Abstract
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.
Highlights
In the context of few-body systems, “universality” refers to two, three, and four-body systems that have properties which are independent of the details of the underlying interaction
EM properties have a wealth of experimental data, including phase shifts and electromagnetic properties, all of which allow us to look at the effects of finite- on the low-energy properties of NN, NNN, and even NNNN systems
That calculation was carried out to next-to-next-to-next-to-leading order (N3LO) in the large-scattering-length effective field theory (EFT). From this calculation it is very clear that /|a| corrections are crucial to getting an accurate description of the energy dependence of the deuteron photodisintegration cross section in the photon energy range from threshold up to 10 MeV. Once these corrections are accounted for, and both the E1 and M1 transitions considered, the predictions of the EFT were consistent with all extant data in that energy range at the level of accuracy expected given that the first omitted correction is of order (r/a
Summary
In the context of few-body systems, “universality” refers to two-, three-, and four-body systems that have properties which are independent of the details of the underlying interaction. Under the rubric of “universality” we collect systems as diverse as cold atoms, the X(3872), halo nuclei, and few-nucleon systems We see that their bound (and, in some cases, low-energy scattering) states share certain common features, even though the microscopic interactions are quite different in all cases. EM properties have a wealth of experimental data, including phase shifts and electromagnetic properties, all of which allow us to look at the effects of finite- on the low-energy properties of NN, NNN, and even NNNN systems. EPJ Web of Conferences tend to examine observables as a function of energy, but at fixed a, while in atomic recombination we work at fixed (or, to be more precise, some average) energy but variable a Both kinds of investigation provide useful ways to look for effects beyond universality.
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