Introduction to Nuclear physics; The nucleus a complex system

1. Introduction to Nuclear physics; The nucleus a complex system Héloïse Goutte GANIL Caen, France goutte@ganil.fr 1

2. 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. III) Examples of recent studies 3

4. Figure of merit of the present approaches 4

5. 1 Theoretical (MeV) 0.1 0.1 1 Experimental (MeV) Figure of merit of a mean field based approach (1) Comparisons between theoretical and experimental data Systematics of the first 2+ excitation energy in even-even nuclei with the Gogny interaction, G. Bertsch, et al. PRL 99, 032502 (2007) Elimination of 16 light nuclei with Z or N < 8 among the 557 experimentally observed Why light elements are not calculated ? 5

6. Figure of merit of a mean field based approach (2)  2+ excitation energy spans 3 orders of magnitude : a challenge for any theory !! Z = 80 – 82 , N = 104 Strongly deformed actinides It is clear that this theory performs much better for strongly deformed nuclei than for others. 6

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

8. 2) Exotic nuclei 9

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10. 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. 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 Predictions from HFB calculations with D1S Gogny force Stability line Proton drip-line Neutron drip-line Up to 5000 to 7000 bound exotic nuclei to be discovered up to drip-lines 12

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

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

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16. 3) New magic numbers in exotic nuclei ? 18

17. 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 ? 126 82 50 28 20 8 2 19

18. d3/2 p3/2 p3/2 p3/2 s1/2 s1/2 28 f7/2 d5/2 f7/2 d5/2 f7/2 d5/2 p n p p n n 46Ar 42Si 44S 14 14 28 28 16 The N=28 magic number Ar Ca Si S N=28 Experimental difficulty Z=16 Z=14 Z=18 20

19. Mean Field Shell Model Ca Si S Ar More and more exotic S. Péru et al. EPJA 9, 35 (2000) F. Nowacki and A. Poves, PRC 79, 014310 (2009) Agreement on the reduction of the shell gap N=28 in exotic nuclei 22

20. How to sign experimentally a magic number ? 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.

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

22. 4) Isomers 25

23. Isomers Metastable states (T1/2 > ns) Their decay is inhibited because their internal structure is very different from the states below energy Spin isomer Fission isomer Shape isomer deformation 26

24. An example of spin isomer 31 years isomeric state 27

25. Spin isomers in odd nuclei 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

26. Magnetic moment of spin isomers The magnetic moment  depends on the spin s of the state and on the orbital moment l =gl l + gs 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 gl= 1 gs=5.586 for proton gl=0 gs=-3.826 for neutron 29

27. N1-N2 R(t)= N1+N2 Détecteur Germanium 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 30

28. 1g7/2 1g 1g9/2 2p1/2 40 1f5/2 488ns 7/2- 2p 2p3/2 1f 3/2 320 1f7/2 7/2 3/2- 20 1d3/2 43S 2s1/2 2s 50 1d 1d5/2 H.O +L2 +L.S 28 20 Example of 43S (Z=16, N=27) Pure 1 f7/2 state l = 3 s=1/2 Pure 1 p3/2 state l = 1 s=1/2 Exp Schmidt f7/2 -0.546 -0.317 p3/2 -1.275 31

29. Shape and fission isomers 32

30. Shape and fission isomers Fission isomer Shape isomer deformation 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) 33

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

32. Number of detected photons 35

33. E Fission isomers: predictions in actinides q20 • Global decrease of the energy of the isomer when A increases • Superdeformed ground states ? 36

34. Stability of these 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 ? Super Deformed Ground states ? * Z. Ren, PRC 65 (2002) 051304(R) I. Muntian et al. PLB 586 (2004) 254 37

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

36. 5) Shape coexistence 39

37. 74Kr  6+ 8+ oblate prolate 6+ 4+ 4+ 2+ 2+ 0+ 0+  Shape coexistence in krypton isotopes 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. M. Bender, et al. PRC 74 (2006) 024312. 40

38. Shape coexistence in krypton isotopes: experiment Shape coexistence in light krypton isotopes was studied in low energy Coulomb excitation experiments using radioactive 74Kr and 76Kr 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. 41

39. Shape coexistence in krypton isotopes: results (mostly…) prolateoblateK=2  vibration E. Clément et al., Phys. Rev. C 75, 054313 (2007). 42

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

42. 6) New structures ? 45

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

44. Alpha cluster model calculations 47

45. The Ikeda picture 48

46. 10Be Alpha decay threshold : 7.409 MeV M. Freer, Rep. Prog. Phys. 70 (2007) 2149. 49

47. Alpha clustering in 12C Hoyle state : it seems impossible to get it from usual shell model calculations -> a loosely bound 3- state in 12C* 8Be +  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. 7) Super heavy elements 51

49. 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 Zmax=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. 8) Fundamental symmetries and interactions 53