H. W. Hammer

Updated dispersion-theoretical analysis of the nucleon electromagnetic form factors

Abstract.In the light of the new data on the various neutron and proton electromagnetic form factors taken in recent years, we update the dispersion-theoretical analysis of the nucleon electromagnetic form factors from the mid-nineties. The parametrization of the spectral functions includes constraints from unitarity, perturbative QCD, and recent measurements of the neutron charge radius. We obtain a good description of most modern form factor data, with the exception of the Jefferson Lab data on GEp/GMp in the four-momentum transfer range

Universal Properties of the Four-Body System with Large Scattering Length

Q^2 = 3 \ldots 6

The size of the proton - closing in on the radius puzzle

GeV2. For the magnetic radii of the proton and the neutron we find rMp = 0.857 fm and rMn = 0.879 fm, which is consistent with the recent determinations using continued-fraction expansions.

Efimov Physics in Cold Atoms

Abstract.Few-body systems with large scattering length have universal properties that do not depend on the details of their interactions at short distances. We study the universal bound-state properties of the four-boson system with large scattering length in an effective quantum mechanics approach. We compute the four-body binding energies using the Yakubovsky equations for positive and negative scattering length. Moreover, we study the correlation between three- and four-body energies and present a generalized Efimov plot for the four-body system. These results are useful for understanding the cluster structure of nuclei and for the creation of weakly bound tetramers with cold atoms close to a Feshbach resonance.

Universal properties and structure of halo nuclei

We analyze the recent electron-proton scattering data from Mainz using a dispersive framework that respects the constraints from analyticity and unitarity on the nucleon structure. We also perform a continued fraction analysis of these data. We find a small electric proton charge radius, rEp = 0.84−0.01+0.01 fm, consistent with the recent determination from muonic hydrogen measurements and earlier dispersive analyses. We also extract the proton magnetic radius, rMp = 0.86−0.03+0.02 fm, consistent with earlier determinations based on dispersion relations.

Efimov States in Nuclear and Particle Physics

Abstract Atoms with a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-atom sector, the universal properties are familiar and depend only on the scattering length. In the 3-atom sector for identical bosons, the universal properties include the existence of a sequence of shallow triatomic molecules called Efimov trimers and log-periodic dependence of scattering observables on the energy and the scattering length. In this review, we summarize the universal results that are currently known. We also summarize the experimental information that is currently available with an emphasis on 3-atom loss processes.

Three-body problem in heteronuclear mixtures with resonant interspecies interaction

The universal properties and structure of halo nuclei composed of two neutrons (2n) and a core are investigated within an effective quantum mechanics framework. We construct an effective interaction potential that exploits the separation of scales in halo nuclei and treat the nucleus as an effective three-body system. The uncertainty from higher orders in the expansion is quantified through theoretical error bands. First, we investigate the possibility to observe excited Efimov states in 2n halo nuclei. Based on the experimental data, 20C is the only halo nucleus candidate to possibly have an Efimov excited state, with an energy less than 7 keV below the scattering threshold. Second, we study the structure of 20C and other 2n halo nuclei. In particular, we calculate their matter form factors, radii, and two-neutron opening angles.

Topological phases for bound states moving in a finite volume

Particles with resonant short-range interactions have universal properties that do not depend on the details of their structure or their interactions at short distances. In the three-body system, these properties include the existence of a geometric spectrum of three-body Efimov states and a discrete scaling symmetry, which leads to log-periodic dependence of observables on the scattering length. Similar universal properties appear in the four-body system and possibly higher-body systems as well. For example, universal four-body states have recently been predicted and observed in experiments. These phenomena are often referred to as Efimov physics. We review their theoretical description and discuss applications in different areas of physics with a special emphasis on nuclear and particle physics.

Range corrections for two-neutron halo nuclei in effective theory

We use the zero-range approximation to study a system of two identical bosons interacting resonantly with a third particle. The method is derived from effective field theory. It reduces the three-body problem to an integral equation which we then solve numerically. We also develop an alternative approach which gives analytic solutions of the integral equation in coordinate representation in the limit of vanishing total energy. The atom-dimer scattering length, the rates of atom-dimer relaxation, and the three-body recombination to shallow and to deep molecular states are calculated either analytically or numerically with a well-controlled accuracy for various energies as functions of the mass ratio, scattering length, and three-body parameter. We discuss in detail the relative positions of the recombination loss peaks, which in the universal limit depend only on the mass ratio. Our results have implications for ongoing and future experiments on Bose-Bose and Bose-Fermi atomic mixtures.

On the strong energy dependence of the e+e−↔pp¯ amplitude near threshold

We show that bound states moving in a finite periodic volume have an energy correction which is topological in origin and universal in character. The topological volume corrections contain information about the number and mass of the constituents of the bound states. These results have broad applications to lattice calculations involving nucleons, nuclei, hadronic molecules, and cold atoms. We illustrate and verify the analytical results with several numerical lattice calculations.