Coherence and Decoherence in Collisions of Complex Nuclei D.J. Hinde, M. Dasgupta, A. Diaz-Torres Department of Nuclear Physics Research School of Physical.

Coherence and Decoherence in Collisions of Complex Nuclei

D.J. Hinde, M. Dasgupta, A. Diaz-TorresDepartment of Nuclear PhysicsResearch School of Physical Sciences and EngineeringAustralian National University

G.J. MilburnDepartment of PhysicsUniversity of Queensland

Quantum Information and Many-body Physics, PITP (UBC), Vancouver, Dec’07

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

+++

+

++

Nucleus-nucleus collisions+

++

+++

++

++

Long-range Coulomb repulsion Short-range nuclear attraction Potential barrier – capture or fusion barrier

R

Potential Energy

R

VC Z1*Z2/RCoulomb repulsion

Nuclear attraction Z1 Z2

Fusion Barrier (typically 100 MeV)

rB

VB

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 radiusFind 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?

Inter-nuclear potential

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

Nucleus-nucleus collisions

..

ground state

Many excited states

Interacting nuclei are in a linear superposition of various states

197Au

0

77

269 279

keV

Effectively changes the interaction potential

C.H. Dasso et al., Nucl. Phys. A405 (1982) 381

Coupled-channels model

Etc.

197Au 16O 16O

6037

Coupled-channels model

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)

+ VJ(r) +n – E n(r) +h2 d2

2 dr2 ][ Vnm (r) m(r) = 0m=n/

VJ(r) = VN + VC +J(J+1)h2/2r2

Coupled-channels model

Simplifying approximations for illustration: Two channels n << 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!

Single-barrier

VB0

E

1

VB2

EVB1

VB3

Distribution of

barrier energies

- eigenchannels

Probability

Probability

nuclei in a superposition of states

Fusion barrier distribution

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

Wei et al., Phys. Rev. Lett. (1991)

Morton et al., Phys. Rev. Lett. (1994)

Concept:Review: Dasgupta et al., Annu. Rev. Nucl. Part. Sci 48 (1998) 401

Rowley et al., Phys. Lett. B254 (1991) 25

3-

0+

2+

4+

6+

8+

10+

12+

0+

Z1Z2 = 496

-200

0

200

400

600

90 95 100 105 110 115

Ec.m. (MeV)

d2 (E

s )/d

E2

ANU

1 ph in each nucleus

58Ni + 60Ni : Z1Z2 = 784Fusion barrier distribution

2+

2+

0+

0+

-200

0

200

400

600

90 95 100 105 110 115

Ec.m. (MeV)

d2 (E

s )/d

E2

ANU

2 ph in each nucleus

Fusion barrier distribution

0+

2+ 2+

2+

58Ni + 60Ni : Z1Z2 = 784

-200

0

200

400

600

90 95 100 105 110 115

Ec.m. (MeV)

d2 (E

s )/d

E2

ANU

3 ph in each nucleus

Looks pretty good!

What’s the problem? – why should we treat decoherence explicitly?

Doesn’t it seem to be “invisible” inside the barrier?

Fusion barrier distribution

2+ 2+ 2+

2+

0+

2+ 2+

58Ni + 60Ni : Z1Z2 = 784

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

ScatteringBreakup, no capture- Irreversible ?

Breakup+capture- irreversible

Radioactive neutron-halo nucleus 6He (E < VB)

Hot target nucleus- irreversible

Slow neutrons

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)

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

Probing larger nuclear density overlap

E

large matter overlap small

J=0

J=100

J=70

r

Large Z1*Z2

J=0

J=100

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

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 : 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?

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

Measurements sensitive to decoherence?

Fusion barrier distributions for larger Z1*Z2

Lose sharp structures in barrier distributions – decoherence?

-100

0

100

200

300

400

500

600

130 135 140 145 150 155 160

EC.M. (MeV)

d2E

/dE

2 (

mb

MeV

-1)

DE = 1.5-2.0 MeV

1 ph S,1 ph Pb

2 ph S, 2ph Pb

DE = 2.0-3.0 MeV

32S+208Pb: Z1Z2=1312

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)

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

Mott scattering

0

100

200

300

400

500

600

700

35 37 39 41 43 45

Theta lab (deg)

Co

un

ts

Experimental data Theoretical curve

0

100

200

300

400

500

600

700

35 36 37 38 39 40 41 42 43 44 45

Theta lab (deg)

Cou

nts

Experimental Data Theoretical Curve

Below fusion barrier

Above fusion barrier

36S + 36S : Z1Z2 = 256

Need to account for flux loss to fusion

208Pb +208Pb : Z1Z2 = 6724

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?

Wrong Way Go Back

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)

Fusion barrier radius(absorption)