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

D.J. HindeDepartment of Nuclear Physics

Research School of Physics and EngineeringThe Australian National University

With M. Dasgupta, M. EversDepartment of Nuclear Physics

Research School of Physics and EngineeringThe Australian National University

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

Introduction

r

r

V

Geiger, Marsden, Rutherford (1909) : +197Au Discovered atomic nucleus Low energy – Coulomb field only Elastic (Rutherford) Scattering

E. Schrödinger

The first experiment studying nuclear collisions

Higher energy, Z1Z2 – inelastic scattering (excited states) Describe pure elastic scattering: optical model

Schrödinger eqn. + phenomenological imaginary potential Detector makes measurement

K.E.

dd

r

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

Characterizing a “hot” nucleus

Fermi Gas Permutations of nucleon excitations Level density exp(aEx)1/2

Low energy collective states Surface vibrational states Rotational states Volume vibrational states

Excita

tion E

nerg

y

Collective states

Ground state

Including excitations of colliding nuclei

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.

Excita

tion E

nerg

y

Collective states

Ground state

Coupled-channels equation: key variable separation (r)

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

+ VJ(r) +n – E φn(r) +h2 d2

2 dr2 ][ Vnm (r) φm(r) = 0m=n/

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


+ VJ(r) +n – E φn(r) +h2 d2

2 dr2 ][ Vnm (r) φm(r) = 0m=n/

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

r

Coherent superposition

Below-barrier


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

+ VJ(r) +n – E φn(r) +h2 d2

2 dr2 ][ Vnm (r) φm(r) = 0m=n/

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


+ VJ(r) +n – E φn(r) +h2 d2

2 dr2 ][ Vnm (r) φm(r) = 0m=n/

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

r


Above-barrier?

? = Excited “Molecular” (compound nucleus) states

Irreversible nuclear collision (fusion)

Neutron interaction with nucleus Bohr’s compound nucleus model Energy spread amongst nucleons Capture – “compound nucleus” Thermalization – Heat Bath

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

Nature 1936 N. Bohr

Coupled-channels model

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!

+ VJ(r) +n – E φn(r) +h2 d2

2 dr2 ][ Vnm (r) φm(r) = 0m=n/

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

Barrier-passing picture – inside barrier(i) imaginary potential(ii) incoming wave boundary

condition Lost probability fusion

K.E. lost to complex excitations

Colliding nuclei lose individual identities – merge together

Fusion - completely irreversible

Coupled channels equations

Fusion – physical picture: Fusion – as modelled:

Nuclei in superposition of states (Include limited number of low lying collective

states, Purely quantal – reversible dynamics)

Irreversible Coherent superposition - reversible

r

Above-barrier

Elastic scattering

Superposition of states

Channel couplings: scattering

Nuclei in ground-states

208Pb 3-

Inelastic scattering

Nucleon transfer reactions

TKEL (MeV)

Single-barrier

VB0

E

1

VB2

EVB1

VB3

Approximation:

3 eigen-channels

3 eigen-barriers

Probability

Probability

Superposition of 3 states

Channel couplings: barrier distribution

Nuclei in ground-states

Reflected flux - scattering

Transmitted flux - fusion

X. Wei et al., Phys. Rev. Lett. (1991) C.R. Morton et al., Phys. Rev. Lett. (1994)

3-

0+2+4+6+8+

10+

12+

0+

Z1Z2 = 496

Superposition, barrier distribution essential to describe near-barrier fusion!

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

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

Near barrier energies - coherence and dissipation

• Quantum: Coherent superposition - scattering, fusion barrier distribution

• Dissipative (irreversible energy dissipation)

- deep inelastic collisions

- compound nucleus formation

Classical or Semiclassical

treatment

GRAZING

Coupled channels formalism

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

r

Irreversible dissipation

Coherent superposition – reversible couplings

r

Where is the transition?It is gradual or sharp?

How does it affect fusion?

Smooth transition from superposition to dissipation

Low Z1Z2

High Z1Z2

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

Mapping energy to radial separation

Radial dependence of probabilities

r

r

V

Sub-barrier energy dissipation – nucleon transfer

16O + 208Pb

Nucleon cluster transfer (2p,

208Pb 3-

n

p

2p

TKEL (MeV)

32S + 208Pb E/VB = 0.96


g.s.


Z=2: E* ~ 5-25 MeV, peak at 12 MeV

2p and -transfer (cluster transfer)

32S + 208Pb

DIC Energy loss: (TKEL or E*)

40Ca + 208Pb E/VB = 1.05

S. Silzner et al., PRC 71(2005)044610

Eloss ~ 40 MeV

10-6

10-5

10-4

10-3

10-2

10-1

100

101

103

102

55 65 75 85 95 105

EC.M. (MeV)

(m

b)

Transfer or Deep-Inelastic? Doesn’t matter what we call it Energy irreversibly lost

VB

19F + 232Th fission > 6 MeV (fission barrier)

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”

103

19F D.J. Hinde unpublished

E* in heavy nucleus – thermalized - fission

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)

• Quantum decoherence – “dynamical dislocalization of Q.M.

superpositions”

(H.D. Zeh arXiv:quant-ph/0512078 v2) coherence shared with (lost in) environment

Idealized isolated system

Superposition of basis states

Described by coherent Q.M.Irreversible outcome (classical)

System “entangled” with environmentLoss of coherence in smaller

system

system

Complex environment

Sub-system

Larger system

Sub-system entangled with rest of system

Example: Electron entanglement with a surface

Interference fringes

Heig

ht

ab

ove s

urf

ace

Splitter

Screen

Semiconductor

surface

Double-slit type experiment with single electrons

Electron passing above disturbs electrons in semiconductor

“which way” information destroys spatial coherence

Semi-conductor surface

RefocusSource

Steep radial dependence Probability at RB ~ 0.1

Inside RB larger Nuclear interaction

Radial dependence of Z=2 probability

10-1

100

10-2

10-3

r

32S + 208Pb

RB

Pro

babili

ty

Nuclei isolated – not external environment but internal

Nuclei overlap, interact strongly – nucleonic d.o.f. opened up

• Effectively irreversible Eloss from CC

space• Need to model dynamics outside CC space• Within Q.M. framework

P-space

Q-space

CC space

Nucleonic d.o.f.

relative motion + few channels

(collective, transfer?)

CC space

Scattering to discrete

states

– only need CC + Imaginary

potFeschbach formalism

Nucleonic d.o.f.

DIC – energy dissipation

in scattered flux

Probing decoherence through fusion

E

large matter overlap small

J=0

J=70

r

Large Z1*Z2

J=0

J=100


Compound nucleus

Decoherence

Reduction in fusion at above barrier energies

46 fusion excitation functions

Newton et al., PRC 70 (2004) 024605

increased reduction of fusion with Z1Z2

Fusion suppression above-barrier

Reported deep inelastic probability

close to VB

Wolfs, PRC 36 (1987) 1379Wolfs et al, NP 196 (1987) 113Keller et al, PRC36 (1987) 1364

Abov-b

arr

ier

suppre

ssio

n

Fusion below and above the barrier inconsistent

– need to go beyond current models

– need to incorporate transition to irreversibility

explicitly

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

10

-12 -10 -8 -6 -4 -2 0E - B (MeV)

(mb)

16O+208Pb

16O+204Pb

a = 0.66 fm

a = 1.65 fm

a = 1.18 fm

101

100

10-1

10-2

10-3

10-4

10-5

10-6

16O+208Pb

16O+204Pb

16O + 208Pb

16O + 204Pb

a = 0.66 fm

a = 1.18 fm

a = 1.65 fm

Ec.m. – VB (MeV)

0

500

1000

1500

-10 0 10 20 30 40

E - B (MeV)

(m

b)

a = 1.18 fm

a = 0.66 fm

a = 1.65 fm

a = 0.66 fm

a = 1.18 fm

a = 1.65 fm

Ec.m. – VB (MeV)

(mb)

M. Dasgupta et al., PRL 99 (2007) 192701Ni+Ni: C.L. Jiang et al., PRL 93 (2004) 012701

Discussion points

• Extend coupled-channels model (or CRC)

• Nucleonic d.o.f. of separate nuclei vs. “molecular” nucleonic d.o.f. ?

• Links with decoherence in other quantum systems (here we are!)

- 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 ?

• Feschbach model – P+Q vs. degrees of freedom

• Decoherence without dissipation ? (Mott scattering ?)

Vtot

r (fm)

l =0

Woods-Saxon a = 0.66 fm

a = 1.18 fm

Qfus

Vtot

Elongation (fm)


adiabaticsudden

Vtot

r (fm)

l =0

l =60

Woods-Saxon

a = 0.66 fm

a = 1.18 fm

Vtot

Qfus

Vtot

Elongation (fm)


adiabaticsudden

Wolfs, PRC 36 (1987) 1379

Kinetic energy losses > 20 MeV

Deep inelastic reactions at E < VB

VB

Wolfs et al., PLB 196 (1987) 113

Keller et al., PRC 36 (1987) 1364

Near-barrier DIC: 58Ni+112Sn

Recent density matrix model with coherence and

decoherence A. Diaz-Torres et al., Phys. Rev. C78(2008)064604

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

GDRNucleonic d.o.f.

(ZP)(ZT)Nucleonic d.o.f.

(ZP-2)(ZT+2)

CC space

transfe

r

Doorway

states

(ZP+ZT)

Molecular C.N. d.o.f.

Example: observation of collisional decoherence

Collision with a gas molecule localizes C70 destroys spatial

coherence

Independent point

source of

C70

diffraction

interference pattern measured

Single collision sufficient to destroy interference

Hornberger et al, PRL 90 (2003) 160401

Fringe visibility decreases with increasing pressure

System - environment interaction (measurement) - decoherence

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.80.2 0.4 0.6 0.80.2 0.4 0.6 0.80.2 0.4 0.6 0.8

E=143.2 MeV E=147.6 MeV E=152.0 MeV E=159.9 MeV E=168.2 MeV

[deg

] c

.m.

coun

ts

102

103

104

1

10

x 0.20 x 0.05 x 0.10

MR

x 0.15

50

100

150

180

45

135

90

0

0

32S + 232Th MAD vs. E/VB (Timescale ~10-20 s)E/VB =

0.93E/VB = 0.96

E/VB = 0.98

E/VB = 1.03

E/VB = 1.09

D.J. Hinde et al., PRL 101 (2008) 092702R. 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

(Shown effect of entrance channel dominant over EX)D.J. Hinde et al., PRL 100 (2008) 202701

Mass-Angle Distributions for quasi-fission

235 MeV 48Ti

48Ti + 196Pt 48Ti + 186W 48Ti + 154Sm

MRMR MR

C.M.

Elastic, quasi-elastic and deep inelastic events

Detector acceptance

0

45

90

135

180

0 0.5 1MR

(d

eg.)

(deg

.)

0

0.5

1

0 20 40 60 80Time

MR

04590

135180

0 20 40 60 80Time

(d

eg.)

MAD – mass-equilibration and rotation (GSI 1980’s)

Miminal mass-angle correlationStrong mass-angle correlation

160o

20o Scission

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

102

10

10.4 0.2 0.4 0.20.0 0.2 0.4 0.0 0.2 0.4

b)a)

0.2

0.4

0.0

0.4

0.2

v [

cm/n

s]

v - v [cm/ns]|| c.m.

232Th – fission after peripheral collision – Eloss – transfer/DIC

Energy dissipated → EX target → deformation energy → fissionE/VB = 0.96

E/VB = 1.03

16O D.J. Hinde et al., PRC 53 (1996) 1290

E* in heavy fragment - thermalized

32S D.J. Hinde et al., PRL 101 (2008) 092702

32S + 232Th fission: Velocity of fissioning nucleus w.r.t. C.M. velocity

d.j. hinde department of nuclear physics research school of physics and engineering

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