2010 - 19th Annual NC State Undergraduate Research Spring Symposium

Session Time : 4/22/10 12:15 PM - 4/22/10 1:30 PM

Content Area : Physics

Student Presenters :
Michelle Jane Pine Physics

Mentors and/or Co-Authors :
Dean Lee Physics

Abstract Title : Reflection Phase Shifts for Composite-Body Scattering off of Hard-Wall Boundaries

Abstract :
In order to understand the properties of a classical object, it is convenient to bounce it off of a surface and see how fast it bounces back. For example, if we throw a baseball and a foam Nerf ball against a wall we expect the Nerf ball to bounce off the wall slower than the baseball due to the greater compressibility of the Nerf ball. If, instead of balls we throw composite bodies composed of particles against a wall we can use the scattering phase shift to probe the structure of these bodies. The short-range interactions of such bodies are not well understood. However, for low energy reflection we can systematically replace these complicated interactions with effective interactions using effective field theory. We consider a two-body bound state of identical bosons in one dimension scattering off of a hard-wall boundary and use effective field theory to derive the reflection phase shift. The effective field theory results are compared, in the low energy limit, to results obtained analytically, via the Bethe Ansatz method, and numerically, via sparse matrix methods.