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- Two categories of magic numbers : Harmonic Oscillator and Spin Orbit

Experimental progresses and challenges in the evolution of shell closures O. Sorlin (GANIL). N=4. 82. 2d. 40. 50. 1g. g 9/2. 40. N=3. 40. p 1/2. 2p. f 5/2. p 3/2. 1f. 28. 20. f 7/2. 20. 20. N=2. d 3/2. 2s. s 1/2. 1d. 14. 8. d 5/2. 8. N=1. L 2. +. L.S. H.O. +.

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- Two categories of magic numbers : Harmonic Oscillator and Spin Orbit

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  1. Experimental progresses and challenges in the evolution of shell closures O. Sorlin (GANIL) N=4 82 2d 40 50 1g g9/2 40 N=3 40 p1/2 2p f5/2 p3/2 1f 28 20 f7/2 20 20 N=2 d3/2 2s s1/2 1d 14 8 d5/2 8 N=1 L2 + L.S H.O + ESNT 2010 - Saclay • - Two categories of magic numbers : • Harmonic Oscillator and Spin Orbit • - The role of proton-neutron interactions • Disappearance of magic numbers • Appearance of new magic numbers • What do we mean by SO magic numbers ? • Influence of binding energy on nuclear force ? • Note that • Structural variations better seen in light nuclei • Extract general empirical rules / symmetries… • -> extrapolate to other regions Mean-field approach for atomic nuclei

  2. The N=20 shell closure A prototypical case of HO shell number

  3. N=20 4 3 E(2+) [MeV] 2 40 20Ca 20 36Ca 14Si 1 12Mg 30 16S 20 0 S2N (MeV) 12 16 20 24 20 Neutron Number 45Ca 27Mg 10 400 35Mg N=20 40Ca sdfp B(E2) [e2fm4] 36S 200 16 20 24 sd 32Mg Neutron Number N 40Ca 38Ar 30Ne 36S 34Si 32Mg N/Z N=20 magic number Disappears !

  4. ESPE in N=20 isotones and island of inversion s1/2 d5/2 d3/2 1) Reduction of the N=20 shell gap N=20 Occupancy of fp states grows at N=20 occupancy 0f7/2 Island of inversion J. R. Terry et al., PRC 77 (2008) 014316. Neutron Role of the Vpnd5/2d3/2 and Vpnd5/2(fp) interactions Attractive and repulsive tensor terms, respectively T. Utsuno et al. PRC (1999) 2) Presence of intruder fp states, f and p reversed ? 3) New magic number at N=16 ?

  5. 24Ne(d,p)25Ne with TIARA+EXOGAM+VAMOS (GANIL) Protons -> TIARA Gammas -> Exogam Nuclei -> Vamos  = 1 4030 0.73 ( = 3),7/2- 3330 0.75  = 1, 3/2-  = 2 2030  = 2, 3/2+ 0.44 1680 0.15  = 2  = 2, 5/2+ hole  = 1  = 0, ½+ 0.80 (SF) 25Ne Jp  = 3 W. Catford et al., PRL 2010 - Proximity of f and p states to sd ones - p and f states reversed, N=28 gap

  6. The ‘sizes’ of the N=20 and N=16 gaps in Oxygen (RIKEN) 22O(d,p)23O reaction to probe the neutron N=16, 20 shell closures Gated on neutrons Gated on 4 MeV neutron peak N=20 : 1.3 MeV L=2 N=16 : 4.0 MeV Elekes et al. PRL98 (2007) 102502 23O 5/2+ observed PRL99 (2007) hole

  7. Nuclear interaction in the sd shell s1/2 d3/2 d5/2 N=20 28O Island of inversion 16 34Si 40Ca A ‘critical’ view : Mechanism of inversion not proven : 0+2 not yet observed in 34Si and 32Mg Hard to get 28O unbound using standard Vnn No ‘direct’ (easy) determination of Vd5/2d3/2 due to deformation So far monopole assumed constant whatever neutron and proton binding energy True or not ? Can we check it ? Neutron -> Study of 26F Utsuno, Otsuka et al.

  8. 26F 25O p d5/2 Sn 24O 24O Vpn (d3/2d5/2) d3/2 168.38 n interact USDa exp Sp Hoffman PRL 100(2008) Stanoiu thesis 2003,E(J=2) Jurado PLB 649 (2007) 1 26Ffree ? 3 +Sp Sn 2 2 183.46 25F 4 1 1 exp J USDa J BE(MeV) Empirical determination of Vd5/2d3/2 Exp monopole ~ 600keV weaker than Shell Model ! continuum effects … ?? Where is the 4+ ? Isomer ?

  9. Generalization to other HO shell gaps

  10. Great similarity between the three cases of HO shell numbers N=20 N=8 N=40 O. S. , MG Porquet PPNP (2008) • Same mechanism at play : • Drop in 2+ energy at N=8, 20 and 40 • Inversion between normal and intruder states at N=40 • Search for a (super)deformed 0+2 in 68Ni • Prove the extreme deformation of 64Cr

  11. Evolution of Harmonic Oscillator shell closures d5/2 d5/2 N=14 s1/2 s1/2 p1/2 8 N~8 p1/2 6 6 p3/2 p3/2 p3/2 p3/2 n [ ] n p p Z=6 Z=2 p3/2 p3/2 f7/2 N=28 N~20 f7/2 20 d3/2 d3/2 16 s1/2 s1/2 14 14 d5/2 [ ] d5/2 d5/2 d5/2 p n p n Z=14 Z=8 d5/2 d5/2 N=50 g9/2 g9/2 N~40 f5/2 40 34 p1/2 p1/2 f5/2 32 p3/2 p3/2 28 28 f7/2 f7/2 [ ] f7/2 p Small gaps p f7/2 n n Z=28 Z=20 Large N/Z Role of the p p3/2- n p1/2 interaction Role of the p d5/2- n d3/2 interaction SPIN –FLIP Dl=0 INTERACTION Role of the p f7/2- n f5/2 interaction ?

  12. The making of ‘SO’ magic numbers Which physics ? Which interactions ?

  13. Evolution of neutron SPE in the Ca isotopic chain Energy [MeV] Binding energy 28 28 28 20 28 Neutrons 20 28 20 28 Neutrons Courtesy M.G Porquet No increase of the N=28 shell gap when nf7/2 is filled Same with realistic VlowK interaction -> 3 body ?

  14. Building SO magic numbers by neutron-neutron interactions From data around 90Zr Sn(23O) O E*(17O) Ca Ni 0 78Ni 68Ni d5/2 Sn(17O) - 4 Sn(22O) N=50 ? g9/2 - 8 42 44 46 48 40 50 24 20 22 26 28 Neutron number Neutron number Extracted from BE’s, spectroscopy and SF’s In collab with MG Porquet > Same increase of the neutron shell gaps by about 3 MeV ! > Same mechanism at play to create SO magic numbers -> empirical rule to be used to constraint these spacing for heavier nuclei

  15. The study of the N=28 shell closure : a way to probe nuclear force N=20 N=28 Ca,Z=20 40Ca 48Ca f5/2 p1/2 p3/2 s1/2 proton sd removed d3/2 Dj=2 28 14 Dj=2 S, Z=16 36S d5/2 [ ] f7/2 [ ] n p Si, Z=14 34Si neutron f7/2filling 1- compression of proton orbits 2- Evolutionof neutron orbits due to pn interactions • Enhanced E2 collectivity due to Dj=2 46Ar 44S 42Si > Role of nuclear forces: Modification of the N=28 shell gap ? SO and Tensor interaction ?

  16. p • Use of 46Ar (d,p) transfer reaction • Size of the N=28 shell gap • Reduction of SO splitting L. Gaudefroy et al. PRL 97 (2006), d qp 18 f5/2 p1/2 p3/2 28 f5/2 0 f7/2 ESPE(MeV) p1/2 - 2 +280keV per proton added in d3/2 f5/2 - 4 p3/2 28 - 6 -210keV f7/2 28 - 8 d3/2 f7/2 1.33 s1/2 p n Tensor interaction (Otsuka) pd3/2 –n( f7/2-f5/2 ) - 10 47Ar 49Ca 18 20 Variation of single particle energies (SPE) Evolution of SPE’s from tensor part of the proton-neutron interaction

  17. Global trend of single particle energies between 49Ca and 43Si derived from experimentally-constrained monopole variations + 2 N=29 SPE(MeV) 0 p1/2 f5/2 p3/2 - 2 28 p1/2 - 4 f7/2 28 p3/2 28 - 6 28 - 8 0 0 f7/2 - 10 43Si 47Ar 45S 49Ca 14 18 16 20 • A shrink of SPE’s due to two-body p-n interactions… • Favor particle-hole excitations and E2 collectivity • Spherical, shape coexistence in 44S and deformation in 42Si

  18. Electron spectroscopy to probe shape coexistence in 44S 1365 02+ 2.62(2) ms Qi ~ 55 42(2) 2+ 1330 r(E0) = 8.7(5) 10-3 BE2(0+2→ 2+1) BE2(0+1→ 2+1) 44S 63(18) ~1/7 BE2 e2fm4 01+ 44S Qi ~ 0 Glasmacher et al., PLB 395 (97) C. Force, S. Grévyet al. to be published 1365 keV e- conv e+ e- Weak mixing between prolate and spherical shapes in the 0+ Ee- (keV)

  19. Collapse of the N=28 shell closure in 42Si 42Si p3/2 p3/2 [ ] d3/2 d3/2 [ ] 28 f7/2 s1/2 s1/2 n [ ] [ ] f7/2 n 14 14 SPIN-FLIP Dl=1 INTERACTION 42Si [ ] [ ] 48Ca d5/2 d5/2 14 20 p p B. Bastin, S. Grévy et al., PRL 99 (2007) N=28 Role of the p d3/2 – n f7/2 interaction Decrease of the N=28 gap by ~1MeV for 6 protons

  20. d5/2 [ ] N=14 shell closure in 22O and 20C s1/2 n p1/2 6 20C [ ] 6 20C p3/2 20C 6 p 5 O E(2+) (MeV) C 0 5 10 20 15 Neutron Number Thirolf et al. PLB 485 (2000) M. Stanoiu et al. PRC 69 (2004) and (2009) s1/2 N=14 14 [ ] p1/2 [ ] d5/2 n 6 [ ] p3/2 22O 8 p Role of the p p1/2 – n d5/2 interaction Decrease of the N=14 by ~1.6 MeV for 2 protons

  21. s1/2 d5/2 [ ] N=14 s1/2 14 n [ ] p1/2 [ ] p1/2 d5/2 N=14 N=28 n 6 6 [ ] p3/2 [ ] 22O 6 20C p3/2 20C 8 6 p p p3/2 p3/2 [ ] N=28 d3/2 d3/2 [ ] 28 f7/2 s1/2 s1/2 n [ ] [ ] f7/2 n 14 14 SPIN-FLIP Dl=1 INTERACTION 42Si [ ] [ ] 48Ca d5/2 d5/2 14 20 p p d5/2 d5/2 N=50 50 f5/2 f5/2 [ ] 50 g9/2 [ ] p3/2 p3/2 n [ ] N=50 ?? g9/2 n 28 28 [ ] [ ] f7/2 d5/2 78Ni 90Zr p p 50 40 f7/2 f7/2 N=82 82 d5/2 d5/2 [ ] 82 [ ] g7/2 h11/2 g7/2 [ ] [ ] h11/2 N=82 strong n n 50 28 [ ] [ ] g9/2 g9/2 132Sn 152Gd p p 50 64

  22. The N=50 shell closure at 78Ni50 40Ca 4 48Ca 34Si 3 68Ni ? 2+ energy (MeV) 2 1 42Si 0.5 1 0 Occupation probability « Monopole propose, quadrupole dispose » A. Zuker

  23. Some Conclusions Robust effect of NN inteactions : Proton Neutron interaction DL=0 plays an essential role to modify HO shell gaps Proton Neutron interaction DL=1 plays an certain role to modify SO shell gaps ->Perhaps not strong enough to supress the magicity in 78Ni50 Role of Vnn to create SO magic numbers -> Same increase of neutron shell gap (3MeV) for all SO magic numbers ! Modification of Vpndue to the presence of continuum ? Vpn d5/2d3/2 (26F) ~ 60% of canonical value only ! -> Other candidates YES !!! Special thanks : S. Grévy, L. Gaudefroy, D. Sohler, Z. Dombradi, M. Stanoiu, M. G. Porquet, F. Nowacki and F. Azaiez

  24. 28 V lowk NN No N=28 shell gap formation with realistic interactions ! The N=28 shell gap and the role of 3 body forces Holt, Otsuka, Schwenk, Suzuki

  25. Evolution of the neutron SPE below 48Ca 20 p • Use of 46Ar (d,p) transfer reaction • Size of the N=28 shell gap • Reduction of SO splitting L. Gaudefroy et al. PRL 97 (2006) d qp 18 f5/2 p1/2 p3/2 28 f7/2 p 46Ar p3/2 f 47Ar p1/2 f5/2 (2J+1)C2S=1.7 (2J+1)C2S=2.44 f7/2 f p C2Sf=0.64 C2Sg=0.34 (2J+1)C2S=1.36 : reduced by 330keV

  26. d5/2 50 g9/2 (jn>) p1/2 neutrons f5/2 (jp<) p3/2 28 f7/2 (jp>) protons 78Ni 42Si and 78Ni are ‘mirror’ systems Development of collectivity in 42Si f5/2 p1/2 p3/2 28 Dℓ=2 f7/2 (jn>) neutrons d3/2 (jp<) s1/2 Dℓ=2 14 d5/2 (jp>) protons 42Si Doubly magic numbers originating from spin-orbit interaction Mutual reductions proton and neutron gaps depends on the strength the tensor force The proton and neutron gaps are connected by Dℓ=2 connections with valence states

  27. Role of proton-neutron forces in the N=28 region d3/2 f7/2 E(1/2+) – E(3/2+) (keV) 16 n s1/2 p Neutron Number Cu (Z=29) exp f5/2 Around 78Ni 1000 g9/2 E(5/2-) – E(3/2-) (keV) 32 n p3/2 0 ?? 28 40 42 44 46 48 50 f7/2 p Neutron Number in the N=50 region

  28. Change of SO splitting for p orbits f5/2 0 SPE(MeV) p1/2 - 2 - 4 p3/2 28 - 6 28 - 8 f7/2 - 10 47Ar 49Ca 18 20 -No change of np1/2-p3/2 splitting between 41Ca and 37S after removal of 4 protons from pd3/2 -Reduction of splitting due to ps1/2 p1/2 +170keV per proton p3/2 -85keV 0.66 s1/2 p n Central density dependence (Piekarewicz) Gaudefroy et al. PRL 2007

  29. Probe the density dependence of the SO interaction in 36S and 34Si N=16 disappears ! B.G Todd Rutel et al. PRC 69 (2004) 1301(R) M. Grasso et al. NPA 2009 SO reduced 34Si 36S RMF calculations using NL3 interaction Reduction of the SO splitting by 70% MF / Skyrme or Gogny forces Reduction of the SO splitting by 40% SM calculations spdf-NR Reduction of SO splitting by 30% Bare forces VlowK reduction by 7% only 36S 34Si Analysis GANIL in progress

  30. Insert here one or two slides on the effect of continuum…

  31. Part I :Properties of shell closures of ‘HO’ origin The N=8 shell closure

  32. Evolution of the N=8 shell closure 14C p1/2 p3/2 Z 6 8 2 4 -1 11Be e [1/2- - 1/2+] - E [1-] -2 12Be -3 -4 13C -5 15O -6 14C -7 16O 12Be d5/2 Dl= 2 d5/2 p1/2 s1/2 s1/2 8 p1/2 6 6 p3/2 p3/2 11Be 15O 12Be : Iwasaki et al., PLB 481 (2000) 7 Quadrupole excitations favored in Be First ‘Island of inversion’ ? 12Be g.s. strongly mixed (Navin et al PRL85; Pain et al. 96) Role of the pp3/2-np1/2 interaction

  33. From Wikipedia, the free encyclopedia The Magic Numbers Magic Numbers are a four-piece rock band from England comprising two pairs of brother and sister who previously went to The Cardinal Wiseman Roman Catholic High School in Greenford. The group was formed in 2002, releasing their critically acclaimed album titled The Magic Numbers in June 2005…. Summary - Two classes of shell closures (magic numbers) : HO and SO - Proton-neutron interactions usually act to destroy them - Takes root in NN bare forces – link in progress - Forces be strong enough to destroy shell closures in heavy nuclei ? - Astrophysical consequences expected - Extrapolation to superheavies or unknown regions ? The

  34. Nuclear Shell Structure Evolution Around 132Sn N>>Z, drip-line 126 p1/2 h9/2 f5/2 f5/2 i13/2 p1/2 p3/2 3 p3/2 h9/2 f7/2 f7/2 82 1 82 h11/2 d3/2 g7/2 2 h11/2 d3/2 s1/2 g7/2 s1/2 d5/2 d5/2 g9/2 50 ? g9/2 Reduced spin-orbit Tensor forces Mean field for N>>Z ? Effect of continuum ? Mean field near stability Strong spin-orbit interaction Adapted from J Dobaczewski • Major consequences : 1 : Reduction/disappearence of shell gaps -> modify the shape of r abundance peaks 2 : Change of g7/2 energy, increase the g7/2→ g9/2 GT transition, shorten b-decay lifetimes 3 : The valence p states appear at weak excitation energy, favor neutron capure with ln =0

  35. Searching for a new N=16 shell closure In-beam g-ray spectroscopy using double step fragmentation Size of N=16 > 4 MeV No bound excited state in 23O and 24O M. Stanoiu et al. PRC 69 (2004)

  36. After this point the talk is finished… Extra slides only !

  37. Evidence of intruder configurations in neutron-rich Ne isotopes J.R. Terry, Phys. Lett. B 640 (2006) 86 A. Obertelli Phys. Lett. B633 (2006)33 26Ne(d,p)27Ne in thick CD2 target 2 states at 765 and 885keV Inclusive s for 765keV, compatible with intruder L=0 L=1 L=2 28Ne(-1n)27Ne transition between 765 and 885keV Intruder state (765keV) has L1 from momentum distrib. L1 Cross section 1/2+ 3/2- p// (Gev/c) Reduction of the N=20 shell gap ?

  38. neutrons gammas 23O 22O 40Ar CD2 22O(d,p)23O reaction to probe the neutron N=16, 20 shell closures protons d qp RIKEN f7/2 d3/2 16 s1/2 14 d5/2 Elekes et al. PRL98 (2007) 102502 22O14

  39. Collapse of the N=28 shell closure in 42Si 42Si B. Bastin, S. Grévy et al., PRL 99 (2007) 20C 5 O E(2+) (MeV) C 0 5 10 20 15 Neutron Number M. Stanoiu submitted

  40. Knock-out reaction 12Be(-1n) to probe g.s. composition of 12Be 11Be unbound 1/2+ Pain et al., PRL 96 (2006) 032502 E*(MeV) J g l =0 2.7 (3/2 -) 1.8 (5/2 +) 12Be 1/2- Sn 1/2 - 0.3 l =1 1/2 + 0. 11Be Almost equal SF values Navin et al., PRL 85 (2000) 266 1.8 Admixtures of s, p and d states N=8 shell closure no longer present Erel (MeV) Confirms that the N=8 gap has collapsed

  41. Large quadrupole deformation in the N=20 isotones below Z=14 Proton inelastic scattering thick Liquid H target Island of inversion Y. Yanagisa et al., PLB 566 (2003) 84 sdfp SM predictions sd

  42. p3/2 fp f7/2 20 2p-2h excitations 20 d3/2 16 s1/2 sd 14 14 d5/2 8 8 p1/2 n n at Z=14 at Z=12

  43. p1/2 h9/2 p3/2 f7/2 82 50 d3/2 g9/2 h11/2 p1/2 s1/2 d5/2 g7/2 protons neutrons 130Cd pg9/2 Known T1/2 Need for good extrapolations far from known regions Understand bulk evolution of nucleus Always protons removed in the same g9/2 shell Proton(p)-neutron(n) interactions involving the g9/2 orbit, e.g. pg9/2 -ng7/2

  44. Evolution of the N=20 shell closure d5/2 ! • Onset of deformation around 32Mg • Specific role of the pd5/2 – nd3/2 and pd5/2 – nf7/2 interac. • No longer determine the size of the spherical N=20 gap • Some consequences … s1/2 d3/2 • Evolution of BE shows that : • N=20 gap remains large and constant as long as protons occupy d3/2 and s1/2 orbits • pn interactions involved have similar strength Vpn(d3/2f7/2)  Vpn(d3/2d3/2) Vpn(s1/2f7/2)  Vpn(s1/2d3/2) 40Ca 34Si 28O 7/2-

  45. Large N/Z 19K d3/2 d3/2 s1/2 s1/2 [ ] f7/2 f7/2 14 14 n n d5/2 d5/2 p p N=20 N=28 29Cu f5/2 g9/2 p3/2 p3/2 f5/2 n [ ] g9/2 SPIN-FLIP Dl=1 INTERACTION 28 28 n f7/2 f7/2 p p N=40 N=44 51Sb g7/2 d3/2 d3/2 d5/2 d5/2 g7/2 h11/2 h11/2 [ ] s1/2 s1/2 50 50 n n g9/2 g9/2 p p N≤64 N=70

  46. 5 O E(2+) (MeV) C 0 5 d3/2 d3/2 d5/2 0 16 s1/2 Effective Single Particle Energy (MeV) 16 s1/2 d5/2 14 -5 5 10 20 10 5 20 15 15 Neutron Number Neutron Number

  47. N=4 2d 40 50 1g g9/2 40 N=3 40 p1/2 2p f5/2 p3/2 1f 28 20 f7/2 20 20 N=2 d3/2 2s s1/2 1d 14 8 d5/2 8 N=1 L2 + L.S H.O + Simplified mean-field approach for atomic nuclei How will proton-neutron interactions (Dlnp=0,1)change this picture ? For large N/Z ratios, the L2 and L.S terms are expected to be reduced

  48. f7/2 N~20 f7/2 20 d3/2 d3/2 16 s1/2 s1/2 14 14 d5/2 [ ] d5/2 d5/2 d5/2 p n p n Z=14 Z=8

  49. ESPE in N=20 isotones and island of inversion Vpn(d3/2d5/2) >> Vpn(d3/2d3/2) d5/2 s1/2 d3/2 N=20 0f7/2 Island of inversion T. Otsuka EPJA (2004) 69

  50. Z=8 Z=20 Z=14 p3/2 p3/2 p3/2 Dl= 2 f7/2 f7/2 f7/2 d3/2 20 20 16 d3/2 d3/2 d3/2 d3/2 [ ] s1/2 s1/2 s1/2 s1/2 s1/2 14 14 14 d5/2 d5/2 [ ] [ ] d5/2 d5/2 d5/2 d5/2 p p p n n n unbound

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