The EMC Effect Problem
The EMC effect was discovered more than 30 years ago . 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 , p. 281, , 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 , p. 281, , p. 202). It means that the -width of quarks of heavier nuclei is smaller than that of lighter nuclei.
Figure 1: QCD compatible predictions . Figure 2: Actual measurements .
The increase of the quarks’ Fermi motion increases the width of the -dependence of the graph of the scattering cross section (see , 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.
As shown in the first report on the EMC effect , QCD, which is the prevailing strong interaction theory, has provided predictions that are inconsistent with the effect (see fig. 1 and fig. 2). Report  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  “During this time no single explanation for the effect has been forthcoming” and in  “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  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 (, 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?
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