nuclear break-up of exotic nuclei

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

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

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

t

0 r

0 r

F

0 r

0 r

0 r

F

Jass

Action

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


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


Jass

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


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

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

Evolution of a wave function via the


Evolution of a wave function via the


Initial wave function

Towing ModeTowing Mode

TargetWS

Projectile WSEinc = 44 MeV/A

t = 0t = 130 fm/c

Jass

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 ()

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




Jass

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

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

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

GANIL

SPEG

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

SISSI

Jass

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

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

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.




Jass

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

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

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

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



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

nuclear break-up of exotic nuclei

Documents