Decoherence in Nuclear Fusion?

1. Decoherence in Nuclear Fusion? M. Dasgupta Department of Nuclear Physics The Australian National University Canberra, AUSTRALIA With: D.J. Hinde, A. Diaz-Torres, B. Bouriquet, C. Low, J.O. Newton G. J. Milburn

2. Repulsive electrostatic Potential energy Barrier against fusion r attractive nuclear Fusion – massive rearrangement of many body quantum system due to Attractive nuclear interactions – represented by a short-range potential

3. V r complete dissipation of the K.E. into internal excitations Multitude of excitations Inclusion of coherent superposition of distinct physical states of the separated nuclei Decoherence? Black hole Coupled-channels model (2) Are effects of decoherence observed? r Described by single potential model (1) Is this description adequate?

4. Probing decoherence – collisions with small separation Fusion at energies well above the barrier – significant overlap at the barrier radius V Fusion at energies well below the lowest barrier – increasing overlap between barrier radius and inner turning point total potential r nuclear potential But…need to know the nuclear potential!

5. Fusion at energies well above the barrier – potential dominated (determined by nuclear potential shape) characterized by diffuseness In the framework of the current model (coupled channels): Fusion at energies well below the lowest barrier – tunnelling dominated (slope determined by barrier width) characterized by potential diffuseness Fusion at energies around the barrier – coupling dominated (barrier distribution)

6. Measurements of fusion of 16O with 208Pb and 204Pb Magic nuclei – theoretically easier 16O beam 208Pb target

7. Fusion - evaporation

8. Fusion - fission

9. evaporation residue n fission Fusion products Alpha decay of residues 16O + 208Pb 16O + 204Pb Direct detection Fusion yield = evaporation residues yield + fission yield

10. Measuring fusion yields – the challenges Fusion cross-sections – At best 10-9 of atomic cross-sections – Large background of Coulomb scattered beam particles (108 - 1015) –fusioncross-section  exp { k (E – B) } Beam – Energy needs to be very well defined Target – thin targets to minimize energy integration, target impurity < ppm Separation and detection – identify fusion products amongst large background Precision measurements require – highly efficient detection systems, – sophisticated techniques

11. Accelerator facility, Australian National University ions injected Terminal voltage: 15 Million Volts experimental equipment Beam 0.1c

13. Fission Measurements • Measure fission fragment positions • Measure flight times • Deduce velocity vectors

14. 16O + 208Pb this work 16O + 208Pb Morton et al (1997) 16O + 204Pb this work Measured fusion cross-sections Dasgupta et al, PRL 99 (2007) 192701 s(mb) E. – B (MeV) One event per hour

15. 16O + 208Pb this work 16O + 208Pb Morton et al (1997) 16O + 204Pb this work Fusion cross-section: σ = R2 ħω / (2E) ln [ 1 + exp { 2π/ħω (E – B) } ] E > B E < B π R2 [ E-B ] /E exp { 2π/ħω (E – B) } s(mb) E. – B (MeV)

16. d [ln(E)] d [ln(E)] Parabolic barrier: E  exp[(2p/ћw )(E – B)] dE dE = 2p/ћw Value independent of B Below barrier shape deviates from parabolic d ln(E) /dE increases Logarithmic slope • cross-sections over several decades to be plotted on a linear scale • comparison of tunnelling gradient independent of the weight of the lowest barrier Hagino et al, PRC67(2003) 054603

17. 16O + 208Pb this work 16O + 208PbMorton et al (1997) 16O + 204Pb this work Logarithmic slope of the measured fusion cross-sections d(ln(E)/dE E – B (MeV)

18. a = 0.66 fm, coupled a = 0.66 fm no coupling s (mb) E – B (MeV) Standard Woods-Saxon potential with and without coupling (E-shifted) d [ln(E)]/dE Diffuseness: Double folding model E - B

19. a = 0.66 fm d [ln(E)]/dE Factor of 1.5 of discrepancy in logarithmic derivative s (mb) > Factor of 20 discrepancy in measured and predicted cross-sections E – B (MeV)

20. a = 1.18 fm, coupled a = 1.18 fm no coupling d [ln(E)]/dE s (mb) E – B (MeV) larger diffuseness of Woods-Saxon potential Below barrier slope not explained Data well-above barrier well represented

21. a = 1.65 fm Below barrier slope reproduced d [ln(E)]/dE Data well-above barrier not reproduced s (mb) E – B (MeV)

22. 16O + 208Pb 16O + 204Pb • (mb) a = 0.66 fm a = 1.18 fm a = 1.65 fm a = 0.66 fm a = 1.18 fm a = 1.65 fm Ec.m. – B (MeV) Ec.m. – B (MeV) simultaneous description of fusion well-above and well-below the barrier is not obtained Some physical effect not being included → affects fusion in both energy regimes Dasgupta et al, PRL 99 (2007) 192701

23. Fusion well-below and well-above the barrier For a given above barrier E – cross-section determined by the limiting l →determined by high-l barrier, R r Rl at smaller separations than R0 Highl V (MeV) Inner turning point for a below barrier E appears at same separation distance as the top of the high l –barrier Lowl Two parts of fusion excitation function probe the same separation (True independent of the particular form of the nuclear potential) r (fm)

24. Any physical mechanism invoked to explain below barrier cross-sections – should also reproduce above barrier results • Not true for explanations so far: • Shallow nuclear potential (~ 10 MeV) → leads to no trapping potential pocket for higher l –value • Large diffuseness used for above barrier results → fail to describe below barrier cross-sections Is decoherence the answer to our woes?

25. Will decoherence help? • A gradual onset of decoherence – with increasing overlap → system becomes more classical → tunnelling increasingly suppressed as E is reduced • It can result in energy dissipation – giving angular momentum and energy loss → changes the above barrier cross-section

26. Suppression of tunnelling – system dependent 16O + Pb s (mb) expectation 64Ni + 64Ni Jiang et al, PRL 93 (2004) 012701 E – B (MeV) • Ni + Ni – charge product is larger – barrier at smaller separation than O +Pb – increased decoherence?

27. Astrophysical interest E << B V Deviations observed at E ~ 10% below B r • Ni + Ni results extrapolated (by others) to reactions of astrophysical interest e.g. C + C • O + Pb data do not support such extrapolation • Need to have an understanding of the correct physics • Is there another probe?

28. Log (probability) elastic Giant resonances 50 100 Measured energy (MeV) • Reflected flux complementary to tunnelling • Deep inelastic events (events with large energy loss) even at deep-sub-barrier energies • Experiments done and more planned

29. Summary and outlook • Measurements of fusion cross-sections for well-below to well-above barrier for 16O + 204,208Pb • Cross-sections in tunnelling regime fall much faster than • predicted (>factor of 20 disagreement in cross-sections) • Commonly used coherent coupled channels model fails to provide a consistent description of fusion • Need to go beyond this model – consistent description with decoherence? • Modelling an isolated system with couplings having a strong radial dependence - interesting area for new developments