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The EMC Effect

Extensive structure function measurements have been made on nuclear targets. The European Muon Collaboration used muon scattering to measure nuclear structure functions [1]. The initial goal of using nuclear targets was to increase luminosity by increasing the target thickness, but the structure functions measured in scattering from iron and deuterium differed substantially. When they compared the cross section per nucleon, they saw an enhancement in iron below $x \approx 0.3$ and a suppression at larger values of x. Figure 1 shows the ratio $\sigma_{Fe}/\sigma_D$ as a function of x for measurements by the EMC collaboration [1], the BCDMS collaboration [2], and SLAC experiment E139 [3]. This nuclear dependence, termed the EMC effect, has since been measured for several targets and mapped out over a large kinematical range. Following these measurements, several models have tried to explain the effect. While it is now possible to identify some of the necessary ingredients in an explanation of the nuclear dependence of the structure function, there are still competing models that lead to significantly different pictures of the effect. An overview of measurements and models of the EMC effect can be found in ref. [4].

Figure 1: $(\sigma_{Fe}/\sigma_D)$ ratios as a function of x from EMC (hollow circles), SLAC (solid circles), and BCDMS (squares). The data have been averaged over Q2 and corrected for neutron excess (i.e. for isoscaler nuclei).
\centerline{\epsfysize=6cm \epsfbox{}}\end{figure}

Several approaches have been used to try to explain the observed nuclear dependence of the cross section. If one expresses the nuclear structure function as a convolution of the proton and neutron structure functions, the modification can be generated in one of two ways. Either the nucleon structure is modified when in the nuclear medium, or the nuclear structure function is modified in the convolution due to multi-nucleon effects (binding, exchange pions, N-N correlations, etc...). Models using both types of explanation have attempted to explain the EMC effect. While many of these models have had some success, they typically reproduce only part of the observed enhancement or suppression, explain a limited x range, or are in conflict with other measurements. Calculations which simply include the momentum distribution of the nucleons predicted that the effect would be below the few percent level for $x \leq 0.6 $ [5] (i.e. away from the quasielastic peak), which is significantly smaller than is observed. Models which also include the removal energy of the nucleon (Akulinichev et al. [6], Ciofi degli Atti and Luiti [7]) have been able to reproduce certain aspects of the data, but have either failed to reproduce the magnitude or the low x behavior of the effect. The nuclear dependence has also been modeled in terms of a change in the confinement radius of a nucleon bound in a nucleus. This leads to a `swollen' nucleon, which will have a softer valence quark distribution. While this picture can reproduce the magnitude and x-dependence of the EMC effect fairly well, it requires a significant increase in the size of the nucleon ($\sim$15% for iron). This would have observable effects in other experiments, and a swelling of this size appears to be ruled out [8,9,10]. The EMC effect has also been modeled in terms of an enhancement of the pion field within a nucleus. The pion exchange piece of the nucleon-nucleon interaction leads to a modification of the virtual pion cloud in the nucleus, producing a shifting of strength in x. However, this requires a pion excess that is too large to be consistent with a Drell-Yan measurement of the pion modification in nuclei [11]. Ultimately, the EMC effect may be fully described by one of the mechanisms currently being examined, by some new approach, or by some combination of these models. In order to determine which model best describes reality, we need to measure the EMC effect over as broad a range in x, Q2, and A as possible to separate models by their specific predictions.

The most complete measurements of the EMC effect for $x \mathrel{\raise.3ex\hbox{$\gt$}\mkern-14mu
 \lower0.6ex\hbox{$\sim$}}0.3$ come from SLAC experiment E139 [3]. They measured ratios to deuterium for 4He, 9Be, 12C, 27Al, 40Ca, 56Fe, 108Ag, and 197Au targets for a few Q2 bins (Q2=2 and 5 (GeV/c)2 for x < 0.3; Q2=2, 5, and 10 for $0.3 \leq x \leq 0.5$; Q2=5 and 10 for x > 0.5). Figure 1 shows the E139 EMC ratio for iron as a function of x, averaged over Q2. In addition to measuring the x-dependence, E139 examined the Q2-dependence and A-dependence of the effect. They found no significant Q2-dependence in the measured cross section ratios. The ratio does have a strong target dependence which, at fixed x, can be well described as a function of mass number ($\sigma_A / \sigma_D =
C(x)A^{\alpha(x)}$) or as a function of $\rho$, the average nuclear density ($\sigma_A / \sigma_D = D(x) [1+\beta(x)\rho(A)]$). For the SLAC analysis (and in this proposal) $\rho$ is taken to be the nuclear density (nucleons/fm3) determined assuming a uniform sphere with a radius equal to the RMS electron scattering charge radius [3,12]. Figure 2 shows the measured target dependence of the EMC effect, along with fits to a $\log(A)$ dependence, and a density dependence [3]. While the 4He/D ratio provides the greatest sensitivity for determining if the nuclear dependence is best described as an A-dependence or a $\rho$-dependence, the uncertainty in the present data is large and the ratio is consistent with both parameterizations. In addition, for very light nuclei it is not clear if either of these descriptions is adequate to describe the nuclear dependence of the EMC effect. A better measurement of the A-dependence for light nuclei is necessary if we want to extend models of the EMC effect to the deuteron.

Figure 2: $(\sigma_A/\sigma_D)$ ratios at x=0.6 from E139 plotted as a function of mass number and nuclear density. The data is averaged over all Q2 and corrected for neutron excess. Errors include statistical uncertainties, point-to-point and target-to-target systematic uncertainties. The hollow point is 4He, and the arrow indicates the location of 3He.
\centerline{\epsfysize=12cm \epsfbox{}}\end{figure}

For heavy nuclei ($A \geq 9$), the magnitude of the EMC effect (the deviation from unity of $\sigma_A/\sigma_D$) varies with A, but the x-dependence is nearly constant. Most parameterizations of the EMC effect assume that the shape is constant or depends very weakly on A for all nuclei, except at very large values of x (x > 0.8), where $\sigma_A/\sigma_D$ is dominated by the Fermi smearing. The x-dependence in 4He is consistent with the heavier nuclei, but the uncertainties in the measurement are much larger, and it is not possible to rule out a significant difference in shape. Recent work by Smirnov [13] has suggested that the target ratios for $A \leq 4$will differ from the EMC effect in heavy nuclei not only in the size of the effect, but also in the shape. He predicts that both the point of maximum suppression and the point where the EMC ratio crosses unity (at very large x) will be at lower x in 3He than in 4He.

At Jefferson Lab, we can improve our understanding of nuclear effects in light nuclei by measuring the EMC effect in 3He and 4He. Table 1 shows A, $\rho$, and the ratio of $\rho$ to $\log(A)$ (taken relative to 27Al) for selected nuclear targets. For the carbon and the heavier targets the difference between a linear density dependence and an $A^\alpha$ dependence is relatively small ($\rho/\log(A)$ varies at the 10-15% level). However, 3He and 4He have a significantly different dependence of density on mass number. 4He is the lightest nucleus for which the EMC effect has been measured, and while it can in principle distinguish a logarithmic (A) dependence from a linear density dependence, the current measurement is not sufficient to distinguish between the two models. The proposed measurement will use a significantly denser 4He target and will improve the systematic uncertainty in the ratio, which was dominated by the uncertainty in the target thickness for E139. In addition, we will improve the statistical precision of the measurement. We expect to reduce the total uncertainty in $\sigma_{^4He}/\sigma_D$ by nearly a factor of two. 3He is lower in both mass number and nuclear density than any nucleus for which the EMC effect has been measured, so the addition of data on 3He will be important in parameterizing the nuclear dependence of the EMC effect in light nuclei.

Table 1: Mass number and nuclear density for 3He and the nuclei used in E139. The density is determined assuming a uniform sphere with a radius equal to the RMS charge radius determined from electron scattering. For 3He, the proton radius is significantly different than the neutron radius. Using a calculated value for the neutron radius, or assuming that the 3He neutron radius is equal to the 3H proton radius, the value extracted for the nuclear density becomes somewhat higher (0.053-0.055)
Nucleus A $\rho$(fm-3) [$\rho/\log(A)$]/[$\rho/\log(A)$]Al
2H 2 0.024 1.08
3He 3 0.051 1.44
4He 4 0.089 2.00
9Be 9 0.062 0.88
12C 12 0.089 1.11
27Al 27 0.106 1.00
40Ca 40 0.105 0.87
56Fe 56 0.117 0.90
108Ag 108 0.126 0.84
197Au 197 0.147 0.87

We propose to measure the EMC ratio $(\sigma_A/\sigma_D)$ for 3He and 4He, covering $x \mathrel{\raise.3ex\hbox{$\gt$}\mkern-14mu
 \lower0.6ex\hbox{$\sim$}}0.3$. We will improve the uncertainty for 4He, which will significantly improve our ability to distinguish and A-dependence from a $\rho$-dependence for the EMC effect. We will also make the first measurement of the EMC effect for A=3 and large x, which will increase our range in A (and in $\rho$) compared to the previous measurements. The HERMES collaboration has measured $\sigma_A/\sigma_D$[14] for 3He, but the bulk of the data is at extremely small x values (in the shadowing region). They have measurements at larger x values, but the uncertainties are large for x>0.5, and while the shape is consistent with the EMC effect observed in other nuclei, the ratio is not inconsistent with unity (no nuclear effects). In addition to improving the measurements of the EMC effect in light nuclei, the proposed measurement will extend the kinematics to somewhat lower Q2 than the previous measurements. While the SLAC measurements showed no indication of a Q2 dependence, most of the measurements are above $Q^2 \approx 5$ (GeV/c)2. Most of the data at lower Q2 is for x<0.5, where the deviation of the EMC ratio from unity is very small and therefore only a large relative change in this deviation would be observable in the data. The proposed measurement will allow us to investigate the Q2 dependence down to $Q^2 \sim 1-2$ (GeV/c)2.

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Next: Neutron Structure Function Up: MOTIVATION Previous: MOTIVATION