1. Héloïse Goutte CERN Summer student program 2009 Introduction to Nuclear physics; The nucleus a complex system Héloïse Goutte CEA, DAM, DIF Heloise.goutte@cea.fr 1

2. Héloïse Goutte CERN Summer student program 2009 The nucleus : a complex system I) Some features about the nucleus discovery radius binding energy nucleon-nucleon interaction life time applications II) Modeling of the nucleus liquid drop shell model mean field III) Examples of recent studies figure of merit of the present approaches exotic nuclei isomers shape coexistence super heavy test of fundamental symmetries IV) Toward a microscopic description of the fission process 2

3. Héloïse Goutte CERN Summer student program 2009 III) Examples of recent studies 3

4. Héloïse Goutte CERN Summer student program 2009 1)Figure of merit of the present approaches 4

5. Héloïse Goutte CERN Summer student program 2009 Figure of merit of a mean field based approach (1) 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 Systematics 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

6. Héloïse Goutte CERN Summer student program 2009 Figure of merit of a mean field based approach (2)  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

7. Héloïse Goutte CERN Summer student program 2009 160 Dy, 170,174,176 Yb and 180 W; the sign of their moments is not exp. known -> they are here all predicted to be prolate with a negative quadrupole moment Systematics of quadrupole moments with the Gogny interaction The theory appears to be reliable : predictions possible 8

8. Héloïse Goutte CERN Summer student program 2009 2) Exotic nuclei 9

9. Héloïse Goutte CERN Summer student program 2009 10

10. Héloïse Goutte CERN Summer student program 2009 Exotic nuclei : some open questions 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

11. Héloïse Goutte CERN Summer student program 2009 Proton and neutron drip-lines (1) 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 12

12. Héloïse Goutte CERN Summer student program 2009 Proton and neutron drip-lines (2) * Proton drip-line not to far from stability * Neutron drip line far from stability : very neutron –rich nuclei -> Theoretical and experimental challenge to locate drip-lines -> Excellent means of testing nuclear models -> Need a very big accuracy for the nuclear masses 13

13. Héloïse Goutte CERN Summer student program 2009 Nuclear masses from microscopic calculations S. Goriely, S. Hilaire, M. Girod, and S. Péru, accepted in PRL. HFB calculations (infinite basis correction) Difference between theo. and exp. D1M : new force adjusted to stable and exotic nuclei 14

14. Héloïse Goutte CERN Summer student program 2009 5DCH calculations (Beyond mean field calculations) Rms 3 MeV for D1S Rms 795 keV S. Goriely, S. Hilaire, M. Girod, and S. Péru, accepted in PRL. 15

15. Héloïse Goutte CERN Summer student program 2009 16

16. Héloïse Goutte CERN Summer student program 2009 3) New magic numbers in exotic nuclei ? 18

17. Héloïse Goutte CERN Summer student program 2009 What about shell effects far from stability ? (1) 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 » 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 ? 2 8 20 28 50 82 126 19

18. Héloïse Goutte CERN Summer student program 2009 20 The N=28 magic number 28 f 7/2 p 3/2 16 d 5/2 d 3/2 s 1/2 14  28 f 7/2 p 3/2 d 5/2 s 1/2 14  46 Ar 44 S 28 f 7/2 p 3/2 d 5/2  42 Si Experimental difficulty N=28 Ca Ar S Si Z=18 Z=14Z=16

19. Héloïse Goutte CERN Summer student program 2009 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

20. Héloïse Goutte CERN Summer student program 2009 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 ?

21. Héloïse Goutte CERN Summer student program 2009 O. Sorlin, M.G. Porquet, Prog. Part. Nucl. Phys. 61, 602 (2008) 23 N= 28 is not a magic number for exotic nuclei.

22. Héloïse Goutte CERN Summer student program 2009 4) Isomers 25

23. Héloïse Goutte CERN Summer student program 2009 Metastable states (T 1/2 > ns) Their decay is inhibited because their internal structure is very different from the states below Spin isomer Shape isomer Fission isomer Isomers energy deformation 26

24. Héloïse Goutte CERN Summer student program 2009 An example of spin isomer 27 31 years isomeric state

25. Héloïse Goutte CERN Summer student program 2009 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 Spin isomers in odd nuclei Past measurements have proven that spins often observed in odd exotic nuclei do not correspond to expectations based on extrapolation from known nuclei. 28

26. Héloïse Goutte CERN Summer student program 2009 Magnetic moment of spin isomers The magnetic moment  depends on the spin s of the state and on the orbital moment l  =g l l + g s s The gyromagnetic factor g =  I It provides information on the orbital moment of the occupied level and on the existence (or not) of configuration mixing g l = 1 g s =5.586 for proton g l =0 g s =-3.826 for neutron 29

27. Héloïse Goutte CERN Summer student program 2009 Measurement of magnetic moment of isomers Nuclei produced by fragmentation : the nuclei in their isomeric states have aligned spins -> all  emitted in a given direction Isomers are put in a magnetic field -> they rotate with the Larmor frequency isomer ground state  Noyau Spin Détecteur Germanium R(t)= N1-N2 N1+N2 30

28. Héloïse Goutte CERN Summer student program 2009 1g 2p 1f 1d 2s 40 20 H.O +L2 +L.S 50 20 28 1g 7/2 1g 9/2 2p 1/2 1f 7/2 1f 5/2 2s 1/2 1d 3/2 1d 5/2 2p 3/2 7/2 3/2 Example of 43 S (Z=16, N=27) Pure 1 f 7/2 state l = 3 s=1/2 Pure 1 p 3/2 state l = 1 s=1/2 Schmidt Exp f 7/2 p 3/2 -0.546 -1.275 -0.317 3/2 - 7/2 - 43 S 320 488ns 31

29. Héloïse Goutte CERN Summer student program 2009 Shape and fission isomers 32

30. Héloïse Goutte CERN Summer student program 2009 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 80s’ 90’s * important for fission (resonances) Shape and fission isomers Shape isomer Fission isomer deformation 33

31. Héloïse Goutte CERN Summer student program 2009 Shape isomer and superdeformed band a b b/a ~ 2/1 A.N. Wilson et al. Phys. Rev. C 54 (1996) 559 energy deformation 34

32. Héloïse Goutte CERN Summer student program 2009 Number of detected photons 35

33. Héloïse Goutte CERN Summer student program 2009 Global decrease of the energy of the isomer when A increases Superdeformed ground states ? E q 20 Fission isomers: predictions in actinides 36

34. Héloïse Goutte CERN Summer student program 2009 Super Deformed Ground states ? Since these states are located Only a few keV below the barrier They may not survive as bound states Controversial question * : Do superdeformed ground states exist in superheavy nuclei ? Stability of these states ? * Z. Ren, PRC 65 (2002) 051304(R) I. Muntian et al. PLB 586 (2004) 254 37

35. Héloïse Goutte CERN Summer student program 2009 Resonant transmission Bandhead states Cross Section (barn) Excitation Energy (MeV) Cross Section (barn) Neutron Energy (MeV) 239 U Influence of superdeformed and (hyperdeformed) states on the fission cross section Results from P. Romain, B. Morillon et H. Duarte 38

36. Héloïse Goutte CERN Summer student program 2009 5) Shape coexistence 39

37. Héloïse Goutte CERN Summer student program 2009 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

38. Héloïse Goutte CERN Summer student program 2009 Shape coexistence in light krypton isotopes was studied in low energy Coulomb excitation experiments using radioactive 74 Kr and 76 Kr beams from the SPIRAL facility at GANIL ( g.s band up to 8 + via multistep Coulomb excitation and several non-yrast states) In both isotopes, the spectroscopic quadrupole moments for the g.s. and the bands based on excited 0 + 2 states are found to have opposite signs. E. Clément, et al., PRC 75 (2007) 054313. Shape coexistence in krypton isotopes: experiment 41

39. Héloïse Goutte CERN Summer student program 2009 (mostly…) prolate oblate K=2  vibration E. Clément et al., Phys. Rev. C 75, 054313 (2007). Shape coexistence in krypton isotopes: results 42

40. Héloïse Goutte CERN Summer student program 2009 43

41. Héloïse Goutte CERN Summer student program 2009 Shape transition in light selenium isotopes  70-72 Se : Shape transition in the yrast band (red and blue) 68 Se : G.s. band oblate (black) excited prolate shapes (green) J. Ljungvall et al., Phys. Rev. Lett. 100, 102502 (2008). 44

42. Héloïse Goutte CERN Summer student program 2009 6) New structures ? 45

43. Héloïse Goutte CERN Summer student program 2009 A Borromean system Borromean nuclei possess the property that none of the two-particle subsystems are bound Ex: 10 Li not bound I. Tanihata et al., PRL 55 (1985) 2676 I. Tanihata and R. Kanungo, CR Physique (2003) 437 A Halo nucleus New forms in exotic nuclei ? Ex: 11 Li From P. Chomaz 46

44. Héloïse Goutte CERN Summer student program 2009 Alpha cluster model calculations 47

45. Héloïse Goutte CERN Summer student program 2009 The Ikeda picture 48

46. Héloïse Goutte CERN Summer student program 2009 10 Be Alpha decay threshold : 7.409 MeV M. Freer, Rep. Prog. Phys. 70 (2007) 2149. 49

47. Héloïse Goutte CERN Summer student program 2009 Alpha clustering in 12 C Hoyle state : it seems impossible to get it from usual shell model calculations -> a loosely bound 3-  state in 12 C* 8 Be +  7.27 MeV (threshold) Hoyle showed that the observed amount of carbon in the cosmos could be made in stars only if there was an excited 0 + state in C at 7.6 MeV 50

48. Héloïse Goutte CERN Summer student program 2009 7) Super heavy elements 51

49. Héloïse Goutte CERN Summer student program 2009 Super heavy nuclei Balance between strong interaction which tends to bind the nucleons together and the Coulomb interaction which tends to push the proton apart. Liquid drop model Z max =104 The SHE owe their existence to microscopic nuclear effects that give additional stability Magic numbers from 2 to 82 are common to both Z and N so the next should be Z = 126 But controversary (Z,N) = (114,184) Macro-micro (120,172) Relativistic (126,184) Non relativistic 52

50. Héloïse Goutte CERN Summer student program 2009 8) Fundamental symmetries and interactions 53

51. Héloïse Goutte CERN Summer student program 2009 Fundamental symmetries and interactions Experiments in nuclear  -decay contribute : 1* to test unitarity of the CKM matrix 2* to test fundamental symmetries of the weak interaction (Parity and Time reversal) 3* investigate the structure of the weak interaction. For 1: need for precision measurements of Q value, branching ratio, half-life -> use of traps (Penning, Paul, ) For 2 and 3 : need for correlations betweens the spins and momenta of the particles involved -> need for polarized nuclei 54

52. Héloïse Goutte CERN Summer student program 2009 Precise testing of CKM Weak interaction mix the quark flavours : quarks participate in the weak interaction with a mixture of their mass eigenstates -> This mixing is described by the Cabibbo Kobayashi Maskawa matrix The standard Model implies unitary conditions V ud 2 +V us 2 +V ub 2 =1 V ud can be extracted from superallowed nuclear beta decay -> need for precision measurement of mass measurements 55

53. Héloïse Goutte CERN Summer student program 2009 Test of fundamental symmetries The weak interaction in the standard model has been introduced as a pure vector –axial vector interaction. The presence of non Standard Model V-A interactions as well as of other more exotic interactions can be probed by observing various types of correlations between the spins and the momenta of the particles involved in the  -decay. 56

54. Héloïse Goutte CERN Summer student program 2009 Examples of recent studies: summary Exotic nuclei Drip – lines not experimentally reached more than 5000 nuclei predicted new shell structures Exotic structures halo nuclei alpha clusters shape coexistence Isomers spin isomers (individual excitations) shape isomers Search for super heavy nuclei Test of fundamental symmetries … 57