@article{rokash_pine_elhatisari_lee_epelbaum_krebs_2015, title={Scattering cluster wave functions on the lattice using the adiabatic projection method}, volume={92}, ISSN={["1089-490X"]}, DOI={10.1103/physrevc.92.054612}, abstractNote={The adiabatic projection method is a general framework for studying scattering and reactions on the lattice. It provides a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time. Previous studies have used the adiabatic projection method to extract scattering phase shifts from finite periodic-box energy levels using L\"uschers method. In this paper we demonstrate that scattering observables can be computed directly from asymptotic cluster wave functions. For a variety of examples in one and three spatial dimensions, we extract elastic phase shifts from asymptotic cluster standing waves corresponding to spherical wall boundary conditions. We find that this approach of extracting scattering wave functions from the adiabatic Hamiltonian to be less sensitive to small stochastic and systematic errors as compared with using periodic-box energy levels.}, number={5}, journal={PHYSICAL REVIEW C}, author={Rokash, Alexander and Pine, Michelle and Elhatisari, Serdar and Lee, Dean and Epelbaum, Evgeny and Krebs, Hermann}, year={2015}, month={Nov} }
@article{pine_lee_rupak_2013, title={Adiabatic projection method for scattering and reactions on the lattice}, volume={49}, ISSN={["1434-601X"]}, DOI={10.1140/epja/i2013-13151-3}, abstractNote={We demonstrate and test the adiabatic projection method, a general new framework for calculating scattering and reactions on the lattice. The method is based upon calculating a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time. As a detailed example we calculate the adiabatic two-body Hamiltonian for elastic fermion-dimer scattering in lattice effective field theory. Our calculation corresponds to neutron-deuteron scattering in the spin-quartet channel at leading order in pionless effective field theory. We show that the spectrum of the adiabatic Hamiltonian reproduces the spectrum of the original Hamiltonian below the inelastic threshold to arbitrary accuracy. We also show that the calculated s -wave phase shift reproduces the known exact result in the continuum and infinite-volume limits. When extended to more than one scattering channel, the adiabatic projection method can be used to calculate inelastic reactions on the lattice in future work.}, number={12}, journal={EUROPEAN PHYSICAL JOURNAL A}, author={Pine, Michelle and Lee, Dean and Rupak, Gautam}, year={2013}, month={Dec} }
@article{pine_lee_2013, title={Effective field theory for bound state reflection}, volume={331}, ISSN={["1096-035X"]}, DOI={10.1016/j.aop.2012.12.009}, abstractNote={Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory for elastic reflection of shallow dimers from hard-wall surfaces using effective field theory. We show that there is a small expansion parameter for analytic calculations of the reflection scattering length. We present a calculation up to second order in the effective Hamiltonian in one, two, and three dimensions. We also provide numerical lattice results for all three cases as a comparison with our effective field theory results. Finally, we provide an analysis of the compressibility of the alpha particle confined to a cubic lattice with vanishing Dirichlet boundaries.}, journal={ANNALS OF PHYSICS}, author={Pine, Michelle and Lee, Dean}, year={2013}, month={Apr}, pages={24–50} }