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Nucleus-nucleus collision as superposition of nucleon-nucleus collisions
ELSEVIER
Nuclear Physics B (Proc. Suppl.) 71 (1999) 330-334
PROCEEDINGS SUPPLEMENTS
Nucleus-Nucleus Collision as Superposition of Nucleon-Nucleus Collisions EMU-01 COLLABORATION: G.I.Orlova 12, M.I.Adamovich 12, M.M.Aggarwal 3, Y.A.Alexandrov 12, N.P.Andreeva 1, S.K.Badyal 7, E.S.Basova 14, K.B.Bhalla 6, A.Bhasin 7, V.S.Bhatia 3, V.Bradnova ~, V.I.Bubnov 1, X.Cai 16, I.Y.Chasnikov 1, G.M.Chen ~, L.P.Chernova 15, M.M.Chernyavsky 12, S.Dhamija 3, K.E1 Chenawi 1°, D.Felea a, S.Q.Feng 16, A.S.Gaitinov 1, E.R.Ganssauge 11, S.Garpman 1°, S.G.Gerassimov 12, A.Gheata 3, M.Gheata 3, J.Grote 13, K.G.Gulamov 15, S.K.Gupta 6, V.K.Gupta 7, U.Henjes 11 , B.Jakobsson 1°, E.K.Kanygina 1, M.Karabova 8, S.P. Kharlamov12 A.D. Kovalenko ~, S.A. KrasnovS, V. Kumar 6, V.G.Larionova 12, Y.X.Li 4, L.S.Liu 16, S.Lokanathan 6, J.J.Lord 13, N.S.Lukicheva 15, Y.Lu 2 , S.B.Luo 9 , L.K.Mangotra z, I.Manhas 7, I.S.Mittra 3, A.K.Musaeva 1, S.Z.Nasyrov 14, V.S.Navotny 15, J.Nystrand 1°, I.Otterlund 1°, N.G.Peresadko 12, W.Y.Qian 16, Y.M.Qin 9, R.Raniwala 6, N . K . R a J , M.Roeper H , V.V.Rusakova 5, N.Saidkhanov 15, N.A.Salmanova 12, A.M.Seitimbetov 1, R.Sethi 3, B.Singh 6, D.Skelding 13, K.Soderstrem 1°, E.Stenlund 1°, L.N.Svechnikova 15, T.Svensson 1°, A.M .Tawfik 11, M.Tothova s, M.I.Tretyakova 12, T.P.Trofimova 14, U.I.Tuleeva 14, Vani Vashisht 3, S.Vokal s, J.Vrlakova s, H.Q.Wang 2, X.R.Wang 16, Z.Q.Weng 4, R.J.Wilkes 13, C.B.Yang 16, Z.B.Yin 16, L.Z.Yu 16, D.H.Zhang 9, P.Y.Zheng ~, S.I.Zhokhova is, D.C.Zhou 16. 1 High Energy Physics Institute, Almaty, Kazakstan 2 Institute of High Energy Physics, Academia Sinica, Beijing, China a Department of Physics, Panjab University, Chandigarh, India 4 Department of Physics, I-Iunan Education Institute, Changsha, Hunan, China b Joint Institute for Nuclear Research (JINR), Dubna, Russia 6 Department of Physics, University of Rajastan, Jaipur, India Department of Physics, University of Jammu, Jammu, India 6 Department of Nuclear Physics and Biophysics, Safarik University, Kosice, Slovacia 9 Department of Physics, Shanxi Normal University, Linfen, Shanxi, China l0 Department of Physics, University of Lund, Lund, Sweden 11 F.B.Physik, Philipps University, Marburg, Germany 12 P.N.Lebedev Institute of Physics, Moscow, Russia 13 Department of Physics, University of Wasington, Seattle, Washington, USA 14 Institute of Nuclear Physics, Tashkent, Uzbekistan 15 Physical-Technical Institute, Tashkent, Uzbekistan 16 Institute of Particle Physics, Hua-Zhong Normal University, Wuhan, Hubei, China lz St.Peterburg Nuclear Physics Institute, St.Peterburg, Russia Angular distributions of charged particles produced in 160 and 32S collisions with nuclear track emulsion were studied at momenta 4.5 and 200 A GeV/c. Comparison with the angular distributions of charged particles produced in proton-nucleus collisions at the same momentum allows to draw the conclusion, that the angular distributions in nucleus-nucleus collisions can be seen as superposition of the angular distributions in nucleon-nucleus collisions taken at the same impact parameter bNA, that is mean impact parameter between the participating projectile nucleons and the center of the target nucleus
1. I n t r o d u c t i o n
The aim of the paper is to show that the pseudorapidity density distributions P(O) of the secondary charged particles from nucleus-nucleus collisi-
0920-5632/98/$19.00 © 1998 ElsevierScience B.V. All rights reserved. PII S0920-5632(98)00362-4
ons can be explained as superposition of pseudorapidity density distributions of the secondary charged particles from nucleon-nucleus collisions taken at the same impact parameter bNA. The data we analyze are taken by the EMU-01
G.L Orlovaet al./Nuclear Physics B (Proc. Suppl.) 71 (1999) 330-334
331
Table 1 Summary of used data Process
p +Em O + Em S +Em p +Em O +Em S + Em
Projectile
lp 160 32S lp 160 32S
P0 in AGeV/c
4.5 4.5 4.5 200 200 200
collaboration using 160 and ass-beams at 200 A GeV/c at the CERN-SPS and at 4.5 A GeV/c at the DUBNA-SF. The proton data at 200 GeV/c are taken at FNAL, at 4.5 GeV/c at DUBNA-SF. Table 1 gives a summary of the data used for this paper. 2. E x p e r i m e n t a l P r o c e d u r e Stacks consisting each of 30-40 NIKFI BR-2 nuclear emulsion pellicles with dimensions 10 x 20 cm 2 and 500#m thick were exposed at 160 and ass beams at CERN-SPS at 200 A GeV/c and at DUBNA-SF at 4.5 A GeV/c. Data of p + Em were taken in the same way at DUBNA at 4.5 GeV and at FNAL at 200 GeV. The beam was parallel to the pellicles. The minimum track ionization was about 35 grains/100 #m. The interactions were found by along-the-track scanning which has a very high detection efficiency. The interactions were analyzed with optical microscopes which were partially equipped with electronic instruments like "digipads" and semi-automatic devices. Only those interactions in which at least one produced particle could be identified were examined, the interactions without produced particles with high probability have been related to quasi-elastice or electromagnetic dissociation type and have been rejected.[5] All secondary charged particles are classified into groups of "multi-charged fragments" N! (Z > 2, momentum about P0), shower particles N~ (/3 >
No. of events
2376 2029 1043 2402 753 926
Accelerator
Dubna Dubna Dubna FNAL CERN CERN
SF SF SF SPS SPS
Ref.
[1] [2] [2] [3] [2,4,5,6] [2,6]
0, 7) and target-associated particles. Grey N e and black Nb tracks (target protons and evaporation target fragments) has been used as it is normally done in nuclear track emulsion experiments (see for instance ref. [7,8]). All the definitions used in the paper are listed in Table 2. The normalization factor K we use takes into account that the effective target mass in an emulsion depends on the projectile mass (see T a b . 2 "Definitions") K(160) = 0.82; K(32S) = 0.77, for (p + Em) collision the normalization factor K(p) is = 1 [9]. The average number of participating projectile nucleons, < Pp,. > is connected with the mass and the charge of the projectile and with Q (the summary charge of the projectile spectators which passed the target without interacting) by equation: < Pp~ > = Ap~-(1 - Q/Zp~).
(1)
3. Analysis and R e s u l t s For the data analysis and the comparison of nucleus-nucleus and proton- nucleus collisions the impact parameter bga is used. The average impact parameter bNA between the participating projectile nucleons and the target center is directly connected with Q for A + Em collisions and with Nh (all target-associeted tracks) for p + Em collisions. Therefore we have divided all minimum bias data of O + Em and S + Em collisions into subgroups according to the value Q, the data of
G.I. Orlova et al./Nuclear Physics B (Proc. Suppl.) 71 (1999) 330-334
332
Table 2 Definitions Apt
Atg K
Q
= = = = = =
~7 0 P bNA
= = = = =
o', P0, r}O
:
gg(Nb) Nh
= = =
Po
mass of the projectile charge of the projectile number of participating projectile nucleons mass of the target < Atg >A,Em / < Atg >p,Em charge flow into the forward cone 8 < 80 with 00 from sin 8o=0.2 GeV/c/po primary momentum of the projectile pseudorapidity: ~1= - I n tan(0/2), with emission angle pseudorapidity density: p _ g . .1. . , dn/dTt mean impact parameter between the participating projectile nucleons and the center of the target v "P'~ IbNAli nucleus: ~ • A.~i=I parameters of the Gaussian fit of the pseudorapidity density distribution number of charged particles produced in the interaction number of grey (black) particles number of "heavy" particles: Nh = Ng + Nb
p + Em collisions on the other hand we have divided into subgroups according to the number Nh of target fragments. To calculate the average impact parameters bgA as a function of Q for A + Em collisions and as a function of Nh for p + Em collisions, we used a simple geometrical model calculation [10] which has not yet been published. It is known that the shower particle pseudorapidity distributions for nucleus-nucleus and protonnucleus collisions could be well fitted by Gaussian distributions. p(~/) = P0" e x p { - ( ~ - ~/0)2/2Cr2}
(2)
The fits are performed in the y-intervals 0.506.00 at 200 A GeV/c and 0.50-2.25 at 4.5 A GeV/c. The cut of the rt-interval is done in order to minimize the contributions from the target Q/ < 0.5) and projectile (7/> 6.0) fragments. These Gaussians are characterized by parameters P0, r/0, and tr, which we analyze in the paper for nucleus-nucleus pseudorapidity density distribution in comparison with proton-nucleus pseudorapidity density distribution (see the next P i g s . l - 4 ) .
We have shown already [11] that there exists a linear relationship between the Gaussian fit parameter - the peak value P0 and the number N~ of produced particles, and that this relation depends on the momentum but not on the mass of the projectile nucleus. Here (see F i g . l ) we show that the same is true for p + Em, and it holds for 200 A GeV as well as for 4.5 A Gev/c. The linear dependence of po(N~) is quite convincing, the peak values are linear functions of the number N,r of produced particles: P0 = (0.25 4- 0.02)N~ at 200 A G e V / c P0 = (0.66 4- 0.03)N~ at 4.5 A G e V / c The cr(bNA)-dependence,the connection between the width of the Gaussian fit and the mean impact parameter (see Fig.2) is very close to a constant: cr -- -(0.0003 -4- O.O001)byA -4- (1.64 4- 0.03) at 200 A GeV/c : --(0.037 4- O.O03)bNA + (0.71 4- 0.02) at 4.5 A GeV/c If we believe that cr(bNA) = const it gives us: a = 1.65 4- 0.04 at 200 A G e V / c cr = 0.84 4- 0.03 at 4.5 A G e V / c The peak position dependence on the impact pa-
G.L Orlova et al./Nuclear Physics B (Proc. Suppl.) 71 (1999) 330-334
d[ 8o
333
D & /
60
/
/
I+._.._÷..... .+..... + ....
1
/
............
/
40 ink" /
20
f
0
2'"
V .
0
°
• /
.
.
.
m
100
.
.
.
.
m
200
.
.
.
.
0
300
,
0
i
--
,
--0-
. . . .
I
,
2
N.
Figure 1. Peak values of the Gaussian as function of the number of produced particles po(N~). The symbols: circles for p + E m data, squares for O + E m data, triangles for S + E m data; open symbols for the data at 4.5 A GeV/c, filled symbols for data at 200 a GeV/c.
rameter ~?o(bNA) (see Pig.3) is also a linear function: ~/0 = (0.38 4- O.02)bgA + (1.89 4- 0.05) at 200 A GeV/c 7/0 = (0.35 4- O.04)bgA + (0.38 4- 0.02) at 4.5 A GeV/c with the slope being independent of the projectile momentum. To investigate the peak value dependence on the impact parameter we use the peak value P0 normalized to the product K. < Ppr >. This allowes us to use the peak value of one participating projectile nucleon corrected according to the fact that in the emulsion the effective target mass depends on the projectile mass. For the normalized peak value Pint =~ PolK" < Ppr > we get again a linear dependence on the impact parameter bNa, shown in Fig.4: Pint = -(1.19 4- O.03)bNa -4- (6.34 4- 0.06) at 200 A GeV/c
........
i
i
I
i
4 bm
Figure 2. Width of the Gaussian as function of the impact parameter: cr(bNa). The symbols are the same as in Fig.1.
Pint = -(0.24 4- O.O1)bNA + (1.50 4- 0.02) at 4.5 A GeV/c As a result all three parameters (~, pint, and ~1o) of the Gaussian fit of the pseudorapidity density distributions of the shower particles from p + Em, O + Em and S + Em collisions depend on the impact parameter bNA of a given subgroup only and do not depend on the projectile mass. This means: If one compares subgroups with the same impact parameter bgA (no matter, whether nucleus-nucleus or proton-nucleus collision is concerned) one finds that the parameters - cr, Pint, and 7?o defining the Gaussian fits of the pseudorapidity density distribution of the shower particles have exactly the same meaning. 4. S u m m a r y a n d C o n c l u s i o n It is shown by analysis of (p + Em), (O + Em), and (S + Em) collisions at 200 A GeV/c and at 4.5 A GeV/c that nucleus-nucleus collisions are superpositions of nucleon-nucleus collisions taken at the same impact parameter bNA. This is due to the
334
G.I. Orlova et al./Nuclear Physics B (Proc. Suppl.) 71 (1999) 330-334
t .
8
...""
6 "-,..
• ......~"
...e.....% "''$"
0
4 r'~A"
~ "~i)~r
O
-O-- _..O...~.~._~ ~ : i b Q
0
~
0
~
i
2
~
~
~
i
i
0
4
b~
Figure 3. Peak position of the Gaussian as function of the impact parameter: ~o(bNA). The symbols are the same as in Fig.1.
i
i
I
2
i
i
i
- _.... I
i
4 b.
Figure 4.
The normalized Gaussian peak value
Pint - p o / K " < Ppr > as function of the impact parameter bNA. The symbols are the same as in
Fig. 1.
fact that all the parameters of the Gaussian fits of the pseudorapidity density distributions of shower particles - pint, 70, and ~ - depend on the impact parameter bNA only and not on the type of the projectile, nucleus or nucleon. 5. A c k n o w l e d g e m e n t s We would like to thank the DFG, the ISF and RFFI for financial support, A. Tawfik thanks the DAAD for making his stay at the PhilippsUniversity Marburg possible. REFERENCES
1. B.P.Bannik et al., Preprint JINR, Dubna, PI13055, (1980). 2. M.I.Adamovich et al., EMU-01 Coll., Phys. Rev. Lett. 69 (1992) 745. 3. M.I.Adamovich et al., Physics of Atomic Nuclei, 26(5), (1977) 1243. 4. M.I.Adamovich et al., EMU-01 Coll., Phys. Lett. B201, N3, (1988) 397.
5. M.I.Adamovich et al., EMU-01 Coll., Phys. Rev. Lett., 62, N24, (1989) 2801. 6. R.J.Wilkes et al., EMU-01 Coll., Nucl. Phys., A544 (1992) 153. 7. M.I.Adamovich et al., EMU-01 Coll., Physics of Atomic Nuclei, 58(6), (1995) 951. 8. M.I.Adamovich et al., EMU-01 Coll., Phys. Lett., B234, N3, (1990) 180. 9. M.I.Adamovich et al., EMU-01 Coll., Modern Phys. Lett., A5 ,N3, (1990) 169. 10. U. Henjes, unpublished; 14th EMU-01 Coll. Meeting, Wuhan, 1995. 11. M.I. Adamovich et al., EMU-01 Coll., Z. Phys., C56, (1992) 509.
Nuclear Physics B (Proc. Suppl.) 71 (1999) 330-334
PROCEEDINGS SUPPLEMENTS
Nucleus-Nucleus Collision as Superposition of Nucleon-Nucleus Collisions EMU-01 COLLABORATION: G.I.Orlova 12, M.I.Adamovich 12, M.M.Aggarwal 3, Y.A.Alexandrov 12, N.P.Andreeva 1, S.K.Badyal 7, E.S.Basova 14, K.B.Bhalla 6, A.Bhasin 7, V.S.Bhatia 3, V.Bradnova ~, V.I.Bubnov 1, X.Cai 16, I.Y.Chasnikov 1, G.M.Chen ~, L.P.Chernova 15, M.M.Chernyavsky 12, S.Dhamija 3, K.E1 Chenawi 1°, D.Felea a, S.Q.Feng 16, A.S.Gaitinov 1, E.R.Ganssauge 11, S.Garpman 1°, S.G.Gerassimov 12, A.Gheata 3, M.Gheata 3, J.Grote 13, K.G.Gulamov 15, S.K.Gupta 6, V.K.Gupta 7, U.Henjes 11 , B.Jakobsson 1°, E.K.Kanygina 1, M.Karabova 8, S.P. Kharlamov12 A.D. Kovalenko ~, S.A. KrasnovS, V. Kumar 6, V.G.Larionova 12, Y.X.Li 4, L.S.Liu 16, S.Lokanathan 6, J.J.Lord 13, N.S.Lukicheva 15, Y.Lu 2 , S.B.Luo 9 , L.K.Mangotra z, I.Manhas 7, I.S.Mittra 3, A.K.Musaeva 1, S.Z.Nasyrov 14, V.S.Navotny 15, J.Nystrand 1°, I.Otterlund 1°, N.G.Peresadko 12, W.Y.Qian 16, Y.M.Qin 9, R.Raniwala 6, N . K . R a J , M.Roeper H , V.V.Rusakova 5, N.Saidkhanov 15, N.A.Salmanova 12, A.M.Seitimbetov 1, R.Sethi 3, B.Singh 6, D.Skelding 13, K.Soderstrem 1°, E.Stenlund 1°, L.N.Svechnikova 15, T.Svensson 1°, A.M .Tawfik 11, M.Tothova s, M.I.Tretyakova 12, T.P.Trofimova 14, U.I.Tuleeva 14, Vani Vashisht 3, S.Vokal s, J.Vrlakova s, H.Q.Wang 2, X.R.Wang 16, Z.Q.Weng 4, R.J.Wilkes 13, C.B.Yang 16, Z.B.Yin 16, L.Z.Yu 16, D.H.Zhang 9, P.Y.Zheng ~, S.I.Zhokhova is, D.C.Zhou 16. 1 High Energy Physics Institute, Almaty, Kazakstan 2 Institute of High Energy Physics, Academia Sinica, Beijing, China a Department of Physics, Panjab University, Chandigarh, India 4 Department of Physics, I-Iunan Education Institute, Changsha, Hunan, China b Joint Institute for Nuclear Research (JINR), Dubna, Russia 6 Department of Physics, University of Rajastan, Jaipur, India Department of Physics, University of Jammu, Jammu, India 6 Department of Nuclear Physics and Biophysics, Safarik University, Kosice, Slovacia 9 Department of Physics, Shanxi Normal University, Linfen, Shanxi, China l0 Department of Physics, University of Lund, Lund, Sweden 11 F.B.Physik, Philipps University, Marburg, Germany 12 P.N.Lebedev Institute of Physics, Moscow, Russia 13 Department of Physics, University of Wasington, Seattle, Washington, USA 14 Institute of Nuclear Physics, Tashkent, Uzbekistan 15 Physical-Technical Institute, Tashkent, Uzbekistan 16 Institute of Particle Physics, Hua-Zhong Normal University, Wuhan, Hubei, China lz St.Peterburg Nuclear Physics Institute, St.Peterburg, Russia Angular distributions of charged particles produced in 160 and 32S collisions with nuclear track emulsion were studied at momenta 4.5 and 200 A GeV/c. Comparison with the angular distributions of charged particles produced in proton-nucleus collisions at the same momentum allows to draw the conclusion, that the angular distributions in nucleus-nucleus collisions can be seen as superposition of the angular distributions in nucleon-nucleus collisions taken at the same impact parameter bNA, that is mean impact parameter between the participating projectile nucleons and the center of the target nucleus
1. I n t r o d u c t i o n
The aim of the paper is to show that the pseudorapidity density distributions P(O) of the secondary charged particles from nucleus-nucleus collisi-
0920-5632/98/$19.00 © 1998 ElsevierScience B.V. All rights reserved. PII S0920-5632(98)00362-4
ons can be explained as superposition of pseudorapidity density distributions of the secondary charged particles from nucleon-nucleus collisions taken at the same impact parameter bNA. The data we analyze are taken by the EMU-01
G.L Orlovaet al./Nuclear Physics B (Proc. Suppl.) 71 (1999) 330-334
331
Table 1 Summary of used data Process
p +Em O + Em S +Em p +Em O +Em S + Em
Projectile
lp 160 32S lp 160 32S
P0 in AGeV/c
4.5 4.5 4.5 200 200 200
collaboration using 160 and ass-beams at 200 A GeV/c at the CERN-SPS and at 4.5 A GeV/c at the DUBNA-SF. The proton data at 200 GeV/c are taken at FNAL, at 4.5 GeV/c at DUBNA-SF. Table 1 gives a summary of the data used for this paper. 2. E x p e r i m e n t a l P r o c e d u r e Stacks consisting each of 30-40 NIKFI BR-2 nuclear emulsion pellicles with dimensions 10 x 20 cm 2 and 500#m thick were exposed at 160 and ass beams at CERN-SPS at 200 A GeV/c and at DUBNA-SF at 4.5 A GeV/c. Data of p + Em were taken in the same way at DUBNA at 4.5 GeV and at FNAL at 200 GeV. The beam was parallel to the pellicles. The minimum track ionization was about 35 grains/100 #m. The interactions were found by along-the-track scanning which has a very high detection efficiency. The interactions were analyzed with optical microscopes which were partially equipped with electronic instruments like "digipads" and semi-automatic devices. Only those interactions in which at least one produced particle could be identified were examined, the interactions without produced particles with high probability have been related to quasi-elastice or electromagnetic dissociation type and have been rejected.[5] All secondary charged particles are classified into groups of "multi-charged fragments" N! (Z > 2, momentum about P0), shower particles N~ (/3 >
No. of events
2376 2029 1043 2402 753 926
Accelerator
Dubna Dubna Dubna FNAL CERN CERN
SF SF SF SPS SPS
Ref.
[1] [2] [2] [3] [2,4,5,6] [2,6]
0, 7) and target-associated particles. Grey N e and black Nb tracks (target protons and evaporation target fragments) has been used as it is normally done in nuclear track emulsion experiments (see for instance ref. [7,8]). All the definitions used in the paper are listed in Table 2. The normalization factor K we use takes into account that the effective target mass in an emulsion depends on the projectile mass (see T a b . 2 "Definitions") K(160) = 0.82; K(32S) = 0.77, for (p + Em) collision the normalization factor K(p) is = 1 [9]. The average number of participating projectile nucleons, < Pp,. > is connected with the mass and the charge of the projectile and with Q (the summary charge of the projectile spectators which passed the target without interacting) by equation: < Pp~ > = Ap~-(1 - Q/Zp~).
(1)
3. Analysis and R e s u l t s For the data analysis and the comparison of nucleus-nucleus and proton- nucleus collisions the impact parameter bga is used. The average impact parameter bNA between the participating projectile nucleons and the target center is directly connected with Q for A + Em collisions and with Nh (all target-associeted tracks) for p + Em collisions. Therefore we have divided all minimum bias data of O + Em and S + Em collisions into subgroups according to the value Q, the data of
G.I. Orlova et al./Nuclear Physics B (Proc. Suppl.) 71 (1999) 330-334
332
Table 2 Definitions Apt
Atg K
Q
= = = = = =
~7 0 P bNA
= = = = =
o', P0, r}O
:
gg(Nb) Nh
= = =
Po
mass of the projectile charge of the projectile number of participating projectile nucleons mass of the target < Atg >A,Em / < Atg >p,Em charge flow into the forward cone 8 < 80 with 00 from sin 8o=0.2 GeV/c/po primary momentum of the projectile pseudorapidity: ~1= - I n tan(0/2), with emission angle pseudorapidity density: p _ g . .1. . , dn/dTt mean impact parameter between the participating projectile nucleons and the center of the target v "P'~ IbNAli nucleus: ~ • A.~i=I parameters of the Gaussian fit of the pseudorapidity density distribution number of charged particles produced in the interaction number of grey (black) particles number of "heavy" particles: Nh = Ng + Nb
p + Em collisions on the other hand we have divided into subgroups according to the number Nh of target fragments. To calculate the average impact parameters bgA as a function of Q for A + Em collisions and as a function of Nh for p + Em collisions, we used a simple geometrical model calculation [10] which has not yet been published. It is known that the shower particle pseudorapidity distributions for nucleus-nucleus and protonnucleus collisions could be well fitted by Gaussian distributions. p(~/) = P0" e x p { - ( ~ - ~/0)2/2Cr2}
(2)
The fits are performed in the y-intervals 0.506.00 at 200 A GeV/c and 0.50-2.25 at 4.5 A GeV/c. The cut of the rt-interval is done in order to minimize the contributions from the target Q/ < 0.5) and projectile (7/> 6.0) fragments. These Gaussians are characterized by parameters P0, r/0, and tr, which we analyze in the paper for nucleus-nucleus pseudorapidity density distribution in comparison with proton-nucleus pseudorapidity density distribution (see the next P i g s . l - 4 ) .
We have shown already [11] that there exists a linear relationship between the Gaussian fit parameter - the peak value P0 and the number N~ of produced particles, and that this relation depends on the momentum but not on the mass of the projectile nucleus. Here (see F i g . l ) we show that the same is true for p + Em, and it holds for 200 A GeV as well as for 4.5 A Gev/c. The linear dependence of po(N~) is quite convincing, the peak values are linear functions of the number N,r of produced particles: P0 = (0.25 4- 0.02)N~ at 200 A G e V / c P0 = (0.66 4- 0.03)N~ at 4.5 A G e V / c The cr(bNA)-dependence,the connection between the width of the Gaussian fit and the mean impact parameter (see Fig.2) is very close to a constant: cr -- -(0.0003 -4- O.O001)byA -4- (1.64 4- 0.03) at 200 A GeV/c : --(0.037 4- O.O03)bNA + (0.71 4- 0.02) at 4.5 A GeV/c If we believe that cr(bNA) = const it gives us: a = 1.65 4- 0.04 at 200 A G e V / c cr = 0.84 4- 0.03 at 4.5 A G e V / c The peak position dependence on the impact pa-
G.L Orlova et al./Nuclear Physics B (Proc. Suppl.) 71 (1999) 330-334
d[ 8o
333
D & /
60
/
/
I+._.._÷..... .+..... + ....
1
/
............
/
40 ink" /
20
f
0
2'"
V .
0
°
• /
.
.
.
m
100
.
.
.
.
m
200
.
.
.
.
0
300
,
0
i
--
,
--0-
. . . .
I
,
2
N.
Figure 1. Peak values of the Gaussian as function of the number of produced particles po(N~). The symbols: circles for p + E m data, squares for O + E m data, triangles for S + E m data; open symbols for the data at 4.5 A GeV/c, filled symbols for data at 200 a GeV/c.
rameter ~?o(bNA) (see Pig.3) is also a linear function: ~/0 = (0.38 4- O.02)bgA + (1.89 4- 0.05) at 200 A GeV/c 7/0 = (0.35 4- O.04)bgA + (0.38 4- 0.02) at 4.5 A GeV/c with the slope being independent of the projectile momentum. To investigate the peak value dependence on the impact parameter we use the peak value P0 normalized to the product K. < Ppr >. This allowes us to use the peak value of one participating projectile nucleon corrected according to the fact that in the emulsion the effective target mass depends on the projectile mass. For the normalized peak value Pint =~ PolK" < Ppr > we get again a linear dependence on the impact parameter bNa, shown in Fig.4: Pint = -(1.19 4- O.03)bNa -4- (6.34 4- 0.06) at 200 A GeV/c
........
i
i
I
i
4 bm
Figure 2. Width of the Gaussian as function of the impact parameter: cr(bNa). The symbols are the same as in Fig.1.
Pint = -(0.24 4- O.O1)bNA + (1.50 4- 0.02) at 4.5 A GeV/c As a result all three parameters (~, pint, and ~1o) of the Gaussian fit of the pseudorapidity density distributions of the shower particles from p + Em, O + Em and S + Em collisions depend on the impact parameter bNA of a given subgroup only and do not depend on the projectile mass. This means: If one compares subgroups with the same impact parameter bgA (no matter, whether nucleus-nucleus or proton-nucleus collision is concerned) one finds that the parameters - cr, Pint, and 7?o defining the Gaussian fits of the pseudorapidity density distribution of the shower particles have exactly the same meaning. 4. S u m m a r y a n d C o n c l u s i o n It is shown by analysis of (p + Em), (O + Em), and (S + Em) collisions at 200 A GeV/c and at 4.5 A GeV/c that nucleus-nucleus collisions are superpositions of nucleon-nucleus collisions taken at the same impact parameter bNA. This is due to the
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t .
8
...""
6 "-,..
• ......~"
...e.....% "''$"
0
4 r'~A"
~ "~i)~r
O
-O-- _..O...~.~._~ ~ : i b Q
0
~
0
~
i
2
~
~
~
i
i
0
4
b~
Figure 3. Peak position of the Gaussian as function of the impact parameter: ~o(bNA). The symbols are the same as in Fig.1.
i
i
I
2
i
i
i
- _.... I
i
4 b.
Figure 4.
The normalized Gaussian peak value
Pint - p o / K " < Ppr > as function of the impact parameter bNA. The symbols are the same as in
Fig. 1.
fact that all the parameters of the Gaussian fits of the pseudorapidity density distributions of shower particles - pint, 70, and ~ - depend on the impact parameter bNA only and not on the type of the projectile, nucleus or nucleon. 5. A c k n o w l e d g e m e n t s We would like to thank the DFG, the ISF and RFFI for financial support, A. Tawfik thanks the DAAD for making his stay at the PhilippsUniversity Marburg possible. REFERENCES
1. B.P.Bannik et al., Preprint JINR, Dubna, PI13055, (1980). 2. M.I.Adamovich et al., EMU-01 Coll., Phys. Rev. Lett. 69 (1992) 745. 3. M.I.Adamovich et al., Physics of Atomic Nuclei, 26(5), (1977) 1243. 4. M.I.Adamovich et al., EMU-01 Coll., Phys. Lett. B201, N3, (1988) 397.
5. M.I.Adamovich et al., EMU-01 Coll., Phys. Rev. Lett., 62, N24, (1989) 2801. 6. R.J.Wilkes et al., EMU-01 Coll., Nucl. Phys., A544 (1992) 153. 7. M.I.Adamovich et al., EMU-01 Coll., Physics of Atomic Nuclei, 58(6), (1995) 951. 8. M.I.Adamovich et al., EMU-01 Coll., Phys. Lett., B234, N3, (1990) 180. 9. M.I.Adamovich et al., EMU-01 Coll., Modern Phys. Lett., A5 ,N3, (1990) 169. 10. U. Henjes, unpublished; 14th EMU-01 Coll. Meeting, Wuhan, 1995. 11. M.I. Adamovich et al., EMU-01 Coll., Z. Phys., C56, (1992) 509.