenomena can be framed, is the existence of one (or many) intermediate, quasi-bound state(s) produced by an initial scattering event, embedded in the continuum represented by one or more fragments of the system under investigation. Depending on the initial kinetic energy of the impinging projectile, the dynamics of the excited target system may undergo a resonant state before decaying. Correlation between system’s many constituents in the intermediate state is the driving force to final decay, possibly leading to several outcomes characterized by a particular set of observables (“channels”). Multichannel outcomes are ultimately the fingerprint of the many-body nature of interactions. We stress that, while scattering events may be driven by different forces coupling the initial and final states, be it Coulomb as in the Auger decay or weak as in β-decay, nevertheless the common platform to all these processes is given by the discretecontinuum interaction, named after FanoFesbach (Fano, 1961). Scattering theory aims to find positive energy solutions (scattering states) of the following many-body Hamiltonian: