Decoherence in Nuclear

Fusion?

With:

D.J. Hinde, A. Diaz-Torres,

B. Bouriquet, C. Low, J.O. Newton

G. J. Milburn

M. Dasgupta

Department of Nuclear Physics

The Australian National University

Canberra, AUSTRALIA

Attractive nuclear interactions – represented by a short-range potential

Fusion – massive rearrangement of many body quantum system

due to

Potential energy

attractive nuclear

Repulsive electrostatic

r

Barrier against fusion

V

r

r

Described by single potential model

Inclusion of coherent superposition of distinct physical states of the separated nuclei

Multitude of excitations

complete dissipation of the K.E. into internal excitations

Coupled-channels modelBlack hole

(1) Is this description adequate?

Decoherence?

(2) Are effects of decoherence observed?

Probing decoherence – collisions with small separation

Fusion at energies well below the lowest barrier –

increasing overlap between barrier radius and inner turning point

V

r

Fusion at energies well above the barrier –

significant overlap at the barrier radius

But…need to know the nuclear potential!

nuclear potential

total potential

Fusion at energies well below the lowest barrier – tunnelling dominated

(slope determined by barrier width)

Fusion at energies around the barrier – coupling dominated

(barrier distribution)

In the framework of the current model (coupled channels):

Fusion at energies well above the barrier – potential dominated

(determined by nuclear potential shape)

characterized by diffuseness

characterized by potential diffuseness

Measurements of fusion of 16O with 208Pb and 204Pb

16O beam 208Pb target

Magic nuclei – theoretically easier

Fusion - evaporation

Fusion - fission

16O + 208Pb

16O + 204Pb

fission

nevaporation residue

Alpha decay of residues

Direct detection

Fusion products

Fusion yield = evaporation residues yield + fission yield

Beam – Energy needs to be very well defined

Target – thin targets to minimize energy integration, target impurity < ppm

Precision measurements require – highly efficient detection systems,

– sophisticated techniques

Separation and detection – identify fusion products amongst large background

– Large background of Coulomb scattered beam

particles (108 - 1015)

– fusion cross-section exp { k (E – B) }

Measuring fusion yields – the challenges

Fusion cross-sections – At best 10-9 of atomic cross-sections

Terminal voltage:

15 Million Volts

experimental equipment

Beam 0.1c

ions injected

Accelerator facility, Australian National University

Fission fragmentdetector 1

Fission fragmentdetector 2

Beam

Monitor detectors(out of plane)

Target

Fissionfragment 1

Fission fragment 2

Fission Measurements

• Measure fission fragment positions• Measure flight times• Deduce velocity vectors

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

-12 -8 -4 0 4 8 12 16 20E - B (MeV)

s (

mb)

16O+208Pb Fusion this work

16O+204Pb Fusion this work

16O+208Pb Fusion PRC60

s (m

b)

16O + 208Pb this work

16O + 208Pb Morton et al (1997)

16O + 204Pb this work

E. – B (MeV)One event per hour

Measured fusion cross-sections

Dasgupta et al, PRL 99 (2007) 192701

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

-12 -8 -4 0 4 8 12 16 20E - B (MeV)

s (

mb)

16O+208Pb Fusion this work

16O+204Pb Fusion this work

16O+208Pb Fusion PRC60

s (m

b)

16O + 208Pb this work

16O + 208Pb Morton et al (1997)

16O + 204Pb this work

E. – B (MeV)

Fusion cross-section: σ = R2 ħω / (2E) ln [ 1 + exp { 2π/ħω (E – B) } ]

E > B

π R2 [ E-B ] /E

E < B

exp { 2π/ħω (E – B) }

Logarithmic slope

d [ln(sE)]

dE

cross-sections over several decades to be plotted on a linear scale

comparison of tunnelling gradient independent of the weight of the lowest barrier

Below barrier shape deviates from parabolic d ln(sE) /dE increases

Parabolic barrier: sE exp[(2/ћ )(E – B)]

= 2ћd [ln(sE)]

dE Value independent of B

Hagino et al, PRC67(2003) 054603

d(ln

(Es)

/dE

E – B (MeV)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-12 -10 -8 -6 -4 -2 0 2 4 6 8

16O+208Pb 2004 (2 MeV)

16O+204Pb 2004 (2 MeV)

16O+208Pb 1997 (2 Mev)

16O + 208Pb this work

16O + 208Pb Morton et al (1997)

16O + 204Pb this work

Logarithmic slope of the measured fusion cross-sections

Standard Woods-Saxon potential with and without coupling

d [ln(sE)]/dE

0

500

1000

1500

-10 0 10 20 30 40

E – B (MeV)

s (mb)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-12 -10 -8 -6 -4 -2 0 2 4 6 8

16O+208Pb 2004 (2 MeV)

16O+204Pb 2004 (2 MeV)

16O+208Pb 1997 (2 Mev)

a=0.66 fm, no coupling, iwbc

a=0.66, coupled, IWBC

a = 0.66 fm, coupled

a = 0.66 fm no coupling

E - B

(E-shifted)

Diffuseness: Double folding model

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

10

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

s (

mb

)

0.0

1.0

2.0

3.0

-12 -8 -4 0 4 8

a = 0.66 fm

Factor of 1.5 of discrepancy in logarithmic derivative

> Factor of 20 discrepancy in measured and predicted cross-sections

E – B (MeV)

d [l

n(sE

)]/d

Es

(mb)

larger diffuseness of Woods-Saxon potential

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-12 -10 -8 -6 -4 -2 0 2 4 6 8

16O+208Pb 2004 (2 MeV)

16O+204Pb 2004 (2 MeV)

16O+208Pb 1997 (2 Mev)

a=1.18 fm, no coupling, iwbc

a=1.18, coupled, IWBC

0

500

1000

1500

-10 0 10 20 30 40

16O+208Pb Fusion

a=1.18, no coupling, IW BC

a=1.18 fm, coupled, IW BC

E – B (MeV)

s (mb)

d [ln(sE)]/dE

a = 1.18 fm, coupled

a = 1.18 fm no coupling

Data well-above barrier well represented

Below barrier slope not explained

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-12 -10 -8 -6 -4 -2 0 2 4 6 8

16O+208Pb 2004 (2 MeV)

16O+204Pb 2004 (2 MeV)

16O+208Pb 1997 (2 Mev)

a=1.65 fm, no coupling, iwbc

0

500

1000

1500

-10 0 10 20 30 40

16O+208Pb Fusion

a=1.65, no coupling

E – B (MeV)

s (mb)

a = 1.65 fm

d [ln(sE)]/dE

Below barrier slope reproduced

Data well-above barrier not reproduced

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

10

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

s (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. – 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

0

500

1000

1500

-10 0 10 20 30 40

E - B (MeV)

s(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. – B (MeV)

s(mb)

Dasgupta et al, PRL 99 (2007) 192701

0

50

100

150

5 10 15 20

Inner turning point for a below

barrier E appears at same

separation distance as the top of

the high l –barrier

Fusion well-below and well-above the barrier

Two parts of fusion excitation function probe the same separation

For a given above barrier E –

cross-section determined by the

limiting l → determined by high-l barrier, R

Rl at smaller separations than R0

Low l

High l

r (fm)

V (

MeV

)

r

(True independent of the particular form of the nuclear potential)

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

Any physical mechanism invoked to explain below barrier cross-sections

– should also reproduce above barrier results

Is decoherence the answer to our woes?

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

Will decoherence help?

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

10

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

s (m

b)

E – B (MeV)

expectation

Suppression of tunnelling – system dependent

64Ni + 64Ni

s (m

b)

Ni + Ni – charge product is larger – barrier at smaller

separation than O +Pb – increased decoherence?

16O + Pb

Jiang et al, PRL 93 (2004) 012701

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?

V

r

Deviations observed at E ~ 10% below B

Astrophysical interest

E << B

Reflected flux complementary to tunnelling

Deep inelastic events (events with large energy loss) even at deep-sub-barrier energies

Experiments done and more planned

Log

(pro

babi

lity)

Measured energy (MeV)50 100

Giant resonances

elastic

Summary and outlook

Cross-sections in tunnelling regime fall much faster than

predicted (>factor of 20 disagreement in cross-sections)

Measurements of fusion cross-sections for well-below to well-above

barrier for 16O + 204,208Pb

Need to go beyond this model – consistent description with

decoherence?

Commonly used coherent coupled channels model fails to provide a

consistent description of fusion

Modelling an isolated system with couplings having a strong radial

dependence - interesting area for new developments