Does the 3<i>N</i>force have a hard core?

Eden, J. A.; Gari, M.

doi:10.1103/physrevc.53.1510

Cited by 36 publications

(41 citation statements)

References 37 publications

(35 reference statements)

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“…3 has the topological structure of the well-known Fujita-Miyazawa [10] diagram. Similar forms (where the exchanged pion rescatters before being absorbed), are the basic ansatz for building the pion part of the irreducible 3N forces, such as the Tucson-Melbourne [11], Ruhr [12], Brazil [13], or Texas [14] 3N interactions. However, this scheme provides at the same time also another set of irreducible 3N diagrams which must be considered as well; these are given in Fig.…”

Section: Discussionmentioning

confidence: 99%

Practical approximation scheme for the pion dynamics in the three-nucleon system

2001

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We discuss a working approximation scheme to a recently developed formulation of the coupled πNNN-NNN problem. The approximation scheme is based on the physical assumption that, at low energies, the 2N-subsystem dynamics in the elastic channel is conveniently described by the usual 2N-potential approach, while the explicit pion dynamics describes small, correction-type effects. Using the standard separable-expansion method, we obtain a dynamical equation of the Alt-Grassberger-Sandhas (AGS) type. This is an important result, because the computational techniques used for solving the normal AGS equation can also be used to describe the pion dynamics in the 3N system once the matrix dimension is increased by one component. We have also shown that this approximation scheme treats the conventional 3N problem once the pion degrees of freedom are projected out. Then the 3N system is described with an extended AGS-type equation where the spin-off of the pion dynamics (beyond the 2N potential) is taken into account in additional contributions to the driving term. These new terms are shown to reproduce the diagrams leading to modern 3N-force models. We also recover two sets of irreducible diagrams that are commonly neglected in 3N-force discussions, and conclude that these sets should be further investigated, because a claimed cancellation is questionable.PACS numbers: 25.10.+s, 21.45.+v, 25.80.Hp, and 21.30.Fe Typeset using REVT E X 1 Preprint DFPD 00/TH/22

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Section: Discussionmentioning

confidence: 99%

Practical approximation scheme for the pion dynamics in the three-nucleon system

2001

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“…Finally, the operators corresponding to the last two graphs in Fig. 5 read 45) and 46) where the ω's refer to the pionic free energy in the isospin limit and H (2) denotes the isospin-violating ππNN vertex from the Lagrangian L (2) proportional to the LEC c 5 . Performing a straightforward evaluation of the matrix elements of these operators, we obtain the following result for the leading CSB 2PE potential:…”

Section: Consider Now Diagrams (E)-(h) Inmentioning

confidence: 99%

“…Further, C T is one of the two leading order four-nucleon LECs [16]. Notice that these nonvanishing contributions are in strong contrast to the corresponding isospin-invariant 3NF forces ∝ g [44][45][46]. We also emphasize that these 3NF contributions were not explicitly evaluated in Ref.…”

Section: Consistency Of the 2n And 3n Forcesmentioning

confidence: 99%

Isospin-violating nucleon-nucleon forces using the method of unitary transformation

Epelbaum

Meißner

2005

Phys. Rev. C

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Recently, we have derived the leading and subleading isospin-breaking three-nucleon forces using the method of unitary transformation. In the present work we extend this analysis and consider the corresponding two-nucleon forces using the same approach. Certain contributions to the isospin-violating one-and two-pion-exchange potential have already been discussed by various groups within the effective field theory framework. Our findings agree with the previously obtained results. In addition, we present the expressions for the subleading charge-symmetry-breaking two-pion exchange potential which were not considered before. These corrections turn out to be numerically important. Together with the three-nucleon force results presented in our previous work, the results of the present study specify completely isospin-violating nuclear forces up to the order q 5 / 5 , where q ( ) denotes the soft (hard) scale.

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“…(2). It is, however, well known that the leading 3N force at this order vanishes provided one uses an energyindependent formulation such as the method of unitary transformation [8,20], see also [21][22][23]. Consequently, only the 2N interaction needs to be taken into account at NLO, which is already completely fixed from the 2N system.…”

Section: Three and More Nucleonsmentioning

confidence: 99%