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The Similarities between the Nuclear and the Molecular Potential

Experimental findings show a striking similarity between the nuclear force and the force between atoms of noble gas. Figures 1 and 2 both show the potential of these forces as a function of the distance between the particles. Another similarity is the success of the nuclear liquid drop model, where a nucleus is described as an incompressible liquid drop (see [1], p. 139). The nuclear force is regarded as a residual force of strong interactions, while the force between noble gas atoms is a residual force of the electromagnetic force (see [1], pp. 100-102).

Research topic #1: Why is there a striking similarity between the nuclear force and the force between atoms of a noble gas?

Research topic #2: Does the similarities suggest something about the origin of the nuclear force?

Remark #1: The Yukawa force, whose form is (see [3], p. 122)

cannot be regarded as an acceptable expression for the nuclear force.

Figure 1: Nuclear Force. (See [1], p. 97)        Figure 2: Molecular force. (See [2], p. 16).

Indeed, fig. 1 shows that at a short distance between nucleons, the nuclear force is strongly repulsive, whereas the Yukawa force (1) is attractive at this region.

Remark #2: In the previous decade an attempt was made to derive the nucleon-nucleon potential from QCD principles [4, 5]. However, the following arguments prove that this attempt is unacceptable. For example, [4] uses a pion mass of =0:36 GeV, whereas the actual pion mass is below 0.14 GeV [6].

Another important discrepancy of [4] is that this article uses the mesons as interaction mediators. This is unacceptable. Indeed, an interaction mediating quantum function takes the form , where denotes a single set of the four space-time coordinates. It means that describes an elementary pointlike particle. For example, the textbook [7] (p. 300) says that this is a general attribute of presently accepted field theories: “all field theories used in current theories of elementary particles have Lagrangians of this form”. By contrast, mesons are composite states which are quark-antiquark bound systems and their function takes the form .

Furthermore, the pion’s radius is about the same as that of the proton [6]. Therefore meaning it is not a pointlike particle, which is required by an interaction mediating particle.


[1] S. S. M. Wong, Introductory Nuclear Physics (Wiley, New York, 1998).

[2] H. Haken and H. C. Wolf, Molecular Physics and Elements of Quantum Chemistry (Springer, Berlin, 2004), 2nd edition.

[3] M. E. Peskin and D. V. Schroeder An Introduction to Quantum Field Theory (Addison-Wesley, Reading Mass., 1995).

[4] N. Ishii, Aoki and T. Hatsuda, Phys. Rev. Lett., 99, 022001 (2007).

[5] F. Wilczek, Nature, 445, 156 (2007).

[6] M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 010001 (2018).

[7] S.Weinberg, The Quantum Theory of Fields, Vol. I (Cambridge University Press, Cambridge, 1995). pp. 58-74.