THREEBODY SCATTERING THEORY AND ITS APPLICATIONS
Yasuro Koike
 THREEBODY SCATTERING THERORY
 Review of twobody scattering theory
 Thresholds in threebody systems
 Faddeev equations
 Boundary conditions and the kernel of integral equation
 Some ideas about the method of solution
 NUCLEONDEUTERON SCATTERING
 Nuclear interactions
 Triton binding energy
 Success in low energy nucleondeuteron scattering and Ay puzzle
 Intermediate pd scattering and the threebody interaction
 Some topics on threenucleon breakup reactions
 Some new trials
 UNSTABLE THREEBODY SYSTEMS AND THREEBODY RESONANCES
 Several systems which can be treated as threebody systems
 Complexity of the thresholds
 Threebody resonances
 Unstable nulei as threebody systems
 Efimov effect
 A NEW THEORETICAL APPROACH WHICH MAY OPEN THE DOOR TO THE FOURBODY 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 threebody scattering theory, which brought us a remarkable success in the protondeuteron scattering, in the world wide
collaborations between theory(Bochum group, LosAlamos group, Hanover group,
Pisa group and groups in Japan) and experiments(TokyoRIKEN, Kyushu, TUNL
and many), and will bring us further remarkable successes.
Assuming a basic idea about twobody scattering theory, I will show how the
threebody 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 twobody scattering theory,
and is the same in the threebody 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 threebody equations
are usually solved in momentum space. This gives the audience an idea how the
theoreticians solve the nucleondeuteron scattering. This is the first part of
my lecture.
In the second part of my lecture, I will describe basic aspects of the
nucleondeuteron scattering. The study of this fundamental systems has been
done since the early stage of the fewbody 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
twonucleon potentials are used. Only recently, the threenucleon interactions
are found to be important to describe the experiment. Learning from the basic
features of the threenucleon scattering, we try to figure out about further
steps in this fundamental system.
In the third part of my lecture, I will discuss other threebody 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 spinparity 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 threebody system.
Singularities make the threebody phenomena interesting. But at the same time,
it makes threebody scattering complicated to treat. It has been very difficult to figure out how the fourbody scattering equations can be solved at higher
energies where fourbody 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 fewbody scattering theory more popular among new generation of nuclear
physicists.
