Shell Eects in Atomic Nuclei
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1 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 1/37 Shell Eects in Atomic Nuclei Laurent Gaudefroy 1 Alexandre Obertelli 2 1 CEA, DAM, DIF - France 2 CEA, Irfu - France Shell Eects in Finite Quantum Systems Erice-Sicily July 25-31, 2010
2 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 2/37 The atomic nucleus General properties Z Protons: J π = 1/2 + ; N Neutrons: J π = 1/2 + ; A = N + Z fermions. Strong interaction range: 2 fm Nuclear radius: R r 0 A 1/3 fm, r fm. Nucleon mean free path: > R.
3 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 3/37 From nucleon-nucleon to nuclear interaction Nuclei description Strong short-range repulsion; A (N+Z) interacting fermions; Ab initio approach Nuclear mean eld Created by the (A-1) nucleons; Replaces NN-interaction. Shell Model or Mean Field approaches.
4 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 4/37 Magic numbers: 2, 8, 20, 28, 50, 82, 126 Goeppert Mayer & Jensen From M. Goeppert Mayer Nobel Lecture (1963) "What makes a number magic is that a conguration of a magic number of neutrons, or of protons, is unusually stable whatever the associated number of the other nucleons.[... ] We found that there were a few nuclei which had greater isotopic as well as cosmic abundance than our theory or any other reasonable theory could explain. Then I found those nuclei had something in common: they either had 82 neutrons, [... ] or 50 neutrons."
5 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 5/37 Spin-Orbit interaction Harmonic oscillator potential U(r) = 1 2 Mω2 r 2 Magic numbers: 2, 8, 20, 40, 70 Angular momentum and spin-orbit U (r) = U(r) + l 2 + ls Magic numbers: 2, 8, 20, 28, 50, 82
6 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 6/37 Success and failure of the nuclear shell model Good features 1 Accounts for known magic numbers. 2 Reproduces J π, E, Q, µ... Bad features 1 Built from knowledge on stable nuclei. 2 (Dis)appearance of magic numbers in unstable nuclei.
7 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 7/37 Outline Today 1 Few body systems. Haloes. Clusters. 2 Heavier systems. Shell evolution: general view. Studies at N = 28. Tomorrow 1 Shapes and coexistence. 2 Super heavy elements.
8 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 8/37 Few-body systems Why? 1 Nuclear interaction A 1/3 2 Strong shell eects expected 3 Exotic phenomena Haloes Clusters
9 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 9/37 Density distributions in He isotopes S.C. Pieper & R.B. Wiringa Annu. Rev. Nucl. Part. Sci.51, 53(2001). Add 2 neutrons to 4 He ρ(r > 2) factor of He 8 He
10 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 9/37 Density distributions in He isotopes S.C. Pieper & R.B. Wiringa Annu. Rev. Nucl. Part. Sci.51, 53(2001). Add 2 neutrons to 4 He ρ(r > 2) factor of He 8 He From 40 Ca to 42 Ca No signicant change.
11 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 9/37 Density distributions in He isotopes S.C. Pieper & R.B. Wiringa Annu. Rev. Nucl. Part. Sci.51, 53(2001). Add 2 neutrons to 4 He ρ(r > 2) factor of He 8 He From 40 Ca to 42 Ca No signicant change. idem for 44 Ca...
12 Density distributions in He isotopes S.C. Pieper & R.B. Wiringa Annu. Rev. Nucl. Part. Sci.51, 53(2001). Add 2 neutrons to 4 He ρ(r > 2) factor of He 8 He From 40 Ca to 42 Ca No signicant change. idem for 44 Ca neutrons latter ρ(r > 2). L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 9/37
13 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 10/37 Halo nuclei An exotic phenomenon Weakly bound nuclei. Extension of neutron wave function out of the interaction range! Linked to shell structure (s or p waves).
14 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 11/37 Halo nuclei: Experimental evidence R from reaction cross section: σ = π(r Target + R Proj ) 2. I. Tanihata, J. Phys. G: Nucl. Part. Phys.22, 157 (1996).
15 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 11/37 Halo nuclei: Experimental evidence R from reaction cross section: σ = π(r Target + R Proj ) 2. Does not follow A 1/3 law for: ( 6,8 He), 11 Li, 11,14 Be and 17 B. (Near) Drip line nuclei. I. Tanihata, J. Phys. G: Nucl. Part. Phys.22, 157 (1996).
16 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 12/37 Halo nuclei: Shell eect
17 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 12/37 Halo nuclei: Shell eect Drip-line Loosely bound systems Ψ(r) e Snr r. Low l Centrifugal force.
18 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 13/37 Halo nuclei: Shell eect Drip-line Loosely bound systems Ψ(r) e Snr r. Low l Centrifugal force.
19 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 14/37 Halo nuclei: Shell eect Structural eect From N = 9 to N = 14: νd 5/2 lling. Strong shell eect Shell rearrangement.
20 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 14/37 Halo nuclei: Shell eect Structural eect From 15 C 9 to 22 C 16 νs 1/2 orbit as GS. Not yet quantitatively understood.
21 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 15/37 Halo nuclei Summary 1 Extension of nucleon wave function out of interaction range. 2 Appear in light loosely bound nuclei. 3 Shell eects orbital reordering.
22 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 16/37 Density distribution in 8 Be. Unbound GS: T 1/ s 8 Be 4 He + 4 He. 0 + : two structures 4 He cluster. α: N = Z = 2. Clusters might appear in light N = Z nuclei. R. B. Wiringa et al., Phys. Rev. C 62, (2000).
23 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 17/37 Clusters in nuclei Energy threshold for clustering Must be energetically allowed. 8 Be 2α 4n X nα Cluster phase expected around E = decay threshold. K. Ikeda et.al, Prog. Theor. Phys. (Suppl.), 464. (1968)
24 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 18/37 Clusters & Shell eects Adapted from: M. Freer, Rep. Prog. Phys. 70, 2149 (2007).
25 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 18/37 Clusters & Shell eects Adapted from: M. Freer, Rep. Prog. Phys. 70, 2149 (2007).
26 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 18/37 Clusters & Shell eects Adapted from: M. Freer, Rep. Prog. Phys. 70, 2149 (2007).
27 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 18/37 Clusters & Shell eects Adapted from: M. Freer, Rep. Prog. Phys. 70, 2149 (2007).
28 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 19/37 Clusters in nuclei. Summary α clusters appear in N=Z light nuclei. Close to decay threshold. Strong deformation leading to shell rearrangement. Experimental evidence: Eg. look for deformed structure.
29 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 20/37 Digression: 12 C, life and clusters. Synthesis of 12 C Insucient production for 12 C; F. Hoyle (1954) predicted a 7.27 MeV state
30 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 20/37 Digression: 12 C, life and clusters. Synthesis of 12 C Insucient production for 12 C; F. Hoyle (1954) predicted a 7.27 MeV state Triple α process: Fowler (Nobel Prize 1983).
31 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 21/37 Few Body Systems Summary 1 Benchmarks for models. 2 Strong shell eects. 3 exotic phenomena: 4 haloes, clusters, molecules,...
32 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 22/37 Outline Today 1 Few body systems. 2 Heavier systems. Shell evolution: quick tour. Studies at N = 28.
33 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 23/37 Shell evolution: overview N = O 8 : E(2 + ) 7 MeV 12 4 Be 8 : E(2 + ) 2 MeV 2s 1/2 intruding and breaking the gap.
34 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 24/37 Shell evolution: overview N = Ca 20: E(2 + ) 7 MeV Mg 20: E(2 + ) 0.9 MeV Island of deformation near Mg 20.
35 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 25/37 Shell evolution: overview N = Ca 28: E(2 + ) 4 MeV Si 28: E(2 + ) 0.8 MeV Island of deformation near Si 28.
36 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 25/37 Shell evolution: overview N = Ca 28: E(2 + ) 4 MeV Si 28: E(2 + ) 0.8 MeV Island of deformation near Si 28.
37 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 26/37 Shell evolution: overview 50, 82 Predicted to disappear in exotic (enough) nuclei. 14, 16, 32, 40 Observed magic properties in neutron-rich nuclei. 70 Predicted as magic number in exotic nuclei.
38 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 27/37 The N = 28 magic number 1 st Spin-Orbit magic number
39 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 27/37 The N = 28 magic number 1 st Spin-Orbit magic number
40 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 27/37 The N = 28 magic number 1 st Spin-Orbit magic number
41 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 27/37 The N = 28 magic number 1 st Spin-Orbit magic number
42 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 27/37 The N = 28 magic number 1 st Spin-Orbit magic number Study of exotic nuclei A way to access part of NN interaction not at play in stable nuclei.
43 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 28/ excitation energy Onset of correlations - Indirect evidence 1 N = 20, 28: magic at Z = 20.
44 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 28/ excitation energy Onset of correlations - Indirect evidence 1 N = 20, 28: magic at Z = Deacrease at Z = and at Z = 14 as well. N = 20 remains rigid up to Z = 14, while N = 28 vanishes.
45 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 29/37 Basic interpretation 2 + congurations Neutron excitations across N = 28. (νf 7/2 νp 3/2 ) Jπ =2 +.
46 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 29/37 Basic interpretation 2 + congurations Neutron excitations across N = 28. (νf 7/2 νp 3/2 ) Jπ =2 +. Shell gap reduced E(2 + ) reduced. Neglects correlations.
47 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 30/37 Transfer reaction Interest Direct way to probe shell structure Possible for relatively high intensity beam (> 10 4 pps) Performed on the radioactive Ar 28 nucleus.
48 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 31/37 Transfer reaction: 46 Ar(d, p) 47 Ar Experimental Setup: SPEG at GANIL
49 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 31/37 Transfer reaction: 46 Ar(d, p) 47 Ar Experimental Setup: SPEG at GANIL
50 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 31/37 Transfer reaction: 46 Ar(d, p) 47 Ar Experimental Setup: SPEG at GANIL
51 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 31/37 Transfer reaction: 46 Ar(d, p) 47 Ar Experimental Setup: SPEG at GANIL
52 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 32/37 46 Ar(d, p) 47 Ar: Results Level scheme State congurations
53 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 32/37 46 Ar(d, p) 47 Ar: Results Level scheme State congurations
54 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 32/37 46 Ar(d, p) 47 Ar: Results Level scheme State congurations Conclusions 1 Still single particle states in 47 Ar. 2 7/2 intruder state. 3 Slight erosion of N = 28 (by 300keV).
55 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 33/37 Shell evolution from 20 Ca to 14 Si
56 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 33/37 Shell evolution from 20 Ca to 14 Si 1 πs 1/2 and d 3/2 orbits degenerate. 2 Attractive πd 3/2 -νf 7/2 interaction.
57 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 33/37 Shell evolution from 20 Ca to 14 Si 1 πs 1/2 and d 3/2 orbits degenerate. 2 Attractive πd 3/2 -νf 7/2 interaction.
58 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 33/37 Shell evolution from 20 Ca to 14 Si 1 πs 1/2 and d 3/2 orbits degenerate. 2 Attractive πd 3/2 -νf 7/2 interaction. 3 Not strong enough eect.
59 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 34/37 Shell evolution: what else? Correlations H Mono main component: H = H Mono + H Multi V Mono = J J (2J + 1)Vij (2J + 1) J H Multi : correlations (pairing, quadrupole,... ).
60 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 35/37 Onset of correlation at N = Ca: Less than gap size
61 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 35/37 Onset of correlation at N = Ca: Less than gap size 46 Ar: Promote 2 neutrons L. Gaudefroy et al., Phys. Rev. Lett.97, (2006).
62 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 35/37 Onset of correlation at N = Ca: Less than gap size 46 Ar: Promote 2 neutrons L. Gaudefroy et al., Phys. Rev. Lett.97, (2006). 44 S: Spher./Def. shape coex. S. Grévy et al., Submit. to Phys. Rev. Lett. 42 Si: Deformed nucleus. B. Bastin et al., Phys. Rev. Lett.99, (2007).
63 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 36/37 Shell evolution at N = 28: Summary
64 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 36/37 Shell evolution at N = 28: Summary
65 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 36/37 Shell evolution at N = 28: Summary
66 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 36/37 Shell evolution at N = 28: Summary
67 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 36/37 Shell evolution at N = 28: Summary
68 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 37/37 Concluding remarks 1 Atomic nuclei: A interacting fermions. 2 Shell structure and magic numbers.
69 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 37/37 Concluding remarks 1 Atomic nuclei: A interacting fermions. 2 Shell structure and magic numbers. 3 Shell eects: orbital reordering. 4 Few-body systems: exotic phenomena (Haloes, Clusters).
70 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 37/37 Concluding remarks 1 Atomic nuclei: A interacting fermions. 2 Shell structure and magic numbers. 3 Shell eects: orbital reordering. 4 Few-body systems: exotic phenomena (Haloes, Clusters). 5 Original models from stable nuclei. 6 Exotic nuclei: a probe for NN-interaction. 7 Larger systems: from magic to strongly correlated.
71 L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 37/37 Concluding remarks 1 Atomic nuclei: A interacting fermions. 2 Shell structure and magic numbers. 3 Shell eects: orbital reordering. 4 Few-body systems: exotic phenomena (Haloes, Clusters). 5 Original models from stable nuclei. 6 Exotic nuclei: a probe for NN-interaction. 7 Larger systems: from magic to strongly correlated. 8 Correlations deformation - Alexandre's lecture.
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