Novel applications of the dispersive optical model

Abstract

A review of recent developments of the dispersive optical model (DOM) is presented. Starting from the original work of Mahaux and Sartor, several necessary steps are developed and illustrated which increase the scope of the DOM allowing its interpretation as generating an experimentally constrained functional form of the nucleon self-energy. The method could therefore be renamed as the dispersive self-energy method. The aforementioned steps include the introduction of simultaneous fits of data for chains of isotopes or isotones allowing a data-driven extrapolation for the prediction of scattering cross sections and level properties in the direction of the respective drip lines. In addition, the energy domain for data was enlarged to include results up to 200 MeV where available. An important application of this work was implemented by employing these DOM potentials to the analysis of the (d, p) transfer reaction using the adiabatic distorted wave approximation. We review these calculations which suggest that physically meaningful results are easier to obtain by employing DOM ingredients as compared to the traditional approach which relies on a phenomenologically-adjusted bound-state wave function combined with a global (nondispersive) optical-model potential. Application to the exotic 132Sn nucleus also shows great promise for the extrapolation of DOM potentials towards the drip line with attendant relevance for the physics of FRIB. We note that the DOM method combines structure and reaction information on the same footing providing a unique approach to the analysis of exotic nuclei. We illustrate the importance of abandoning the custom of representing the non-local Hartree–Fock (HF) potential in the DOM by an energy-dependent local potential as it impedes the proper normalization of the solution of the Dyson equation. This important step allows for the interpretation of the DOM potential as representing the nucleon self-energy permitting the calculations of spectral amplitudes and spectral functions above and below the Fermi energy. The latter feature provides access to quantities like the momentum distribution, charge density, and particle number which were not available in the original work of Mahaux and Sartor. When employing a non-local HF potential, but local dispersive contributions (as originally proposed by Mahaux and Sartor), we illustrate that it is impossible to reproduce the particle number and the measured charge density. Indeed, the use of local absorptive potentials leads to a substantial overestimate of particle number. However from detailed comparisons with self-energies calculated with ab initio many-body methods that include both short- and long-range correlations, we demonstrate that it is essential to introduce non-local absorptive potentials in order to remediate these deficiencies. We review the fully non-local DOM potential fitted to 40Ca where elastic-scattering data, level information, particle number, charge density and high-momentum-removal cross sections obtained at Jefferson Lab were included in the analysis. All these quantities are accurately described by assuming more or less traditional functional forms for the potentials but allowing for non-locality and the abandonment of complete symmetry around the Fermi energy for surface absorption which is suggested by ab initio theory. An important consequence of this new analysis is the finding that the spectroscopic factor for the removal of valence protons in this nucleus comes out larger by about 0.15 than the results obtained from the NIKHEF analysis of their data. This issue is discussed in detail and its implications clarified. Another important consequence of this analysis is that it can shed light on the relative importance of two-body and three-body interactions as far as their contribution to the energy of the ground state is concerned through application of the energy sum rule.