1 / 50

Transfer reactions: From Bound to Unbound states

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

lesley
Download Presentation

Transfer reactions: From Bound to Unbound states

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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 PISA,February 2005Sydney Galès

  2. 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 PISA,February 2005Sydney Galès

  3. Long Range CorrelationsCoupling to (1p-1h) ,…, (np-nh) na 1 IPM E Ef na 1 IPM+Corr E Ef Depletion of the fermi sea 15% PISA,February 2005Sydney Galès

  4. Proton Stripping reaction Single-particle states208Pb+1p Above 2.5 MeV strong fragmentation of Single –particle strengths !!! PISA,February 2005Sydney Galès

  5. Spectroscopic Factors & sum-rule Pick-upS-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 SfSlj = < F0(A)/ a+a/ F0(A)>= nlj number of nucleons lj in the ground state Sum of all final fragments limited in Energy short range correlations (up to high Ex) Two obvious problems in deducing absolute values for this sum-rule Accuracy of reaction models Cross-sections dependence on form factors , Optical parameters PISA,February 2005Sydney Galès

  6. Reaction model for one-nucleon transfer • DWBA A+a B+b b=a+/-1n one-step • TBA= draA drbB C b-* (kb,rbB) F(raA ,r bB) C a+ (ka,raA) • 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 OM elas channels PISA,February 2005Sydney Galès

  7. Bound states and polarized beams in transfer State of the art :OSAKA 1993 2p3/2 2p1/2 P=80% 30KeV PISA,February 2005Sydney Galès

  8. Examples : Angular distributions and asymmetries2p3/2 ,2p1/2 in 49Ca L=1 J=3/2 L=1 J=1/2 PISA,February 2005Sydney Galès

  9. From stripping and pick-up :occupation numbers and shell closure Excellent closure of f7/2 >95% Open sd shell 15-25% PISA,February 2005Sydney Galès

  10. (e,e’,p) State of the art PISA,February 2005Sydney Galès

  11. LRC and SRC PISA,February 2005Sydney Galès

  12. Persistence of s-p motion at high excitation energy ?First evidence of deeply-bound hole states in heavy nuclei PISA,February 2005Sydney Galès

  13. Spin of deep-hole states 1g9/2neutron-hole in 120Sn GR like structure (1-2MeV) IUCF 1980 Broad peak 1MeV 9/2+ 7/2+ PISA,February 2005Sydney Galès

  14. Selectivity for large L transfer (5-8) Direct observation of Spin-orbit partners PISA,February 2005Sydney Galès

  15. 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 Transfer to Unbound states PISA,February 2005Sydney Galès

  16. Damping Mechanism G =2P<V>2r =2<W> PISA,February 2005Sydney Galès

  17. Experimental observation of the damping steps (1p-1h) to (np-nh) PISA,February 2005Sydney Galès

  18. 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) PISA,February 2005Sydney Galès

  19. Structure of 11Be g.s. through (p,d) reaction H(11Be,10Be)2H E = 35 A.MeV (ds/dW)exp=S(ds/dW)calc S(2+) = 0.2 S(2+) + S(0+) 10Be (coinc with 2H) 0.4o  lab  1.2o S. Fortier et al. PLB 461 (1999) 22 J.S. Winfield et al. NPA 683 (2001) 48 PISA,February 2005Sydney Galès

  20. Structure of 10Li G. S via transfer reactions 105 11Be /s S.Pita PhD thesis Orsay,2000 PISA,February 2005Sydney Galès

  21. 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 PISA,February 2005Sydney Galès

  22. Low energy RNB > 1013 fiss./s 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

  23. 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

  24. 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 PISA,February 2005Sydney Galès

  25. **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. PISA,February 2005Sydney Galès

  26. END PISA,February 2005Sydney Galès

  27. Neutron rich C & O isotopes PISA,February 2005Sydney Galès

  28. Isopin dependence ofspin-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 PISA,February 2005Sydney Galès

  29. Spin-Orbit Splittingeso=aso l.s. dr/dr=1/2(2L+1) xx=<1/V.dV/dr>=g(A) .f(n) • protons neutrons • Nucleus nl eso nl eso • 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.Mairle Phys.lett B 1993 PISA,February 2005Sydney Galès

  30. Neutron Transfer on 132Sn EXOGAM MUSTx VAMOS g p 132Sn D 15A.MeV 133Sn • Determine neutron-captures at stellar temperatures • Spectroscopic factors • Statistical models not valid at magic shells • Direct capture component • Compound nucleus component CN 9/2- 132Sn 1/2- Sn=2.7 MeV 3/2- DC 7/2- 133Sn PISA,February 2005Sydney Galès

  31. TIARA University of Surrey TIARA is designed to be used with EXOGAM and VAMOS at GANIL 4p particle + 20% g (EXOGAM) DE:500 keV DE:50 keV W N CATFORD 68+nNi E* ; Lp ; S Bound States PISA,February 2005Sydney Galès DARESBURY

  32. Absolute Spectroscopic factors from Nuclear knock-out reactionsBrown,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 • sth(nlj)= Sj Snlj ssp(Bn,lj) R= sexp/sth • ssp(Bn,lj) calculated from a define set of parameters S-Matrix from free nn np cross-sections, dinteractionor 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 ? PISA,February 2005Sydney Galès

  33. 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. PISA,February 2005Sydney Galès

  34. S-P response function: Exp versus QPM PISA,February 2005Sydney Galès

  35. Single Particle states - 1970Early experimental evidences Light-Nuclei :Well separated shells Broad inner 1s shell Medium and heavy nuclei Rapidly overlapping shells PISA,February 2005Sydney Galès

  36. Energy dependence of the dampingwidth for s-p responsefunction PISA,February 2005Sydney Galès

  37. Single –Particle strenghts from IAS PISA,February 2005Sydney Galès

  38. Transfer to continuum and reaction model Bonnacorso,Brink PISA,February 2005Sydney Galès

  39. Decay of single-particle states PISA,February 2005Sydney Galès

  40. Gamma-decay of overlapping sub shells in 111Sn PISA,February 2005Sydney Galès

  41. Damping of deep-hole in 208PbExperiment and HF+RPA Model PISA,February 2005Sydney Galès

  42. Nuclear Models: Damping MechanismsMass ,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) PISA,February 2005Sydney Galès

  43. Comparison of Hadronic and electromagnetic processes PISA,February 2005Sydney Galès

  44. 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

  45. Fragmentation and damping of S-P strengths for valence and deeply-bound states in e,e’p PISA,February 2005Sydney Galès

  46. PISA,February 2005Sydney Galès

  47. PISA,February 2005Sydney Galès

  48. Proton knock-out process: (e, e ‘,p) PISA,February 2005Sydney Galès

  49. Advantages and limitations (e,e’p) versus Transfer PISA,February 2005Sydney Galès

  50. PISA,February 2005Sydney Galès

More Related