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D.J. Hinde Department of Nuclear Physics Research School of Physics and Engineering

Quantum Coherence and Decoherence in Low Energy Nuclear Collisions: from Superposition to Irreversible Outcomes. With M. Dasgupta, M. Evers Department of Nuclear Physics Research School of Physics and Engineering The Australian National University. D.J. Hinde Department of Nuclear Physics

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D.J. Hinde Department of Nuclear Physics Research School of Physics and Engineering

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  1. Quantum Coherence and Decoherence in Low Energy Nuclear Collisions: from Superposition to Irreversible Outcomes With M. Dasgupta, M. Evers Department of Nuclear Physics Research School of Physics and Engineering The Australian National University D.J. Hinde Department of Nuclear Physics Research School of Physics and Engineering The Australian National University

  2. r Introduction V • Collision of two nuclei – relative co-ordinate r • Coulomb repulsion – long range • Nuclear attraction – short range – nucleonic d.o.f. • Inter-nuclear potential • Isolated from external environments • Mini-Universe MeV, fm (10-15m), zs (10-21s) • Describe all constituents, all interactions • Fully coherent q.m. description of collision r

  3. dsdW K.E. r The first experiment studying nuclear collisions • Geiger, Marsden, Rutherford (1909) : a+197Au • Discovered atomic nucleus • Low energy – Coulomb field only • Elastic (Rutherford) Scattering • Higher energy, Z1Z2 – inelastic scattering (excited states) • Describe pure elastic scattering: optical model Schrödinger eqn. + phenomenological imaginary potential • Detector makes measurement E. Schrödinger

  4. Irreversible nuclear collision (fusion) • Neutron interaction with nucleus • Bohr’s compound nucleus model • Energy spread amongst nucleons • Capture – “compound nucleus” • Thermalization – Heat Bath • Effectively irreversible • “Measurement” on neutron performed by nucleus (nucleons) Nature 1936 N. Bohr

  5. Characterizing a “hot” nucleus Excitation Energy • Fermi Gas • Permutations of nucleon excitations • Level density r~ exp(aEx)1/2 • Low energy collective states • Surface vibrational states • Rotational states • Volume vibrational states Collective states Ground state

  6. Including excitations of colliding nuclei Excitation Energy • Fermi Gas • Permutations of nucleonic excitations • Level density • Collective surface vibrations, rotations • Collective volume vibrations • Excited states of separated nuclei • Coulomb field • Nuclear interaction • Relative motion • Coupling to (collective) states • Includes some nucleonic d.o.f. Collective states Ground state

  7. [ ] h2 d2  Vnm (r)φm(r)= 0 + VJ(r) +en – Eφn(r) + 2 dr2 m=n / Coupled-channels equation: key variable separation (r) VJ(r) = VN + VC +J(J+1)h2/2mr2 (Superposition of all J) • Channels (n,m) : combination of Projectile,Target states • Strongly-coupled (collective) channels • Reversible couplings (Vnm= Vmn) • Boundary conditions : • Below-barrier scattering: distant boundary: • Incoming plane wave in channel “0” (both nuclei in ground states) • Outgoing spherical waves in all channels

  8. [ ] h2 d2  Vnm (r)φm(r)= 0 + VJ(r) +en – Eφn(r) + 2 dr2 m=n / r Coherent superposition Coupled-channels equation: key variable separation (r) VJ(r) = VN + VC +J(J+1)h2/2mr2 Below-barrier

  9. [ ] h2 d2  Vnm (r)φm(r)= 0 + VJ(r) +en – Eφn(r) + 2 dr2 m=n / Coupled-channels equation: key variable separation (r) VJ(r) = VN + VC +J(J+1)h2/2mr2 (Superposition of all J) • Channels (n,m) : combination of Projectile,Target states • Strongly-coupled (collective) channels • Reversible couplings (Vnm= Vmn) • Boundary conditions : • Below-barrier scattering: distant boundary: • Incoming plane wave in channel “0” (both nuclei in ground states) • Outgoing spherical waves in all channels

  10. [ ] h2 d2  Vnm (r)φm(r)= 0 + VJ(r) +en – Eφn(r) + 2 dr2 m=n / r Coherent superposition Coupled-channels equation: key variable separation (r) VJ(r) = VN + VC +J(J+1)h2/2mr2 Above-barrier ? ? = Excited “Molecular” (compound nucleus) states

  11. Irreversible nuclear collision (fusion) • Neutron interaction with nucleus • Bohr’s compound nucleus model • Energy spread amongst nucleons • Capture – “compound nucleus” • Thermalization – Heat Bath Nature 1936 N. Bohr • Fusion is irreversible (no superposition of fusion, elastic scattering) • Energy dissipation to other d.o.f. – c.n. nucleonic “heat bath” • CC model does include nucleonic degrees of freedom explicitly

  12. [ ] h2 d2  Vnm (r)φm(r)= 0 + VJ(r) +en – Eφn(r) + 2 dr2 m=n / Coupled-channels model VJ(r) = VN + VC +J(J+1)h2/2mr2 • Channels: combination of P,T states (n,m) • Include strongly-coupled (collective) channels • Reversible couplings (Vnm= Vmn) • How is this physics inside the barrier treated in CC model ? • Ingoing wave in superposition of all channels – “black hole” – IWBC • Imaginary potential acting on wavefunction – attenuation, absorption • Flux remains in superposition (scattered) or is “lost without trace” • Lost flux identified with fusion – in barrier passing picture, loss should only be inside barrier!

  13. Irreversible K.E. lost to complex excitations Colliding nuclei lose individual identities – merge together Fusion - completely irreversible Barrier-passing picture – inside barrier (i) imaginary potential (ii) incoming wave boundary condition Lost probability fusion Above-barrier r Coherent superposition - reversible Fusion – physical picture: Fusion – as modelled: Nuclei in superposition of states Coupled channels equations (Include limited number of low lying collective states, Purely quantal – reversible dynamics)

  14. Channel couplings: scattering Nuclei in ground-states 208Pb 3- Elastic scattering Superposition of states Inelastic scattering Nucleon transfer reactions TKEL (MeV)

  15. Channel couplings: barrier distribution Nuclei in ground-states 1 Single-barrier Probability Superposition of 3 states E VB0 Approximation: 3 eigen-channels 3 eigen-barriers Probability Reflected flux - scattering Transmitted flux - fusion E VB2 VB3 VB1

  16. Z1Z2 = 496 3- 12+ 10+ 8+ 6+ 4+ 2+ 0+ 0+ C.R. Morton et al., Phys. Rev. Lett. (1994) X. Wei et al., Phys. Rev. Lett. (1991) Concept: N. Rowley et al., Phys. Lett. B254 (1991) 25 Review: M. Dasgupta et al., Annu. Rev. Nucl. Part. Sci. 48 (1998) 401 Superposition, barrier distribution essential to describe near-barrier fusion!

  17. Near barrier energies - coherence and dissipation • Quantum: Coherent superposition • - scattering, fusion barrier distribution Coupled channels formalism • Dissipative (irreversible energy dissipation) • - deep inelastic collisions • - compound nucleus formation Classical or Semiclassical treatment GRAZING Imposed mathematical conditions • Strong divide between two classes of model • do not include KE-dissipation out of CC model space in scattering • unable to include superposition in classical dissipative models

  18. Low Z1Z2 High Z1Z2 Smooth transition from superposition to dissipation r r Coherent superposition – reversible couplings Irreversible dissipation Where is the transition? It is gradual or sharp? How does it affect fusion?

  19. Information from energy dissipative reactions • Fusion – energy- damping “invisible” inside barrier ? • Deep inelastic events – energy damping mechanism? • Deep-inelastic measurements – systematics of E-dissipation • Fusion – above-barrier cross sections – quantum tunnelling probability

  20. Radial dependence of probabilities • Mapping energy to radial separation r V r

  21. Sub-barrier energy dissipation – nucleon transfer

  22. Nucleon cluster transfer (2p, a) 16O + 208Pb 208Pb 3- 2p n p TKEL (MeV)

  23. Sub-barrier energy dissipation – nucleon transfer 32S + 208Pb E/VB = 0.96 g.s.

  24. Sub-barrier energy dissipation – nucleon transfer 32S + 208Pb DZ=2: E* ~ 5-25 MeV, peak at 12 MeV 2p and a-transfer (cluster transfer)

  25. DIC Energy loss:(TKEL or E*) S. Silzner et al., PRC 71(2005)044610 Eloss ~ 40 MeV 40Ca + 208Pb E/VB = 1.05

  26. 103 E* in heavy nucleus – thermalized - fission 19F + 232Th fission > 6 MeV (fission barrier) • Transfer or Deep-Inelastic? • Doesn’t matter what we call it • Energy irreversibly lost Fusion-fission Peripheral • Some flux in superposition • Some flux with energy dissipation • Lost to complex nucleonic degrees of freedom – heat bath • Standard quantum models or classical models cannot simultaneously describe • Need to model “quantum to classical” VB 19F D.J. Hinde unpublished

  27. Sub-system Larger system system Complex environment From coherent superposition to irreversible outcome W.H. Zurek, Rev. Mod. Phys. 75 (2003) 715; Phys. Today 44 (1991) 36 M. Schlosshauer, Decoherence and the quantum to classical transition, Springer (2007) Idealized isolated system Superposition of basis states Sub-system entangled with rest of system System “entangled” with environment Loss of coherence in smaller system Described by coherent Q.M. Irreversible outcome (classical) • Quantum decoherence– “dynamical dislocalization of Q.M. superpositions” • (H.D. Zeh arXiv:quant-ph/0512078 v2) coherence shared with (lost in) environment

  28. Example: Electron entanglement with a surface Height above surface Interference fringes Screen Splitter Refocus Source Semiconductor surface Semi-conductor surface • Double-slit type experiment with single electrons • Electron passing abovedisturbs electrons in semiconductor • “whichway” information  destroys spatial coherence

  29. Radial dependence of DZ=2 probability • Steep radial dependence • Probability at RB ~ 0.1 • Inside RB  larger • Nuclear interaction 100 Probability 32S + 208Pb 10-1 10-2 10-3 r RB

  30. P-space CC space Q-space Nucleonic d.o.f. CC space Nucleonic d.o.f. relative motion + few channels (collective, transfer?) Nuclei isolated – not external environment but internal Scattering to discrete states – only need CC + Imaginary pot Nuclei overlap, interact strongly – nucleonic d.o.f. opened up Feschbach formalism DIC – energy dissipation in scattered flux • Effectively irreversible Eloss from CC space • Need to model dynamics outside CC space • Within Q.M. framework

  31. Probing decoherence through fusion Decoherence Compound nucleus Coherent superposition J=100 Large Z1*Z2 J=70 E J=0 J=0 r large matter overlap small

  32. Reduction in fusion at above barrier energies Fusion suppression above-barrier increased reduction of fusion with Z1Z2 Abov-barrier suppression 46 fusion excitation functions Newton et al., PRC 70 (2004) 024605 Wolfs, PRC 36 (1987) 1379 Wolfs et al, NP 196 (1987) 113 Keller et al, PRC36 (1987) 1364 Reported deep inelastic probability close to VB

  33. 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. – VB (MeV) Ec.m. – VB (MeV) Fusion below and above the barrier inconsistent – need to go beyond current models – need to incorporate transition to irreversibility explicitly Ni+Ni: C.L. Jiang et al., PRL 93 (2004) 012701 M. Dasgupta et al., PRL 99 (2007) 192701

  34. Discussion points • Extend coupled-channels model (or CRC) - include many states at high Ex ? - generic treatment or case-by-case (experiment) ? - eliminate need for imaginary potential ? - eliminate need for “friction” at high J (Bass model) ? - describe DIC and coherent phenomena ? • Nucleonic d.o.f. of separate nuclei vs. “molecular” nucleonic d.o.f. ? • Feschbach model – P+Q vs. degrees of freedom • Decoherence without dissipation ? (Mott scattering ?) • Links with decoherence in other quantum systems (here we are!)

  35. a = 0.66 fm a = 0.66 fm a = 1.18 fm adiabatic Woods-Saxon Woods-Saxon sudden l =0 Vtot Vtot Qfus r (fm) Elongation (fm)

  36. a = 0.66 fm Woods-Saxon Woods-Saxon l =60 adiabatic sudden Vtot Vtot Vtot l =0 a = 0.66 fm Qfus a = 1.18 fm r (fm) Elongation (fm)

  37. VB Near-barrier DIC: 58Ni+112Sn Kinetic energy losses > 20 MeV Deep inelastic reactions at E < VB Wolfs, PRC 36 (1987) 1379 Wolfs et al., PLB 196 (1987) 113 Keller et al., PRC 36 (1987) 1364

  38. (ZP+ZT) Doorway states Molecular C.N. d.o.f. GDR Nucleonic d.o.f. (ZP)(ZT) Nucleonic d.o.f. (ZP-2)(ZT+2) Recent density matrix model with coherence and decoherence A. Diaz-Torres et al., Phys. Rev. C78(2008)064604 transfer CC space relative motion + few channels (collective, transfer) Track energy dissipated through different mechanisms Suppresses quantum tunnelling (sub-barrier fusion) Future applications: deep sub-barrier fusion – astrophysics

  39. Example: observation of collisional decoherence Hornberger et al, PRL 90 (2003) 160401 Independent point source of C70 interference pattern measured diffraction • Collision with a gas molecule localizes C70  destroys spatial coherence • Single collision sufficient to destroy interference • Fringe visibility decreases with increasing pressure • System - environment interaction (measurement) - decoherence

  40. (Shown effect of entrance channel dominant over EX) D.J. Hinde et al., PRL 100 (2008) 202701 E/VB = 0.93 E/VB = 0.96 E/VB = 0.98 E/VB = 1.03 E/VB = 1.09 32S + 232Th MAD vs. E/VB (Timescale ~10-20 s) R. Bock et al., NP A388 (1982) 334 J. Toke et al., NP A440 (1985) 327 W.Q. Shen at al., PRC 36 (1987) 115 B.B. Back et al., PRC 53 (1996) 1734 D.J. Hinde et al., PRL 101 (2008) 092702

  41. Detector acceptance Mass-Angle Distributions for quasi-fission 235 MeV 48Ti 48Ti + 196Pt 48Ti + 186W 48Ti + 154Sm qC.M. MR MR MR Elastic, quasi-elastic and deep inelastic events

  42. 160o 20o R. Bock et al., NP A388 (1982) 334 J. Toke et al., NP A440 (1985) 327 W.Q. Shen at al., PRC 36 (1987) 115 B.B. Back et al., PRC 53 (1996) 1734 MAD – mass-equilibration and rotation (GSI 1980’s) Miminal mass-angle correlation Strong mass-angle correlation Scission q (deg.)

  43. E/VB = 0.96 E/VB = 1.03 16O D.J. Hinde et al., PRC 53 (1996) 1290 32S D.J. Hinde et al., PRL 101 (2008) 092702 E* in heavy fragment - thermalized 232Th – fission after peripheral collision – Eloss– transfer/DIC Energy dissipated → EX target→ deformation energy → fission 32S + 232Th fission: Velocity of fissioning nucleus w.r.t. C.M. velocity

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