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Bietenholz, W., Göckeler, M., Horsley, R., Nakamura, Y., Pleiter, D., Rakow, P.E.L., et al. (2010) Pion in a Box. Physics Letters B, 687, 410-414.
https://doi.org/10.1016/j.physletb.2010.03.063

has been cited by the following article:

• TITLE: Finite Size Effects and the Mechanism of Nucleon-Nucleon Attraction

  AUTHORS: Nicolae Bogdan Mandache

  KEYWORDS: Covalent Bonding, Particle Exchange, Average Localization Radius, Finite Size Effects, Residual Mass of Pion, Attraction Mechanism, Central Nucleon-Nucleon Potential

  JOURNAL NAME: Journal of Modern Physics, Vol.17 No.1, January 16, 2026

  ABSTRACT: The kinetic energy of a particle confined in a finite volume decreases with increasing volume. In the covalent bonding, the delocalization of electrons exchanged between atoms of the molecule is equivalent to an increase in their localization volume compared to their localization volume in the individual atoms. This results in a decrease in their kinetic energies, which is at the origin of the attraction mechanism of the atoms in the molecule. The quantum mechanical approach to the covalent bonding (Valence Bond Picture) used to describe the delocalization of the two exchanged electrons in the hydrogen molecule is used to describe the delocalization of the two exchanged pions in the nucleon-nucleon system. In particular, the increase in the average localization radius of each pion in the nucleon-nucleon system compared to its average localization radius in an individual nucleon is calculated. This increase in average localization radius is correlated with the Lattice QCD data on the decrease in the residual mass of a pion confined in a finite volume with increasing volume. The decrease of the residual masses of delocalized pions in the nucleon-nucleon system compared with their residual masses in individual nucleons is at the origin of the mechanism of nucleon-nucleon attraction. An expression for the central nucleon-nucleon potential due to two-pion exchange is obtained.