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Nuclear break-up of exotic nuclei History of the towing mode in stable nucl the 40 Ar+ 58 Ni @ 40 MeV/A case I The TDSE calculation II The case of the 11 Be break-up V The extension to borromean nuclei Conclusions - Perspectives J a s s
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Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Dec 18, 2015

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Page 1: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Nuclear break-up of exotic nuclei

I History of the towing mode in stable nucleithe 40Ar+58Ni @ 40 MeV/A case

II The TDSE calculationIII The case of the 11Be break-up IV The extension to borromean nucleiV Conclusions - Perspectives

Jass

Page 2: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Inelastic Channel-projectile=ejectileInelastic Channel-projectile=ejectile

A

AA

AA

A+1

A A A A

InelasticInelasticScatteringScattering

GR and multiphononsGR and multiphonons

KnockKnockOutOut

Pick-upPick-upBreak-upBreak-up

New New mechanismmechanism??

TargetTarget

ProjectileProjectile

1 emitted particle1 or several emitted particle(s)Jass

Page 3: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Angular distribution of nucleon emitted in 58Ni(40Ar, 40Ar + n or p)

p or n

58Ni

40Ar

40Ar

lab

Jass

Feeding of the first hole states of the daughter

nucleus

Page 4: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

t

0 r

0 r

F

0 r

0 r

0 r

F

Jass

Action

Page 5: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

What happens when a force acts on a mass for a given period of time ?

F = m.x..

tc = d

vp

d (ro . A1/3)= 4 fm

vp= 10+23 fm.s-1

tc = 4. 10-23 s

{m F

x

x = . tc + xo

. Fm

.

F = 15 MeV.fm-1 xo = 0.

x =. 15 . 9 . 10+46

900.4. 10-23 = 6.10+22 fm.s-1

V

0 r

40

3 fm

E ~ 40 MeV/A

Right order of magnitude!Jass

Action

Page 6: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Nuclear break-up of exotic nuclei

I History of the towing mode in stable nuclei the 40Ar+58Ni @ 40 MeV/A case

II The TDSE calculationIII The case of the 11Be break-up IV The extension to borromean nucleiV Conclusions - Perspectives

Jass

Page 7: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

H = . diagonalization eigen states, eigen values

Evolution of a one-particle wave function via the

resolution of time dependent Schrödinger

Evolution of a one-particle wave function via the

resolution of time dependent Schrödinger

H = p2

2.m + U0

1+e(r-r0)

a0

∂2

∂x2 φ(xn) ≈ φ(xn+1) + φ(xn-1) - 2. φ(xn)

Static solutions ^

Jass

J.A. S.D. LacroixPh. Chomaz

Time dependent solutions

ih ddt

= H (t+dt) = e- i Hdth ( t )

e- iHt

h ≈e-ihp

2

2mt2.e-i

hVt.e-i

hp

2

2mt2

H = p2

2.m + U 0

target

1+e(r -r0(t))

a0

+ U 0proj

1+e(r-r0(t))

a0

e- ih

p2

2m t2 .( , )=p t e-i

hp2

2mt2.( , )p t

e- ih

V t .( , )=x t e-ih V t.( , )x t

and

^ FFT of (x,t)

. . .

^ projtarget

Split operator

D.Lacroix et al. Nucl. Phys. A658 (1999) p273

Exact up to 2sd order

Page 8: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

The calculation includes : • TDSE for a wave function in a moving potential• diffraction (refraction!) through the nuclear potential • single particle excitations to unbound states • n-core excitations (!!)• « shaking  » of the core (Coulomb classical trajectory)

The calculation does not include :• spin-orbit, pairing

No structure info• core or target excitations (not excluded either)• nucleon-nucleon dissipation• quantum relative motion• energy conservation

Resolution of time dependent Schrödinger equation on a mesh

non perturbative calculation

proj

target

proj

target

Jass

Page 9: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Evolution of a wave function via the

resolution of time dependent Schrödinger

Evolution of a wave function via the

resolution of time dependent Schrödinger

Initial wave function

Towing ModeTowing Mode

TargetWS

Projectile WSEinc = 44 MeV/A

t = 0t = 130 fm/c

Jass

Page 10: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Initial Density Probabilityin the target potentialat rest in the lab frame.

Density probablility after the projectile has passed

Fourier transform of theformer density probability.

y

x

px

py

Jass

0,00

0,05

0,10

0,15

0 60 120 180

Neutrons

lab

Same density probability after subtraction of the bound

eigen states

y

x

Angular distribution of the emitted particle

Evolution

FFT

d/d ()

Page 11: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

0,00

0,05

0,10

0,15

0 60 120 180

Neutrons

lab

58Ni(40Ar,40Ar+p or n)

2p calculation, b from 10 to 12 fmPlus flat background

0,00

0,05

0,10

0,15

0 60 120 180

Neutrons

lab

b=10 fm

40Ar

58Ni

Jass

~50°

px

py

~50°

2s

Page 12: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Nuclear break-up of exotic nuclei

I History of the towing mode in stable nuclei the 40Ar+58Ni @ 40 MeV/A case

II The TDSE calculationIII The case of the 11Be break-up IV The extension to borromean nucleiV Conclusions - Perspectives

Jass

Page 13: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

11Be break-up calculationsWS potential to bound the 2s by 0.5 MeV

Need to use a Coulomb trajectory :

Weakly bound neutron Large Coulomb break up

Runge Kutta r(t+dt) = r(t-dt) + 2.dt.p(t)/mp(t) = p(t-2dt) + 2.dt.F(t-dt)/m

13 fm 2000

8015

1

Density of 2s

Imaginary time evolution extract a stable eigen state (M.Fallot...) for the cartesian mesh

Interpolation ...

Does not change when using N.Vinh Mau potential

Jass

Page 14: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Neutron angular distributionsAu,Ti,Be (11Be, 10Be + n) @ 41 Mev/A

Data from : R.Anne et al.,Nucl.Phys. A575 (1994) 125

M.Fallot, J.A.Scarpaci, D.Lacroix, Ph. Chomaz et J.Margueron, Nuclear Physics A700 (2002) 70

Large b (Coulomb break-up) = forward peaked emitted neutronSmall b (nuclear break-up) = responsible for neutrons emitted at large angle

neutron neutron neutronlab lab lab

The nuclear break-up is fully reproduced by the interaction of the particlewith the mean field of the target - no need of n-n interaction….

Jass

Page 15: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Jass

11Be a halo nucleus

Neutron bound by 0.504 MeV

GS (J=1/2+):

|GS>= |2s1/2 0+> + |1d5/2 2+>

10Be

n

2 (S2s) et 2 (S1d):spectroscopic factors

10Be 2+ state of 2=0.74Ref: Auton et al. NP A

322(1970) 305

E=3.37 MeV

Page 16: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

GANIL

SPEG

• Primary beam of 13C @ 75 A.MeV• Secondary beam of 80000 11Be/s @ 41 A.MeV.

SISSI

Jass

Page 17: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Experimental set-up

48Ti11Be

3 m

n-detectors

10Be

SPEG

Château de cristal

10Be

48Ti

TDSE Calculation

Jass

11Be 10Be + n + @ 41 MeV/A

Experimental set-up & results

10 -3

10 -2

10 -1

100

101

0 10 20 30 40 50 60 70

Ti

/ ( / )d d barn sr

lab

Our data

1994 data from R.Anne et al., Nucl. Phys. A575 (1994) 125.

TDSE calculationsM.Fallot et al., Nucl. Phys. A 700 (2001) 70-82.

Neutron angular spectra

Page 18: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

S1d= 0,50 ± 0,20 S1p= 3.9

incoincidence

V.Lima et al., Bormio 2004V.Lima, Ph.D. Paris XI, oct 2004V.Lima et al., in preparation

4*1p

0.5*1d

S2s = 0,47± 0,04

no-

Neutron energy spectra

TDSE calc.2s

11Be 10Be + n + @ 41 MeV/A

10Be

48Ti

48Ti11Be

3 m

n-detectors

10Be

SPEG

Château de cristal

TDSE Calculation

Jass

Experimental set-up & results

Page 19: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Break-up reactions (11Be,10Be)@ 520 MeV/u Palit et al., PR. C 68, 034318 (2003)

Large diversity of S2s

The G.S. of 11Be

Transfer reaction p(11Be,10Be)d: GANIL

Fortier et al., PL B 461(1999)22-27

|GS> ~ |2s1/2 0+> + |1d5/2 2+> S2s ≈ 85-36% S1d ≈ ?%

Break-up reactions (11Be,10Be)

@ 60 MeV/u and eikonal modelsT. Aumann et al.,

P.R.L.84 (2000) 35-38

Our work

B.Zwieglinski et al.Nucl.Phys.A315, 124 (1979)

N.K.Timofeyuk et al.P.R.C59, 1545 (1999)

DWBAexcitation and break-up

nucl.

elect.

Page 20: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Nuclear break-up of exotic nuclei

I History of the towing mode in stable nuclei the 40Ar+58Ni @ 40 MeV/A case

II The TDSE calculationIII The case of the 11Be break-up IV The extension to borromean nucleiV Conclusions - Perspectives

Jass

Page 21: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Study of neutron correlationswith nuclear break-up

6He is an archetype of a Borromean nucleus ; high intensities most suitable nucleus to investigate new experimental

approach and develop new theoretical tools

Cigar configuration

Zhukov et al., Phys. Rep. 231 (1993) 151

Di-neutron configuration

Jass

three-body descriptionexpansions on hyperspherical harmonics

coordinate space Faddeev approach

Page 22: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Some experiments on 6He…• Transfer reactions 4He( 6He,6He) 4He

dominated by di-neutron conf…Yu.Oganessian et al. (1999) : Dao T.Khoa and W.von Oertzen (2004)

• Radiative capture 6He(p,)x @ 40 MeV/A - no + t decay

large distance between the two neutrons… (cigar like)E.Sauvan et al. (2001)

• Coulomb break-up6He + C, Pb @ 30-60 MeV/A large distance between the two neutrons… (cigar like)

Invariant mass ≠ interferometry … depending on impact parameter cuts…

G.Normand et al. (2004) rn-n 7.7 fm, 9.4 fm

F.M.Marques et al. (2000) rn-n 5.9 fm@ 240 MeV/A 6,8He + Pb @ 700 MeV/A

L.V.Chulkov et al. (2005) QFS dominateslow lying 1- states 3-6 MeV core plus 2 or 4 neutrons

8He = small 6He + 2nNo consensus on the n-n configuration

Open to more experimentsJass

Page 23: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Neutron angular emission

Large impact parametersCoulomb break-up

cigar di-neutron

n

d/d

60°0°

Small differencesin relative angles

G.Normand, PhD thesis 2004F.M.Marques, PR C64, 2001

Measure neutrons at large anglesNeeds a theoretical development

Small impact parametersNuclear break-upcigar di-neutron

n

d/d

60°0°

di-neutron

cigar

extension of TDHF (TDDM)(M.Assie-D.Lacroix)Jass

Page 24: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Set-up

65°

Faraday cup

Neutron wall

Additionalneutron detectors

n

n

5 mg/cm2

Pb target

4He

Si det.

High neutron angular coverage up to 90° : neutron wall + 20 additional detectorsSi detector for 4He covering from 5° to 15°

6He20 MeV/u

Page 25: Nuclear break-up of exotic nuclei I History of the towing mode in stable nuclei the 40 Ar+ 58 Ni @ 40 MeV/A case IIThe TDSE calculation IIIThe case of.

Nuclear break-up of exotic nuclei

I History of the towing mode in stable nuclei the 40Ar+58Ni @ 40 MeV/A case

II The TDSE calculationIII The case of the 11Be break-up IV The extension to borromean nuclei

V Conclusions - Perspectives

• Reaction mechanism plays an important role in the break-uptowing Mode, a spectroscopic toolneed of good theoretical description to infer spectroscopic factors

• Development required for two-particle wave function evolutionextension of TDHF - Marlène Assié, Denis Lacroix

• Possible application to cluster studies!observation of emission in 40Ca break-up

Jass