Coherence and Decoherence in Collisions of Complex Nuclei

1. Quantum Information and Many-body Physics, PITP (UBC), Vancouver, Dec’07 Coherence and Decoherence in Collisions of Complex Nuclei D.J. Hinde, M. Dasgupta, A. Diaz-Torres Department of Nuclear Physics Research School of Physical Sciences and Engineering Australian National University G.J. Milburn Department of Physics University of Queensland

2. + + + + + + Atomic nucleus – a complex many-body system • ~ 6 to 250 constituent nucleons • Protons, neutrons - Fermions • Well-defined internal excitations • Single-particle excitations (one n or p to new orbital) • Coherent collective excitations – many nucleons • Many collective modes (0.06 -20 MeV) • Vibrational excitations – surface or volume modes • Rotational excitations – nuclear deformation (shapes) • Vary systematically – nuclear structure • Shells gaps play crucial role – magic (extra-stable) nuclei • Nuclear structure, interactions from first principles? - NO

3. + + + + + + + + + + Nucleus-nucleus collisions • Long-range Coulomb repulsion • Short-range nuclear attraction • Potential barrier – capture or fusion barrier Fusion Barrier (typically 100 MeV) VB Coulomb repulsion rB Nuclear attraction VC a Z1*Z2/R Potential Energy Z1 Z2 R R

4. Inter-nuclear potential • Coulomb potential exactly calculable • Nuclear potential is not so easy • Options: • Double folding model (also for Coulomb interaction) Fold matter densities with phenomenological n-n interaction Exponential at and outside barrier radius (not closed expression) • Simple, convenient expression VN(r)=V0/(1+exp(r-R0)/a) [Woods-Saxon potential] Exponential at and outside barrier radius Find parameters by fitting experimental data • Fit peripheral part of double-folding potential with Woods-Saxon form • Problem in region inside barrier radius: • Re-organization of nuclear matter to find lowest energy configuration • Does system have time to “find” this configuration – adiabatic?

5. Nucleus-nucleus collisions • Currently two theoretical approaches • Classical or semi-classical – trajectory (Sommerfeld parameter) • Coherent time-independent quantum description (1980s-1990s) • Classical trajectory model • Distance of closest approach defines minimum surface separation • Kinetic energy loss – macroscopic friction - irreversible • No quantum tunnelling • Coupled-channels model • Time-independent Schrodinger eqn • Radial separation r is key variable • Coupling of relative motion to specific internal excitations • No energy loss – reversible • Trapping inside barrier by playing a trick ..

6. 6037 Coupled-channels model Etc. keV Many excited states 279 269 77 ground state 0 197Au 16O 197Au 16O Interacting nuclei are in a linear superposition of various states Effectively changes the interaction potential C.H. Dasso et al., Nucl. Phys. A405 (1982) 381

7. Coupled-channels model VJ(r) = VN + VC +J(J+1)h2/2mr2 [ ] h2 d2  Vnm (r) ym(r) = 0 + VJ(r) +en – E yn(r) + 2 dr2 m=n / • Each combination of energy levels (m) is a “channel” • Collective, strongly-coupled channels should be included (Vnm= Vmn) • Isocentrifugal approximation • The centrifugal energy is independent of the channel • It is incorporated in the inter-nuclear potential (up to J~100, E~100 MeV) • Boundary conditions at two positions: • Distant boundary: • Incoming Coulomb wave in channel “0” (nuclei in ground states) • Outgoing Coulomb waves in all channels • Inside the barrier only an incoming wave (or imaginary potential)

8. Coupled-channels model • Simplifying approximations for illustration: • Two channels • en << Vnm (e.g rotational nuclei) • Solve coupled equations at each value of r • Then VJ(r) {VJ(r) + VCoupling(r)} and {VJ(r) – VCoupling(r)} • The potential barrier is “split” into two barriers (eigenchannel picture) • More channels, more barriers • Coupling matrix elements proportional to Z1*Z2 • like the uncoupled barrier energy itself • Width of barrier distributions ~ 0.1 VB – large effect!

9. Fusion barrier distribution 1 Single-barrier Probability E nuclei in a superposition of states VB0 Probability Distribution of barrier energies - eigenchannels E VB2 VB3 VB1

10. Coupled-channels model • Energy E below VJ(rB) • Incoming wave b.c. inside rB plays no role • Reaction processes are elastic and inelastic scattering • Observables are the populations and energies of “physical” channels m • Shows the strongly coupled channels • Energy E above VJ(rB) • Incoming wave b.c. inside rB acts like a black hole calculate fusion • Irreversibility inside rB - BUT - no effect on coherence! • Always assumed irreversibility does not reach out to rB “invisible” • Potential (fusion) barrier acts as a filter at rB • Measuring the distribution of barrier energies and probabilities allows us to see the eigenchannels of the system at the barrier radius

11. Concept: Review: Dasgupta et al., Annu. Rev. Nucl. Part. Sci 48 (1998) 401 Rowley et al., Phys. Lett. B254 (1991) 25 Z1Z2 = 496 3- 12+ 10+ 8+ 6+ 4+ 2+ 0+ 0+ Wei et al., Phys. Rev. Lett. (1991) Morton et al., Phys. Rev. Lett. (1994)

12. Fusion barrier distribution 58Ni + 60Ni : Z1Z2 = 784 2+ 2+ 0+ 0+

13. Fusion barrier distribution 2+ 2+ 58Ni + 60Ni : Z1Z2 = 784 2+ 0+

14. Fusion barrier distribution 2+ 2+ 2+ 2+ 2+ 58Ni + 60Ni : Z1Z2 = 784 2+ 0+ Looks pretty good! What’s the problem? – why should we treat decoherence explicitly? Doesn’t it seem to be “invisible” inside the barrier?

15. Problem area #1 • Breakup of weakly-bound nuclei • Excited to energy above breakup threshold outside rB • Coupling to continuum - and back again! (Vnm= Vmn) • No irreversibility in CC model –wavefunction exists in linear superposition of fragmented and not fragmented at all distances

16. Radioactive neutron-halo nucleus 6He (E < VB) Scattering Breakup, no capture - Irreversible ? Slow neutrons Breakup+capture - irreversible Hot target nucleus - irreversible Excitation of low-E state - reversible Stable target nucleus Classical trajectory model with stochastically sampled breakup function A. Diaz-Torres et al., Phys. Rev. Lett. (2007)

17. Problem area #2 • Probing inside the fusion barrier • High J values (larger Vn to counter centrifugal pot) • High Z1*Z2 (larger Vn to counter Coulomb pot) • Deep sub-barrier tunnelling

18. Probing larger nuclear density overlap J=100 J=100 Large Z1*Z2 E J=70 J=0 J=0 r large matter overlap small

19. High E,J, large Z1*Z2 • High E,J and large Z1*Z2 (Classical limit) • No potential pocket • Large overlap of matter distributions • Dominant process is KE loss, J-loss, no capture • Deep-inelastic scattering – up to hundreds of MeV E loss • Energy dissipated into heat – irreversible! • Modelled classically – trajectory, friction (1970’s) • High E,J or large Z1*Z2 at low E,J • Less matter overlap • Dominant process is capture (fusion) • Still see deep-inelastic products with finite probability

20. A new model is needed • Treat irreversibility in a consistent way • Include effect of irreversibility on coherent superpositions • Decoherence • Need to identify mechanism(s) for decoherence • Must be internal to colliding nuclear system (mini universe) • Associated with density of levels of system (size of environment) • i.e. lowest energy excited states will not lead to decoherence • Fermi gas level density r: exp[2(AU/k)1/2] U=thermal energy • A=200, k=8 MeV, U=20 MeV 1015 levels/MeV ! • U = E - V • At inner turning point U = 0, at top of barrier U=0 • Coupling to high energy collective vibrations can result in decoherence even when U=0 – how?

21. Coupling to Giant Resonances • Giant Resonances: volume oscillations – dipole, quadrupole…. • Highly collective (large coupling strength ~ 80% of sum-rule) • High energy (10-20 MeV) • Identified as likely doorways for energy loss already in 1976 (semi-classical picture) R.A. Broglia, C.H. Dasso, Aa. Winther, Phys Lett 61B(1976)113 • Giant resonance states have ~ 10 MeV width • Rapidly decay to 1015 non-collective states in same energy range! • Environment even when “classically” U=0! • Lindblad equation, wave packet (A. Diaz-Torres, ANU) • Quantitative coupling to environment • Energy loss • Trapping inside fusion barrier • Wave packet is currently wide (8% energy spread – want <1%) • Need additional decoherence where U>0 inside fusion barrier

22. Measurements sensitive to decoherence? • Fusion barrier distributions for larger Z1*Z2 • Lose sharp structures in barrier distributions – decoherence? 32S+208Pb: Z1Z2=1312

23. Measurements sensitive to decoherence? • Deep-sub-barrier tunnelling probability (next talk) • Reduced tunnelling probability – decoherence? • Deep-inelastic probabilities and energy spectra • Evidence for role of giant resonances in decoherence • Measure properties of reflected flux (next talk)

24. Measurements sensitive to decoherence? • Mott scattering of identical nuclei • Loss of amplitude of interference fringes – decoherence? Rmin Probability of excitation depends exponentially on Rmin Weak measurement distinguishing paths

25. Mott scattering 36S + 36S : Z1Z2 = 256 208Pb +208Pb : Z1Z2 = 6724 Below fusion barrier Above fusion barrier Need to account for flux loss to fusion

26. Conclusions • Irreversibility needs to be correctly incorporated into quantum mechanical picture of nuclear collisions • Decoherence through couplings with giant resonance • Quantitative couplings to resonances and environment • Breakup of weakly-bound nuclei • Irreversibility is clearly necessary • Decoherence in fusion • Next talk • Deep-inelastic reactions – irreversible energy loss • Complementary to fusion (scattered back from barrier) • Decoherence in Mott scattering • May be a sensitive probe?

27. Wrong Way Go Back

28. Fusion barrier radius (absorption) Breakup probabilities vs. Rmin Extrapolated prompt breakup probability at fusion barrier radii: PBU = 0.36 to 0.58 (Depends on L) Incomplete fusion probability: PICF = 0.32 (Average over L) (Hinde et al., Phys. Rev. Lett. 89 (2002) 272701)