THREE-BODY SCATTERING THEORY AND ITS APPLICATIONS
Yasuro Koike

  1. THREE-BODY SCATTERING THERORY
    • Review of two-body scattering theory
    • Thresholds in three-body systems
    • Faddeev equations
    • Boundary conditions and the kernel of integral equation
    • Some ideas about the method of solution
  2. NUCLEON-DEUTERON SCATTERING
    • Nuclear interactions
    • Triton binding energy
    • Success in low energy nucleon-deuteron scattering and Ay puzzle
    • Intermediate p-d scattering and the three-body interaction
    • Some topics on three-nucleon breakup reactions
    • Some new trials
  3. UNSTABLE THREE-BODY SYSTEMS AND THREE-BODY RESONANCES
    • Several systems which can be treated as three-body systems
    • Complexity of the thresholds
    • Three-body resonances
    • Unstable nulei as three-body systems
    • Efimov effect
  4. A NEW THEORETICAL APPROACH WHICH MAY OPEN THE DOOR TO THE FOUR-BODY SCATTERING
    • Contour deformation --- Analytical continuation in the complex momentum space
    • Complex energy method ---Analytical continuation in the total energy of the system

I will give a series of lectures on three-body scattering theory, which brought us a remarkable success in the proton-deuteron scattering, in the world wide collaborations between theory(Bochum group, Los-Alamos group, Hanover group, Pisa group and groups in Japan) and experiments(Tokyo-RIKEN, Kyushu, TUNL and many), and will bring us further remarkable successes.

Assuming a basic idea about two-body scattering theory, I will show how the three-body scattering theory described in the integral equations, which contains the boundary conditions. The boundary conditions are described in the Green's functions as singularities. This is known in the two-body scattering theory, and is the same in the three-body scattering theory with more complexity. I will demonstrate how the singularities look like. It is in momentum space. In the coordinate space it is more complicated. That is why three-body equations are usually solved in momentum space. This gives the audience an idea how the theoreticians solve the nucleon-deuteron scattering. This is the first part of my lecture.

In the second part of my lecture, I will describe basic aspects of the nucleon-deuteron scattering. The study of this fundamental systems has been done since the early stage of the few-body studies at 60's. Only in the last 15 years, the study has become realistic. In the first stage, the study has done with phenomenological separable potential. In the second stage, realistic two-nucleon potentials are used. Only recently, the three-nucleon interactions are found to be important to describe the experiment. Learning from the basic features of the three-nucleon scattering, we try to figure out about further steps in this fundamental system.

In the third part of my lecture, I will discuss other three-body systems in nuclear physics. Especially interesting systems are in unstable nuclei as well as in hypernuclei. Applying the idea discussed in the first lecture, I will show the audience how thresholds affect these systems especially in resonances. I will show that the spin-parity assignments sometimes will be given definitely from the position and the width of the resonance in the relation to the location of the thresholds. Very interesting phenomena known as Efimov effect will be discussed. This famous effect can not be understood without the argument of singularities or boundary conditions of the three-body system.

Singularities make the three-body phenomena interesting. But at the same time, it makes three-body scattering complicated to treat. It has been very difficult to figure out how the four-body scattering equations can be solved at higher energies where four-body breakup channel opens up. The singularities become very complicated. To conclude my lecture, I will propose a method in which complicated singularities may be almost forgotten. This method makes the solution of Faddeev equations in the scattering region much easier, and therefore, makes the few-body scattering theory more popular among new generation of nuclear physicists.

Lecture Note

CISS02 Program