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Reaction cross sections of unstable nuclei

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

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Reaction cross sections of unstable nuclei

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

  2. Density distributions (r ) of stable nuclei Text book says…… • RµA1/3 • Neutron radii ≈ proton radii even for 48Ca, 208Pb • Diffuseness is constant.a ~ 0.6 fm Same radii for mirror pairs No thick neutron skin! How are unstable nuclei?

  3. How to deduce r of unstable nuclei (H. Sakaguchi et al., PRC57(98)1749) • 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 (11Be: M. Fukuda et al., Phys. Lett. B 268 (1991) 339. )

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

  5. Glauber model Optical Limit approximation (Zero range calculations) T(r):Transmission function sR s:effective NN cross-sections s r of target r of projectile Harmonic-oscillator type (p-shell) Mean square radii rP(r) = 2p-3/2l-3 (1-1/A)-3/2 exp(-x2) (1+ (N-2) /3x2) x = (r/l)2

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

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

  8. Assumption for shape of densities r(r) = HO(a)-type (r < rc) Y exp(-lr)/r2 (r ≥ rc) rc

  9. Example : Effective r of 11Li Famous two neutron halo nucleus C target by energy dependence Finite range Density (nucleon/fm3) sR (mb) by target dependence Zero range PLB287(1992)307 Energy (A MeV) r (fm) Deduced r is consistent with one deduced by other method.

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

  11. Measurements of sR at intermediate energies RIBLL in IMP Z.Sun et al., NIMA503(2003)496 E/A<50 MeV Br -DE-TOF/Br -DE-TOF is possible.

  12. Results of particle identification Before reaction target After reaction target 8 14Be 5 6 14Be 4 11Li 9Li DE (a.u.) Z 4 11Li 9Li 3 8He 2 2 8He 0 3.0 3.4 3.8 4.2 20 40 60 80 A/Z TOF (ns) Good particle identification!

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

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

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

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

  17. 14C D.Q.Fang et al., PRC 69 (2004) 034613. 15C Pure s1/2 Pure p1/2 RIPS data RIPS data T.Zheng et al., NPA709(2002)103. C.Wu et al., NPA 739 (2004) 3. 16C Pure s1/2 17C RIPS data RIPS data

  18. (Preliminary) 18C RIPS data

  19. Summary • Reaction cross section (sR) measurements are powerful tools to investigate matter density distributions (r ) of unstable nuclei. • sR with low energy can be measured at RIBLL and RIPS. • We deduced r for 14-18C. Relatively large tail for 15-18C. • 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 (23Al) and Wu-san (17C)

  20. List of collaborators A.Ozawa1, X.Z.Cai2, Z.Q.Chen2, M.Chiba3, D.Q.Fang2, M.Fukuda4, Z.G.Guo5, N.Iwasa6, T.Izumikawa7, R.Kanungo8, R.Koyama7, J.X.Li5, R.S.Mao5, T.Ohnishi3, T.Ohtsubo7, W.Q.Shen2, W.Shinozaki7, T.Suda3, Z.Y.Sun5, T.Suzuki9, M.Takahashi7, I.Tanihata8, W.D.Tian5, J.S.Wang5, M.Wang5, Y.B.Wei2, C.Wu10, G.Q.Xiao5, Z.G.Xiao5, T.Yamaguchi9, Y.Yamaguchi3, A.Yoshida3, W.L.Zhan5, H.Y.Zhang2, T.Zheng10, C.Zhong2 1University of Tsukuba, 2Shanghai Institute of Applied Physics, 3RIKEN, 4Osaka University,5Institute of Modern Physics, 6Tohoku University,7Niigata University, 8TRIUMF, 9Saitama University, 10Peking University I strongly appreciate Chinese collaborators!

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