Physics
Nuclear Energy Functionals
I am very interested in the development of novel energy functionals for the purpose of constructing a global mass table for nuclei.
Alternate representations of NN potentials
NB: I am by no means an expert on ab initio approaches to nuclear interactions and my understanding of the current state of the field may be incorrect. My interest lies in the mathematical techniques used on the following topic.
The continuing advancements made in nuclear structure through ab initio methods hing greatly on the various realistic two-nucleon (NN) potentials now available [for a historical review see R. Machleidt, Adv. Nucl. Phys. 19 (1989)]. While computationally dificult to implement in describing heavy nuclei, the NN potentials provide a sophisticated model for nuclear interactions. With increasing complexity, the choice of a momentum of configuration spatial representation of the potential becomes important.
In more recent times, NN potentials tend to be formulated in momentum space. With the new ground made by [pmath size=10]V_{low-k}[/pmath] interactions (through chiral perturbative EFTs), it may not come as a surprise that momentum has become the space “of choice.” A (very) small set of the advantages of momentum space representations is the ease with which they can be constructed fully relativistically and that experimental measurements are infact made in this representation, making comparison more direct. In response to the latter advantage in particular I have developed an interest change of basis transformations for NN potentials in configuration space (work which led to a M.Sc. thesis).
While at first glance it may seem an uninteresting topic since the transformation from configuration basis to a momentum basis is clearly given by a Fourier transform. However, the Fourier transforms of these functions are far from trivial to compute analytically. Taking the form of Yukawa-like potentials, these functions have many apparent singularities that must be properly dealt with. My previous work was specifically on the Reid potential (a quite antiquated interaction from several decades ago). However there are more recent (and still referenced) potentials whose basis transformation would be interesting to study, such Av18.
It is true, though, that momentum space NN potentials may not be as easily visualized as those in configurations space.