1. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Introduction to Nuclear Physics S.PÉRU 3/3

2. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru The nucleus : a complex system I) Some features about the nucleus discovery radius, shape binding energy nucleon-nucleon interaction stability and life time nuclear reactions applications III) Examples of recent studies figures of merit of mean field approaches exotic nuclei isomers shape coexistence IV) Toward a microscopic description of the fission process II) Modeling of the nucleus liquid drop shell model mean field

3. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru 0.1 1 Experimental (MeV) 0.1 1 Theoretical (MeV) Why light elements are not calculated ? Elimination of 16 light nuclei with Z or N < 8 among the 557 experimentally observed Systematic of the first 2 + excitation energy in even-even nuclei with the Gogny interaction G. Bertsch, et al. PRL 99, 032502 (2007) Comparisons between theoretical and experimental data 5 Figure of merit of mean field approaches and beyond: 5DCH

4. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru 2 + excitation energy spans 3 orders of magnitude : a challenge for any theory !! Strongly deformed actinides Z = 80 – 82, N = 104 It is clear that this theory performs much better for strongly deformed nuclei than for others. 6 Figure of merit of mean field approaches and beyond: 5DCH

5. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru spurious state IS GMR GQR IV GDR Monopole Dipole Quadrupole Octupole IV GMR Figure of merit of mean field approaches and beyond: (Q)RPA Giant resonances are related to nuclear matter properties

6. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Iso vectorIso scalar Monopole (GMR) Dipole (GDR) Quadrupole (GQR) P. Adrich animations

7. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Figure of merit of mean field approaches and beyond: (Q)RPA S. Péru and H. Goutte, PRC 77, 04413 (208)

8. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru IV Dipole S. Péru and H. Goutte, PRC 77, 04413 (208) Figure of merit of mean field approaches and beyond: (Q)RPA

9. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Quadrupole D.H. Youngblood, Y.-W. Lui, and H.L. Clark, Phys.Rev.C 60 (1999)014304 D.H. Youngblood, Y.-W. Lui, and H.L.Clark, Phys. Rev. C, 65, (2002) 034302

10. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Monopolaire Quadripolaire Dipolaire Octupolaire 1-1- 3-3- 2+2+ 0+0+ + 716800 h (~82 y) cpu time 7 ✕200 runs on 256 and 512 proc. Figure of merit of mean field approaches and beyond: (Q)RPA

11. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru 10

12. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru What are the limits to nuclear existence ? What new forms will be found in nuclei ? What happens to the well-known shell structure seen in stable nuclei as we move away from stability ? 11 Exotic nuclei: some open questions A drip-line is defined by the locus of the values of Z and N for which the last nucleon is no longer bound Stability line Neutron drip-line Proton drip-line Predictions from HFB calculations with D1S Gogny force Up to 5000 to 7000 bound exotic nuclei to be discovered up to drip-lines Neutron drip line far from stability : very neutron –rich nuclei Proton drip-line not to far from stability -> Theoretical and experimental challenge to locate drip-lines -> Excellent means of testing nuclear models -> Need a very big accuracy for the nuclear masses

13. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru What about shell effects far from stability ? Characteristic shell gaps that appear in the single-particle spectrum induce particular properties of nuclei that have the numbers of protons or neutrons equal to the so-called « magic numbers ». 2 8 20 28 50 82 126 19 Magic numbers well established for nuclides in the vicinity of the valley of stability: 2, 8, 20, 28, 50, 82, 126 Are these magic number still valid for exotic nuclei ?

14. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru S. Péru et al. EPJA 9, 35 (2000) Mean Field F. Nowacki and A. Poves, PRC 79, 014310 (2009) Shell Model Agreement on the reduction of the shell gap N=28 in exotic nuclei Ca ArSSi More and more exotic 22 Is N=28 a magic number for exotic nuclei ? TiCr

15. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Magic nuclei have increased particle stability, spherical form, and require a larger energy to be excited Magic gaps are signaled by peaks in the 2 + energies and dips in B(E2, 2 + ->0 + ) values in even-even nuclei. How to sign experimentally a magic number ? O. Sorlin, M.G. Porquet, Prog. Part. Nucl. Phys. 61, 602 (2008) N= 28 is not a magic number for exotic nuclei !

16. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Densities Transition densities PDR GDR PDR GDR Paar et al. Rep. Prog. Phys. 70 (2007) 691-793 Pygmy resonances in exotic nuclei Dipolar response

17. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru 26 Ne B(E1)  = 0.49 ± 0.16 e 2 fm 2 %STRK = 4.9 ± 1.6 @ 9 MeV J. Gibelin et al, PRL 101, 212503 (2008) B(E1)=0.173 e 2 fm 2 @ 10.69 MeV B(E1)=0.237e 2 fm 2 @ 14.2 MeV B(E1)=0.107 @ 9.52 MeV B(E1)=0.106 @ 13.68 MeV Exotic nuclei: Dipolar responses in Neon isotopes 20 Ne 22 Ne 24 Ne 26 Ne 28 Ne 18 Ne GDR Pygmy

18. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Transition densities Evolution with A Pygmy or piccolo?

19. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Isomers Spin isomer Shape isomer Fission isomer energy deformation Metastable states (T 1/2 > ns) Their decay is inhibited because their internal structure is very different from the states below deformation energy

20. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Spin isomer

21. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Spin isomers correspond to individual excitations. -> pure states -> possibility to pin down the structure of these states (deformation, spin, parity, g-factor …) -> important information for theory Past measurements have proven that spins often observed in odd exotic nuclei do not correspond to expectations based on extrapolation from known nuclei. 28 Spin isomer in odd nuclei S. Péru, PhD 1997 Shape and spin isomer 

22. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru 33 Shape and fission isomer Why is it interesting to study shape and fission isomers ? In the case of fission and shape isomers, isomers are of collective nature (almost all nucleons participate) * extensive search for superdeformed states in the 80’s 90’s * important for fission (resonances) A.N. Wilson et al. Phys. Rev. C 54 (1996) 559

23. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Main experimental evidence for shape coexistence : Observation of a low-lying 0 + 2 state in even-even nuclei Physical reason for the shape coexistence :  Due to the competition of large shell gaps in the particle level scheme for both oblate and prolate deformation at Z/N numbers 34, 36, and 38. 74 Kr   0+0+ 0+0+ 2+2+ 2+2+ 4+4+ 4+4+ 6+6+ 6+6+ 8+8+ oblateprolate M. Bender, et al. PRC 74 (2006) 024312. Shape coexistence in krypton isotopes 40

24. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru The nucleus : a complex system I) Some features about the nucleus discovery radius, shape binding energy nucleon-nucleon interaction stability and life time nuclear reactions applications III) Examples of recent studies exotic nuclei isomers shape coexistence IV) Toward a microscopic description of the fission process II) Modeling of the nucleus liquid drop shell model mean field

25. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru The fission process Fissile nucleus E = 8.5 A/2 + 8.5 A/2 - 7.5 A ≈ 200MeV

26. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru A/2 A Q F ≈200 MeV Instability Mass fission fragments fissile nucleus marble Potential energy The fission process

27. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru spontaneous Induced by neutron, Gamma, nucleus … The fission process Only 19 nuclei are known to fission spontaneously

28. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Competition between coulomb repulsion and the attractive nuclear interaction : -> oscillation of the nucleus due two this competition -> the system goes through the saddle point (a critical point) after which the potential energy decreases. Then rapid increase of the deformation up to the scission point (break into two fragments) Then separation of the fragments decay of the fragments A schematic description of the fission process energy deformation Evolution of the liquid drop energy during the fission process Saddle point Scission point Equilibrium state (spherical in the liquid drop model)

29. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru The fission process Compound nucleus promptdelayed Decay Stable nuclei

30. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Fission Prompt neutrons gammas Beta + delayed neutrons Compound nucleus Scission Primary fragments Fission products > 10 -19 s10 -17 s10 -14 s> 10 -6 s J.F. Berger, lecture at « Ecole Joliot Curie 2006 » The fission process: Time scale

31. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru High energy released per fission  200 MeV to compare :  combustion of 1 atom of carbon = 4 ev  fission of 1 g of 235 U releases the same amount of energy than 2.55 tons of coal The  200 MeV of energy release are shared as:  Kinetic energy of the fission products 168 MeV  Kinetic energy of the neutrons 5 MeV  Prompt  emission 7 MeV  Delayed  emission 6 MeV  Delayed  emission 7 MeV  Neutrinos 10 MeV The fission process: Energy balance

32. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru * From a theoretical point of view, fission appears as a large amplitude motion, in which intervene: * A large rearrangement of the internal structure of the nucleus with an important role played by the shell effects * Many types of deformation simultaneously * Dynamical effects: couplings between collective modes, couplings between collective modes and intrinsic excitations.  A laboratory for theoretical predictions The fission process: a challenge for the theory

33. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru energy deformationDeformed ground state Isomeric well (fission isomer ) Liquid drop energy + Microscopic shell corrections Spontaneous fission Very favored induced fission What is missing in this description ? Description of the dynamics (time evolution) Description of the different fragmentations The fission process: a challenge for the theory

34. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Fission dynamics is governed by the evolution of a few collective parameters q i (elongation and asymmetry) Why these two degrees of freedom are important ? * Internal structure is at equilibrium at each step of the collective movement  Assumption valid only for low-energy fission Fission dynamics results from a time evolution in a collective space The fission process: a challenge for the theory Assumptions of the present approach

35. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru 1) Static results: * Properties of the fissioning system potential energy landscape of the fissioning system * Properties of the fragments definition of the scission configurations total kinetic energy deformation number of evaporated neutrons 2) Dynamical results fission fragment mass distributions The fission process: a challenge for the theory Results

36. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru The fission process: a challenge for the theory Results

37. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru The fission process: a challenge for the theory Topology of the 2D surfaces 258 100 Fm 158 226 90 Th 136 238 92 U 146

38. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru 2 fragments with the same mass Breaking in two fragments with different masses The fission process: a challenge for the theory Scission configurations H. Goutte, P. Casoli, J.-F. Berger, Nucl. Phys. A 734, 217 (2004)

39. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru S. Pommé et al. Nucl. Phys. A572 (1994) Good overall agreement Over-estimation (up to 6%) H. Goutte, J.-F. Berger, P. Casoli and D. Gogny, Phys. Rev. C 71, 024316 (2005) 238 U The fission process: a challenge for the theory Total kinetic energy distribution

40. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Comparisons between 1D and « dynamical » distributions Same location of the maxima  Due to properties of the potential energy surface (well-known shell effects) Spreading of the peaks  Due to dynamical effects : ( interaction between the 2 collective modes via potential energy surface and tensor of inertia) Good agreement with experiment Yield « 1D » « DYNAMICAL » WAHL H. Goutte, J.-F. Berger, P. Casoli and D. Gogny, Phys. Rev. C71 (2005) 024316 The fission process: a challenge for the theory Dynamical effects on mass distributions

41. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru « Coherent » determination of the properties of the fissioning system, the fission dynamics, and observables of the fragments. -> good qualitative agreement with the exp. data, even if there are no free parameters -> this strengthen our idea that microscopic approaches based on the mean field (and the Gogny force) are pertinent for the study of nuclear structure and fission. The fission process: a challenge for the theory Conclusions

42. CERN Summer student program 2011 Introduction to Nuclear Physics S. Péru Current subjects under study in the community (non exhaustive list) Structure of exotic nuclei Nuclear interaction in the medium Theoretical approaches for the many-body problem Coherent approach for both nuclear structure and nuclear reaction (ex: fission process) Interplay with astrophysics research … It is still human size physics. SOME GENERAL CONCLUSIONS ABOUT THE NUCLEAR PHYSICS “Nuclear physics both experimental and theoretical is a very fantastic subject.” H.G.