1. Reaction cross sections of carbon isotopes incident on proton and 12 C International Nuclear Physics Conference, Tokyo, Japan June 3-8, 2007 W. Horiuchi (Niigata) B. Abu-Ibrahim (Cairo), A. Kohama (RIKEN) Y. Suzuki (Niigata)

2. Motivation Reaction and interaction cross sections have been measured up to 20 C on a 12 C target. Analysis of 19,20,22 C+p is in progress at RIKEN (QW-005). → Prediction of reaction cross sections of carbon isotopes. A. Ozawa et al., Nucl. Phys. A693, 32(2001). Contents 1.Reaction model: the Glauber theory. 2.Densities of C isotopes. 3.σ R on a 12 C target. 4.σ R on a proton target. 5.Comparison of the two targets. 6.Summary ～ 900AMeV

3. Reaction model: Glauber theory For a proton target Reaction cross section: Optical Limit Approximation For a 12 C target Input: p and n density distribution. Profile function. NTG: OLA + higher order correction. NTO: Eikonal Approx. with the global optical potential (N- 12 C). Profile function:

4. p- 12 C and 12 C- 12 C Excellent agreement with experiment in a wide range energy. Non-adjustable parameters. p- 12 C reaction cross section

5. How to construct the densities Slater determinant generated from a mean field potential of Woods-Saxon form. Potential strength → determined to reproduce S n and S p. To go beyond the mean field description. A core+n model (core: A-1 C) for odd nuclei. A core+n+n three-body model for 16 C and 22 C. – 16 C: (1s 1/2 )(0d 5/2 ) mixing (W.H., Y. Suzuki, PRC73,037304(2006), QM-064) – 22 C: Borromean (W.H., Y. Suzuki,PRC74, 034304(2006), QM-064)

6. Reaction cross sections of carbon isotopes on a 12 C Good agreement with experiment at high energy except for 15,17 C.

7. On a proton target Reaction cross section of C+p 40MeV Empirical S 2n : 0.423±1.140 MeV 22 C: 20 C+n+n 3-body cal.

8. Proton vs 12 C target We define the quantity σ R (b) as the same definition of the reaction cross section: (upper limit of integral is limited to b) Comparing the reaction cross section at low energy (40MeV) with that at high energy (800MeV). proton neutron matter

9. σ R (b)/σ R of 22 C 12 C target p target ⊿ b: 2.0fm ⊿ b: 1.6fm 800AMeV 40AMeV → A proton target is more sensitive for neutron distribution than a 12 C target. 90%

10. Summary We have investigated reaction cross sections of carbon isotopes systematically in the Glauber model. –Even: densities constructed by a mean field model. –Odd: core+n model is used. – 22 C: 20 C+n+n three-body model. On a 12 C (W.H., B. Abu-Ibrahim, Y. Suzuki, A. Kohama,PRC75, 044607(2007)) – 12 C+ 12 C reaction are reproduced very well. –Reaction cross sections of other isotopes are in reasonable agreement (except for 15,17 C+ 12 C reaction). On a proton (in preparation) –We predict reaction cross section of 22 C. 960-1000 mb at 40MeV on a proton (very large A ～ 60) –p target is more advantageous than 12 C target to probe extended neutron distribution.