Large-angle quasi-elastic scattering around the Coulomb barrier

1. Large-angle quasi-elastic scattering around the Coulomb barrier Kouichi Hagino (Tohoku University) 　　萩野浩一　　　　　（東北大学） PRC69(’04)054610 PRC71(’05)044612 PRC73(’06)034607 • Introduction • Complementary process: quasi-elastic scattering • 3. Applications • Heavy-ion fusion reactions around the Coulomb barrier • Nuclear structure effects and Fusion barrier distribution • Quasi-elastic barrier distribution • Advantages over fusion • Structure of neutron-rich nuclei • Inter-nucleus potential

2. Sendai （仙台） 「藤野先生」

3. Introduction Aim of nuclear reaction physics 1. Investigate the dynamical aspects of many-body system 2. Nuclear reaction as a tool to investigate nuclear structure e.g. Heavy-ion fusion reactions at energies around the Coulomb barrier Nuclear Structure Effect Enhancement of sfus Fusion: sensitive to nuclear structure

4. Fusion Barrier Distribution Fusion Cross sections Very strong exponential energy dependence Difficult to see differences due to details of nuclear structure Plot cross sections in a different way: Fusion barrier distribution N. Rowley, G.R. Satchler, P.H. Stelson, PLB254(’91)25 Function which is sensitive to details of nuclear structure

5. 16O 154Sm Nuclear Structure Effect Barrier Distribution Dfus : gives a prob. distribution for each potential as a fnct’n of the barrier height • Barrier Distributions: • Very sensitive to nucl. structure • But, need high precision data for sfus

6. Fusion Quasi-elastic Future experiments with radioactive beams Fusion barrier distribution: requires high precision measurements for sfus Radioactive beams:much lower beam intensity than beams of stable nuclei Unlikely for high precision data at this moment Possible to extract barrier distribution in other ways? Exploit reflection prob. instead of penetrability P + R = 1 Quasi-elastic scattering

7. 16O 154Sm Quasi-elastic barrier distribution: H. Timmers et al., NPA584(’95)190 Complementary process: Quasi-elastic scattering Quasi-elastic scattering A sum of all the reaction processes other than fusion (elastic + inelastic + transfer + breakup……) cf. fusion and Qel: inclusive complementary to each other

8. Quasi-elastic barrier distribution: H. Timmers et al., NPA584(’95)190 Complementary process: Quasi-elastic scattering 16O + 152Sm Also, next talk by prof. Liu Huanqiao Zhang et al.,PRC57(’98)R1047

9. Comparison between Dfus and Dqel H. Timmers et al., NPA584(’95)190 A gross feature is similar to each other K.H. and N. Rowley, PRC69(’04)054610

10. Suitable for low intensity exotic beams Experimental advantages for Dqel ・ less accuracy is required in the data (1st vs. 2nd derivative) ・ much easier to be measured Qel：a sum of everything a very simple charged-particle detector Fusion： requires a specializedrecoil separator to separate ER from the incident beam ER + fission for heavy systems ・several effective energies can be measured at a single-beam energy relation between a scattering angle and an impact parameter measurements with a cyclotron accelerator: possible Qel: will open up a possibility to study the structure of unstable nuclei

11. Dqel measurements with radioactive beams 32Mg: breaking of the N=20 shell? Expt. at RIKEN and GANIL: large B(E2) and small E2+ deformation? MF calculationsspherical? Low intensity radioactive beams: High precision fusion measurements still difficult Quasi-elastic measurements may be possible (0+,2+,4+) (0+,3-) Example: 32Mg + 208Pb E4+/E2+ = 2.62 Investigation of collective excitations unique to n-rich nuclei K.H. and N. Rowley, PRC69(’04)054610

12. VC.b. Surface diffuseness problem VN(r) = -V0/[1+exp((r-R0)/a)] Scattering processes: a ~ 0.63 fm Fusion: a = 0.75 ~ 1.5 fm C.L. Jiang et al., PRL93(’04)012701

13. QEL at deep subbarrier energies: sensitive only to the surface region Quasi-elastic scattering at deep subbarrier energies? K.H., T. Takehi, A.B. Balantekin, and N. Takigawa, PRC71(’05) 044612 K. Washiyama, K.H., M. Dasgupta, PRC73(’06) 034607 16O + 154Sm

14. Summary • Barrier distributions: sensitive to nuclear structure • Quasi-elastic b.d. Dqel(E) counterpart of fusion b.d. Dfus(E) • Dqel(E): allows measurements with a cyclotronaccelerator • Dqel(E): well suited to future expt. with low-intensity exotic beams Dqel(E): may be opening up a novel way to probe the structure of neutron-rich nuclei • QEL at deep subbarrier energies: an ideal tool to investigate • the surface property of ion-ion potential

15. Nuclear effects Semi-classical perturbation theory Tunneling effect smears the delta function Fusion test function Classical fusion cross section: Quasi-elastic test function Classical elastic cross section (in the limit of a strong Coulomb):

16. Fusion Barrier Distribution N. Rowley, G.R. Satchler, P.H. Stelson, PLB254(’91)25 P0 E B E B Representation of fusion barrier distribution from experimental data: E B1 B2 B3

17. Reference cross sections Does break-up hinder/enhance fusion cross sections? How to choose reference cross sections? Fusion enhancement/hindrance compared to what? 6He i) Comparison to tightly-bound systems 11Be + 209Bi 10Be + 209Bi 6He + 238U 4He + 238U 4He Separation between static and dynamical effects? M. Trotta et al. PRL84(’00)2342 ii) Measurement of average fusion barrier Fusion barrier distribution 9Be + 208Pb 6,7Li + 209Bi M. Dasgupta et al. PRL82(’99)1395 Neutron-rich nuclei Dqel(E)