Marchenko method with incomplete data and singular nucleon scattering

Extra dimensions, SN1987a, and nucleon-nucleon scattering data

One of the strongest constraints on the existence of large, compact, “gravityonly” dimensions comes from SN1987a. If the rate of energy loss into these putative extra dimensions is too high, then the neutrino pulse from the supernova will differ from that actually seen. The dominant mechanism for the production of Kaluza-Klein gravitons and dilatons in the supernova is via gravistrahlung and di...

Inverse Scattering on the Line with Incomplete Scattering Data

The Schrödinger equation is considered on the line when the potential is real valued, compactly supported, and square integrable. The nonuniqueness is analyzed in the recovery of such a potential from the data consisting of the ratio of a corresponding reflection coefficient to the transmission coefficient. It is shown that there are a discrete number of potentials corresponding to the data and...

Partially-Quenched Nucleon-Nucleon Scattering

Nucleon-nucleon scattering is studied to next-to-leading order in a partially-quenched extension of an effective field theory used to describe multinucleon systems in QCD. The partially-quenched nucleon-nucleon amplitudes will play an important role in relating lattice simulations of the two-nucleon sector to nature.

Image Reconstruction from Incomplete Data

Implementation of the Marchenko method

The Marchenko method makes it possible to compute subsurface-to-surface Green’s functions from reflection measurements at the surface. Applications of the Marchenko method have already been discussed in many papers, but its implementation aspects have not yet been discussed in detail. Solving the Marchenko equation is an inverse problem. The Marchenko method computes a solution of the Marchenko...