Recent developments for the optical model of nuclei

Abstract

A brief overview of various approaches to the optical-model description of nuclei is presented. A survey of some of the formal aspects is given which links the Feshbach formulation for either the hole or particle Green's function to the time-ordered quantity of many-body theory. The link between the reducible self-energy and the elastic nucleon-nucleus scattering amplitude is also presented using the development of Villars. A brief summary of the essential elements of the multiple-scattering approach is also included. Several ingredients contained in the time-ordered Green's function are summarized for the formal framework of the dispersive optical model (DOM). Empirical approaches to the optical potential are reviewed with emphasis on the latest global parametrizations for nucleons and composites. Various calculations that start from an underlying realistic nucleon-nucleon interaction are discussed with emphasis on more recent work. The efficacy of the DOM is illustrated in relating nuclear structure and nuclear reaction information. Its use as an intermediate between experimental data and theoretical calculations is advocated. Applications of the use of optical models are pointed out in the context of the description of nuclear reactions other than elastic nucleon-nucleus scattering. arXiv:1811.03111v1 [nucl-th] 7 Nov 2018The number of works that are encompassed by the title of "optical model" is immense and any review must be selective. The topics and studies present in this review are biased by the interests of the authors. We start with several theoretical derivations of the optical potential and its connection to the self-energy in many-body formulations in Sec. 2. In Sec. 2.1 the analysis of Capuzzi and Mahaux [6] will be employed to link the Feshbach approach to the many-body perspective provided by the time-ordered Green's function. We complement this in Sec. 2.2 with a derivation by Villars [7] that formalizes the work of Ref.[8] that demonstrates the equivalence of the nucleon-nucleus T -matrix to the on-shell reducible nucleon self-energy Σ red associated with the time-ordered Green's function. This approach is important as it can be extended to the description of more complicated reactions involving composite projectiles or ejectiles. In Sec. 2.3 we briefly summarize some elements of the multiple-scattering approach but refrain from a detailed presentation which is available in Ref. [9]. We will take particular interest in the empirical dispersive optical model (DOM) where the real and imaginary potentials are connected by dispersion relations thereby enforcing causality. This approach allows one to exploit the formal properties of the time-ordered Green's function including its link to the nucleon self-energy through the Dyson equation [10,11]. As the dispersion relations require the optical potentials to be defined at both positive and negative energy, the formalism makes connections between nuclear reactions and nuclear structure needed for a better understanding of rare isotopes. Some ingredients...

Investigating the link between proton reaction cross sections and the quenching of proton spectroscopic factors in 48Ca

“…This is not consistent with corresponding results of transfer reactions reviewed in Ref. [11] or the single-nucleon removal experiments recently reported in Refs. [12,13].…”

Generic nature of asymptotic completeness in dissipative scattering theory

“…In this context, the pseudo-Hamiltonian H considered previously is given by a dissipative Schrödinger operator. See [12,14] for a thorough exposition of various versions of the model and their physical interpretations, and [6] for more recent developments. Hence, in this section, we focus on the nuclear optical model, setting…”

Point-Particle Catalysis

“…In many cases it is overkill to track all of the possible final state products of a particular interaction. This is especially the case in nuclear physics, where a summation over many unobserved final states is the basis of the highly successful optical model [14,15]. The price one pays for the convenience of ignoring certain states is the loss of unitarity, and such a non-unitary point-particle EFT was the subject of Plestid et al [13].…”

“…In that case, the flavor-violating crosssection appears as an absorptive interaction when restricting to the particle 1 subspace of the theory. In this way, our toy model can be seen as a particular unitary completion of a model with a single particle subject to a non-self-adjoint Hamiltonian, as studied in Plestid et al [13] and frequently used in the form of nuclear optical models [14,15].…”