The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

Chapter 1
Introduction
Nuclear physics as a science has a long history of almost 100 years. In 1911 Rutherford demonstrated
that large-angle alpha-particle scattering can only be explained in terms of a positively
charged nucleus of a radius of about 10-12 cm, which is much smaller than the typical atomic
radii of the size rv 10-8 cm. This important discovery allowed to make a crucial progress in
understanding the atomic structure and stimulated the development of new theoretical concepts
[1], [2]. A few years later Heisenberg [3] and Schrödinger [4] formulated rigorously the principles
of quantum mechanics.
In spite of advances in the knowledge of atomic systems, the concept of the structure of the nucleus
remained unclear until 1932 when a neutral particle, the neutron, was discovered by Chadwick [5].
After that it was proposed that nuclei are composed of neutrons and protons which have nearly
the same mass. Already at that time Heisenberg suggested that the neutron and proton can be
looked upon as corresponding to two states of the same particle [6]. Four years later Cassen and
Condon introduced the concept of isotopic spin to describe these two states [7].
The basic problem in nuclear physics is determining the nature of the interactions between neutrons
and protons. Only if these forces are known we can understand various properties of nucleL
The first and very successful concept of nuclear forces was proposed by Yukawa [8], who assumed
that nucleons interact due to the exchange of massive scalar particles (mesons).
Although the meson-exchange theory of nuclear forces has undergone many developments and
modifications within the last 60 years, Yukawa's fundamental idea about a meson exchange origin
of nuclear forces is still valid today. In order to keep the manuscript consistent, we would like to
briefly summarize basic historical developments of the meson exchange models of nuclear forces.
More detailed historical reviews can be found in [10], [11].
First modifications of Yukawa's theory were due to Proca [12] and Kemmer [13]. They extended
Yukawa's model to pseudoscalar and pseudovector particles. A few years later models including
combinations of pseudoscalar and pseudovector fields were considered by M�ller and Rosenfeld
[14] and by Schwinger [15]. In 1946 Pauli [16] predicted the existence of an isovector pseudoscalar
meson since the exchange of particles with these quantum numbers could correctly explain the
sign of the quadrupole moment um of the deuteron which was measured in 1939 [17] . Few years
later 1l"-mesons were observed experimentally [9] and identified with the particles predicted by
Pauli.
In 1951 Taketani, Nakamura and Sasaki [18] introduced a new concept. The whole range of
nucleon-nucleon interactions is divided into three regions: a long range part (r 2: 2 fm), an
intermediate region (1 fm � r � 2 fm) and a short range or core part with r � 1 fm. Since the
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