nuclear break-up of exotic nuclei i history of the towing mode in stable nuclei the 40 ar+ 58 ni @...
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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
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
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
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
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
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
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
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.
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
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
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
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