1. Reaction cross sections of unstable nuclei Contents What is reaction cross section (  R )?  R Effective matter density distributions of unstable nuclei How to measure  R. RIBLL in IMP, RIPS in RIKEN Recent results in 14-18 C isotopes Summary A. Ozawa (University of Tsukuba)

2. Density distributions (  ) of stable nuclei R  A 1/3 Neutron radii ≈ proton radii even for 48 Ca, 208 Pb Diffuseness is constant. a ~ 0.6 fm How are unstable nuclei? No thick neutron skin! Text book says…… Same radii for mirror pairs

3. How to deduce  of unstable nuclei Proton elastic scattering at ~400 MeV Tested for stable nuclei R&D for unstable nuclei Electron scattering Charge distribution can be deduced. R&D for unstable nuclei (SCRIT in RIBF etc. ) Reaction cross section (interaction cross section) with different energies Already applied to unstable nuclei ( 11 Be: M. Fukuda et al., Phys. Lett. B 268 (1991) 339. ) (H. Sakaguchi et al., PRC57(98)1749)

4. Interaction cross-section (  I ) and reaction cross section (  R ) Interaction cross-section (  I ) and reaction cross section (  R ) Definition of interaction cross-section (  I ); Cross section for the change of Z and/or N in incident nucleus Reaction cross-section (  R )  R =  I +  inela,  inela : inelastic cross-section If  inela is small enough,  R ≈  I. At relativistic energy (~1 A GeV)

5. Glauber model Optical Limit approximation RR  T(r):Transmission function  :effective NN cross-sections  of target  of projectile Mean square radii (Zero range calculations)  P (r) = 2  -3/2 -3 (1-1/A) -3/2 exp(-x 2 ) (1+ (N-2) /3x 2 ) x = (r/ ) 2 Harmonic-oscillator type (p-shell)

6.  NN has an energy dependence. Energy at RIBF Energy at GSI Glauber model Energy at RIPS/RIBLL

7. Sensitivity of  R to the densities 30 A MeV 300 A MeV radius( 12 C+ 12 C)

8. Assumption for shape of densities  (r) = HO(  )-type(r < r c ) Y exp(- r)/r 2 (r ≥ r c ) rcrc

9. Example : Effective  of 11 Li Energy (A MeV)  R (mb) r (fm) Density (nucleon/fm 3 ) Finite range Zero range by energy dependence by target dependence PLB287(1992)307 C target Famous two neutron halo nucleus Deduced  is consistent with one deduced by other method.

10. Principle of measurement  I = -1/t log(N o /N i ) Target (thickness t) Ni(AZ)Ni(AZ) No(AZ)No(AZ) Transmission method Carbon  R =  I +  inela Particle identification is important! Estimation of  inela is also important.

11. RIBLL in IMP B  -  E  -TOF/B  -  E-TOF is possible. E/A<50 MeV Z.Sun et al., NIMA503(2003)496 Measurements of  R at intermediate energies

12. 14 Be 11 Li 8 He 9 Li 0 20406080 TOF (ns) 2 4 6 8  E (a.u.) 2 3 4 5 Z 3.03.44.23.8 A/ZA/Z Good particle identification! Results of particle identification Before reaction targetAfter reaction target

13. Results in RIBLL We obtained only interaction cross sections (  I ) with large error bars…… A.Ozawa et al., NIMB in press Predictions by phenomenological formulae  I (mb)

14. Experimental setup in RIPS RIPS in RIKEN Good transmission! Large momentum acceptance p // of fragments E/A<100 MeV Q: Quadrupole Magnet D: Dipole Magnet F1~3: Focus 1~3

15. Results of particle identification After reaction target Case for 16 C Identification is not so easy….. However, good transmission is achieved after the reaction target.

16. Recent results in C isotopes (in RIPS/FRS)

17. 14 C RIPS data Pure p 1/2 Pure s 1/2 D.Q.Fang et al., PRC 69 (2004) 034613. 15 C RIPS data 16 C RIPS data 17 C C.Wu et al., NPA 739 (2004) 3. T.Zheng et al., NPA709(2002)103. Pure s 1/2

18. 18 C (Preliminary) RIPS data

19. Summary Reaction cross section (  R ) measurements are powerful tools to investigate matter density distributions (  ) of unstable nuclei.  R with low energy can be measured at RIBLL and RIPS. We deduced  for 14-18 C. Relatively large tail for 15-18 C. We will extend the measurements to other heavier nuclei in RIBF in RIKEN and CSR in IMP. Related topics in this symposium: by Wang-san ( 23 Al) and Wu-san ( 17 C)

20. List of collaborators A.Ozawa 1, X.Z.Cai 2, Z.Q.Chen 2, M.Chiba 3, D.Q.Fang 2, M.Fukuda 4, Z.G.Guo 5, N.Iwasa 6, T.Izumikawa 7, R.Kanungo 8, R.Koyama 7, J.X.Li 5, R.S.Mao 5, T.Ohnishi 3, T.Ohtsubo 7, W.Q.Shen 2, W.Shinozaki 7, T.Suda 3, Z.Y.Sun 5, T.Suzuki 9, M.Takahashi 7, I.Tanihata 8, W.D.Tian 5, J.S.Wang 5, M.Wang 5, Y.B.Wei 2, C.Wu 10, G.Q.Xiao 5, Z.G.Xiao 5, T.Yamaguchi 9, Y.Yamaguchi 3, A.Yoshida 3, W.L.Zhan 5, H.Y.Zhang 2, T.Zheng 10, C.Zhong 2 1 University of Tsukuba, 2 Shanghai Institute of Applied Physics, 3 RIKEN, 4 Osaka University, 5 Institute of Modern Physics, 6 Tohoku University, 7 Niigata University, 8 TRIUMF, 9 Saitama University, 10 Peking University I strongly appreciate Chinese collaborators!