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The EMC Effect Problem

The EMC effect was discovered more than 30 years ago [1]. The experiment measured the ratio between the -distribution of quarks of the iron nucleus and the corresponding quantity of the deuteron. The data are limited to <0:7. The curved lines of fig. 1 provide a description of QCD-compatible predictions of . It turns out that these predictions strongly disagree with the experimental data (see the decreasing line in fig. 2). Other experiments have later confirmed the EMC effect at the region of <0:7 and demonstrated that the effect increases with the nucleon number A of nuclei. The new experiments also contain data of higher and show that the graph of the ratio R changes direction and turns upwards for >0:75 [2, 3, 4].

This evidence does not change the general features of the experiment, because the actual number of quarks at >0:75 is negligible (see [5], p. 281, [6], p. 202).

In order to find the mean momentum of quarks, one must multiply the data represented in fig. 2 by the -population of quarks. It turns out that most quarks are found at small (see [5], p. 281, [6], p. 202). It means that the -width of quarks of heavier nuclei is smaller than that of lighter nuclei.

Figure 1: QCD compatible predictions [1].    Figure 2: Actual measurements [1].


The increase of the quarks’ Fermi motion increases the width of the -dependence of the graph of the scattering cross section (see [5], p. 268-269). The smaller Fermi motion of quarks of heavy nuclei and the uncertainty principle mean that the average self-volume of quarks increases with the nuclear number A.

QCD Inconsistency

As shown in the first report on the EMC effect [1], QCD, which is the prevailing strong interaction theory, has provided predictions that are inconsistent with the effect (see fig. 1 and fig. 2). Report [1] concludes: “We are not aware of any published detailed prediction presently available, which can explain the behavior of these data.” To date, this inconsistency is still a mystery, as concluded in [7] “During this time no single explanation for the effect has been forthcoming” and in [4] “So, while the experimental signature is clear, the interpretation of the effect is, at present, ambiguous.”

The Significance of the Liquid Drop Model

It turns out that a similar effect is well known in electrons. Conductors are extreme phenomenon and their electrons move freely along a macroscopic distance.

Electronic bands of solids and of liquids [8] indicate that the self-volume of electrons of a single molecule is smaller than that of electrons of the same molecules in a condense matter state. In the case of electrons, the increase of the electron’s volume in a condensed matter state is a self-evident phenomenon. Here electrons of a neighboring molecule screen the Coulomb attraction of the molecule’s nuclei and the reduced attraction yields an increase of the electron’s self-volume. Therefore, a theory that explains the nuclear liquid drop model ([9], pp. 139-141) could provide a successful interpretation to this phenomenon as well.

Research topic #1: What is a theoretically consistent explanation for the EMC effect?

Research topic #2: Is the similarity between quarks in nuclei and electrons in a liquid drop relevant to the first problem?


[1] J. J. Aubert et al. (EMC), Phys. Lett. 123B, 275 (1983).

[2] J. Gomez et. al., Phys. Rev. D49, 4348 (1994).

[3] O. Hen, G. A. Miller, E. Piasetzky and L. B. Weinstein, Rev. Mod. Phys. 89, 045002-1 (2017).

[4] J. Arrington, J. Phys. Conference Series, 69, 012024 (2007).

[5] D. H. Perkins, Introduction to High Energy Physics (Addison-Wesley, Menlo Park CA, 1987).

[6] M. Thomson, Modern Particle Physics (Cambridge University Press, Cambridge, 2013).

[7] P R Norton, Rep. Prog. Phys. 66, 1253 (2003).

[8] J. B. Pendry, J. Phys. C13, 3357 (1980).

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

[10] C. F. von Weizscker, Zeit. Phys. 96, 431(1935).

[11] E. Comay, Elect. J. Theor. Phys., 9, 93-118 (2012).

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16 April 2023

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