transfer reactions: from bound to unbound states

PISA,February 2005PISA,February 2005Sydney GalèsSydney Galès11

Transfer reactions:Transfer reactions:From Bound to Unbound statesFrom 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


Nucleon-NucleusNucleon-Nucleus mean field 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)+ V(r,E)

Potential depth

A independent

Dynamical

content of IPM


Long Range CorrelationsLong Range CorrelationsCoupling to (1p-1h) ,…, (np-Coupling to (1p-1h) ,…, (np-

nh)nh)

IPM

1

n

EEf

IPM+Corr

1

n

EEf

Depletion of the fermi sea 15%


Proton Stripping reactionProton Stripping reaction

Single-particle states Single-particle states 208208Pb+1pPb+1p

Above 2.5 MeV strong fragmentation of Single –particle strengths !!!


Accuracy of reaction models

Cross-sections dependence on form factors ,

Optical parameters

Spectroscopic Factors & sum-ruleSpectroscopic Factors & sum-rule Pick-up S-

lj(A,A-1)= /<f(A-1)/alj /

Stripping S+lj(A,A+1)= /<f(A+1)/a+

lj /

Sum-Rule Sum of Slj on all final sates f with lj quantum numbers give

fSlj = < a+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)


Reaction model for one-nucleon transferReaction model for one-nucleon transfer

• DWBA A+a B+b b=a+/-1n one-step

• TBA= draA drbB bkb,rbB) F(raA ,r bB) a

ka,raA)

• EFR-DWBA d/dEXP

= C2Slj. K. [ TBA]2= C2S ddEFR-DW

. 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 (rbn)l0

2) the form factor flj(r) . Calculated in WS potential ,to reproduce correct binding (SE, energy dependence) . d/dDW

displays strong dependence on the radius

OM elas channels


State of the art :OSAKA 1993

P=80%30KeV

2p3/2

2p1/2

Bound states and polarized beams Bound states and polarized beams in transferin transfer


Examples : Angular distributions and asymmetries

2p3/2 ,2p1/2 in 49Ca

L=1

J=3/2

L=1

J=1/2


From stripping and pick-up :occupation From stripping and pick-up :occupation

numbers and shell closurenumbers and shell closure

Excellent closure

of f7/2

>95%

Open sd shell

15-25%


(e,e(e,e’’,p) ,p) State of the State of the

artart


LRC and SRC LRC and SRC


Persistence of s-p motion at high excitation energy ?Persistence of s-p motion at high excitation energy ? First evidence of deeply-bound hole states in heavy First evidence of deeply-bound hole states in heavy

nucleinuclei


Spin of deep-hole statesSpin of deep-hole states

1g9/2neutron-hole in 120Sn GR like structure (1-2MeV)

IUCF 1980

Broad peak1MeV

9/2+

7/2+


Selectivity for large L transfer (5-8)

Direct observation

of

Spin-orbit

partners


Transfer to Unbound statesTransfer to Unbound states

Standard DWBA • Unbound state Form Factor• Gamov function pole of the

Green s-p wave function

• gRlj(r,kr) =( ljh2kr) ei

lj Olj

Solution of Schrodinger equation for the complex energy

ERes= ER –i


Damping MechanismDamping Mechanism

=2<V>2=2<W>


Experimental observation of the Experimental observation of the damping steps (1p-1h) to (np-nh)damping steps (1p-1h) to (np-nh)


John Elbfas, 1535, Storkyrkan, Stockholm

1p splitting , 8He,12-14Be,20C,22O Mainly Pol (p,d) and (d,p)

Single-particle motion far of stabilitySingle-particle motion far of stability


H(11Be,10Be)2H E = 35 A.MeV

10Be (coinc with 2H) 0.4o lab 1.2o

.....1220 2102/10102/1..114 dBeSsBeSBe sg

(d/d)exp=S(d/d)calc

S(2+)

S(2+) + S(0+)= 0.2

Structure of 11Be g.s. through (p,d) reaction

S. Fortier et al. PLB 461 (1999) 22J.S. Winfield et al. NPA 683 (2001) 48


Structure of Structure of 1010Li G. S Li G. S via transfer reactionsvia transfer reactions

S.Pita PhD thesis Orsay,2000

105 11Be /s


Structural changes with neutron Structural changes with neutron excessexcess

Diffuse Nuclear Surface Leads to vanishing Spin-orbit splitting

New « magic numbers »Test cases N=20, 1d splitting 28,30Ne,32Mg,34SiZ=20 N=28-40 46Ar Z=28 N=28-40,1f56Ni,68Ni

N=50-82,1g,2d 116-134Sn

RFQ - 0.75A MeV

ECRIS-HI 1mA

“SILHI-deuteron” 5mA

CIME Cyclotron RNB (fission-fragments)

E < 6-7 MeV/u,132Sn 109pps

SC - LINACE = 14.5 AMeV

HI A/Q=3E = 40 MeV - 2H

Production Cave

C converter+UCx target

Low energy RNB

> 1013 fiss./s

2. Fusion reaction with n-rich beams

1. Fission products (with converter)

4. N=Z Isol+In-flight

5. Transfermiums In-flight

3. Fission products (without converter)

Primary beams: deuterons heavy ions

Regions of the Chart of Nuclei Accesible with SPIRAL 2 beams

Regions of the Chart of Nuclei Accesible with SPIRAL 2 beams

7. High Intensity Light RIB

6. SHE

8. Deep Inelastic Reactions with RNB


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


**Conclusions**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.


END


Neutron rich C & O isotopesNeutron rich C & O isotopes


Isopin dependence ofIsopin dependence ofspin-orbit interactionspin-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 spin-orbit interaction becomes important


Spin-Orbit SplittingSpin-Orbit Splittingsoso=a=aso so l.l.s. ds. ddr=dr=/2(2L+1) /2(2L+1)

1/V.dV/dr>=g(A) .f(n)1/V.dV/dr>=g(A) .f(n)• protons neutrons• Nucleus nl so nl so

• 12C 1p 8.24 1p 8.5 • 16O 1p 6.88 1p 6.7• 40Ca 1d 6.7 1d 6.7• 2p 2.1 48Ca 1f 8.9 2p 1.9 90Zr 1f 6.3 1g 7.9 2p 1.1 2d 2.4 140Ce 1h 6.5 2d 1.7 208Pb 1h 5.8 1i 6.4 2f 1.7 2f 1.8

G.MairlePhys.lett B1993


D132Sn

p

133Sn

VAMOS

EXOGAM

MU

STx

133Sn

132SnSn=2.7 MeV

Determine neutron-captures at stellar temperaturesSpectroscopic factors

Statistical models not valid at magic shells- Direct capture component- Compound nucleus component

15A.MeV

3/2-

7/2-

1/2-9/2-

CN

DC

Neutron Transfer on Neutron Transfer on 132132SnSn


TIARA

E* ; Lp ; SBound States

TIARA is designed to be usedwith EXOGAM and VAMOS at GANIL

W N

CA

TF

OR

D

University of Surrey

DARESBURY

68+nNi

E:500 keV

E:50 keV

44 particle + 20% particle + 20% EXOGAMEXOGAM


Absolute Spectroscopic factors from Nuclear Absolute Spectroscopic factors from Nuclear knock-out reactionsknock-out reactions

Brown,Hansen,Sherill,TostevinBrown,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 th(nlj) has been calculated using shell model predictions for the s-f and eikonal reaction theory

• th(nlj)= j Snlj sp(Bn,lj) R= exp/ th

sp(Bn,lj) calculated from a define set of parameters S-Matrix from free nn np cross-sections, interactionor 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 ?


Inclusive single -particle spectra Inclusive single -particle spectra

Strength functions for resonance in the continuumStrength functions for resonance in the continuum

Exclusive experiments and decay properties.Exclusive experiments and decay properties.

Persistence of s-p motion Persistence of s-p motion at high excitation energy ?at high excitation energy ?


S-P response function: Exp versus QPMS-P response function: Exp versus QPM


Single Particle states - 1970Single Particle states - 1970Early experimental evidencesEarly experimental evidences

Light-Nuclei :Well separated shells Broad inner 1s shell

Medium and heavy nucleiRapidly overlapping shells


Energy dependence of the dampingEnergy dependence of the damping

width for s-p responsewidth for s-p response functionfunction


Single –Particle strenghts from Single –Particle strenghts from IASIAS


Transfer to continuum and reaction Transfer to continuum and reaction model Bonnacorso,Brinkmodel Bonnacorso,Brink


Decay of single-particle statesDecay of single-particle states


Gamma-decay of overlapping sub Gamma-decay of overlapping sub shells in shells in 111111SnSn


Damping of deep-hole in 208PbDamping of deep-hole in 208PbExperiment and HF+RPA ModelExperiment and HF+RPA Model


Nuclear Models: Damping MechanismsNuclear Models: Damping MechanismsMass ,Energy Dependence of S(E),Mass ,Energy Dependence of S(E),

• 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)


Comparison of Hadronic and Comparison of Hadronic and electromagnetic processeselectromagnetic processes


Quenching of S-P strengthsQuenching 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 ep* If ep up by 10% n increases from 50 to 70%


Fragmentation and damping of S-P Fragmentation and damping of S-P strengths for valence and deeply-strengths for valence and deeply-

bound states in e,e’pbound states in e,e’p


Proton knock-out process: (e, e Proton knock-out process: (e, e ‘‘,p),p)


Advantages and limitations Advantages and limitations (e,e’p) versus Transfer(e,e’p) versus Transfer

transfer reactions: from bound to unbound states

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