1. Overview of sub barrier fusion Aradhana Shrivastava, BARC

2. Sub barrier fusion How interest in sub-barrier fusion with heavy ion started (in ~1980s) ? Two apparent reasons: Discovering new elements (SHE) Nuclear astrophysics

4. Reaction channels around the Coulomb Barrier A P,Z P A T,Z T b Nucleon/cluster transfer/ Incomplete Fusion Inelastic scattering/ breakup Elastic scattering Complete Fusion Interconnectivity of reaction channels Multidimensional quantum tunneling

5. A potential between the projectile and the target is given by a function of the relative distance r between them. V (r) = V N (r) + V C (r), nuclear potential + Coulomb potential V C (r) = Z P Z T e 2 /r Interaction Potential double folding procedure v NN effective nucleon-nucleon interaction, and ρ P and ρ T densities of the projectile and the target Nuclear potential

6. Woods-Saxon form Akyuz -Winther Parametriation

7. Coulomb Barrier V C (r) = Z P Z T e 2 /r r> Ro = Z e [3Ro 2 – r 2 ]/ 2Ro 3 r<Ro 12C +154Sm

8. L. C. Vaz, J.M. Alexander and G.R. Satchler, Phys. Rep. 69 (1981) 373.

9. One dimensional barrier penetration Parabolic shape for barrier Hill -Wheeler extension of WKB approximation Transmission coefficient 1 dim: depends only on inter-nuclear separation - r Considering nuclei as inert spheres

10. Rounded barrier, semi-classical approx.  Wong formula: The fusion process: a simple approach Tunnelling through a 1-dim barrier 1-dim: the interaction depends only upon the distance The system enters the “pocket”: fusion Fusion cross-section: Radial distance Potential Coulomb Nuclear VBVB RBRB E Potential: Coulomb + Nuclear+ centrifugal Energy Fusion probability in Log Barrier

12. Discrepancies enhancement

17. Fusion and degrees of freedom Stokstad et al, PRL 41 (1978) 465 Leigh et al, PRC 52 (1995) 3151 M. Beckerman et al, PRL 45 (1980) 1472 Enhancement of the fusion cross section 154 Sm is strongly deformed  height of the barrier depends on orientation 58 Ni + 64 Ni positive Q-value for transfer Coupled-channels formalism

18. total transmission is a weighted sum of the transmission for the potentials V -F and V + F. coupling to another channel effectively splits the potential barrier into two barriers

21. Fusion barrier distribution Po – transmission co efficient for uncoupled barrier Wi= IUioI 2 overlap of gnd state with eigen vector with eigen value i

23. Investigate nuclear shape through barrier distribution

24. Barrier Distribution from Quasi elastic T= 1 – R, dT/dE = -dR/dE

26. Reduced scale To compare data for different systems, it is necessary to suppress trivial differences, arising from sizes & charges of the collision partners.

27. Reaction Dynamics near the Coulomb Barrier stable beams: what we learnt? Rich interplay between reaction channels, coupling to inelastic and transfer reactions – Fusion enhancement barrier distribution broadening of, Energy dependence optical potential- Elastic scattering Weakly bound stable(6,7Li, 9Be): low lying continuum - importance of breakup, observation of suppression in fusion at E>Vb Weakly bound radio active nuclei: exotic shapes, unusual neutron or proton asymmetry, large probability of transfer of valence nucleon, Transfer (+Q) (neutron rich) vs BU Recent interest: sub barrier fusion with weakly bound stable and unstable (RIB) deep sub barrier fusion

28. Challenges Experimental complication Excitation functions with only few data points Statistical and systematic uncertainties Definition of fusion: total, complete, incomplete vs transfer Theoretical Models Definition of fusion Include couplings to direct processes – reduced real potential – effective potential from CDCC calculations Lack of reliable OM parameters:  need for elastic scattering measurements Independent measurement of strength of other channels  break-up and transfer cross-sections  Comparison with stable companion Light system: no difference Heavier system: angular momentum

29. Methods Fissile target: Z > 90 Charged particle detectors 11,9 Be + 238 U 6,4 He + 238 U 7 Be, 7 Li + 238 U Fission  -emitters: 84 < Z < 90 Charged particle detectors 11,9 Be + 209 Bi 6 He + 209 Bi  Recoil separators but low velocities! E.R. E.R. decay by EC Si-Li detectors 4,6 He + 64 Zn X (delayed) Decay scheme of E.R. Large  -detector array 4,6,8 He + Cu KX-  - ray coinc 8 He + 197 Au 

30. Reactions with unstable nuclei Lightest Borromean Nuclei 6 He Addition to Weak binding – large isospin Exotic structure – Halos and skin 4 He + n +n cigar Di-neutron t + t Inert  core, known  -n interaction

31. Vol 431 No 7010 pp823-826Fusion......and the fat helium Fusion and the fat helium

32. Controversial ! Fusion and the fat helium The halo Extended neutron matter distribution  strong force begins acting at a larger distance Deformation Large part of dipole strength present at low energy  coupling to fusion The weak binding Strong direct reaction channels: transfer break-up??

33. The fission cross section Large enhancement of the fission cross-section for 6 He+ 238 U below the barrier 4,6 He + 238 U fission

34. Two-neutron transfer and (no) fusion No enhancement of the fusion cross section Below the barrier, the two-neutron transfer dominates

35. He isotopic chain: Nucleon emission threshold from 20.5 MeV to 0.9 MeV 6 He and 8 He “Borromean” structures 8 He : 4 He + 4n 6 He+2n (double Borromean) Charge radius of 6 He > 8 He, Neutron separation energy 6 He < 8 He 8 He: largest N/Z ratio, strong di-neutron correlations Neutrons in 8 He interesting case : interconnectivity of intrinsic structure with reaction dynamics

36. 8 He: Tunneling of most neutron rich nuclei Detection: sensitive off beam technique 8 He ~4x10 5 pps X ray-gamma ray coinc sensitivity selectivity Primary beam: 13 C (75 MeV/A) on thick graphite, Secondary beam: 8 He, fully purified and reaccelerated at CIME Target : 197 Au (6mg/cm 2 ) (stack 197 Au +Al) Fusion ERs 199 - 202 Tl

37. Fusion and Neutron Transfer Transfer x-section larger than fusion A. Lemasson et al PRL 103, 232701 (2009) Couple channel calculations –1n,2n neutron transfer Evaporation residues from CN 205 Tl Accuracy similar to stable beams for low x-sec at sub-barrier: first time with low intensity RIB Good agreement with statistical model calculation 1n,2n Transfer: 198,199 Au

38. Comparison of tunneling in He isotopes  fus ( 6,8 He >  fus ( 4 He)  fus ( 6 He) ~  fus ( 8 He) A. Lemasson et al PRL 103, 232701 (2009) 8 He -easier to transfer excess neutron in peripheral reaction than to tunnel fusion cross-section larger for more neutron rich isotope

39. Li isotopes – unique case of clustering Heaviest isotope: 11 Li : two neutron halo Borrowmean 9 Li + 2n cluster PRL 100, 192502 (2008) 9 Li: 6 He + t PRC 85 (2012)024303 Lighter isotopes (weakly bound stable) : 6,7 Li :  + d ( BE1.45 ),  + t ( BE 2.47 MeV) Link between stable and RIB 7 Li : 5 He+ d (BE 9.5 MeV) : 6 He+ p (BE 9.8 MeV)

40. Fusion 11 Li+ 208 Pb 1.2x10 3 p/s TRIUMF A.M. Vinodkumar, W. Loveland et al. The α decay of the stopped evaporation residues (ERs) was detected in an α-detector array at each beam energy in the beam-off period 40

42. Halo nuclei

43. 1n halo 9,11 Be + 209 Bi Signorini, Eur. Phys. J. A 13 (2002) 129 Delayed  –particles Below the barrier: 9 Be and 11 Be are unexpectedly similar  halo not important? Above the barrier: difference too large, not explained Other calculations: reduction of the cross-section above the barrier for 9 Be + 209 Bi  effect of the break-up channel More accurate data needed

44. 15 C: 1n halo

45. 1n halo lowest energies an enhancement is observed for the neutron-halo nucleus 15 C (solid points). From Alcorta et al., 2011.

46. Proton halo no special enhancement of fusion for 8 B is observed Aguilera et al. (2011) (58Ni) and Pakou et al. (2013) (28Si + 8B).

47. Fusion with heavy projectile Z. Kohley et al PRL 107, 202701 (2011) influence of transfer channels on the fusion of is very weak with no significant differences observed in the reduced excitation functions

48. Summary Influence of Exotic shape, larger size, neutron transfer channels Not as spectacular as was expected !!!