Transfer reactions:
From Bound to Unbound states
I- Single-particle motion in nuclei
Spectroscopic factors ,Sum-rules
II Experimental quest : One nucleon
Transfer and e,e’ p Knock out .
III Beyond bound states :transfer to
resonances in the continuum
Single particle states far of Stability
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PISA,February 2005Sydney Galès
Nucleon-Nucleus mean field
°Mean field concept similar for
bound (shell model ) and scattering
(optical model) states.
°°In real nuclei the mean field is
non-local. V(r,r ’) velocity dependence
Fluctuations of V give rise to collective
modes . Coupling of s-p motion to
Collective modes leads to V(r,r’,E).
°°°Local equivalent
V(r,E)=VHF (r,E)+ DV(r,E)
Dynamical
content of IPM
Potential depth
A independent
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Long Range Correlations
Coupling to (1p-1h) ,…, (np-nh)
na
1
IPM
Ef
E
na
1
IPM+Corr
Ef
E
Depletion of the fermi sea 15%
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PISA,February 2005Sydney Galès
Proton Stripping reaction
Single-particle states 208Pb+1p
Above 2.5 MeV strong fragmentation of
Single –particle strengths !!!
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Spectroscopic Factors & sum-rule
Pick-up
S-lj(A,A-1)= /<Ff(A-1)/alj /F0(A)>/2
Stripping
S+lj(A,A+1)= /<Ff(A+1)/a+lj /F0(A)>/2
Sum-Rule
Sum of Slj on all final sates f with lj quantum numbers give
Sf Slj = < F0(A)/ a+a/ F0(A)>= nlj
number of nucleons lj in the ground state
Two obvious problems in
deducing absolute values for
this sum-rule
Sum of all final fragments limited in Energy
short range correlations (up to high Ex)
Accuracy of reaction models
Cross-sections dependence on form factors ,
Optical parameters
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PISA,February 2005Sydney Galès
Reaction model for one-nucleon transfer
• DWBA A+a
• TBA=
B+b b=a+/-1n one-step
draA drbB C b-* (kb,rbB) F(raA ,r bB) C a+ (ka,raA)
OM elas channels
• EFR-DWBA
ds/dwEXP (q) = C2Slj. K. [ TBA]2= C2S ds/dw EFR-DW (q)
. F contains
1) the Vnb interaction between the ejectile b and the transferred
nucleon n (from n-n or n-b phase shifts at low energies)
Zero Range Vnb= Do d(rbn)dl0
2) the form factor flj(r) . Calculated in WS potential ,to reproduce
correct binding (SE, energy dependence) . ds/dwDW (q) displays
strong dependence on the radius
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PISA,February 2005Sydney Galès
Bound states and polarized beams
in transfer
State of the art
:OSAKA 1993
2p3/2
2p1/2
P=80%
30KeV
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PISA,February 2005Sydney Galès
Examples :
Angular distributions and asymmetries
2p3/2 ,2p1/2 in 49Ca
L=1
J=3/2
L=1
J=1/2
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PISA,February 2005Sydney Galès
From stripping and pick-up :occupation
numbers and shell closure
Excellent closure
of f7/2
>95%
Open sd shell
15-25%
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(e,e’,p)
State of the
art
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LRC and SRC
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Persistence of s-p motion at high excitation energy ?
First evidence of deeply-bound hole states in heavy
nuclei
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PISA,February 2005Sydney Galès
Spin of deep-hole states
1g9/2neutron-hole in 120Sn
GR like structure (1-2MeV)
Broad peak
1MeV
IUCF 1980
9/2+
7/2
+
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PISA,February 2005Sydney Galès
Selectivity for large L transfer (5-8)
Direct
observation of
Spin-orbit
partners
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Transfer to Unbound states
Standard DWBA
• Unbound state Form Factor
• Gamov function pole of the
Green s-p wave function
• gRlj(r,kr) =( mGlj /h2kr) eixlj Olj
Solution of Schrodinger equation
for the complex energy
ERes= ER –i G/2
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PISA,February 2005Sydney Galès
Damping Mechanism
G =2P<V>2r =2<W>
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Experimental observation of the
damping steps (1p-1h) to (np-nh)
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PISA,February 2005Sydney Galès
Single-particle motion far of stability
John Elbfas, 1535,
Storkyrkan, Stockholm
1p splitting , 8He,12-14Be,20C,22O
Mainly Pol (p,d) and (d,p)
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PISA,February 2005Sydney Galès
Structure of 11Be g.s. through (p,d) reaction
Beg.s. =S1/2(0+ )10Be0+2s +S1/2(2+ )10Be2+1d +.....
H(11Be,10Be)2H
E = 35 A.MeV
11
4
(ds/dW)exp=S(ds/dW)calc
S(2+)
= 0.2
S(2+) + S(0+)
10Be
(coinc with 2H)
0.4o  qlab  1.2o
S. Fortier et al. PLB 461 (1999) 22
J.S. Winfield et al. NPA 683 (2001) 48
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PISA,February 2005Sydney Galès
Structure of 10Li G. S via
transfer reactions
105
11Be
/s
S.Pita
PhD thesis
Orsay,2000
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PISA,February 2005Sydney Galès
Structural changes with neutron
excess
Diffuse Nuclear
Surface
Leads to vanishing
Spin-orbit splitting
New « magic
numbers »
Test cases
N=20, 1d splitting
28,30Ne,32Mg,34Si
Z=20 N=28-40
46Ar
Z=28 N=28-40,1f
56Ni,68Ni
N=50-82,1g,2d
116-134Sn
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PISA,February 2005Sydney Galès
> 1013 fiss./s
Low energy RNB
Production Cave
C converter+UCx target
CIME Cyclotron
RNB (fission-fragments)
E < 6-7 MeV/u,132Sn 109pps
SC - LINAC
E = 14.5 AMeV
HI A/Q=3
E = 40 MeV - 2H
“SILHI-deuteron” 5mA
ECRIS-HI 1mA
RFQ - 0.75A MeV
Regions of the Chart of Nuclei Accesible
with SPIRAL 2 beams
Primary beams:
 deuterons
 heavy ions
6. SHE
4. N=Z Isol+In-flight
5. Transfermiums
In-flight
2. Fusion reaction
with n-rich beams
1. Fission products (with converter)
3. Fission products (without converter)
8. Deep Inelastic Reactions with RNB
7. High Intensity Light RIB
NuPPEC Roadmap for the European Strategic Forum for Research
Infrastructures (March 2005)
NuPECC recommends the construction of 2 ‘next generation’ RIB
infrastructures in Europe, i.e. one ISOL and one in-flight facility. The
in-flight machine would arise from a major upgrade of the current GSI
facility.
Among the intermediate steps on the road to “the EU Isol facility”
EURISOL (2014) ,SPIRALII has a clear EU dimension in terms of
size,investment(130M€) and site (GANIL).
Latest News
To build strong collaboations within European low energy communities
for both stable and RIB,,GANIL and Legnaro are in the way to
establish a new European laboratory ,open to all french and italian
communities and later to others. Loi are presently submitted to a
steering committee and a workshop is being prepared (April 8&9
,Legnaro ) where the scientifc goals of this new initiative will be
discussed
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PISA,February 2005Sydney Galès
**Conclusions
•
•
•
•
•
Absolute spectroscopic factors for strong s-p bound valence states
with are within reach ,combining careful analysis from nucleon transfer
and electron knock-out with an accuracy of (10% at best)
But s-p have partial occupation ,rest of the strength at very high(
Ex>100 MeV)
outside shell model space
SM describes only 70% of nucleons due to SRC (15%) and LRC (15%)
Highly fragmented sp strengths, in particular for unbound resonances
embedded in the continuum suffer greatly from the use of inadequate
« standard » parameters (E dependence of form factors , continuum) .
Form factors from HF-RPA or QPM models may improve the accuracy.
For exotic nuclei coupling to continuum occurs even more rapidly as
a function of Ex . Careful analysis of deduced SF needed to
establish for exemple
SPIN-ORBIT SPLITTING
Nuclear Knock-out seems promising, in particular for “exotic”
nuclei,careful evaluation of the reaction model parameters and
various kinematics ,and target conditions are certainly needed to
assess the potential of this approach.
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END
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Neutron rich C & O isotopes
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PISA,February 2005Sydney Galès
Isopin dependence of
spin-orbit interaction
The Spin-orbit interaction
is proportional to the
nuclear distribution in a
stable nucleus. In an
unstable nucleus, the
differential of the proton
and the neutron
distribution have peaks at
different distances,
therefore isospin
dependence of the spinorbit interaction becomes
important
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PISA,February 2005Sydney Galès
Spin-Orbit Splitting
eso=aso l.s. dr/dr=1/2(2L+1) x
x=<1/V.dV/dr>=g(A) .f(n)
•
• Nucleus
• 12C
• 16O
• 40Ca
•
48Ca
90Zr
protons
nl
eso
1p 8.24
1p 6.88
1d 6.7
1f
6.3
1h
2f
5.8
1.7
140Ce
208Pb
neutrons
nl
eso
1p
8.5
1p
6.7
1d
6.7
2p
2.1
1f
8.9
2p
1.9
1g
7.9
2p 1.1
2d 2.4
1h 6.5
2d 1.7
1i
6.4
2f 1.8
G.Mairle
Phys.lett B
1993
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Neutron Transfer on 132Sn
EXOGAM
g
p
132Sn
15A.MeV
D
Determine neutron-captures at stellar temperatures
Spectroscopic factors
CN
Sn=2.7 MeV
133Sn
9/2-1/2
3/27/2-
132Sn
DC
Statistical models not valid at magic shells
- Direct capture component
- Compound nucleus component
133Sn
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PISA,February 2005Sydney Galès
4p particle + 20% g (EXOGAM)
W N CATFORD
DE:500 keV
TIARA
DE:50 keV
68+nNi
E* ; Lp ; S
Bound States
University of Surrey
TIARA
is designed to be used
with EXOGAM and VAMOS at GANILPISA,February 2005Sydney Galès
DARESBURY
31
Absolute Spectroscopic factors from Nuclear
knock-out reactions
Brown,Hansen,Sherill,Tostevin
•
•
One nucleon removal partial cross-sections to final identified (nlj) bound states have
been measured for about 25 nuclei in sd shell and on 12C and 16O
Theoretical s-p removal cross-sections sth(nlj) has been calculated using shell model
predictions for the s-f and eikonal reaction theory
R= sexp/s th
•
sth(nlj)= Sj Snlj ssp(Bn,lj)

ssp(Bn,lj) calculated from a define set of parameters
S-Matrix from free nn np cross-sections, d interaction or Gaussian range functions
n-core w-f calculated with empirical W-S (r,a) standard set
Outcome
R=1 for l=0 and 2 transitions for 25-27Si, 10,11 Be, 14-18C
R=0.5-0.6 for n and p hole in12C and 16O g.s .Strong quenching like in e,e’ p !!
How we understand that ? How it compares to p,2p knock out ?
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PISA,February 2005Sydney Galès
Persistence of s-p motion
at high excitation energy ?
Inclusive single -particle spectra
Strength functions for resonance in the
continuum
Exclusive experiments and decay properties.
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PISA,February 2005Sydney Galès
S-P response function: Exp versus QPM
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PISA,February 2005Sydney Galès
Single Particle states - 1970
Early experimental evidences
Light-Nuclei :Well separated shells
Broad inner 1s shell
Medium and heavy nuclei
Rapidly overlapping 35
shells
PISA,February 2005Sydney Galès
Energy dependence of the damping
width for s-p response function
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Single –Particle strenghts from IAS
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Transfer to continuum and reaction
model Bonnacorso,Brink
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Decay of single-particle states
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Gamma-decay of overlapping sub
shells in 111Sn
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Damping of deep-hole in 208Pb
Experiment and HF+RPA Model
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Nuclear Models: Damping Mechanisms
Mass ,Energy Dependence of S(E),G
• A) HF+RPA N. Van Giai et al Pb
Bertsch, Broglia, Bortignon Sn, Pb self-consistent or effective coupling
B) Mean field + Dispersion Relation C. Mahaux et al
40Ca to 208Pb
Empirical –Optical potential W-S .All coupling included
C) Semi-classical description Brink & Bonnacorso, n-N optical model
D) Quasiparticle-Phonon Model
V.G.Soloviev,Ch.Stoyanov,A.I.Vdovin,V.Voronov et al From Zr to Pb
H= Hsp+Hpair+
Hmultipole+Hspin-multipole
WS
Monopole Multipole
spin-multipole
part-part part-hole
part-hole
Large basis s-p ,phonons (up to 25 MeV,l>5)
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PISA,February 2005Sydney Galès
Comparison of Hadronic and
electromagnetic processes
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PISA,February 2005Sydney Galès
Quenching of S-P strengths
Summary 1
A) For bound states close the Fermi sea
e,e’p observed a severe quenching
(50+/-10%) not observed in transfer
reactions (90+-15%)
B) One can reconcile partly e,e’p and
transfer reactions values using the
radius determined in knock out
experiments
,
12C,16O,40Ca,90Zr,208Pb
( 70+/-15%)
Two questions remains :
How realistic is the use of this
radius ? (pm shift in ang. dist)
Is there hidden inconsistencies
in the analysis of e,e’p
Renormalization of quasi-elastic
Coulomb coupling sep*
If sep up by 10%
n increases from 50 to 70%
PISA,February 2005Sydney Galès
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Fragmentation and damping of S-P
strengths for valence and deeplybound states in e,e’p
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Proton knock-out process: (e, e ‘,p)
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Advantages and limitations
(e,e’p) versus Transfer
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