1. The total charge-changing cross sections and the partial cross sections of 84Kr fragmentation on Al, C and CH2 targets
Luo-Huan Wang1, Liang-Di Huo1, Jia-Huan Zhu1, Hui-Ling Li1, Jun-Sheng Li1, S. Kodaira2, N. Yasuda3, Dong-Hai Zhang1*
1 Institute of Modern Physics, Shanxi Normal University, Linfen , China
2 Radiation Measurement Research Section, National Institute of Radiological Sciences, Anagawa, Inage, Chiba , Japan
3 The Research Institute of Nuclear Engineering, University of Fukui, Kanawa 1-2-4, Tsuruga, Fukui, , Japan
Jun. 22, 2019

2. Motivation:
1. Mechanism of nucleus fragmentation or multifragmentation.
2. The astrophysical problemes of propagation of cosmic ray nuclei through the interstellar medium.
In order to describe the physical process of heavy ion fragmentation at intermediate and high energy, it is necessary to make a systematic study of the total charge-changing cross sections and the partial cross section of Pfproduction. These studies can help us to understand the emission mechanism of the production of PFs.
1500 A MeV 84Kr, Phys. Rev. C36(1987)1870
1502, 1198, 700 A MeV 84Kr, Phys. Rev. C52(1995)3277
1050 A MeV 80Kr, Phys. Rev. C74(2006)044608
200, 500 A MeV 84,86Kr, Phys. Lett. B262(1991)6; Nucl. Phys. A578(1994)659

3. Experimental Details
Three targets: Al-target, 3mm; C-target, 5mm;
CH2-target, 10mm.
Beam: 400 A MeV 84Kr from HIMAC NIRS, the energy is the beam
energy on the up surface of the first target.

4. After the exposure, the CR-39 detector is etched in 7N NaOH aqueous solution at temperature of 70oC for 30 hours. The images of ion tracks are scanned and analyzed automatically by HSP-1000 microscope system and the PitFit measurement software, then checked manually.

5. (a)
(b)
(d)
(c)
(a) and (b) show the difference dx and dy in the front surface and back surface on a CR-39 sheet, (c) and (d) show the difference dx and dy before and after the target

6. Experimental results
3.1, The total charge-changing cross sections
Experimental:
H-target:
Bradt-Peters semi-empirical formula , where r0= 1.35fm, b0= 0.83; Ap and AT are the projectile and target mass number.

7. Experimental results
3.2, The partial charge-changing cross sections
Experimental:
If Ninf=0, then

8. Experimental results

9. Experimental results
3.3, Factorization
Factorization is based on the concept that the cross section for a given projectile and target can be separated into a factor that is independent of the target and a factor that is independent of the fragment. Then the cross section for the production of a fragment F from a projectile nucleus P interacting with a target nucleus T can be written:
Here is a factor which depends only on the species of projectile and fragment but not the target, and is a factor which depends only on the species of projectile and target but not the fragment. Cross sections which follow this format are said to follow “weak factorization” as opposed to “strong factorization” which restricts the dependence of second factor to the target only.

10. Experimental results
Considering the beam energy dependence of cross section, Cummings et al. (Phys. Rev. C42(1990)2530) parametrized their global power-low expression for nonhydrogen target as:
and for a hydrogen target as:
Nilson et al.(Phys. Rev. C52(1995)3277) proposed a parametrized cross section expression as:

11. Experimental results
Fit of Cummings et al. formula to the measured cross sections of Kr on Al at 395 A MeV(left) and 359 A MeV(right), plotted as a function of charge change △Z. The fission peak can be clearly seen.

12. Fit of Cummings et al. formula to the measured cross sections of Kr on C at 395 A MeV(left) and 354 A MeV(right), plotted as a function of charge change △Z. The fission peak can be clearly seen.

13. Experimental results
Fit of Cummings et al. formula to the measured cross sections of Kr on CH2 at 395 A MeV(left) and 341 A MeV(right), plotted as a function of charge change △Z. The fission peak can be clearly seen.

14. Experimental results Fitting parameters (Cummings et al.):
395 A MeV Kr+Al A MeV Kr+Al
395 A MeV Kr+C A MeV Kr+C
395 A MeV Kr+CH A MeV Kr+CH2

15. Experimental results
Fit of Nilsen et al. formula to the measured cross sections of Kr on Al at 395 A MeV(left) and 359 A MeV(right), plotted as a function of charge change △Z. The fission peak can be clearly seen.

16. Experimental results
Fit of Nilsen et al. formula to the measured cross sections of Kr on C at 395 A MeV(left) and 354 A MeV(right), plotted as a function of charge change △Z. The fission peak can be clearly seen.

17. Experimental results
Fit of Nilsen et al. formula to the measured cross sections of Kr on CH2 at 395 A MeV(left) and 341 A MeV(right), plotted as a function of charge change △Z. The fission peak can be clearly seen.

18. Experimental results
Fit of Nilsen et al. formula to the measured cross sections of Kr on H at 395 A MeV(left) and 348 A MeV(right), plotted as a function of charge change △Z.

19. Experimental results Fitting parameters (Nilsen et al.):
395 A MeV Kr+Al A MeV Kr+Al
395 A MeV Kr+C A MeV Kr+C
395 A MeV Kr+CH A MeV Kr+CH2
395 A MeV Kr+H A MeV Kr+H

20. Thank you for your attention!
Conclusion Remarks:
The total charge changing cross section is independent of the beam energy and can be well described by the Bradt-Peters formula. The total cross section increases as a function of target mass number.
The partial cross sections of PF productions are target dependent, and no obvious beam energy dependence are observed.
The partial cross sections are fitted using parametric formula proposed by Cummings et al. and Nilsen et al., respectively.
For the same target and the same parametric fitting formula, the fitting parameter are the same within fitting errors.
Thank you for your attention!