Coulomb excitation with radioactive ion beams

1. Motivation and introduction Theoretical aspects of Coulomb excitation Experimental considerations, set-ups and analysis techniques Recent highlights and future perspectives Coulomb excitation with radioactive ion beams Lecture given at the Euroschool 2009 in Leuven Wolfram KORTEN CEA Saclay Euroschool Leuven – September 2009

2. 126 stable double-magic nuclei 4He, 16O, 40Ca, 48Ca, 208Pb 82 radioactive: 56Ni, 132Sn, magic ? 48Ni, 78Ni, 100Sn 50 protons 28 82 20 70Ca ? 50 8 48Ca 28 neutrons no 28O ! 2 20 40Ca 8 2 42Si 32Mg Shell structure of atomic nuclei Euroschool Leuven – September 2009

3. 126 82 110Zr70 132Sn82 “drip line” 50 stabil f7/2 f7/2 protons h11/2 82 70 h11/2 28 g7/2 82 N/Z d3/2 d3/2 20 s1/2 s1/2 g7/2 d5/2 50 g9/2 d5/2 8 28 neutrons 2 20 50 40 8 g9/2 2 p1/2 p1/2 Changes in the nuclear shell structure Spin-orbit term of the nuclear int. ? Only observable in heavy nuciei: (Z,N) > 40 Euroschool Leuven – September 2009

4. N=20 4 3 E(2+) [MeV] 2 20Ca 1 12Mg 16S 0 N 12 16 20 24 400 N=20 sd+fp B(E2) [e2fm4] 200 sd 40Ca 38Ar 30Ne 36S 34Si 32Mg N/Z Changes in the nuclear shell structure Observables: Masses and separation energies Properties of 2+ states Example: “Island of inversion” around 32Mg  deformed ground state Euroschool Leuven – September 2009

5. 126 Nilssondiagramm Z, N = magic numbers 82 50 Closed shell = spherical shape 28 50 sngle particle enegies protons 20 28 82 20 Prolate Oblate 50 2 8 8 28 neutrons 2 20 Spherical 8 2 Deformed elongation Shapes of atomic nuclei The vast majority of all nuclei shows a non-sphericalmass distribution Euroschool Leuven – September 2009

6. Quadrupole deformation of nuclei M. Girod, CEA Coulomb excitation can, in principal, map the shape of all atomic nuclei Euroschool Leuven – September 2009

7. N=Z Oblate Prolate Quadrupole deformation of nuclei Pb & Bi N~Z Fission fragments M. Girod, CEA Oblate deformed nuclei are far less abundant than prolate nuclei Shape coexistence possible for certain regions of N & Z Euroschool Leuven – September 2009

8. N+3 shell 108Cd 235U 152Dy N+2 shell N+1 shell N shell Fermi level Energy Z=48 Deformation HD ND SD Shape variations and intruder orbitals  i13/2 single-particle energy (Woods-Saxon) • (N+1) intruder  normal deformed, e.g. 235U quadrupole deformation • (N+2) super-intruder  Superdeformation, e.g. 152Dy, 80Zr • (N+3) hyper-intruder  Hyperdeformationin 108Cd, ? Euroschool Leuven – September 2009

9. quadrupole oblate non-collective Lund convention octupole prolate collective  spherical 2 : elongation hexadecapole g: triaxiality prolate non-collective oblate collective Exotic shapes and “deformation” parameters Generic nuclear shapes can be described by a development of spherical harmonics alm:deformation parameters Tetrahedral Y32 deformation Triaxial Y22 deformation Static  rotation Dynamic vibration Euroschool Leuven – September 2009

10. Coulomb excitation – an introduction Euroschool Leuven – September 2009

11. Elastic scattering of charged particles (point-like monopoles) under the influence of the Coulomb field FC = Z1Z2e2/r2 with r(t) = |r1(t) – r2(t)|  hyperbolic relative motion of the reaction partners Rutherford cross section ds/dq = Z1Z2e2/Ecm2 sin-4(qcm/2) Rutherford scattering – some reminders target b r(t) projectile a beam energy b = impact parameter Euroschool Leuven – September 2009

12. small impact parameter • back scattering • close approach • strong EM field • large impact parameter • forward scattering • large distance • weak EM field Coulomb excitation – some basics Nuclear excitation by the electromagnetic interaction acting between two colliding nuclei. target b projectile • Target and projectile excitation possible • often heavy, magic nucleus (e.g. 208Pb) • as projectile  target Coulomb excitation • as target  projectile Coulomb excitation (important technique for radioactive beams) Coulomb trajectories only if the colliding nuclei do not reach the “Coulomb barrier” purely electromagnetic process, no nuclear interaction, calculable with high precision Euroschool Leuven – September 2009

13. VC= Z1Z2e2/rb (1-a/rb) rb = 1.07(A11/3+A21/3) + 2.72 fm a=0.63 fm (surface diffuseness) sexp/sRuth Reactions below the Coulomb barrier • Beam energy per nucleon (EB/A) rather constant, e.g. for 208Pb target 5.6 to 6 A.MeV • Inelastic scattering (e.m/nucl.) • Transfer reactions • Fusion Pure Coulomb excitation requires a much larger distance between the nuclei ”safe energy” requirement Euroschool Leuven – September 2009

14. Rutherford scattering only if the distance of closest approach is large compared to nuclear radii + surfaces: „Simple“ approach using the liquid-drop model Dmin rs = [1.25 (A11/3 + A21/3) + 5] fm More realistic approach using the half-density radius of a Fermi mass distribution of the nuclei : Ci = Ri(1-Ri-2) with R = 1.28 A1/3 - 0.76 + 0.8 A-1/3  Dmin rs = [ C1 + C2 + S ] fm target b Dmin projectile  „Safe“ energy requirement Euroschool Leuven – September 2009

15. sexp/sRuth „Safe“ energy requirement Dmin  Empirical data on surface distance S as function of half-density radii Cirequiredistance of closest approachS > 5 - 8 fmchoose adequate beam energy (D > Dmin for all )low-energy Coulomb excitation limit scattering angle, i.e. select impact parameter b > Dmin,high-energy Coulomb excitation Euroschool Leuven – September 2009

16. Pb Ar O He Validity of classical Coulomb trajectories target projectile b=0 D=2a • Sommerfeld parameter •  >> 1 requirement for a semi classical treatment of equations of motion • measures the strength of the monopole-monopole interaction • equivalent to the number of exchanged photons needed to force the nuclei on a hyperbolic orbit Euroschool Leuven – September 2009

17. target b D(q) projectile  Coulomb trajectories – some more definitions r (w) = a (e sinh w + 1) t (w) = a/v (e cosh w + w) a = Zp Zt e2 E-1 Principal assumption >>1  classical description of the relative motion of the center-of-mass of the two nuclei  hyperbolic trajectories • distance of closest approach (for w=0): • impact parameter: • angular momentum : Euroschool Leuven – September 2009

18. Coulomb excitation – the principal process target b vi projectile vf Inelastic scattering: kinetic energy is transformed into nuclear excitation energy e.g. rotation vibration Excitation probability (or cross section) is a measure of the collectivity of the nuclear state of interest  complementary to, e.g., transfer reactions Euroschool Leuven – September 2009

19. Coulomb excitation – “sudden impact” Excitation occurs only if nuclear time scale is long compared to the collision time: „sudden impact“ if nucl >>  coll ~ a/v  10 fm / 0.1c  2-310-22 s coll ~ nucl ~ ћ/E adiabatic limit for (single-step) excitations • : adiabacity paramater sometimes also () with D() instead of a Limitation in the excitation energyDE for single-step excitations in particular for low-energy reactions (v<c) Euroschool Leuven – September 2009

20. Coulomb excitation – first conclusions Maximal transferable excitation energy and spin in heavy-ion collisions =1 Euroschool Leuven – September 2009

21. Coulomb excitation – the different energy regimes Low-energy regime (< 5 MeV/u) High-energy regime (>>5 MeV/u) Energy cut-off Spin cut-off: DL up to 30ћDL~ nl with n~1 Euroschool Leuven – September 2009

22. Coulomb excitation is a purely electro-magnetic excitation process of nuclear states due to the Coulomb field of two colliding nuclei. Coulomb excitation is a very precise tool to measure the collectivity of nuclear excitations and in particular nuclear shapes. Coulomb excitation appears in all nuclear reactions (at least in the incoming channel) and can lead to doorway states for other excitations. Pure electro-magnetic interaction (which can be readily calculated without the knowledge of optical potentials etc.) requires “safe” distance between the partners at all times. Summary Euroschool Leuven – September 2009