1 / 39

A microscopic version of CDCC P. Descouvemont Université Libre de Bruxelles, Belgium

A microscopic version of CDCC P. Descouvemont Université Libre de Bruxelles, Belgium In collaboration with M.S. Hussein (USP) E.C. Pinilla ( ULB) J . Grineviciute (ULB). Introduction Spectroscopy of light nuclei – theoretical models (cluster models )

coty
Télécharger la présentation

A microscopic version of CDCC P. Descouvemont Université Libre de Bruxelles, Belgium

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. A microscopic version of CDCC • P. Descouvemont • Université Libre de Bruxelles, Belgium • In collaboration with • M.S. Hussein (USP) • E.C. Pinilla (ULB) • J. Grineviciute (ULB)

  2. Introduction Spectroscopy of light nuclei – theoreticalmodels (cluster models) Application to nucleus-nucleus scattering Outline of microscopic CDCC The R-matrix method Application to 7Li+208Pb near the Coulomb barrierP.D., M. Hussein, Phys. Rev. Lett. 111 (2013) 082701 Application to 7Li+12C and 7Li+28Si at high energiesE.C. Pinilla, P.D., Phys. Rev. C, in press Application to 17F+208PbJ. Griveniciute, P.D., Phys. Rev. C., submitted Application to 8B+208Pb, 8B+58NiVerypreliminary! Conclusion

  3. 1. Introduction • Main goal in nuclearphysics: understanding the structure of exoticnuclei • Available data: • Elastic (inelastic) scattering • Breakup • Fusion • Etc • Role of the theory: how to interpretthesescattering data? • Combination of twoingredients • Description of the scatteringprocess • Lowenergies(around the Coulomb barrier): optical model, CDCC • High energies (typically ~50-100 MeV/u): eikonal (+variants) • Description of the projectile • 2-body, 3-body • Microscopic

  4. Spectroscopy of light nuclei

  5. 2. Spectroscopy of light nuclei – theoreticalmodels Non-microscopicmodels: 2-body or 3-body r

  6. 2. Spectroscopy of light nuclei – theoreticalmodels • Microscopicmodels • Pauli principletakenintoaccount • Depend on a nucleon-nucleon (NN) interaction  more predictive power • Twoapproaches

  7. 2. Spectroscopy of light nuclei – theoreticalmodels  Nextstep: usingmicroscopicwavefunctions in collisions target

  8. Application to nucleus-nucleus scattering

  9. 3. Application to nucleus-nucleus scattering • The CDCC method(Continuum DiscretizedCoupledChannel) • Structure of the targetisneglected • Validatlowenergies (partial-waveexpansion the total wavefunction) • Introduced to describedeuteroninducedreactions (deuteronweaklybound) G. Rawitscher, Phys. Rev. C 9 (1974) 2210 N. Austern et al., Phys. Rep. 154 (1987) 126 Standard CDCC (2-body projectile) fragment target core Microscopic CDCC (2-cluster projectile)

  10. 3. Application to nucleus-nucleus scattering Comparisonbetweenbothvariants

  11. Outline of microscopic CDCC

  12. 4. Outline of microscopic CDCC First step: wavefunctions of the projectile Solve for several: ground-state but alsoadditional valueswith: physical states: pseudostates (approximation of the continuum)= : combination of Slater determinants (RGM) Example: deuteron d=p+n PS:E>0 Ground state: E<0

  13. 4. Outline of microscopic CDCC Second step: wavefunction for projectile + target • Expansion over projectile states: • Wedefine, : projectile state (bound states + continuum states) L: relative angularmomentumbetween projectile and target •  Set of coupledequations R Microscopicwf • Common to all CDCC variants • Solvedwith: Numerovalgorithm/ R-matrix method • Fromasymptoticbehaviour of :  scattering matrix  cross sections

  14. 4. Outline of microscopic CDCC • Coupling potentials • =combination of Slater determinants • =nucleon-target interaction (including Coulomb) • Standard one-body matrix element (such as kineticenergy, rms radius…) • Must beexpanded in multipoles:

  15. 4. Outline of microscopic CDCC • Two calculationmethods: • Brink’s formula for Slater determinants • One-body matrix elements (kineticenergy, rms radius, densities, etc.) • Matrix elementsbetweenindividualorbitals : • Overlap matrix • Angularmomentum projection • Foldingprocedure • With =nucleardensities • expandedin multipoles as • Test of the calculation • 2ndmethod more efficient sincechanging the potentialis a minorwork

  16. 4. Outline of microscopic CDCC • In practice: • foldingpotentials are computedwith Fourier transforms • obtained from with additionalangularmomenumcouplings

  17. The R-matrix method

  18. 5. The R-matrix method • Scattering matrices, cross sections • Asymptoticform of the relative wavefunctions • , =incoming/outgoing Coulomb functions • =entrance channel • =scattering matrix  cross sections: elastic, inelastic, transfer, etc. R-matrix theory: based on 2 regions (channel radius a)Lane and Thomas, Rev. Mod. Phys. 30 (1958) 257 P.D. and D. Baye, Rep. Prog. Phys.73 (2010) 036301 Internalregion: Externalregion: R Full Hamiltonian expanded over a basis (N functions) Only Coulomb has itsasymptoticform matching atR=aprovides: scattering matrices  cross sections

  19. 5. The R-matrix method Matrix elements • In general: integral over R (fromR=0 to R=a)Lagrange mesh: value of the potentialat the mesh points  veryfast • From matrix C  R matrix •  Collision matrix U  phase shifts, cross sections • Typical sizes: ~100-200 channels c, N~30-40 • Test: collision matrix Udoes not depend on N, a • Choice of a: compromize (atoosmall: R-matrix not valid, atoo large: N large)

  20. The Lagrange-meshmethod (D. Baye, Phys. Stat. Sol. 243 (2006) 1095) • Gauss approximation: • N= order of the Gauss approximation • xk=roots of an orthogonal polynomial, lk=weights • If interval [0,a]: Legendre polynomials [0,]: Laguerre polynomials • Lagrange functions for [0,1]: fi(x)~PN(2x-1)/(x-xi) • xi are roots of PN(2xi-1)=0 • with the Lagrange property: • Matrix elements with Lagrange functions: Gauss approximation is used no integral neededvery simple!

  21. Propagation techniques • Computer time: 2 main parts • Matrix elements: veryfastwith Lagrange functions • Inversion of (complex) matrix C R-matrix (long times for large matrices) • For reactionsinvolving halo nuclei: • Long range of the potentials(Coulomb) • Radius a must be large • Many basis functions (N large) •  • Distorted Coulomb functions (FRESCO) • Propagation techniquesin the R-matrix (wellknown in atomicphysics)Ref.: Baluja et al. Comp. Phys. Comm. 27 (1982) 299Welladapted to Lagrange-meshcalculations Can be large (large quadrupole moments of PS)

  22. Application to at lowenergies P.D., M. Hussein, Phys. Rev. Lett. 111 (2013) 082701

  23. 6. Application to • Data: Elab=27 to 60 MeV (Coulomb barrier ~ 35 MeV) • Non-microscopiccalculationat 27 MeV: • Parkar et al, PRC78 (2008) 021601 • uses α and t potentials renormalized by 0.6! • Microscopic calculation • wave functions: include gs,1/2-,7/2-,5/2- and pseudostates (E>0)Nucleon-nucleonpotential: Minnesota interactionReproduces7Li/7Be, a+3He scattering, 3He(a,g)7Be cross section • Q(3/2-)=−37.0 e.mb(GCM), −e.mb (exp.)B(E2, 3/2− → 1/2−)=7.5 e2fm4 (GCM), e2fm4 (exp) • n potential: local potential of Koning-Delaroche (Nucl. Phys. A 713 (2003) 231) • ppotential: onlyCoulomb (Ep=27/7 ~4 MeV, Coulomb barrier ~12 MeV) • No parameter

  24. 6. Application to • Convergence test: single-channel:twochannels: multichannel:pseudostates up to 20 MeV ElasticscatteringatElab=27 MeV Inelasticscattering

  25. 6. Application to Elab=35 MeV

  26. 6. Application to Elab=39 MeV

  27. 6. Application to Elab=44 MeV • Underestimationat large angles and high energies • N. Timofeuyk and R. Johnson (Phys. Rev. Lett. 110, 2013, 112501 ) • suggestthat the nucleonenergy in A(d,p) reactionmushbelargerthan Ed/2 • Similareffecthere? • Role of target excitations?

  28. Application to and at 350 MeV E.C. Pinilla, P.D., Phys. Rev. C, in press

  29. 7. Application to and at 350 MeV Data fromNadasen et al., Phys. Rev. C 52 (1995) 1894 : 7Li bound states 7Li breakup j=1/2  j=11/2 7Li bound states 7Li breakup j=1/2  j=11/2

  30. 7. Application to and at 350 MeV Influence of the cut-off energy 7 MeV 15,19 MeV

  31. 7. Application to and at 350 MeV Influence of the nucleon-targetopticalpotential Koning, Delaroche, Nucl. Phys. A713 (2003) 231 (volume + surface) Weppner et al., Phys. Rev. C80 (2009) 034608 (volume + surface) Madland, arXiv.nucl-th/9702035v1 (volume only) 28Si+n 28Si+7Li MD WP KD 28Si+p

  32. Application to J. Gineviciute, P.D., Phys. Rev. C, submitted

  33. 8. Application to • 17F described by 16O+p • NN interaction: Minnesota + spin-orbit • Q(5/2+)=-7.3 e.fm2 (exp: -10±2 e.fm2) • B(E2)=19.1 W.u., exp=25.0±0.5 W.u. • Ref. D. Baye, P.D., M. Hesse, PRC 58 (1998) 545 16O+p phase shifts 16O(p,g)17F radiative capture

  34. 8. Application to • Data fromLiang et al., PLB681 (2009) 22; PRC65 (2002) 051603 • Renormalization: real part x0.65 • Weakeffect of breakupchannels • Similar to Y. Kucuk, A. Moro, PRC86 (2012) 034601 • Data from M. Romoli et al. PRC69 (2004) 064614 • Poor agreement withexperiment!

  35. Application to +nucleus scattering Verypreliminary!!

  36. 9. Application to + nucleus The model canbeextended to 3-cluster projectiles: many data with6He, 9Be, 8B, 8Li • Sametheory • J(8B)=0,1,2,3,4 (Gs=2+)(7Be)=0,1,2,3 (gs=3/2-) • L(p-7Be):0 to 7 manychannels for 8B • Calculationsmuch longer • 2 generatorcoordinates • Angular-momentum projection 8B target P.D., Phys. Rev. C70, 065802 (2004)

  37. 9. Application to 8B+208Pb at Elab=170.3 MeV Data from Y. Yang et al., Phys. Rev. C 87, 044613 Calculationwith the KD nucleon-208Pb potential Weak influence of breakupchannels

  38. 9. Application to 8B+58Ni around the Coulomb barrier Data from E. Aguilera et al., Phys. Rev. C 79, 021601(R) (2009) Calculationwith the KD nucleon-58Ni potential 8B+58Ni at Elab=20.68 MeV 8B+58Ni at Elab=25.32 MeV

  39. 10. Conclusion • Microscopic CDCC • Combination of CDCC and microscopic cluster model for the projectile • Excited states of the projectile are included • Continuum simulated by pseudostates (bins are possible) • Only a nucleon-targetisnecessary • Open issues • Target excitations • Around the Coulomb barrier, weakconstraint for the p-targetpotential(Elab/A muchsmallerthan the CB  Rutherford cross section) • Multichannel description of the projectile: • Elastic, inelastic OK • Breakup: pseudostatescontain a mixing of all channels  PS methodcannotbeapplied • Future works: core excitations (11Be), fusion, etc.

More Related