Test of weak and strong factorization in nucleus-nucleuscollisions atseveral hundred MeV/nucleon Page: 1 of 13
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Test of weak and strong factorization in nucleus-nucleus collisions at several hundred
C. La Tessa,' * L. Sihver,'2 C. Zeitlin,3 J. Miller,3 S. Guetersloh,3
L. Heilbronn,3 D. Mancusi,1 Y. Iwata,4 and T. Murakami4
'Nuclear Engineering, Applied Physics, Chalmers University of Technology, 412 96 Gothenburg, Sweden
2Department of Mathematics, Computer Science and Physics, Roanoke College, Salem, VA, USA
3Lawrence Berkeley National Laboratory, Berkeley, CA, USA
4Division of Accelerator Physics and Engineering National Institute of Radiological Sciences, Chiba, Japan
Total and partial charge-changing cross sections have been measured for argon projectiles at 400
MeV/nucleon in carbon, aluminum, copper, tin and lead targets; cross sections for hydrogen were
also obtained, using a polyethylene target. The validity of weak and strong factorization properties
has been investigated for partial charge-changing cross sections; preliminary cross section values
obtained for carbon, neon and silicon at 290 and 400 MeV/nucleon and iron at 400 MeV/nucleon, in
carbon, aluminum, copper, tin and lead targets have been also used for testing these properties. Two
different analysis methods were applied and both indicated that these properties are valid, without
any significant difference between weak and strong factorization. The factorization parameters have
then been calculated and analyzed in order to find some systematic behavior useful for modeling
to write the fragmentation cross section as:
Heavy ions collisions at beam energies around a few
hundred MeV/nucleon, well above the nuclear binding
energy but below the energy at which resonance pro-
duction becomes important, have distinct characteristics.
Over the past three decades, fragmentation cross sections
at these energies have been measured for many projectile-
target combinations. In order to elucidate the underlying
physics, it is useful to identify a systematic behavior in
the fragmentation cross sections. One such behavior is
factorization , a concept originally from high energy
physics and subsequently extended to heavy ion interac-
tion . It states that at high enough beam energies the
partial charge-changing cross section can be written as:
o(P, T, F) =F'YPT
weak factorization (1)
o(P, T, F) = F'YT
strong factorization (2)
o(P, T, F) is the fragmentation cross section for the pro-
jectile P incident upon the target T and producing the
fragment F, u is a factor depending only upon the pro-
jectile and the fragment while the target factors 'PT and
iT depend respectively upon the target and the projectile
and only upon the target.
One important application of the factorization prop-
erty is the rescaling procedure, which is the base of sev-
eral cross section prediction models [3, 4]. Under the
assumption that weak factorization holds, it is possible
*Corresponding author. E-mail address: chiaranephy.chalmers.
se; tel: +46 31 7722911; fax: +46 31 7723079.
o(P, T, F) =(P, T, F) %PT
where %P,T and yPT are the target factors for a specific
target T and the reference target T. The target factors
are generally obtained using simple semi-empirical for-
mulas (e.g. Eq. 11); the value of o(P, T, F) can be calcu-
lated with semi-empirical algorithms. In particular, the
models discussed in  and  use hydrogen as a reference
target, because of the large amount of target fragmenta-
tion cross sections measured for protons projectiles, that
can be reversed as projectiles fragmentation cross sec-
tions on hydrogen target.
Weak factorization is also one of the basic predictions
in the abrasion-ablation theory  and the investigation
of its validity could therefore be useful for testing the
goodness of this model.
In this work fragmentation cross sections have been
measured for different projectile-energy-target combina-
tions and analyzed in order to test if the data followed
the factorization rules. We describe herein the analysis
procedure for obtaining cross sections as well as the two
methods, graphical and analytical, used for validating
weak and strong factorization. The factorization param-
eters defined in Eq. 1 and 2 have been calculated; in
particular the target factors have been fitted with appro-
priate equations in order to investigate their dependence
upon the target mass number. Finally the results have
been compared with data from literature.
II. EXPERIMENT DESCRIPTION
All the experiments have been performed at the Heavy
Ion Medical Accelerator at Chiba (HIMAC) ; the pro-
jectiles, their kinetic energy at extraction from the accel-
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La Tessa, Chiara; Sihver, Lembit; Zeitlin, Cary; Miller, Jack; Guetersloh, Stephen; Heilbronn, Lawrence et al. Test of weak and strong factorization in nucleus-nucleuscollisions atseveral hundred MeV/nucleon, article, June 21, 2006; United States. (digital.library.unt.edu/ark:/67531/metadc897399/m1/1/: accessed February 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.