In the past years various new hadronic states were discovered in the charm and bottom meson sector by experiments like Belle, BES and Babar. Many of these states fit into the conventional charmonium or bottomonium spectrum, but a growing number of them does not. Especially, the charged ones which can definitely be no conventional hadrons motivate the term exotic hadrons to classify particles which are neither conventional baryons nor conventional mesons. Their substructure is not yet clear due to the often poor experimental knowledge and there are many different interpretations for these exotic particles. One very popular idea is the hadronic molecule interpretation which states that two ordinary hadrons can form a loosely bound pair similar to the deuteron made of a proton and a neutron. However, in the latter system it is known that after adding a third nucleon there appears a three particle bound state, the triton. The emergence of such a three-body state can be explained by the Efimov effect as a low-energy universality phenomenon. The question which will be answered in this work is if there exists also an Efimov effect in systems of hadronic molecules which scatter off a third meson or baryon. Since the number of candidate systems is large (and still growing due to ongoing experiments) it is useful to find a general expression that tells us if the Efimov effect is present. Moreover, this expression should only depend on the basic particle properties like mass, spin and isospin. Such a relation will be derived in this work for a generic three particle system that can be described in a pionless effective field theory. It will then be applied to a set of possible hadronic molecule systems in order to check if the Efimov effect occurs. The thesis is organized as follows: after an introduction of quantum chromodynamics and a review of the classification of hadrons we continue with a summary, firstly, of experimental observations concerning exotic hadrons, secondly, of the idea of effective field theories and thirdly, of basic scattering theory. In chapter 2 the three identical boson system will be discussed in order to explain the Efimov effect more quantitatively. With this knowledge it is possible to derive the mentioned general expression regarding the existence of Efimov physics in a generic three particle system. After the detailed derivation in chapter 3 (using the information given in the appendices) the results will be applied to scattering processes where known hadronic molecules as well as hypothetical ones are involved. This is done in order to either search for the Efimov effect or - for the hypothetical molecular states - to predict under which conditions an Efimov trimer is expected. For system without Efimov effect we will calculate in chapter 5 for a selected example S-wave observables of the in this case elastic scattering process. The thesis is completed by a summary of the results and an outlook on further work that can be done based on this work.
The interaction of neutrons and nuclei at low energies may potentially lead to scattering lengths several orders of magnitude larger than the effective range of the interaction, well beyond the nuclear scale. If such cases existed, they could lead to the observation of the Efimov effect in nuclei, a remarkable universal phenomenon that has been observed only in atoms. The interaction parameters of neutrons scattering off unstable nuclei can be explored in neutron-nucleus systems created after the fast removal of a few nucleons from a slightly heavier beam. The case of the 17 B- n system is considered, and the implications of its potentially huge scattering length on the structure of 19 B as a 17 B- n - n Efimov trimer is discussed.
Continuum structures of three short-range interacting particles in a deformed external one-body field are investigated. We use the equivalent
d method employing noninteger dimension,
d, in a spherical calculation with a dimension-dependent angular momentum barrier. We focus on dimensions close to the critical dimension,
d=dE, between 2 and 3, defined by zero two-body energies, where the Efimov effect can occur. We design for this dimension region a schematic, long-distance realistic, square-well based, three-body spherical model, which is used to derive analytic expressions for the wave functions, scattering lengths, phase shifts, and elastic-scattering cross sections. The procedure and the results are universal, valid for all short-range potentials, and for large scattering lengths. We discuss the properties and validity of the derived expressions by means of the simplest system of three identical bosons. The derived expressions are particularly useful for very small energies, where full numerical calculations are often not feasible. For energies where the numerical calculations can be performed, a good agreement with the analytic results is found. These model results may be tested by scattering experiments for three particles in an equivalent external deformed oscillator potential. The cross sections all vanish in the zero-energy limit for
d<3 with definite
d-dependent power of energy.
By studying the eigenvalue spectrum of the Faddeev kernel in a certain singular limit, we give an independent proof of an effect recently deduced by Efimov: When three identical particles interact via short-range pairwise potentials, the number of three-body bound states grows without limit when the pairwise scattering length
a becomes large. [The number of bound states is then roughly $(\frac{1}{\ensuremath{\pi}})\mathrm{ln}(\ensuremath{\Lambda}|a|)$, where $\ensuremath{\Lambda}$ is a momentum cutoff]. We extend our proof to the case where only two particles are identical and show that Efimov's effect persists in the special limiting cases with two heavy and one light particle, and with two light and one heavy particle.
The quantum three body problem generally has its own complexities and is difficult to solve. It requires rigorous steps and iterations to find the solution. We often encounter three body system in various branches of physics including Nuclear Physics, Particle, Atomic, Molecular physics, and condensed matter. The underlying physics involved is quite complicated. Faddeev in 1961 made a successful attempt and formulated theory of three particle scattering in a rather rigorous mathematical way. Efimov developed a method that enabled one to obtain the universal properties of three particle system and is quite independent of the two body potentials. This article attempts to introduce Efimov effect. The formalism and the salient features are also discussed.