A higher-dimensional model of the nucleon–nucleon central potential

Abstract

Based on a theory of extra dimensional confinement of quantum particles [E. R. Hedin, Physics Essays, 2012, 25(2): 177], a simple model of a nucleon–nucleon (NN) central potential is derived which quantitatively reproduces the radial profile of other models, without adjusting any free parameters. It is postulated that a higher-dimensional simple harmonic oscillator confining potential localizes particles into three-dimensional (3D) space, but allows for an evanescent penetration of the particles into two higher spatial dimensions. Producing an effect identical with the relativistic quantum phenomenon of zitterbewegung, the higher-dimensional oscillations of amplitude ħ/(mc) can be alternatively viewed as a localized curvature of 3D space back and forth into the higher dimensions. The overall spatial curvature is proportional to the particle’s extra-dimensional ground state wave function in the higher-dimensional harmonic confining potential well. Minimizing the overlapping curvature (proportional to the energy) of two particles in proximity to each other, subject to the constraint that for the two particles to occupy the same spatial location one of them must be excited into the 1^st excited state of the harmonic potential well, gives the desired NN potential. Specifying only the nucleon masses, the resulting potential well and repulsive core reproduces the radial profile of several published NN central potential models. In addition, the predicted height of the repulsive core, when used to estimate the maximum neutron star mass, matches well with the best estimates from relativistic theory incorporating standard nuclear matter equations of state. Nucleon spin, Coulomb interactions, and internal nucleon structure are not considered in the theory as presented in this article.

Graphical abstract

Keywords

nucleon–nucleon potential / higher-dimensional theory / neutron star mass limit

References

[1] H. Yukawa, On the interaction of elementary particles, Proc. Phys.-Math. Soc. Jpn., 1935, 17: 48

[2] R. A. Bryan and B. L. Scott, Nucleon–nucleon scattering from one-boson-exchange potentials (III): S waves included, Phys. Rev., 1969, 17(4): 1435

[3] M. Lacombe, B. Loiseau, J. M. Richard, R. Vinh Mau, J. Côté, P. Pirès, and R. de Tourreil, Parametrization of the Paris N–N potential, Phys. Rev. C, 1980, 21(3): 861

[4] R. Machleidt, The meson theory of nuclear forces and nuclear structure, Adv. Nucl. Phys., 1989, 19: 189

[5] F. Myhrer and J. Wroldsen, The nucleon–nucleon force and the quark degrees of freedom, Rev. Mod. Phys., 1988, 60(3): 629

[6] S. Weinberg, Nuclear forces from chiral lagrangians, Phys. Lett. B, 1990, 251(2): 288

[7] D. R. Entem and R. Machleidt, Accurate charge-dependent nucleon–nucleon potential at fourth order of chiral perturbation theory, Phys. Rev. C, 2003, 68(4): 041001(R)

[8] N. Ishii, S. Aoki, and T. Hatsuda, Nuclear force from lattice QCD, Phys. Rev. Lett., 2007, 99(2): 022001

[9] C. Downum, J. R. Stone, T. Barnes, E. S. Swanson, I. Vidaña, V. Crede, P. Eugenio, and A. Ostrovidov, Nucleonnucleon interactions from the quark model, AIP Conf. Proc., 2010, 1257: 538

[10] B. Singh, M. Bhuyan, S. K. Patra, and R. K. Gupta, Optical potential obtained from relativistic-mean-field theory-based microscopic nucleon–nucleon interaction: Applied to cluster radioactive decays, J. Phys. G, 2012, 39(2): 025101

[11] R. Xu, Z. Ma, E. N. E. van Dalen, and H. Müther, Relativistic nucleon optical potentials with isospin dependence in a Dirac–Brueckner–Hartree–Fock approach, Phys. Rev. C, 2012, 85(3): 034613

[12] E. R. Hedin, Extradimensional confinement of quantum particles, Physics Essays, 2012, 25(2): 177

[13] P. Strange, Relativistic Quantum Mechanics, With Applications in Condensed Matter and Atomic Physics, Cambridge: Cambridge University Press, 1998: 118, 210. The Compton wavelength is defined to be ħ/mc in this citation.

[14] R. Liboff, Introductory Quantum Mechanics, 2nd Ed., Reading: Addison-Wesley, 1992: 185-187

[15] T. Hatsuda [for HAL QCD Collaboration], Nuclear forces from lattice QCD, in: Proc. of Science, 6th International Workshop of Chiral Dynamics, Bern, Switzerland, arXiv: 0909.5637v1, 2009

[16] R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Accurate nucleon–nucleon potential with charge-independence breaking, Phys. Rev. C, 1995, 51(1): 38

[17] S. M. Carroll, An Introduction to General Relativity, Spacetime and Geometry, San Francisco: Addison-Wesley, 2004: 233

[18] H. Heiselberg and V. Pandharipande, Recent progress in neutron star theory, Annu. Rev. Nucl. Part. Sci., 2000, 50(1): 481

[19] B. W. Carroll and D. A. Ostlie, An Introduction to Modern Astrophysics, Reading: Addison-Wesley, 1996: 604

[20] K. S. Krane, Modern Physics, 2nd Ed., Hoboken: John Wiley & Sons, 1996: 508

[21] S. Carroll, Spacetime and Geometry: An Introduction to General Relativity, San Francisco: Addison-Wesley, 2004: 232-233

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Higher Education Press and Springer-Verlag Berlin Heidelberg