Preface
The subject of few body physics has undergone a long journey during the past few
decades, witnessing an upsurge of research activities since the pioneering work of
Faddeev in 1960. While these activities are well documented and published in
standard journals and review articles, we here wish to present only a brief historical
perspective which led to this upsurge [1–6].
Faddeev [7], starting from the Lippmann–Schwinger equation for the three-body
scattering problem, showed how the problem of disconnectedness of the scattering
matrix appearing in the form of d-type singularities inherently present in the
Lippmann–Schwinger equation can be resolved leading to the three-body kernel
which is completely continuous. Subsequently, Lovelace in 1964 [8], following
Faddeev equations, undertook a detailed study and found that in situations where
the two-body systems involved have bound or resonant states, the two-body
T-matrices could be represented in a separable form with the result that resulting
integral equations for the three-body scattering amplitude would involve only a
single variable. Such equations could be easily handled computationally without
resort to further approximations. Prior to this, Mitra in 1960 [9] had already initiated
a three-body approach using two-body separable potentials and in 1963, Mitra and
Bhasin [10] had derived, using three-body Schrodinger equation, the same equations as obtained by Lovelace for the n-d scattering problem. Independently,
Sitenko and Kharchenko [11] also obtained similar equations using Faddeev’s
theory and employing separable two-body T-matrices. During the same period,
Amado and his group [12], starting from the Lee model, developed a three-body
model for n-d scattering which eventually led to similar equations obtained with
separable potentials. Thus, these attempts carried out altogether during 1960–65
sparked off a spectacular interest in research activities in few body nuclear, atomic
and molecular systems at various places all over the world. The major impact of this
was the decision to hold regular international conferences after a period of every
two years in different parts of the world to sustain the interest and encourage the
young researchers in this field of few body physics.
v
The subject of few body physics has undergone a long journey during the past few
decades, witnessing an upsurge of research activities since the pioneering work of
Faddeev in 1960. While these activities are well documented and published in
standard journals and review articles, we here wish to present only a brief historical
perspective which led to this upsurge [1–6].
Faddeev [7], starting from the Lippmann–Schwinger equation for the three-body
scattering problem, showed how the problem of disconnectedness of the scattering
matrix appearing in the form of d-type singularities inherently present in the
Lippmann–Schwinger equation can be resolved leading to the three-body kernel
which is completely continuous. Subsequently, Lovelace in 1964 [8], following
Faddeev equations, undertook a detailed study and found that in situations where
the two-body systems involved have bound or resonant states, the two-body
T-matrices could be represented in a separable form with the result that resulting
integral equations for the three-body scattering amplitude would involve only a
single variable. Such equations could be easily handled computationally without
resort to further approximations. Prior to this, Mitra in 1960 [9] had already initiated
a three-body approach using two-body separable potentials and in 1963, Mitra and
Bhasin [10] had derived, using three-body Schrodinger equation, the same equations as obtained by Lovelace for the n-d scattering problem. Independently,
Sitenko and Kharchenko [11] also obtained similar equations using Faddeev’s
theory and employing separable two-body T-matrices. During the same period,
Amado and his group [12], starting from the Lee model, developed a three-body
model for n-d scattering which eventually led to similar equations obtained with
separable potentials. Thus, these attempts carried out altogether during 1960–65
sparked off a spectacular interest in research activities in few body nuclear, atomic
and molecular systems at various places all over the world. The major impact of this
was the decision to hold regular international conferences after a period of every
two years in different parts of the world to sustain the interest and encourage the
young researchers in this field of few body physics.
v