We have measured the total charge changing cross sections as a function of energy for projectile _(36)Kr nuclei in a wide range of targets ranging from polyethylene to lead. These cross sections are energy dependent and the dependence increases as the target mass increases

Binns, W. R.

Cummings, J. R.

Garrard, T. L.

Klarmann, J.

Nilsen, B. S.

Waddington, C. J.

Caltech Authors - Main

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Fragmentation of UH Nuclei* 
C. J. Waddingtonl, W. R. Binns2, J. R. Cummings3, 
T. L. Garrard3, J. Klarmann2 and B. S. Nilsenl. 
I.University of Minnesota, 2. Washington University, 3. Caltech. 
Abstract 
We have measured the total charge changing cross sections as a function of energy for 
projectile 36Kr nuclei in a wide range of targets ranging from polyethylene to lead. 
These cross sections are energy dependent and the dependence increases as the target 
mass increases. 
Introduction 
In order to better understand the propagation of UH cosmic ray nuclei, 
Z ~ 30, in the interstellar medium we have continued our program of 
studying the fragmentation of heavy relativistic nuclei accelerated at the 
LBL Bevalac. In a new series of runs using a combination of ion 
chambers and Cherenkov counters, see OG 10.1.15, we have extended the 
range of target masses beyond that studied earlierl,2 and have expanded 
the charge range of the projectiles to lighter nuclei. The overall coverage 
of charges of the projectiles and targets as a function of energy is shown 
in Fig.I. 
8 D D D at- + on H, C and Al. Dalso on Cu. 
~' 0 also on Li, Sn and Pb. ell a D D 
-
I. 
.a 6 
a D a D a .. 
Cj 
Q.> 
SS 0 0 0 0 0 ~ 
·~ E4 
+s ~ 0 0 
3 
a 
2 
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 
Projectile energy, GeV/n 
Fig. 1 Projectile charge as a function of energy for three different series of runs. 
Hydrogen cross sections were deduced from subtraction between C and CH2 targets. 
Results and discussion 
From our preliminary analysis of the new data we can now report 
values for the total charge changing cross sections of krypton projectiles 
with energies between 500 and 1500 MeV/n interacting in targets of CH2, 
C, Al, Cu, Sn and Pb. The charge resolution of the fragments produced in 
these interactions is excellent, see e.g.Fig. 2, and we will be able to 
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report later on the partial cross sections for the production of these 
fragments in all these different targets. Here we confine our attention to 
the total charge changing cross sections and their dependence on energy 
and target mass. 200------------------------------------------------
180 
160 
1430 Me V /n Krypton on Carbon 
140 B 
t 120 e 
-e 100 a 
i BO m 
60 l 40 20 0 
400 600 800 1000 1200 1400 1600 
Cherenkov signal 
Fig. 2 A plot of the Cherenkov signal for fragments that have commensurate ion 
chamber signals. For high energy Kr on a carbon target. For clarity the beam peak has 
been suppressed. 
In our previous study2 with projectiles having multiple energies we 
were unable to determine these total cross sections due to the triggering 
requirements imposed during the data taking. As a result our estimates of 
these total cross sections have all been based on data taken earlierl at a 
single energy (the maximum Bevalac energy for the beam) and on a 
limited range of targets (H - Al). 
These runs are shown in Fig. 1 by the symbol +. From these data we 
proposed a modified version of earlier3 overlap models to calculate 
values for beams in this range of charges. This relation, Eq. 1, had the 
form: 
O'total = 101t(l.35)2[ATargl/3+AProj1/3 - p ( ATarg + AProj )q] 2 mb 
with p and q being determined to have values of 0.209 and 0.332 
respectively. This expression differs from previous models in that the 
overlap term is dependent on both the projectile and target masses, but, 
like them, is energy independent. It may be compared with an expression 
proposed recently to fit data on lighter projectiles4 of the form 
O'tota1 = C{ATargl/3 + AProjl/3 _ [(to-t.ATarg)-(b'ATarg113AProjl/3)]}2 
which, however, blows up for large ATarg, predicting a negative overlap. 
In view of the strong energy dependence of the partial cross sections 
found previously2, and the energy dependence of the total cross sections 
observed for lighter projectiles4, it is not surprizing to find from our 
new data that total cross sections for these heavy projectiles are also 
energy dependent. The measured cross sections as a function of energy 
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are compared with those predicted from Eq. l in Fig. 3, which shows the 
cross sections for krypton of three different energies on six different 
targets. It can be seen that there is good agreement with the predictions 
for the lighter targets and the high energies, similar to those used to 
derive Eq. 1, but that the heavier targets and the lower energies have 
cross sections that are not well predicted by this equation. The deviations 
from the prediction values are shown in Fig. 4, which emphasizes how 
poorly the predictions are able to represent the very heavy targets, 
particularly at lower energies. 
5500---~~~~~~~~~~~~~~--~-
5 4500 
.... 
c 
.2 
..... 
C,J 
Qj 
fl') 
~ 3500 
0 
s... 
C,J 
ell 
c 
.Sil 
c 
~ 2500 
Qj 
ell 
s... 
~ 
.c 
u 
1500 
Lead 
Tin 
- - - - - - - - - - - - - -~ - - - - - - - - -
Copper ~ l 
-----------;:- ------1- --
- - - - - - ~~~n~~ - - ~- - - - - - ~- - -
~ Carbon 
- -0 - - - - - - - - - - Q- - - - - - ~- - -
poly 
---o ----------o- - - - - - ~- -
500----------------------------------------' 
500 1000 1500 
Energy, MeV/nucleon 
Fig. 3 Total cross sections as a function of energy. Predicted values from Eq. 1 are 
plotted at 1600 Me V /n 
The measured cross sections are shown as a function of the atomic 
number of the targets in Fig.4, Also shown are logarithmic fits that have 
a fair degree of confidence. It appears that a relation of the form 
<>total = a.exp [b(E) Ztarg.J, 
where a(Atarg,A proj) and b(E) are functions, provides a good 
representation of the cross sections 
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When the data from the silver projectiles, where we have more energies 
and one more target, Li, have been similarly analyzed, we should be able 
to propose a modified version of Eq. I that will allow us to predict these 
cross sections as a function of energy and target mass. At present Eq. 1 
must be used with caution and only in the parameter space where it is 
applicable. 
1500 5000 
~ 
·--
Lead 
s 
§ 1000 
--. ~ 4000 
"'1400 MeV/n ~",. ·-.... 
' 
(,J s ~ Tin 
' Q> 
• ' c f ... .... ' 0 ...... ~,c. 500 ' ' ·-s ' ' ~ 3000 &;o:~~'' • / ~ 0 Cl) / c:: ~ f' = / ~ • 52 - -.--=-~ .... 0 ' ---- u 2000 // .... d;' "'650MeV/n ~ 
·s: 
Q> /~ Q 
-500 1000 
500 1000 1500 2 10 100 
Energy, MeV/nucleon Atomic number of target 
Fig. 4 Deviations of predicted cross section 
from measured value, in mb. Errors are 
suppressed for clarity. 
Conclusions 
Fig. 5 Cross sections as a 
function of the atomic number 
of the target for the three energy 
groups 
The total charge changing cross sections increase with increasing 
energy, and this effect become more significant for the heavier targets. 
Previous predictions are not adequate to represent these cross sections on 
the heaviest targets such as tin and lead. 
1. Binns et al., Phys.Rev. C36, 1870 ( 1987). 
2. Cummings et al. Phys. Rev. C42, 2508 and 2530 (1990) 
3. Westfall et al., Phys. Rev. C19, 1309 (1979) 
4. Webber, W.R., J.C. Kish and D. A. Schrier. Phys. Rev. C41: 520, 533, 547, 
556 (1990). 
* Partially supported by NASA grants 
© Dublin Institute for Advanced Studies • Provided by the NASA Astrophysics Data System 


Fragmentation of UH Nuclei

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Fragmentation of UH Nuclei

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