0 fermi national accelerator laboratorylss.fnal.gov/archive/1982/pub/pub-82-064-e.pdf · 0 fermi...
TRANSCRIPT
0 Fermi National Accelerator Laboratory
FEKMILAB-Pub-82/64-EXP 7160.451 (Submitted to Phys. Rev. D)
EXPERIMENTAL STUDY OF THE A-DEPENDENCE OF INCLUSIVE HADRON FHAGMENTATION
D. S. Barton, G. W. Brandenburg, W. Busza, T. Dobrowolski, J. I. Friedman, C. Halliwell, H. W. Kendall, T. Lyons,
B. Nelson, L. Rosenson, and R. Verdier Massachusetts Institute of Technology Cambridge, Massachusetts 02139 USA
and
M. T. Chiaradia, C. DeMarzo, C. Favuzzi, G. Germinario, L. Guerriero, P. LaVopa, G. Maggi, F. Posa, G. Selvaggi,
P. Spinelli and F. Waldner Istituto di Fisica and Istituto Nazionale di Fisica Nucleare
Bari, Italy
and
D. Cutts, K. S. Dulude, B. W. Hughlock, K. E. Lanou, Jr. and J. T. Massimo
Brown University, Providence, Rhode Island 02912 USA
and
A. E. Brenner, D. C. Carey, J. E. Elias, P. H. Garbincius and V. A. Polychronakos
Fermi National Accelerator Laboratory Batavia, Illinois 60510 USA
and
J. Nassalski and T. Siemiarczuk Institute of Nuclear Research, Warsaw, Poland
September 1982
e Operated by Unlversilles Research Association Inc. under contract with the United States Department of Energy
Experimental Study of the A-Dependence of Inclusive Hadron Fragmentation
D.S. Barton 3 G.FI. Brandenburg,b, W. Busza, T. Dobrownliki,
J.1 Friedman, C. Halliwellc, H.W. Kendall, T. Lyons, B. Nelson, L. Rosenson, and R. Verdier Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139 USA
and
M.T. Chiaradia, C. DeMarzo, C. Favuzzi, G. Germinario! L. Guerriero, P. LaVopa, G. Maggi, F. Posa, G. Selvaggl,
P. Spinelli, and F. Waldner Istituto di Fisica and
Istituto Nazionale di Fisica Nucleare, Bari, Italy
and
D. Cutts, R.S. Duluded,~B.W. Hughlock, R.E. Lanou, Jr., and J.T. Massimo
Brown University, Providence, Rhode Island 02912, US4 :~.
and .-
A.E. Brenner, D.C. Carey, J.E. Elias, P.H. Garbincius,
and V.A. Polychronakose Fermi National Accelerator Laboratory,
Batavia, Illinois 60510 USA :
and
J. Nassalski, T. Siemiarczuk Institute of Nuclear Research, Warsaw, Poland
ABSTRACT Data are presen$ed op the inclusive production of 'II- k, p, and p for KS, and protons iicident on nuclear
TI*,
targets at 100 GeV. The results cover the kinematic range 30.5 P.sTEE ",,eIL;ved for Pt= 0.3 and 0.5 GeV/c. A-dependence of the invariant cross sections exhibits remarkable simplicity, which does not naturally. follow from current models of particle production. The results show that the hypothesis of limiting fragmentation can be extended to include collisions with nuclei.
Page 2
I -z Introduction
The mechanism of hadron fragmentation and resultant
particle production in high energy hadron-hadron collisions
is not well understood. In order to investigate the main
features of the fragmentation process we have carried out an
extensive experimental survey of the forward particle
spectra for incident pions, kaons, and protons, and a broad
range of targets and incident energies. The results on the
projectile and energy dependence of the spectra for a proton
target have been presented previously.’ In this paper we
concentrate on the target dependence of the spectra.
There are several motivations for investigating
projectile fragmentation from such apparently complex
targets as nuclei. From the point of view of the study of
the hypothesis of limiting fragmentation*, nuclear targets
add a new dimension. Consider, for example, a
hadron-nucleus collision in the rest frame of the incident
hadron, i.e., in which the nucleus is the projectile. Two
interesting questions arise:
1) At high energies, do hadron targets fragment in an
energy-independent way for projectiles
considerably more massive and complex
than nucleons?
2) If so, to what extent does the fragmentation depend
on the projectile?
Page 3
We know from previous hadron-nucleus experiments that
at high energies the multiplication of hadrons within a
nucleus is relatively weak.3 This has been interpreted as
evidence of long formation times of the produced particles. 4
If this is a correct interpretation, nuclear targets can be
looked upon as filters analyzing the wave function of the
projectile .5 From this point of view, the leading particle
spectra reflect that part of the wave function which has not
been absorbed by the target.
Finally, the A-dependence of the leading particle
spectra can give information on the rate of energy loss of
strongly interacting particles as they pass through nuclear
matter. 6 In contrast to the extensive knowledge of the
energy loss by ionisation when charged particles pass
through ordinary matter, little is known about the nuclear
stopping power for hadrons. This information is .not only
important for a better understanding of the interactions
that take place when two hadrons pass through each other,
but also is needed for predicting the kind of nuclear
densities that may be achieved in head-on collisions of
large nuclei .6
Previous measurements of the A-dependence of inclusive
processes in the beam fragmentation region include IT’, K’,
p, and F production in proton interactions at 24 GeV7, To,
A0 8 , K’production by protons at 300 GeV , E’ production by s
protons at 400 GeV 9
, and neutron production by protons at 10
400 GeV . In this experiment, we have measured the
Page 4
inclusive production of x’ , K ‘, p, and 3 in 100 GeV K+, K+,
and p collisions with C, Al, Cu, Ag, and Pb targets. Since
essentially the same equipment was used in an earlier
measurement of these same processes for a hydrogen target,
an accurate comparison between hA and hp interactions, free
of many systematic errors, is possible. Preliminary results
of this experiment have been discussed in Ref. 11.
II. The Experimental Method and Measured Cross Sections - -
The data were collected using the Fermilab Single Arm
Spectrometer facility in the M6E beam line. An incident
positive beam of 100 GeV/c was used. The production of the
fast secondaries was measured over a momentum range of 30
GeV -< P -< 88 GeV/c and transverse momentum range 0.18 <- p,i
0.5 GeV/c. Data were taken simultaneously for the nine
reaction types (xx, xK, xp, etc.). Good n-K-p separation
was achieved over the entire kinematic range using the seven
xerenkov counters of the facility. Full details of the
apparatus, data taking, and analysis procedures are
described in Ref. 1.
A list of the targets used in the experiment is given
in Table 1. Typical data consisted of a sequential set of
measurements using the thickest targets of C, Al, Cu, Ag,
and Pb along with an empty target run at a fixed
spectrometer momentum and angle setting. In this way, the
A-dependence of the invariant cross sections for each
Page 5
channel could be studied without requiring detailed
knowledge of absolute acceptance apertures, particle
identification efficiencies, etc. The thinner targets were
used at P = 40 GeV/c and 80 GeV/c to study finite target
thickness effects by extrapolation to zero target thickness.
The average corrections to the thick target data were
x-independent and %~R%.
In a manner similar to that described in Ref. 1, the
interaction rates were corrected for particle absorption and
decay in the spectrometer, multiple scattering losses in the
spectrometer, particle misidentification, and track
reconstruction inefficiencies. The corrected rates were
then used to obtain the invariant differential cross section
for every channel.
In addition to the nuclear targets, data were taken on
a hydrogen target at P = 40 GeV/c and 80 GeV/c for Pt I 0.3
GeV/c. Tbe invariant cross sections for the high statistics
n+p + x+X and pp + pX channels measured in this experiment
agree on the average with those previously quoted1 to 4 -I 2%
in absolute value. Throughout this paper the quoted
hydrogen cross sections are the statistically more accurate
ones measured earlier.
The complete set of measurements of the invariant cross
sections is given in Table 2. The errors are primarily
statistical, but contain a small contribution from particle
misidentification. The overall normalisation uncertainty is
Page 6
estimated to be 10%. The systematic uncertainty due to
particle misidentification, in the reactions with an
outgoing kaon, is less than 5%. As an illustration of these
results, in Figs. 1 - 4 the invariant cross sections for
+ + p+ p, p+ TI , n +n; andx
+ + K+ at Pt = 0.3 GeV/c are 12
plotted as a function of Feynman x.
In order to exhibit explicitly the A-dependence of the
data, at every kinematic point the invariant cross sections
were fitted to the empirical form
3 Ey = o. Aa . ..(l)
Hydrogen data were not included in the fits. A typical data
set and the fit to it are shown in Fig. 5. The results of
all the fits are given in Table 2. As can be seen from
these results, as well as from most other nuclear target
experiments, the extrapolation of equation (1) to A = 1 does
not yield the hydrogen result. This makes clear that
conclusions drawn from experiments that use only one nuclear
target in conjunction with hydrogen should be treated with
caution.
Page 7
III. Discussion of Results -
The A-dependence of the inelastic cross sections on
13 nuclei at 100 GeV can be parameterized as : 25 8A”‘76mb, .
20.9A”‘7gmb 0.72 , and 38.2A + mb for incident II , K’, and
protons respectively. The corresponding hydrogen cross
sections are14 : 20.2mb, 16.7mb, and 31.4mb. A comparison
of these values with those in Table 2 indicates that, over
the entire projectile fragmentation region, and for all
produced particles, the ratio of the inclusive cross section
to the total inelastic cross section is smaller for a
nuclear than for a proton target. Furthermore, this ratio
decreases as the size of the nucleus increases.
As a test of the hypothesis of limiting fragmentation*,
we can compare our incident proton data at 100 GeV with
those of Eichten et al.’ at 24 GeV. We find that the --
absolute values of the cross sections on nuclei are slightly
higher at 24 GeV than at 100 GeV. A similar change is seen
in proton target data over this energy range. l5 The
A-dependences at the two energies are in very good
agreement. We conclude that while the fragmentation of the
projectile does depend on the nature of the target, the
approach to scaling in Feynman x does not.
For the kinematic range covered by this experiment, the
A-dependence as expressed by the exponent c exhibits a
remarkable simplicity. With a few exceptions, discussed
later, it is only a function of x and incident particle
Page a
type. It is independent of the outgoing particle type. To
illustrate these features, in Fig. 6 we plot a as a function
of x for a broad range of proton-induced reactions. In the
interest of clarity, data points with errors in a greater
than kO.03 have been omitted. The curve which has the
functional form a(x) = 0.74 - 0.55x + 0.26x2 is a
polynomial fit to all previous world data and data from this
experiment. It has no particular significance other than to
guide the eye. Although we have not plotted some
statistically less significant results in Fig. 6, it should
be pointed out that all our proton data are well represented
by the fitted curve, with x*/DF = 0.7, (see Fig. 7). Except
for p+ p at 24 GeV and p + z” at 400 GeV, the data in Fig.
6 for x > 0.2 suggest that a is a function of x alone. In
other words, they suggest that, for a given x, the ratios of
the production of various types of particles are independent
of the target and of the incident energy.
If one takes this suggestion seriously and couples it
to the observation that the functional form of dc/dx differs
dramatically for various outgoing particle&, one seems to
arrive at a very strong set of constraints on the possible
mechanisms of particle production. For example, such
behaviour does not follow naturally from models such as the
additive quark model 16
, which assumes that the leading
particle spectrum is a reflection of the momentum spectrum
of those valence quarks which are not absorbed in the
target, nor does it follow from dual-parton models. l7 This
Page 9
is most readily seen in the the similarity of the
A-dependence of channels such as p-+ p, p+ ho, +
orp-tx,
where the projectile and outgoing particle have one or more
valence quarks in common, to the A-dependence of channels
such as p-+r’, p+ Ki, or p-+ Y, where there are no common
valence quarks.
The data are also inconsistent with any mechanism whose
essence is that the hadronic matter from the incident
particle is slowed down as it passes through the target, and
then decays into different particles in ratios independent
of the final momentum of this hadronic matter. If this were
the case, the ratios of particles at a given x on nuclear
targets would be the same as the ratios from a proton target
at a higher value of x, and not at the same x as is
observed.
Finally, it is difficult to see how any multiple
collision model could account for the observed trends, in
particular the constancy as a function of A of the ratios of
the various produced particles at the highest values of x,
i.e., greater than, say, 0.5. One possible mechanism which
could explain such a constancy is that, at high x, particles
are produced in collisions where only one target nucleon is
involved. However, if this were so, a should be independent
of x and should approach a value of about 0.31 for incident
protons. This corresponds to the A-dependence of the
probability of a collision with a single nucleon in the
nucleus.
Page 10
A similar comprehensive study of x+- and K+-induced
reactions is not possible because, as is apparent from Fig.
8, for most channels our statistical accuracy is inadequate,
and no other comparable data exist. The only general
conclusion that can be drawn from these data is that for x+-
and K+-induced reactions, a tends to be higher than for
proton-induced reactions. This may simply be a reflection
of differences in the II, K, and p inelastic cross sections
on nucleons.
Among the r and K data the only channels with
sufficient data to allow us to investigate the x-dependences
are x+ + pi+ and TI+ + TI-. These results are replotted in
Fig. 9, together with the polynomial fit to the proton data
(solid line) and the same fit displaced by 0.045, the
difference in the A-dependence of the inelastic cross
section of pions and protons (broken line). These data
suggest that the x-dependence of a for r-induced reactions
follows a universal curve similar to that observed in the
proton data, but that superimposed on it for these
particular channels there is an enhancement in a around an
x-value of 0.7. This enhancement probably reflects some
coherent nuclear phenomenon. l8 At very low momentum
transfers similar enhancements have been seen by Whalley et -
al lo’ -- in the p + n channel.
Page 11
In the past many experiments using emulsion targets
have claimed that as x increases a first decreases and then
increases towards a value equal to that of the inelastic
cross section. This trend has been interpreted by somel
as an indication of a multiperipheral type of interaction.
We see no evidence for such a trend.
Consistent with earlier experiments over the limited
range in transverse momenta covered by our data, we find no
significant variation of the A-dependence as a function of
pt * In Fig. 10, for example, the difference of c at a Pt
of 0.3 and 0.5 GeV is plotted as a function of x for
+ + 71 +?I ( lr+. -+ 71- + ,p+x ,andp+ p. This behaviour also
excludes the interpretation of particle production in nuclei
in terms of sequential collisions.
To summarize , we observe from our data and from a
comparison of our data with earlier experiments, that the
A-dependence of the inclusive cross sections in the
projectile fragmentation region exhibits a remarkable
simplicity. For most channels the A-dependence is a
universal , weakly-decreasing function of x independent of
the outgoing particle, its transverse momentum, and the
incident energy. The difference of the A-dependences for
various incident particles probably arises from the
different inelastic cross sections on nucleons. We know of
no model which in a natural way predicts such a simple
behaviour . However, it should be pointed out that most
current models have sufficient flexibility to encompass the
Page 12
data. Our results do not rule out a weak dependence of
a on the produced particle, and it is possible that a is
not very sensitive to the mechanism of production. In the
TI+ -+ 71+ channels, there is evidence in our data for the
presence of some coherent phenomena.
ACKNOWLEDGEMENTS
We would like to express our thanks to the many people
at the Fermi National Accelerator Laboratory who have
contributed to the successful operation of this experiment,
and to D. Dubin for assistance in data handling. Two of us
(J.N. and T.S) wish to thank Prof. I.P. Zielinski for
constant encouragement. This work was supported in part by
the U.S. Department of Energy, the National Science
Foundation Special Foreign Currency Program, and the
Istituto Nazionale di Fisica Nucleare, Italy.
I I’
.
Page 13
REFERENCES
(a) Permanent address: Brookhaven National Laboratory,
Upton, Long Island New York 11973.
(b) Permanent address: High Energy Physics Laboratory,
Harvard University, Cambridge, Massachussetts 02138.
(c) Permanent address: Department of Physics,
University of Illinois at Chicago Circle, Chicago,
Illinois 60680.
(d) Present address: GTE, 77 A Street, Bldg. 5,
Needham, Massachusetts 02194.
(e) Permanent address: Brookhaven National Laboratory,
Upton, L 0 ng Island, New York 11973.
1.
2.
3.
4.
5.
6.
7.
A.E. Brenner et al 7160. (Cl%) from
- --, Fermilab-Pub-81/82-EXP 118, to be published in Phys. Rev. D. A slight change in absolute hp + h*X cross sections this reference is due to a corrected treatment
of the multiple interactions in the hydrogen target.
J. Benecke et al., Phys. Rev. 188, 2159 .(196g). -
See, for example, J. Elias et al., Phys. Rev. D22 13 (1980):
--I
See, for example, the reviews by N.N. Nikolaev, sov . J. Part. and Nucl. 12, (1) (1981); W. Busza, Proc . Hakone Seminar on high Energy Nuclear Inter- actions and Properties of Dense Nuclear Matter" Vol.11, p.20, K. Nakai and A.J. Goldhaber, eds., July, 1980.
See, for example, A. Krzywicki et al., Phys. Lett. &, 407 (1979); C. Bertsch et al., Phys. Rev. Lett. 47, 297 (1981).
A.S. Goldhaber, Nature 275, 114 (1978); W. Busza and A.S. Goldhaber, to be published.
T. Eichten et al., Nucl. Phys. 844, 333 (1978). -
---,-~.--~, . .,~ --r__,rr,__. ...~, ^ ~_1- _.,_--.,-..-,..-_,,,,. ..--~- ,---...-,--.-,.
Page 14
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
P. Skubic et al., Fhys. Rev. s, 3115 (1978).
L. Pondrom, private communication.
M.R. Whalley et al, University of Mich UM HE 79-14 (-7p.
igan Report
P.H. Garbincius et al., AIP Conf. Proc (1981); A.E. Brenner et al., -- Fermilab-Conf-80/47-EXP 7160.451; D.S. . --
.g, 74
Barton, Proceedings of the 11th International SympOSiUm On
Multiparticle Dynamics, E. DeWolf and F. Verbeure, Eds., p. 211, Bruges, Belgium, June (1980) and BNL Report 28166; C. Halliwell, Acta Phys. Polon.812, 141 (1981).
For all the targets x is defined as P, (cm)/P,,(max in cm) with the mass of the target tallen to be the nucleon mass.
A.S. Carroll et al., Phys. Lett. EOB, 319 (1979). -
See, for example, the compilation by G. Giacomelli, Phys. Reports 2, 123 (1976).
See, for example, the compilation by F.E. Taylor et al., Phys. Rev. G, 1217 (1976).
-
See, for example, V.V. Anisovich et al Nucl. Phys. B133, 477 (1978); N.N. NikoGeii-a;d S. Pokorsr R. Takagi,
Phys. Lett. 808, 290 (1979); A. Dar and Phys. Rev. Lett. 2, 768 (1980); A.
Bialas and W. Czyz, Nucl. Phys. 8194, 21 (1982).
A. Capella and J. Tran Thanh Van, Particles and Fields to, 249 (1981).
It should be noted that in the b+p + x-X data the invariant cross section shows an enhancement in the same x region. For a possible interpretation of this phenomenon see the discussion in D. Cutts et al., Phys. Rev. Lett. 5, 141 (1978).
-
See for example, N.N. Nikolaev, L.D. Landau ITP Preprint CHERNOGOLOVKA (1976).
Page 15
Table 1. Targets used in this experiment. Most data
were taken with the thicker targets. The
thin targets were used primarily for finite
thickness corrections.
Target A Thickness (g-cm -2)
C 12.0 1.37
3.93
5.79
Al 27.0 5.99
CU 63.5 2.89
5.94
9.94
Ag 107.9 6.71
Pb 207.2 2.06
4.00
7.38
Page 16
Table 2. The measured inclusive invariant differential
cross sections and the results of the fit of
the data to Equation (1). The errors shown
for the measurements are primarily statistical,
but contain a small contribution from particle
misidentification. In addition, there is an
overall normalisation uncertainty estimated to
be 10%.
. . . . . . . . . ..a......... . ...*. . ::Zl . ..O . . . e-0
.
ZF; z; a- .-es n.D .FC ?iz
03 OO.NO u-lo id ,’ 2
. . , . . . . mr(.Oa 00
; :
:NcJ mm :
::2 rf: “i N3’-w -Gz om .mm
.u-l .m-l uio :zd :A 2:
cr..... .I
: NN:Oo O0
. . .
.
:U :: :z ; . :“: *m
.
: :: .
. . . 24 2. 2 “Z mm :na .r( ,-In :z de,DY) \Do ;:d z.: :: al.... Mm.*0 2.:
:
2%. z: .C c,: zx
. on .UIm .a .nm :$
mC*CN 00 4.e.. -” :O-
:c: . .
mm :mN 110 *co ic:
hrn.Cr.2 Loo I.?.... et.7 .*e :2
: .
InuT :cvbl .N v0D.n rJ:
N..nm 00 CCI * . . M-4 ..a00 2 2
.
WI, WI :;p, ;I” :c; 2;
. . nuJ :cw ,111 *NW ;z N(O.\Drn Vla c . , . . rla.c0 42 .
: -0 LON mm .NN 1; $C ,a o-C
g2 C.n.PC no
Fir: z: ***” -t\D .IDO ,’ 2 .
: . * : : . : : : . . . : . : : . : : . : . . . : . . : . . . : : : . . : . . . . . . : . . : : : . . . . : . . : : : . . : : . : . : : : : : : . . . : . . . : : : . .
.
. an .*a .m e-c 22
u-lo.o* 100 10 . * . . Nm*mD 2.:
.
:
f: 3: 7:: ig: “,2 z: m.n O...C rD0
z: YI-‘d’ rnd ,#O 2,: :
,,,..,.,,....,......... .
; x
+” +” +” +- +” l .c F % F c e :
+ + + + + t:
n. +” f I Y
: 2 +E .
.c L c 0 L * : 8 * . .
. . . ..1.....*.......1*..
;
i:z ;z r;: u.. :c.lL. mc .ew ,“L
: “. ? .i : .x3 r*n a0
.a . . * . *s-lo : d et-4 mLo*c)c) Gd
: :
1..:..1......11.11...:..... . . .
;
* ,a.,..
. .bl.l ::2 ig : 2 d :d :
; 0. ,100 mu% .a”7 .#I .a*
0.... c)FI .“30
.
.
.
. Nrl .(Dc) l * IlPd
.m .0.-l -..I. *N .4O
; . .
“(“I ,IC 7: OC .” “; 5.2 :: z.:
. . : .
. :
ma0 *.2* 40 *P-a* .C ,DDN
c . I * * cn ..4C)
: . : iz: :39 g;
.NO 22 . *m :mo .* .m.l
.n\D .\00 01,*. d\D .no ; . i
: : . *mm ::2
L-if, **
:A: $2 :
Pa :nr .n *aa
ro 1.4. -a.. . N” .LnCI
: . ,,.*.,,,.,.....,.....;..... . . ; ;
:k?:: 22 *NO d4
“Z C’..rn e& CaiD *ma .d .!9e4 aLI
::,’ N . * 9 .
,-ID 2: .a. .NP dd
: . : ; i
::: z2 2: -c*n- ::: .\D .*a :T? 2 ‘“. 4: om .NI Loa 0 . , . . #NO -0 .N 40 .no d d . : : . ,.,,.,,,,,,.,,...1,,1 I.... I . . ix
. x I * :
;I .E 1; 1: Be IE Is : . ;t +.t + + t: :m Y ;: 2 2 E :2 :+ +e +& +& +e +e .e :+ ?j .
; . ; . !.a.*.
i: 2 : : g z * a- . : E . iz :.....
I. 4:. ;.. i: @ @ 2-j :) ) ‘3 ‘a ~) 3 IJ 3 ‘) ,
tz;P, )NO 1 . 1 too
. . .
,‘2 m- dd
I..,.,
Ia.0 8-a 1’;:
i; . .
800 00
a* :::
LZ Cd
2; 2:
;i 2: co
24 d d
. . . . .
ri$ ;a
2.2 d d
2: E’; UIO
22 dd
:z k?z Cd Ino . . oa dd
.
.
:
:
:
:
: .
: . .
:
:
: . . . .
:
: .
:
:
:
:
: .
:
: 1
:
:
: .
.
. . , . . . .C)C
::: . . . .a0
. . . z: 4D . . 00
. l . . . .
zs c-4 . .
ao
I . . .
;: : ;Y : 10.
.
. . . . . mu1 z2 ,=E . . 00 dd
. . : : . :,” ig . :“: 10
.
: . .
:
: . . . .
.
.
.
:
:
: .
: 0
: .
:
:
: .
:
: *
: . . . ,
:
:
:
: . .
:
: .
:
: .
;
i,, :Z,:: . . . .00 . . . . .YIC .m.n . ..lm I * * .a0 . .
I .: ., : :,.I, .-IO .a0 . . . .00 : :
: IW . i;: : . . ‘%-I.
: * I$ im SC) t, ‘.. It? .,
: ‘.: . . .
:: . I . ., * . . I2 i: YI .L d :, . . .
i ;i $2
**1.,.
zik $5 d d fd
“; ::
..I,.,
i; :; 4s Gd
D : n . . . .I..,, . .
I..
ci dd
;z 2,:
;; dd
. . . .I.,.
. : . : . . . . . .
: : . . l . .
: l ::
.
.
:,” .Z
:: . 2 .m * . .O
l
i-,E .CIO . 0 . .C10 . . . . .mo ::.Z : ,’ d : .
:z z: 2.0 m+ :z 0’ 2 :
. . .
.
. .
.
: :
--Y) ,““, iz$ fd VT2
!zg $2 mu
2.: : I:
n :. K :: d :<
; i
.I L” Y - .” c c *, -q :.
2: LC ET 22 2:: :’ . .
00 12 4; ,.td YI’: ::
.” ‘, “I 9) zig z:: id 4:
“Irl f-4.” WC z,” 2: :z id ” -’ mL( rlN
:
:: .a-, Liz :
22 dd : : :
;; nm I ,“g :
:d d,‘:
: . l ****:.’
: :
; ; . . :
. . . . . . . . .
2: zs :z ,” -40 l.lP.7 . . . oe .!ld A: i-i : . * :
: .
*PI a,I ::: 2z :d dd
. .
; n :e ;o :: . *
r( tc .
:
s i: m . .
. l , N .e
.
:
$ i: 3 .VI
: :d
:
. : , . i
;: :7
Fiz SD 22
:: L: .d .a- :2 22
: . .’ . . .’ .
: .
: .
.
:
.
.
:
;z 2: m’.4 2:
,.....I
c: :;: iz z”: NC
m..,,.
..I...........,.,
; ; +; +z < $
+ + + + t +
P ,” : : ; d 2 2 g
F c c c L L
1.1..1*.*1.......
I’ . f.
:
9 i
-0 - 0 ;
: . . ..l..,
. . . .
= i; II .r( : :d
: .
. D
::: 0
i;
:” ; Is c *c z :i
: .
. t . .
;: 2: :: 7-z >e 00
* . l I *
. .
.O . ::
.
; ; .
m.,.,. .L .P ,” : 2 . m 2 * b
z .
z ,,I z
.
.11*,1
..*..*.*......*. ; . . x x
* L 1; 1: ,: IX
Y
+ t + + t +
; c c; +c; +e ~ i-” + 2 2 ;
. :’ . : .I *, .
: . .
. .
.
.
; . .
i:
: t .
.: 4
; : : . . . . . . . ..I......
f f
52 Z% . . . . >o 00
5: zz DO LBir( :d d2
5; ;i :,: 2,:
. . * * ,
: 9 :. 2 :: . 1 D a< . .
: : :: N .< r: :< . . I :
: . ii 2:
: :
: :: 10 .c 2 :< . . . . 5 Ii : :< . .
: “1 . . ; :: . l
m .< . . .
2 i: 3 .c
rz :.
:
:
; i:
4 :c . . * .
; :: 10 . .
r: :.
: .
. . .
:
E :: c .<
4 :. .
: .
z :: 3 .I
I: :.
:
ml.7 :mcc Ln. *ml- In\0 .rDr( . I 1 . . 00 100 .
:Lz i . :
-0. . . . :
00. . . . i . : ;
I:: ,“I? :cG %Z :Fz .00 me r(L-4 ON LnyI :dd 22 d: 12 ::d . .
-41 :-I, InI. tow sz i iEL2 c.4 .eo *r(. e-0 , . , . , . . . . . . NO.OO DO. *c)o . . . ; : ;
;; *I ZI
. . . Oa *I
;; Fii 2,’ 42
FE z:: *r( :,: di
a ,” ““1 2:: z: ::, d;
;z ;; :d. d2
i; -- $2 :,: 22
:F4 22 *rl co :.: 2,:
..,..
2: Lou-l 2’:: . . . . DO 00
!r$ ::
:z . . 20 00
ia, .-d z: ..+O (0” :d.G dc: : : .L1sw YW :2: z: :dd ” 40
; r-z .Dwl NPl .OUI ulyl *we . . , . .
.I e-0 . :
wu :w. N. ,.-lo, l c .I.70
. . I 0 1 r-3 ,oo
zz i ; :2:: VI0 * e-0 . . . 00. :dd . . . . . .
“C : :,“, VII-. UC) * :2:: * . * . . .
OP. .C)O : :
: .
2:: : i:: InS). :“.y .Gd : .DO
: : : :
ec. z,“: ifi:
2:: ::2
VY, CI s: :i 2: .:, . . .
i:: zs a00 ON . . . .00 8.42
.
.
. mm :rfw! oN l “Iv
.a. .a* a...* -4.00
$1 c, .
ci
: . :cz~ 003 ..D z: :d; 22
: en ..aP Nrn .Lnrl ..a .(0d
I-.**. NN .00 .
: iz2 z; ,.nD mc :d.G 2.4 .
.
: . . :
: ..I .
**....,....
slg 2; 01 ;: :c
;; Z! C, l-id . rn’
. . .
z i igg
.a0 :dd :
:
i Lz :?S .00 :
,........,*....~.....: . .
f r f’ c I;, ; ” ;i a ‘L t -3 1 ‘I ‘3 ‘1 -2
,.,..,,...,.,.,,........,....,,.,,,..,..,,,.,,..,~......... . . . i:: :“, : 0 :?9 -- . .
E$ 5; m . . . .
: .a0 00 0.. 4n t
;. :; .
;
:,” i$
0 . in :“: .O :
::
: . ‘*+ s:: ::I; rn . . . .C)O kcl .
2; g
i : d d
fE u-lr- :“N
Gc: dd
2: l-c
.n* L%: : N’ dd
. I . , I
: : . . : : . : : : : . . . : : : : : : : . : . . . : . : . : : : : . : : : : : : . : : : . . : : . . l .
:
:
:
: .
:
:
: .
:
:
:
: .
:
:
: .
: .
:
:
.
:
i:: 2: .-- ml-d 5; i; I.. . . . . :“” On Zd N-4 : . ‘Oc3 :22 2: -rN ?$ 2% . . . * . .00 2: 2.: ::: .
z: Kg: h-4 iON. . . . . . 00 00. *
. : :zlc 2: .G+yl rn . , . .NO 2:: . .
22 .C 2,:
sz . . zz
I
. . L.-a0 Z$i z”, m-G*
‘i., 5;
:,: 22: . . .
2:: . . 2:
: :22 ;;E :,” :s .mul .C . 1 . . .
5’: .00 CN 2 d :: :
5; m.4. 2z i 2.2 dd:
. .
..,*,.,11,..,..,.....,., . . ..1........1,1*...I .
. . . . . . :
$2 2:: d” ZN. 2,: 24: .
: * Lz$ :z: em. ;d :d: .
; . : : : : . : : . : . : . . . : : . . . . : : : . . . : . : . l . . . . .
:
:
.
.
.
.
.
.
: . . . . . .
: . . .
: . . .
: l . . . .
:
: . .
: . l
: .
:
: . . . . . . . . .
:
: . . .
: . . .
: t
:
.
.
.
.
. : . : . .
::” .e
:: . :? *n . . .
.
. : : : . . . . . . . . . . : .
. : . : : . : i;z .Nd : d 2 :
g; 22
zs& 22
2: 2:
:& .” :rl
.z:: 2: -N
“; 2.4
x: :z
zi dd
i%: V)N dd
IBe 2: ctd
IF 22 22
g: (Do 2 d
f{ dd
,“2 ca d d
CF LnN 2: 2s ;: 22 Zd .-z: : .
: . i$Z .-lo :2,: : . . .
iz: ..a- :2,: . .
Is: ;1: zz NO *NO Ina C” :z :;,: -* NO A-: 0Tt-z . .
:: (0M. :: i
dd 22: :
. i . :,“, .u?c- .0* * . . .‘O .
:“,- “,I# .P :;;: s2 :rG 2: . . . (00 22 :: i z .
ev. ,,:
2:: 22 ’ . dd. 2::
.
.
“8.. -F, .nN mm cc! “: 2: NIO c+
. . i . u.c 2:; zz .r(, z: “’ 00. . .
.
.N(D
..aN
.*tn ::2
. :z: :: :Fit 22 .a- m-l .V) *cd :::d D: G 2 ; z: .
“; 2:: .1 :; GvT
; . i : ::2 .-Iv . . t *-lo . :
; i :k?: *mtn :4: . : . ::2 .-IO . , . .na : .
?ii *a* 2: i
Gel 22 : :
“; ::
224 c’ : *a
i”, ::: :A: . .
!zz 5% ff :: z 34
. . . . . . . ,.,...,..,.....I.....
. . : : :2 :
mm
: : 2
:
: ii: *to. z:: : ;d 2,: :
;u g ; :: . :: : :CC : . :‘: : .O :: : .
. :I?;: 22 ,zz :: ::“: 2 “. 2 .i ,NO NI h.4 si . .
EZ ,“: i u33.l. IA; 22:
: .*...: . .
: . *
: : .
. . . . . . . . . . ..I...........
. . .
::: . :
: .* *e
g: +: +: +E
x +: +t
. n. ;:+ + + + t +
::p +” :: +?
2 rf ,“?A a G x L s + 4. L
.
.:......*.......... *.*.. : :r ‘: c 1: 1% IX := L c . ,+ + + t t + . :L +u i 2 z z :+x r t + +r +ic x
.
2 . :
ho 8 : . . . . . . :....,i......*,,..,,.,,, ;
. . . . . . . ..I........~..
I I f (’ f’ <’ <~ El -J ‘) 7
,zz $L k2; ZF; . . 2”; :,: c: d 00 dd Prl
. :
cr( 5;:
2;: 2% 2’;: cc
:24 0 .
.I . . -0 \LIN CI- :“N
. * 0 . . . . . . . .
;; mm EL
. . . . NO 00
,I *a “;: :“o
2”: z: Nrn
Car ,>“l
-- “.Y ::
. . $5
2; z2 rnq
“3 ,l
sl: {i
A.: dd
“I c CY 2: cf; 2; :;
. . : . i2z “i srl . 0 .Osn : In :A; : ? 2: NO .
$5 :: 30 :: OI “5
:2 . . IIN 9’ .: 2,:
: . ::iZ .Nsx . . . .NO
: *cI CN -01 .N .m .OD
z3.G L.i Iii -4 rlN
nc On :?i :I% $2 z.2 . . AC: rid :pr NN :::
. . . . . . . . , . . . . : : i, :: z : ::: . . . :r; : . . . :- : : .
: . I.,.. 1.e. . :: ,” : .
z ,%I 0 . . CL c :+ :: :,l d .I eL .x .
. . . . . . . . ...*. .,...,.....*..
ez ea.4 ;: E” :c: s: 2%
. .
+:
. . . * I . r + 2 ‘Y
I
+:
:* x
:: .’ . .I : : .I :N . 9, . : : . ., : . . l
: . . .
:
: .
:
:
: . . . .
:
:
: . .
: . .
: .
:
: .
: . .
:
:
: .
: I
:
: . .
:
: .
:
:
: .
:
: . .
:
:
:
: . *
.
. .
: . .
:
:
:
i
,.1... * +x z + + ;s ,E Y ‘x
.,,.,...1*..*.
+ 3 ‘k
.
:
: . . .
:
:
:
.
.
.
T)* : ;; 0-a
cc) l
:A 22:
:
Z? *I?. sz :
:: ‘.’ 00. .
:
,3 a*. 22 i
:,: 22:
:
.,...: . . .
: . . . . . .
2: $2 i
;: :‘;: 34 001
:
. . . . . . . . . . . . .
-2 b0 B
. , . . .
1: 1: Y Y L I” : IX
+ + t t +
. ,..,.,.,11..,..,........
‘ , ,, i .,, .~ ~.
. : : : : : : . : . . . . . . . : : : . . . : . . . : . . . . : : . . : . . . . . . : . . . . . . . . : . : . : : . . . : : : : : . : . * : : . . . : . : :
: :
: . . . : . : . :
;
: .
:,
: .
.
:
: t . . .
:
:
: .
:
: .
.
.
:
: . .
: . .
.
.
.
:
.
.
.
. .
:
.
:
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
: .
.
: . . . .
. . .
:
:
.
: .
. .
: .
: .
:
: *
.
.
:
:
.
.
:
I .
: .
l .
. * .
* I .
a
.
.
.cJ :: :ki 0
“7 :‘: .o . :
::
. *..1*.
. : z . .
. .
:
;
: . . . 0 . * . .
:
)I )/ % 1 , \ \ ,
:: :*., :2 0 :;2 l m .**
:“: .dN .
.O .
. .
:
:
: .
: * .
~ : .
.
.
:
: . . . . .
; . :2: g” :s z :abl . .
.:: JZ 2: . . ; ;
. . . . . . ..I............
.
. , . I . . : . : * : . : : . : . :
ii
: : . : . . . :
:: 3 i
. . 4
* 1 *
.
.
.
. : : : . . : . . . . : . . . . . . . . : . . : . : . . . . . . . * I : : : : : : :
: . . : : :; * 8 :.
: . . .* :: :. . . . :C :: . . . : . . .
. . . ..I . . . . . . . *
x& i; z; oc . . . . . 4
00 ..d OIC ; . :
: : : : . . : : . . . . . : : : . . . . :, ;, ., :a . : . :I * :t : . :, .I .t :, : . . :I . . . .I : : . . . : : : . : : : : : . :
l
: s . . .
:
:
: z
.
2
:: .d
:: 0
:n \D
. .
.O
.
.
. . :: . . .
: . . . . z . .
: ; . *
. :“cz yIy) ..C TZ ;z . . . .y10 ?I: ;r: .
; . : . . . . . . . : . . : : . . .
: : . . . . : :
zz :: 3. 2.: d. : . .
: : ; I
. . . , : ; : : :
: * . : ; : : : . i
: I : I : , *
: :
I : I . ~ : 0
: : . . . . : . . t . : : : : : : : : . :. : : : . : . . : i.
; . ..aOm .om .Lnrd ;$ ;i . . . .a0 r.?d 2;
; . ::LZ N”: :?I .a* au7 %nII) . . . .OD 4: 22 . . .
NN :nia CN *mm 2: oc .-I*) cm . . . . . . .
O”.DO 00 : .
vtc :,- cd-
g: : 2,: :
.
. : . . . : l
:
: .
:
5: : .lY
;I2 .4 !?I :
2: . . x”,
Y.mJ 0). :zi “,z : 0’ d :
.
. 9
.
.
: . . .
:
: *
:
: .
: . . .
: .
: . . . . . . .
: . . . . l *
:
: .
: . .
:
3
DO r:
..1.,1
-3 .)
; . n* :z z; id d 2
:i rsfi 2:
:d dd
: . . . . . . . . . . . . . . . . . . . ..I t . .
. I
* .
. . . . . . . . . . . . . .
: ii
:. : : :;
i;:
: : : .L . 110. : .+ . &‘ 1%
: a
. :: z i; . :: :d D ip
..,1., :: ? : : $ z . er : ii if . . 2 ::
i; z:: Et: or( :d
oa 2,: 2:
. . ..*1.....,., . ..** 1***...***.,.
= * x x x 1 - n. P &
vz x x x
In UP P Ia ; . . . i: : t
: ,
b + t + +
> +$ ,= : +g d Y I r x
+ + .t +
+$ += +$ +: Y I Y Y ri
* I . .
1..1...1....,,,,.,,,,
1’ ; 1’. 4’~ E., : :‘
l...O......,..
. ;,a ,I P ,3 )
. . . . ,.,......,......,.,,,..,.,,. ,.........* . . . . . ..a........ . .
; D . z
::” *3 l?i SO z :“: .D . . . .
z . . . ..,.,.
. b .
i : I .
2: 2; ;; iz! d ,’ d 2 . . . * 00 rlc
;; z; 00 7: z: dd ,’ : 2,: 2: S-4.
S? z: 2: 7: .m .,-I Gd 2.: z: zz;
..,*.,,,.*.,**..t
g$ E; . . ., 00 cl0
55 2: 00 :: dd
b! Fii A.2 dd
*....
; ; . 0 :
I :’ I :’ . : .
L :I I :: ! :t . . D : :
b :< I :: I :c : .
I il I :’ 10’ . . : I :r , .,
I :< : . I :a / . . II
/ :. . . : . .
~ :; ! :, . * . :, ::
~ :I . : :e :: :t : : : : : : : . : . : : : : . . . . : i : i
.
.
:
: .
:
:
:
: .
:
: *
: .
:
:
: .
: 0
:
:
:
: .
:
:
: .
:
: .
:
: .
:
: .
:
:
:
:
: . .
:
:
:
: .
:
:
:
: , .
:
:
: .
: .
: .
: .
: . . 4
: .
:
: .
:
: . . . . I
. :22 2: $2 .00 00 ..o z: . . . . . . . .PO 00 d ,’ PD .
ii CO, 2: :
. . ..* 00 00,
: :
.
.
. : . : :
.
.
.
.
.
.
.
.
.
.
: . . :: .P
::
:1 .C)
.
.
.
. * . . . . . . . . . . . . . . . . :
.
. . : : : : : : : . : . . : . . . . ; .*..*,
: Nm 2: 5: mr nc:: m* 22 d,: 0’ : 2: dd :
$5 E: d
2:: LDI 22
5% d ,’
c L” z”, d d
:;: Loo d,:
gFj d :
z; d,:
. ig g;i dd p’d: .
;
2: Kg CN mm 2.2 0’;
; z-i:: :2: 00 yI.7, 42 dz: . .
w I Y .a “I !A, “l - ;b2 ES z;: 72 d.4 u: d 4.: z:
:: :z UY Y, “1 IIT.+ m. zz zg 2: :,d 1; :d ” *XT LG:
-4 :z rn,$ 23 :d 2,:
Nrl 5; (110 z: 2: 2l:d ;2 d:
:
;
22 z,” :s .ul .U) .N z.: 24 :;
!G:: co
. . : 2 E”, 2:
.
i : 2: L?: ss . NN h-la : 22 d d ,’ ,: . ;
. . . . * . *
+- I=
t
?i
b
. . . ..I
i :::F; zz 2: :z ::7 7”. .O .r(F) co 24 2: NY) : . ‘.,...,1............. . i
:t + . . .a u :.a 0
+2
00 n
1 . I * .
:
: . . . . .
:
.
:
: . . . .
:
: . .
:
:
:
: .
: 0
: : : . :; ., :< : . :, :I :< . . . :
: . . . : : . :
: - ,” : ,x ,x ,* :‘L c c t E *
:r + + + t + I :o ” 2 2 2 E . .* e n ” ” ”
: ,.l,.............,,,.
I * 6 I,’ i, i :: ‘C . .
zz 2% 00 ?4aD.l* \cr *a ..a= era L(P 2: .* .00 ::: . . . . . . . I . * .
00 00 00 ma e-0 d:
22 z; .rl NC Z$ i; dd c: d l .
C” Fib4
. . . . . . . . . . . . . . ..I
; . . . . . : : . . .
. . : : . . . . . l . . *
: . . l .
.
. l . . . . . . . . . . . . . .
:
: . . . . . . . . . . . . .
: .
: . . .
:
.
.
.
.
.
.
: . . .
:
: .
: . .
:
:
:
.
.
.
.:
:
:I
:r
: :
I : I : / * .
: :
~ : I :
: . l
: . . . . .
: . .
:
: . . . . .
:
:
:
:
: .
: . . .
: .
: .
:
: *
: . .
:
:
:I .’
:.
:
:
:
:
: . . .
:
:
:
: .
.
.
: . . . . .
:
: .
I : , .
{$ Q. ula .ny: z: :z Liz:
dd Ad . . n-l 2,:
g ::: rD- 2: 2.4
*.*., I I
;Fj ii 5; a: :g . . 00 di dd dd dd
%I? 2% 00 InnN dd d d
i E . . . . ::” .z.
::: D . 0 :? .O . .
: . . ,” .
- $1 0 v, . ;; “1 P> 6” V’ - r 22 SC :: c;: s: dd :2 Ad :z A,: :c:
.tn cc,
$N” $2 22 ‘. 00
: : .
j i . . . :
I : I :
9 : . * : .
1 i
~ : . : : . . . . . . . . . : : . . . : . . . . : . . l . . . . .
:
: .
: .
:
:
:
:
:
: . . .
:
:
:
:
:
:
:
:
:
: .
:
: . . . .
:
: 9
; .
:
: .
:
:
: .
:
:
: . *
: I .
: . . . . .
:
:
: . . .
: .
:
: .
: . . .
: .
:
:
2: c 6” 00 zz 22 2;
. .
: . ,” . ; .
: . . . R :
. . . . . . . . . . . . . . . . . :..... . . : ::: z ii . ::: :d . :: . . :..... :: ,”
2 z . P . E : 2 . 2 .
. . . . .
. ..*.*.. . . . . *.,*,
I L +; +; +; +; +z + + t + + + 1 u d 2 : 2 L P cl. n, 0 P
..,.*
.
.
‘3
;
.
. : : . I : : : :s *, . ., : .
. l .
:
: .
: . .
:
:1
:’
:’
: l I
.
.
.
.>
:\ . . .
:< . .L
I :
. . . . . . . . . . . . . . . . . . . . . . . . . . :
; sz ;z si: Pm .t7.0 oa *cm kc2
:2 2 d :: N-‘a0 ‘f: , . . . . 40 .N.OO -0
‘P 3 3 ‘, 3 I 1 3
.a..*.. . . ..I...........,.........,,........................ . . . . . . :2: 5: :2 . z :?‘: .m .u7 :* ; i: -0. s,: i : gi :: 2: : 00 0”. . ..P zz z< i?i,’ . . . . . : I. . . . I FD 00. : 00 Oa 00 ‘- . . ; ;
.” .
:: :0. :L: :22 FG;: Z$ -0 . z :A: N,d G”: 2:‘: IGs d . , b7 my1 “b . . .D . : .
::z : z tc.3 “{ 2:: :: . :;A ff 2.2 . z.: “4 .
i .
z;: i .
E;: . “,? 73: : rnti -a. : . . : .
: l (Dd 5: 55; : ;; zs
. Ezl 00
G d dd: l dd . .
-0 d:, . : . .
: . : . . : . . . : . . . . . .
; . -,
; . .
; . . :.m . . . 2 ii” . Ir(O . . . .
. . . . . . . : : . .
. .
. :z i
: “S l o .
:
:
;; ii
22 dd : . ,: d d. 2
: . .
: i . “E LOO. 22 : : . 2: 22 : . .
: : . .
; . .
i . . .z . . . . . . . . : :: . :u :: ::: : :: .O . . . . :: . . . . : . : : . . . . . . :: . .
i :2,” 22
::: “; 55 orlo 2.: SC:
5:
.
. :CVL? v?F : “. E: “; ,“z
‘O 42
10. n. *r10 :.!I 2: .dn
.
_“l .,I- U.”
::: “(z l VI
=;G 2l.4 kc:
VI. cc 22 22 2: I?;
“.r: -O- 2’. 2:: “.a zr:
“ii? 72 5; 2:
<Y “I P Y ir
.C ;: d 4(D rd.4
big N.
;% 4: z,:
ulvl c’ Y $5
Da ?;t: .Q kt; ;i
.
.
.
:
:
:
:
: .
: . .
:
:
: .
: . I
: . . . . . . .
:
: . . . . . . . .
:
:
: .
:
: .
: .
:
:
:
: .
:
: . .
:
:
:
:
:
: .
:
:
: .
: .
: .
:
:
: . l .
:
: .
: . .
:
:
: .
,“z i .
“ii -0, : 00 -z: :z . 00 2: 22 : : Zd d 2 .
: : VIY ,u: : . F, w vlrl z2: A: : 2; 2: . . . . Ft.4 DD. . 2,’ dd
: . .
lx;; or( . I
oe
g; d,:
Es 2,:
L” ” “,c dd
2: Ns. 2.:
2; 2.:
(Do ,‘!s ci;
“C W”’ :z gs :d 2;
al-d am: : ::: ST2 : : 2: 22 d2: . . 22
z4s NVI .” .* :2 ;j
: . : : .
zr =?a: :Ti: zz *\o ino. .Oe ..I* 22 22 : : d 2 2 2
0 .
22 .N dd
:
* . : : . . : : : : : . . . :. .c .c .E : . . :: .c . IL .
:a :: :c : . . :: I. . IC : : : . : . . . . :c :: :. . . : . . .
.
: .
:;: :‘:
zl; z.0 2.2
; .
:;t \DN E2 :? 10 2.2
;
: . . . . :
. . . * .
; .
: .,,..,.*,.....,..,.. : . *
:: 2 :z .O . :: :d . :: . :
.
; . .
: ; .
i * , . .!s .x . 5 . w . Lz . b . : ;
.
: . , 1
. . . . . . . . ..~..I...... . . ax x x x x x
z:a a. a. L D D e:t + + + + t
!?ic. u 2 2 : f ;;:P a 0. P a L
..*...*.....*.,....,
; : : c”$ : : 00 ;z :z mc : : 2.4 dc: 2.:
: : .
; : :2
:9 pJ
a0 dd
l . . ..i...i..,,,..,......... . . : . . : .X x x x x x . :a (0 I= ID ,P IP . :t * + + t
9 ; i&UL::E 8 LI : :L m a n. a a
. : .,....,,,,..11.,.,1.*.,.*,.
1 * ,‘, j’ , \ “. w, 1s L ,\ \ ., . a . . .
Page 26
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
FIGURE Captions
The invariant differential cross section for pA+ pX plotted as a function of x for an incident momentum of 100 GeV/at transverse momentum of 0.3 GeV/c. c
The invariant differential cross section for pA+ a+X plotted as a function of x for an incident fn;m;;tum of 100 GeVLand transverse momentum of 0.3
The inv_ariant differential cross section for a+A + n X plotted as a function of x for an incident momentum of 100 Gelyand transverse momentum of 0.3 GeV/c. C
The invariant differential cross section for n+A -t K+X plotted as a function of x for an incident momentum of 100 GeV/and transverse momentum of 0.3 GeV/c. C
The invariant differential cross section for pA +pX plotted as a function of A for x = 0.3 and 0.8 at transverse momentum of 0.3 GeV/c. The straight lines are the best fits of the data to equation (1). The variation of the parameter c with x for various particles produced by protons at a transverse momentum of 0.3 GeV/c and for incident energies spanning the range 24 - 400 GeV. The curve is a polynomial fit to the data as discussed in the text.
The variation of the parameter c( with x for our proton data at a transverse momentum of 0.3 GeV/c. The curve is the polynomical fit to the world data as discussed in the text.
The variation of the parameter c with x for the rf data at a transverse momentum of 0.3 GeV/c.
The variation of the parameter CL with x for the TI+ + and r+ -L r- channels at a transverse momentum of 0.3 GeV/c. The solid line is the polynomial fit to the proton data shown in Fig. 6. The broken line is the same fit raised by 0.045. See text.
The measured difference in the parameter c at transverse momentum 0.5 GeV/c and 0.3 GeV/c for various n+- and proton- induced reactions, as a function of x.
+ ‘IT
IO3 -- I I I I I I I I I
PA - PX
Pb * * * 4 + * Q
* Q Q
x * *
4 A A
0 0 0
Ag Q Q Q
cur: * * *
Al A A A
co q O q 1 l
*
e I *
I 1 I I I I 0
I I 0.2 0.4 X 0.6 0.8 1.0
Fig. 1
102=
N z \ IO= z u T “E
bn TJO” ‘- W
0.1 zz
IO3 I I I I I I I I I -J
PA - lT+x
Pb e 4 0 cu * ,
Al 4
c Q
* + 0 *
0 A b
P a
0.01 II 0 0.2
I
+
0.4 I
0.6 X
0.8 I.0
Fig. 2
7T+A -lT-X
IO2
1 N ” ; s ‘;: I01
e
$I? W
I=
Pb *
Ag Q cux ’ AlA * , *
*
c 0 0 0 x * t, *
0 A *
A
A A 0
0 0 0
P =
.
. .
. .
0.11 I I I I I I I I I 0 0.2 0.4 0.6 0.8 I.0
X
Fig. 3
lO2L I I I I I I I I -1
E lT+A - K+ X
N IO= ” > s t:
f
b?l m -0-o
w I=
t f
4 9
t
t
t
0
t
,
t 0 t 9
9
t
t
0.11 I I I I I I I I 0 0.2 0.4 0.6 0.8 1.0
X
Fig. 4
I I”“1 I I I I r
3’ ‘........
km
\ 0.c
\ \ i6 OA - \\
YT d -
\\ ‘~‘01 u urmw
iii $ :a JY
I I I I I I
0.8
d
0.6
0.5
I I I I I I I I I
0 p-7T+ This
O P-P > Experiment
0 p-n Ref. IO
0 P--H0 Ref. 9
0.4 I I I I I I I I I I 0 0.2 0.4 0.6 0.8 I .o
X
Fig. 6
I.0
0.8
0.6
d
0.4
0 .2
0
0
0
A
A
P-P
p- lr+
p- n-
p- K+
p- K-
0 0.2 0.4 0.6 0.8 1.0 X
Fig. 7
;~~ ,~,.~~~., ~.. ..,~.,,~ .,~ ;~ ,, . ..~.~~. .~ ..>.,. ,.. ~. ., .~
1.0
0.8
0.6
d.
0.4
0.2
0 lr+ - 7r+
0 IT+- r-
A T+ - K+
A IT+-- K-
0 ?T+ - p
n 77+ - ir
1
0 0.2 0.4 0.6 0.8 1.0 X
Fig. 8
0.9
0.8
0.7
OL
0.6
\ \
\
0.4 -
0.5
I I I I I I I I I
.
0
sr+A - TT+X
-rr+A -r--x
\ \
\ \
I I I I I I I I I 0 0.2 0.4 0.6
X 0.8 1.0
Fig. 9
I ok I= ‘k - I tttt 00
a:Q,Qa d + i i= k 0 0 0 I a ~~ r-
d
ul d
x
I I I I I I I I I IO ?
7 9 -
0 6 (S.O=‘~)“-q~*o= ;dp