The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

Contents
1 Introduction
2 Low-momentum effective theories for two nucleons 11
2.1 What is effective? . . . . . . . . . . . . 11
2.2 Two nucleons at very low energies . . . . 15
2.3 Going to higher energies: a toy model . . 23
2.3.1 Method of unitary transformation 24
2.3.2 Regularization of the decoupling equation 29
2.3.3 Numerical realization of the projection formalism . 32
2.3.4 Unitary transformation for a potential of the Malfliet-Tjon type 33
2.3.5 Implication for effective theories 37
2.3.6 Coordinate space representation . . . . . . . . . . . 46
3 The derivation of nuclear forces from chiral Lagrangians 48
3.1 Chiral symmetry . . . . . . . . . . . . 48
3.2 Effective Lagrangians . . . . . . . . . . 55
3.3 Chiral perturbation theory with pions 69
3.4 Including nucleons . . . . . . . . . . . 73
3.5 Bloch-Horowitz scheme and the method of unitary transformation 78
3.6 Application to chiral invariant Hamiltonians . . . . . . . . . 81
3.7 Nuclear forces using the method of unitary transformation . 87
3.8 Two-nucleon potential . . . . . . . . . . . . . . . . . . 91
3.8.1 Expressions and discussion . . . . . . . . . . . . . . 91
3.8.2 Renormalization of the N N potential at NLO . . . .
3.8.3 Phenomenological interpretation of some of the 7fN LECs and the role of
100
the ß(1232) . . . 105
3.9 Three-nucleon potential . . . . . . . . . . . .
113
4 The two-nucleon system: numerical results
4.1 Bound and scattering state equations .
4.2 The fits . . . .
4.3 Phase shifts . .
4.3.1 S-waves
4.3.2 P-waves
4.3.3 D- and F-waves
4.3.4 Peripheral waves
4.4 Deuteron properties . .
4.5 Results for the NNLO-ß approach
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