Universality and Beyond
Department of Physics and Astronomy, Ohio University,
2 Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn, D-53115, Bonn, Germany
a e-mail: firstname.lastname@example.org
I discuss the impact of a ﬁnite eﬀective range, r, on systems with a large two-body scattering length, a. In particular, I show how observables can be written as an expansion around the “universal”, or large-scatteringlength limit. The parameter governing this expansion is the ratio r/a. In few-nucleon systems the ratio r/a has a value of about 1/3, and so such corrections are essential in producing good agreement between theory and data. Hence, I ﬁrst show how these eﬀects range play a key role in making the so-called “pionless” eﬀective ﬁeld theory a successful descriptor of low-energy processes in the NN system. I then move to the NNN system, and review predictions for the energy-dependence of observables there. However, the beautiful Eﬁmov physics associated with the presence of a large scattering length is not fully revealed in the NNN system, precisely because r/a corrections are large. I therefore turn to cold atomic gases and show that there are some important recent experiments where physics “beyond universality” aﬀects the data. In the process I demonstrate that an additional piece of short-distance physics is necessary to renormalize scattering-length-dependent observables in the three-body system once corrections ∼ r are considered. Finally, I discuss recent initial eﬀorts to compute r/a corrections to the predictions of universality for the four-body system.
© Owned by the authors, published by EDP Sciences, 2010