- Email: [email protected]
Color transparency and correlation effects in quasielastic electron-nucleus scattering at high momentum transfer
Nuclear Physics A532 (1991) 277c-284c North-Holland, Amsterdam
NUCLEAR PHYSICS A
COLOR TRANSPARENCY AND CORRELATION EFFECTS IN QUASIELASTIC ELECTRON-NUCLEUS SCATTERING AT HIGH MOMENTUM TRANSFER Omar Benhar* INFN, Sezione Sanità Physics Laboratory, Istituto Superiore di Sanità I-00161 Roma, Italy Abstract The effects of NN correlations and color transparency on the final state interaction of the struck particle in electron-nucleus scattering processes at high momentum transfer are discussed. The results of realistic microscopic calculations show that the two mechanisms both lead to an enhancement of the nuclear transparency and correlation effects are larger up to momenta Q - 5 (GeV/c)2 . 1. Introduction The possible occurrence of the effect generally referred to as color transparency (CT) has been predicted by Brodsky [1] and Miller [2] in the early eighties. The mechanism leading to CT can be qualitatively understood considering the expansion of a hadronic wave function on a complete set of Fock states representing free quarks and gluons . Since the amplitudes for exclusive processes involve a factor 1/Q2 for each constituent, at large momentum transfer the valence state, corresponding to the lowest number of constituents, is expected to be dominant . The transparency effect follows from the fact that such a state, having small color electric dipole moment, interacts weakly with nuclear matter. According to this picture, a hadron travelling through the nuclear medium after absorbing a large momentum is initially "small", its typical transverse size being - 1/Q, and evolves back to its standard configuration within a distance from the interaction point which increases with increasing Q2. Explicit models to describe the evolution of the hadronic cross section associated with the occurrence of CT, inspired by the parton model and perturbative quantum chromodinamics (PQCD), have been proposed in ref.[3]. A pioneering experiment to measure the effect of CT in proton-nucleus scattering has been recently carried out at Brookhaven [4] . The data of ref.[4] agree fairly well with the theoretical predictions based on the PQCD model of ref.[3] up to incident proton momenta pi,,, -10 GeV/c, while showing a completely different behaviour at *E-mail address : THEO@IRMISS .BITNET 0375-9474/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved .
D. Benhar I QuasiFlastic electron-nescleus scattering
273c larger momenta.
Experimental evidence of the occurrence of CT can also be obtained from (e, ~!') and (e, e'p) electron scattering experiments at high momentum transfer, studying the A and Q2 dependence of the nuclear absorption of the knocked out proton. In fact, CT is expected to lead to a modification of the final state interaction (FSI) of the struck particle with respect to the prediction of the conventional nuclear physics picture, in which the nucleons are assumed to be structureless. In this paper I discuss a semiclassical treatment of FSI in electron-nucleus scattering which can be readily extended to include the effect of CT. The present approach, which can be regarded as a generalization of the widely employed Glauber theory [5j, allows for a consistent treatment of the dynamical correlation effects arising from the fact that the projectile particle was bound in the nuclear target in the initial state. A short outline of the theory will be given in section 2, whereas in section 3 the results of numerical calculations of the (e, e') cross section VA momentum transfer - 2 eVIc and of the total nuclear transparency evaluated in the kinematical conditions of the NE1S SLAC-NPAS proposal [6] will be discussed. Finally, a summary and the conclusions are contained in section 4. 2. Semiclassical theory of FSI in electron-nucleus scattering at high mo-
mentum transfer
According to Glauber multiple scattering theory [5], the state of a nucleon of momentum - travelling through the nuclear medium is described by the wave function *P(r )
= e P"SPP(r ),
where the function zp(r ), accounting for the effect of nucleon-nucleon (NN) collisions, is related to the scattering potential V by the equation iPP(r ) _
jpP
(b+ pz) = exp i ~v
Z
_
dz'V(b + pz') .
(2)
In eq.(2), v denotes the velocity of the projectile particle, z is the projection of r along the direction of the incident momentum and b is the impact parameter. The scattering potential V is a complex quantity whose imaginary part, responsible for nuclear absorption, is generally written in terms of the forward NN scattering amplitude f and the density distribution of the target nucleus p(r) in the form:
r
sV (r
v
hvO' p(r ), y; sf (P)P( - ) _ - 1 2
a being the total NN scattering cross section. In ref.[7] the Glauber approach has been generalized to the case of a projectile particle initially bound in the target ground state. Due to the strongly repulsive core of the NN interaction, this assumption dramatically affects the shape of the scattering potential V. The underlying mechanism can be
O. Benhar / Quasielastic electron-nucleus scattering
279c
easily understood thinking of the incoming particle as surrounded by a hole produced by the NN repulsion. As a consequence, the nuclear density p entering the definition of Y has to be replaced by the product Gp, where the function G is related to the radial ciistribution function 9(r), yielding the probability of finding two particles at relative distance r in the nuclear ground state. The definition of G reads as follows [7] : 3 1 z d k f(k) d3re ;k.(F_pz' )9(r), G(z) = dz, 2~ (4) z 0 (21r)3 Q and the resulting expression for W is
f
W(r) _
-12 hvo G(z)p(r ).
It clearly appears that CT can be easily included in the present approach by replacing the total NN scattering cross section in eq.(5) with a function o(z) modeling the evolution of state describing the projectile particle.
5
5
4 3 2 1
0
1
2 z (fm)
3
4
0
0
1
2 z (fm)
3
4
Fig. 1. z dependence of the NN cross section of eq.(6) t31 (dashed lines), compared to the quantity o G(z) (see eq.(4)), evaluated using the nuclear matter radial distribution function of ref.[8] (solid lines) . The cross sections are given in units of fm2 . It should be pointed out that short range NN correlations and CT both lead to a suppression of the absorptive part of Y at small z, and have therefore to be regarded as competing mechanisms, whose relative relevance has to be carefully investigated . This problem is illustrated in fig.l, where the z dependence of aG(z) and a(z), calculated according to the PQCD model of ref.[3], are compared for two different values of Q `by2 produced in the kinematical setup of ref.[6] . It turns out tat the "hole" at low z
O. Benhar I Quasielastic electron-nucleus scattering
280c
Q2 NN correlations is much larger than the one associated with CT at whereas the situation is reversed. at Q2 = 7 (GeV/c) 2 .
= 2 (GeVlc)2 ,
3. Numerical results The theoretical procedure described in the previous section has been recently applied to study FSI effects in inclusive electron-nucleus scattering at momentum transfer Q - 2 GeV/c [7] . In ref.[7], the (e, e') cross section has been calculated for infinite nuclear matter, using the spectral function of ref.[9] and including the contributions of both elastic and inelastic electron-nucleon scattering processes . In fig.2 the theoretical results are compared with the empirical nuclear matter cross section obtained from the extrapolation of the existing data to infinite A [10]. The three different curves correspond to different definitions of the absorptive part of the potential felt by the struck nucleon travelling through the nuclear medium. The daslb-dot line represents the results of the standard Glauber prescription of eq.(3), whereas the solid and dashed curves have been obtained using:W defined in egs.(4) and (5), with and without inclusion of CT respectively. The calculations have been performed using the parametrization of the forward NN scattering amplitude given in ref.[11] and the PQCD inspired model of ref.[3] to describe the evolution of the NN cross section associated with CT: 2 > Z + < 9kâ _ ~ x9(L _ z) +4(z _ L) , (6) V(z) 1[L where < QT
>1/2
Q
.35 GeV/c and L = 2p/,&M2 , with Orne = .7 GeV.
It appears that NN correlations and CT both produce an appreciable lowering of the FSI and that CT significantly affects the cross section behavior in the low energy loss wing (w < 800 bbleV, corresponding to Q2 - 2.7 (GeVlc)2 ), bringing the theoretical predictions in good agreement with the data. An experiment designed to study the nuclear and momentum transfer dependence of the quasielastic (e, e'p) scattering, in a kinematical region extended up to Q2 = 7 (GeV/c)2 , has been recently proposed (SLAC-NPAS proposal NE18 [6)). Since in the region of the quasielastic peak the reaction mechanism appears to be well under control and the effect of the nucleon ofd shellness is rather small, it is expected that NE18 data could provide clearcut evidence of the occurrence of CT. However, to get a quantitative understanding of this phenomenon and discriminate between different models describing the evolution of the hadronic cross section, a realistic theoretical calculation of the nucler absorption within standard nuclear physics is needed, and the interplay between NN correlations and CT has to be carefully investigated . Unfortunately, a fully realistic microscopic calculation of the (e, e'p) cross section for finite nuclei is not yet available . However, some information can be obtained considering the total nuclear transparency T, defined as z
T=1 Z
d2bdzp(r)exp? TV
dz'!W(b,z') .
O. Benhar / Quasielastic electron-nucleus scattering
281c
10 -2 a) 0
d
10 -3
10 -4
a b C 10 Nb a
v
10 -5
0 .75
1 1 .5 1 .25 energy loss u (GeV)
1 .75
2
Fig. 2 . Inclusive cross section for electron scattering by nuclear matter at incident energy e = 3.595 GeV and scattering angle 0 = 30°. Dashdot line: Glauber theory. Dashed line: present approach with constant NN cross section. Solid line: present approach with the NN cross section of eq.(6). The results of an estimate of T for 12C, carried out assuming the kinematical conditions of the NE18 proposal, are summarized in fig.3. The calculation has been performed using a nuciear density obtained by a parametrization of the elastic electronnucleus scattering data and different prescriptions for SIV. The dotted and dashed lines show the behaviour of the total transparency estimated using the definition of W of egs.(3) and (5), respectively, and a constant o, = 43.3 mb. The corresponding quantities obtained using the NN cross section of eq.(6) are given by the dash-dot and solid lines. It appears that up to momentum tranfer Qz - 5 (Gev/c)2 NN correlations produce an enhancement of T, with respect to the prediction of Glauber theory, larger than the one associated with CT. Moreover, the CT effect turns out to be appreciably smaller within the present approach than within standard Glauber theory. For instance, at dotted and the dash-dot lines of fig-3 is QZ _= 7 (GeV/c)z the difference between the - 43%, while comparing the dashed and the solid lines one finds a deviation of 28% only. A crude estimate of correlation effects on the nuclear transparency has also been given in ref.[12], where the function G of eq .(4) has been approximated with a step function producing a correlation hole of radius .5 fin, and an enhancement of about 10 -15% has been found . The origin of the larger correlation effect resulting from the
O. Benhar I Quasielastic electron-nucleus scattering
282c
0.9 0.8 0.7 0.6 0.5 0.4
s
'
f
2 .5
e
e
f
f
~
f
s
:
a
~
e
7.5 5 QZ [(GeV/c)2]
e
f
f
~
10
f
f
e
f
~
12 .5
f
e
e
f
15
Fig. 3. Total transparency (eq.(7)) of "'C evaluated as a function of QZ and assuming NE16 kinematics. Potted line: Glauber theory. Dashed .line: present approach with constant a,. Dash-dot line: Glauber theory with or(z) of eq.(6). Solid line: present approach with a(z) of eq.(6). present calculation can be readily understood considering that G(z), shown in fig .1, is rather long ranged and its shape can hardly be approximated by a step function . . Conclusions
The study of the FSI of the struck particle in electron-nucleus scattering at high momentum transfer can provide valuable information on both nuclear and hadronic structure. The strong short range repulsion of the NN force has been shown to play a crucial role in producing a significant enhancement of the nuclear transparency. As a consequence, it has to be carefully taken into account to study the possible occurrence of different mechanisms leading to the same effect, such as color transparency. Fully realistic microscopic calculations of the cross section are certainly needed to firmly establish the possibility of getting quantitative information on CT from (e, e'p) experiments . As it has been pointed out in ref.(12], to get a clean signature of the evolution of the hadronic cross section one should measure the momentum distribution of the single particle states, rather than the total nuclear transparency. However, this requirement obviously puts severe constraints on the missing energy resolution of the experimental apparatus . As a final remark, it should be mentioned that processes other than (e, e') and
0. Benhar / Quasielastic electron-nucleus scattering
283c
(e, e'p) can also be regarded as candidates to study the occurrence of CT in electron-
nucleus scattering (see, e.g., ref.[13]). For instance, exclusive meson photoproduction appears to be particularly well suited, since the relevant Q2 are lower and the nuclear transparency is unaffected by the mechanism associated with NN correlations. Acknowledgments Most of the results discussed in this paper have been obtained in collaboration with A. Fabrocini, S. Fantoni, V.R. Pandharipande and I. Sick, to whom I am deeply indebted for many clarifying discussions . References 1. S.J. Brodsky, in Proceedings of the Thirteenth International Symposium on Multiparticle Dinalnycs. Eds. E.W. Kittel, W. Metzger and A. Stergion (World Scientific, Singapore, 1982)p. 963. 2. A. Mûller, in Proceedings of the Seventeenth Rencontre de Moriond. Ed. J. Thran Thanh Van (Editions Frontières, Gif-sur-Yvette, 1982)p . 13. 3. G.L. Farrar, H. Liu, L.L. Frankfurt and M.I. Strikman, Phys. Rev. Lett . 61 (1988) 686. 4. A.S. Carrol et al, Phys . Rev. Lett. 61 (1988) 1698 . 5. J. Van den Brand et al, SLAC-NPAS proposal NE18 (1990). 6. R.J. Glauber, in Lectures in Theoretical Physics.. Ed. W.E. Brithin et al (Interscience, New York, 1959)p. 315. 7. O. Benhar, A. Fabrocini, S. Fantoni, G.A . Miller, V .R . Pandharipande and I. Sick, preprint SISSA 4/91/CM (1991), submitted to Phys. Rev. C. 8. R. Schiavilla et al, Nucl. Phys. A473 (1987) 267.
9. O . Benhar, A. Fabrocini and S. Fantoni, Nucl. Phys. A505 (1989) 267. 10. D.B. Day et al, Phys. Rev. C 39 (1989) 1011 . 11 . R.H . Bassel and C. Wilkin, Phys. Rev. Lett . 18 (1967) 971.
12. L.L. Frankfurt, M .I. Strikman and M.B . Zalhov, Nucl . Phys . A515 (1990) 599. 13. Pegasys/Mar k II proposal, SLAC-337 (1990) .
NUCLEAR PHYSICS A
COLOR TRANSPARENCY AND CORRELATION EFFECTS IN QUASIELASTIC ELECTRON-NUCLEUS SCATTERING AT HIGH MOMENTUM TRANSFER Omar Benhar* INFN, Sezione Sanità Physics Laboratory, Istituto Superiore di Sanità I-00161 Roma, Italy Abstract The effects of NN correlations and color transparency on the final state interaction of the struck particle in electron-nucleus scattering processes at high momentum transfer are discussed. The results of realistic microscopic calculations show that the two mechanisms both lead to an enhancement of the nuclear transparency and correlation effects are larger up to momenta Q - 5 (GeV/c)2 . 1. Introduction The possible occurrence of the effect generally referred to as color transparency (CT) has been predicted by Brodsky [1] and Miller [2] in the early eighties. The mechanism leading to CT can be qualitatively understood considering the expansion of a hadronic wave function on a complete set of Fock states representing free quarks and gluons . Since the amplitudes for exclusive processes involve a factor 1/Q2 for each constituent, at large momentum transfer the valence state, corresponding to the lowest number of constituents, is expected to be dominant . The transparency effect follows from the fact that such a state, having small color electric dipole moment, interacts weakly with nuclear matter. According to this picture, a hadron travelling through the nuclear medium after absorbing a large momentum is initially "small", its typical transverse size being - 1/Q, and evolves back to its standard configuration within a distance from the interaction point which increases with increasing Q2. Explicit models to describe the evolution of the hadronic cross section associated with the occurrence of CT, inspired by the parton model and perturbative quantum chromodinamics (PQCD), have been proposed in ref.[3]. A pioneering experiment to measure the effect of CT in proton-nucleus scattering has been recently carried out at Brookhaven [4] . The data of ref.[4] agree fairly well with the theoretical predictions based on the PQCD model of ref.[3] up to incident proton momenta pi,,, -10 GeV/c, while showing a completely different behaviour at *E-mail address : THEO@IRMISS .BITNET 0375-9474/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved .
D. Benhar I QuasiFlastic electron-nescleus scattering
273c larger momenta.
Experimental evidence of the occurrence of CT can also be obtained from (e, ~!') and (e, e'p) electron scattering experiments at high momentum transfer, studying the A and Q2 dependence of the nuclear absorption of the knocked out proton. In fact, CT is expected to lead to a modification of the final state interaction (FSI) of the struck particle with respect to the prediction of the conventional nuclear physics picture, in which the nucleons are assumed to be structureless. In this paper I discuss a semiclassical treatment of FSI in electron-nucleus scattering which can be readily extended to include the effect of CT. The present approach, which can be regarded as a generalization of the widely employed Glauber theory [5j, allows for a consistent treatment of the dynamical correlation effects arising from the fact that the projectile particle was bound in the nuclear target in the initial state. A short outline of the theory will be given in section 2, whereas in section 3 the results of numerical calculations of the (e, e') cross section VA momentum transfer - 2 eVIc and of the total nuclear transparency evaluated in the kinematical conditions of the NE1S SLAC-NPAS proposal [6] will be discussed. Finally, a summary and the conclusions are contained in section 4. 2. Semiclassical theory of FSI in electron-nucleus scattering at high mo-
mentum transfer
According to Glauber multiple scattering theory [5], the state of a nucleon of momentum - travelling through the nuclear medium is described by the wave function *P(r )
= e P"SPP(r ),
where the function zp(r ), accounting for the effect of nucleon-nucleon (NN) collisions, is related to the scattering potential V by the equation iPP(r ) _
jpP
(b+ pz) = exp i ~v
Z
_
dz'V(b + pz') .
(2)
In eq.(2), v denotes the velocity of the projectile particle, z is the projection of r along the direction of the incident momentum and b is the impact parameter. The scattering potential V is a complex quantity whose imaginary part, responsible for nuclear absorption, is generally written in terms of the forward NN scattering amplitude f and the density distribution of the target nucleus p(r) in the form:
r
sV (r
v
hvO' p(r ), y; sf (P)P( - ) _ - 1 2
a being the total NN scattering cross section. In ref.[7] the Glauber approach has been generalized to the case of a projectile particle initially bound in the target ground state. Due to the strongly repulsive core of the NN interaction, this assumption dramatically affects the shape of the scattering potential V. The underlying mechanism can be
O. Benhar / Quasielastic electron-nucleus scattering
279c
easily understood thinking of the incoming particle as surrounded by a hole produced by the NN repulsion. As a consequence, the nuclear density p entering the definition of Y has to be replaced by the product Gp, where the function G is related to the radial ciistribution function 9(r), yielding the probability of finding two particles at relative distance r in the nuclear ground state. The definition of G reads as follows [7] : 3 1 z d k f(k) d3re ;k.(F_pz' )9(r), G(z) = dz, 2~ (4) z 0 (21r)3 Q and the resulting expression for W is
f
W(r) _
-12 hvo G(z)p(r ).
It clearly appears that CT can be easily included in the present approach by replacing the total NN scattering cross section in eq.(5) with a function o(z) modeling the evolution of state describing the projectile particle.
5
5
4 3 2 1
0
1
2 z (fm)
3
4
0
0
1
2 z (fm)
3
4
Fig. 1. z dependence of the NN cross section of eq.(6) t31 (dashed lines), compared to the quantity o G(z) (see eq.(4)), evaluated using the nuclear matter radial distribution function of ref.[8] (solid lines) . The cross sections are given in units of fm2 . It should be pointed out that short range NN correlations and CT both lead to a suppression of the absorptive part of Y at small z, and have therefore to be regarded as competing mechanisms, whose relative relevance has to be carefully investigated . This problem is illustrated in fig.l, where the z dependence of aG(z) and a(z), calculated according to the PQCD model of ref.[3], are compared for two different values of Q `by2 produced in the kinematical setup of ref.[6] . It turns out tat the "hole" at low z
O. Benhar I Quasielastic electron-nucleus scattering
280c
Q2 NN correlations is much larger than the one associated with CT at whereas the situation is reversed. at Q2 = 7 (GeV/c) 2 .
= 2 (GeVlc)2 ,
3. Numerical results The theoretical procedure described in the previous section has been recently applied to study FSI effects in inclusive electron-nucleus scattering at momentum transfer Q - 2 GeV/c [7] . In ref.[7], the (e, e') cross section has been calculated for infinite nuclear matter, using the spectral function of ref.[9] and including the contributions of both elastic and inelastic electron-nucleon scattering processes . In fig.2 the theoretical results are compared with the empirical nuclear matter cross section obtained from the extrapolation of the existing data to infinite A [10]. The three different curves correspond to different definitions of the absorptive part of the potential felt by the struck nucleon travelling through the nuclear medium. The daslb-dot line represents the results of the standard Glauber prescription of eq.(3), whereas the solid and dashed curves have been obtained using:W defined in egs.(4) and (5), with and without inclusion of CT respectively. The calculations have been performed using the parametrization of the forward NN scattering amplitude given in ref.[11] and the PQCD inspired model of ref.[3] to describe the evolution of the NN cross section associated with CT: 2 > Z + < 9kâ _ ~ x9(L _ z) +4(z _ L) , (6) V(z) 1[L where < QT
>1/2
Q
.35 GeV/c and L = 2p/,&M2 , with Orne = .7 GeV.
It appears that NN correlations and CT both produce an appreciable lowering of the FSI and that CT significantly affects the cross section behavior in the low energy loss wing (w < 800 bbleV, corresponding to Q2 - 2.7 (GeVlc)2 ), bringing the theoretical predictions in good agreement with the data. An experiment designed to study the nuclear and momentum transfer dependence of the quasielastic (e, e'p) scattering, in a kinematical region extended up to Q2 = 7 (GeV/c)2 , has been recently proposed (SLAC-NPAS proposal NE18 [6)). Since in the region of the quasielastic peak the reaction mechanism appears to be well under control and the effect of the nucleon ofd shellness is rather small, it is expected that NE18 data could provide clearcut evidence of the occurrence of CT. However, to get a quantitative understanding of this phenomenon and discriminate between different models describing the evolution of the hadronic cross section, a realistic theoretical calculation of the nucler absorption within standard nuclear physics is needed, and the interplay between NN correlations and CT has to be carefully investigated . Unfortunately, a fully realistic microscopic calculation of the (e, e'p) cross section for finite nuclei is not yet available . However, some information can be obtained considering the total nuclear transparency T, defined as z
T=1 Z
d2bdzp(r)exp? TV
dz'!W(b,z') .
O. Benhar / Quasielastic electron-nucleus scattering
281c
10 -2 a) 0
d
10 -3
10 -4
a b C 10 Nb a
v
10 -5
0 .75
1 1 .5 1 .25 energy loss u (GeV)
1 .75
2
Fig. 2 . Inclusive cross section for electron scattering by nuclear matter at incident energy e = 3.595 GeV and scattering angle 0 = 30°. Dashdot line: Glauber theory. Dashed line: present approach with constant NN cross section. Solid line: present approach with the NN cross section of eq.(6). The results of an estimate of T for 12C, carried out assuming the kinematical conditions of the NE18 proposal, are summarized in fig.3. The calculation has been performed using a nuciear density obtained by a parametrization of the elastic electronnucleus scattering data and different prescriptions for SIV. The dotted and dashed lines show the behaviour of the total transparency estimated using the definition of W of egs.(3) and (5), respectively, and a constant o, = 43.3 mb. The corresponding quantities obtained using the NN cross section of eq.(6) are given by the dash-dot and solid lines. It appears that up to momentum tranfer Qz - 5 (Gev/c)2 NN correlations produce an enhancement of T, with respect to the prediction of Glauber theory, larger than the one associated with CT. Moreover, the CT effect turns out to be appreciably smaller within the present approach than within standard Glauber theory. For instance, at dotted and the dash-dot lines of fig-3 is QZ _= 7 (GeV/c)z the difference between the - 43%, while comparing the dashed and the solid lines one finds a deviation of 28% only. A crude estimate of correlation effects on the nuclear transparency has also been given in ref.[12], where the function G of eq .(4) has been approximated with a step function producing a correlation hole of radius .5 fin, and an enhancement of about 10 -15% has been found . The origin of the larger correlation effect resulting from the
O. Benhar I Quasielastic electron-nucleus scattering
282c
0.9 0.8 0.7 0.6 0.5 0.4
s
'
f
2 .5
e
e
f
f
~
f
s
:
a
~
e
7.5 5 QZ [(GeV/c)2]
e
f
f
~
10
f
f
e
f
~
12 .5
f
e
e
f
15
Fig. 3. Total transparency (eq.(7)) of "'C evaluated as a function of QZ and assuming NE16 kinematics. Potted line: Glauber theory. Dashed .line: present approach with constant a,. Dash-dot line: Glauber theory with or(z) of eq.(6). Solid line: present approach with a(z) of eq.(6). present calculation can be readily understood considering that G(z), shown in fig .1, is rather long ranged and its shape can hardly be approximated by a step function . . Conclusions
The study of the FSI of the struck particle in electron-nucleus scattering at high momentum transfer can provide valuable information on both nuclear and hadronic structure. The strong short range repulsion of the NN force has been shown to play a crucial role in producing a significant enhancement of the nuclear transparency. As a consequence, it has to be carefully taken into account to study the possible occurrence of different mechanisms leading to the same effect, such as color transparency. Fully realistic microscopic calculations of the cross section are certainly needed to firmly establish the possibility of getting quantitative information on CT from (e, e'p) experiments . As it has been pointed out in ref.(12], to get a clean signature of the evolution of the hadronic cross section one should measure the momentum distribution of the single particle states, rather than the total nuclear transparency. However, this requirement obviously puts severe constraints on the missing energy resolution of the experimental apparatus . As a final remark, it should be mentioned that processes other than (e, e') and
0. Benhar / Quasielastic electron-nucleus scattering
283c
(e, e'p) can also be regarded as candidates to study the occurrence of CT in electron-
nucleus scattering (see, e.g., ref.[13]). For instance, exclusive meson photoproduction appears to be particularly well suited, since the relevant Q2 are lower and the nuclear transparency is unaffected by the mechanism associated with NN correlations. Acknowledgments Most of the results discussed in this paper have been obtained in collaboration with A. Fabrocini, S. Fantoni, V.R. Pandharipande and I. Sick, to whom I am deeply indebted for many clarifying discussions . References 1. S.J. Brodsky, in Proceedings of the Thirteenth International Symposium on Multiparticle Dinalnycs. Eds. E.W. Kittel, W. Metzger and A. Stergion (World Scientific, Singapore, 1982)p. 963. 2. A. Mûller, in Proceedings of the Seventeenth Rencontre de Moriond. Ed. J. Thran Thanh Van (Editions Frontières, Gif-sur-Yvette, 1982)p . 13. 3. G.L. Farrar, H. Liu, L.L. Frankfurt and M.I. Strikman, Phys. Rev. Lett . 61 (1988) 686. 4. A.S. Carrol et al, Phys . Rev. Lett. 61 (1988) 1698 . 5. J. Van den Brand et al, SLAC-NPAS proposal NE18 (1990). 6. R.J. Glauber, in Lectures in Theoretical Physics.. Ed. W.E. Brithin et al (Interscience, New York, 1959)p. 315. 7. O. Benhar, A. Fabrocini, S. Fantoni, G.A . Miller, V .R . Pandharipande and I. Sick, preprint SISSA 4/91/CM (1991), submitted to Phys. Rev. C. 8. R. Schiavilla et al, Nucl. Phys. A473 (1987) 267.
9. O . Benhar, A. Fabrocini and S. Fantoni, Nucl. Phys. A505 (1989) 267. 10. D.B. Day et al, Phys. Rev. C 39 (1989) 1011 . 11 . R.H . Bassel and C. Wilkin, Phys. Rev. Lett . 18 (1967) 971.
12. L.L. Frankfurt, M .I. Strikman and M.B . Zalhov, Nucl . Phys . A515 (1990) 599. 13. Pegasys/Mar k II proposal, SLAC-337 (1990) .