New Trends in the Nuclear Shell Structure O. Sorlin GANIL Caen

Transcription

1 New Trends in the Nuclear Shell Structure O. Sorlin GANIL Caen I. General introduction to the atomic nucleus Charge density, shell gaps, shell occupancies, Nuclear forces, empirical monopoles, additivity, Quadrupole correlations, Role of monopoles, p-n tensor force II. Study of the N=20 shell closure Drip line Spectroscopic properties Change of shell gap A new magic number III. Study of the N=28 shell closure IV. Nuclear astrophysics V. Perspectives O. Sorlin and M.-G. Porquet Prog. In Part. Nucl. Phys. 61 (2008) Ecole Joliot Curie, Maubuisson 2009

2 I. General introduction to the atomic nucleus, shell closures, nuclear forces

3 The atomic nucleus : a world apart! 10 fm Zprotonset N neutrons Understand and model a microscopic system, the constituents of which are in strong and short range interaction ~1fm. Paradoxically, Mean field approach appropriate for heavy nuclei (Pauli) Nucleons are self-generating their mean field (contrary to e- in atoms) Charge density distribution -> mean field potential Nucleons arranged on orbits -> irregular spacing gives rise to shell gaps Shell model approach : Core nucleus on which two body interactions develop BUT differ from the bare NN forces / to which extent? Two quantum fluids ; Vnn (Vpp) ~ 1/3 Vnp due to Pauli principle -> importance of Vnp for structural changes

4 Charge density of the nucleus : ρ(r) F(q) e- Large transferred momentum q provides shape of the central density distribution ρ(r) scaling with A r

5 Probing nuclear orbits with (e,e p) reaction Orbital labelling n,l,j n nodes (n=0,1,2) L angular momentum (s,p,d,f,g,h ) (-1) L parity L-s <J< L+s (2J+1) per shell s 1/2 d 3/2 h 11/2 g 7/ Nuclear orbits 82 Pb N p E * [MeV] example : h 11/2 : L=5, J=11/2, L and s aligned contains 12 nucleons ->Nucleons are arranged on shells -> Gaps are present for certain nucleon numbers -> N p detected follows orbit occupancy -> Mixing with collective states at high E* -> Study limited (so far) to STABLE nuclei

6 Simplified mean-field approach for atomic nuclei ρ(r) U(r) r r N=4 40 N=3 20 N=2 8 N=1 2d 1g 2p 1f 2s 1d g 9/2 p 1/2 f 5/2 p 3/2 f 7/2 d s 3/2 1/2 Spin Orbit 6, 14, 28, 50, 82, 126 Harmonic Oscillator 8, 20, 40 H.O + L 2 + L.S 3 3 U ( r) ρ( r') v( r, r') d r' = ρ( r')[ v0 ( r r')] d r' = v0ρ( r) = vol vol

7 Our vision of MAGIC numbers up to 70 s universality - Large n and p separation energies - High energy of first excited states - Weak excitation probability - Spherical shape

8 Enlarged vision of nuclear structure using worldwide accelerators Haloes and cluster structures Island of superheavy elements Exotic radioactivities Collapse of shell closures To next shell Part IV casa - Chandra Part II Part III Rapid neutron capture nucleosynthesis -> Production of ½ of heavy elements -> Far from stability, new in-medium forces are explored / i.e. tensor forces

9 How can magic numbers (or shell gaps) be modified by nuclear forces?

10 Main features of the in-medium NN interaction Radial overlap (radial WF) : larger when n 1 =n 2 Angular momentum : maximum for l 1 =l 2 P(r) 1s 2p 1f Relative spin orbital momentum orientation : spin-orbit, tensor r l l 2 1 s s 2 1 Radius of the orbits (scales with 1/r or A -1/3 ) smoother changes in structure of heavy nuclei Interaction strength (MeV) Atomic Mass A

11 36 S Empirical determination of proton-neutron interaction d 3/2 p 38 Cl S n V pn (d 3/2 f 7/2 ) 36 S n f 7/2 37 S S p S n + S p 37 Cl TBME 38 Cl free 38 Cl Vpn ( V 7 / 2 3/ 2 < J < 7 / 2 + 3/ 2 pn = J (2J + 1) v J (2J J pn ( + 1) j p, j n )

12 Additive n-p interactions in the 36 S region? 36 S Neutron binding energy -1. MeV/p -1. MeV/p 40 Ca V pn (d 3/2 f 7/2 ) ~ -1 MeV per proton pn pn Δ( 20) = (2 j p + 1) ( Vd 3/ 2 f 7 / 2 Vd 3/ 2d 3/ 2) 4 Vpn (d 3/2 d 3/2 ) ~ -1 MeV per proton The N=20 shell gap is unchanged!

13 V pn (d 3/2 f 7/2 ) The role of quadrupole correlations in atomic nuclei (f 7/2 filling) ESPE p (MeV) 0 ε p (lower energy state observed) -2 ε d3/ ε s1/2 Quadrupole energy can be gained for certain orientations of particles At mid-shell, deviation from linear monopole trend -> correlations / coupling to excitations of the neutron core neutrons pn pn Δ( Z = 16) = 8 ( V d 3/ 2 f 7 / 2 Vs 1/ 2 f 7 / 2)

14 Evolution of proton configurations in the K chain exp monopole Exp :(d,3he) or ee p. [Doll 76, Banks 85, Kramer01] f 7/2 20 Role of pn monopole force Vd 3 f 7 >> Vs 1 f 7 No info on tensor! d 3/2 16 s 1/2 p /2 f7/2 π ν f 7/2 20 s 1/2 14 d 3/2 π 28 p 3/2 ν f 7/2 Z=19K N=20 Z=19K N=28 Proton s 1/2 and d 3/2 orbits degenerate

15 Predictive power : Evolution of sd proton states towards N=28 below Ca (Z=20) Gade et al. PRC 74 (2006) f 7/2 20 monopole d s 3/2 1/2 14 E2 π monopole Riley et al. PRC 78 (2008) 184 kev ~1MeV 43 P f 7/2 20 d s 3/2 1/2 14 π E2? monopole 43 P Degeneracy of proton s 1/2 and d 3/2 orbits preserved Role of monopole interactions similar How is the changed, tensor force? Change of Z=14 gap? From Gade PRC74 (2006) Fridmann et al. PRC 74 (2006)

16 Evolution of the Z=14 shell gap A way to constraint tensor interaction occupancy occupancy S 44 S 1/2 + 5/2 + 0 Exp+Utsuno 2 4(MeV) 3/2 + Exp 3/2 + 5/2 + 1/ E* strength d 3/2 s 1/2 14 d 3/2 s 1/ S S 28 νf 7/ EXP 35 P From N=20 to N=28, the proton is shifted at lower E* and is more fragmented Consistent picture with proton-neutron tensor forces P28 5/2+ 3/2+ 1/ (5/2 + ) EXP Riley + Bastin (5/2 + ) 3/2 + 1/ S(d, 3 He) 35 P 44 S 43 P

17 From spherical to deformed nuclei ESPE (MeV) 0 ε p2 (j n1, l n1 ) j p2, l p2 (j n2, l n2 ) -2 GAP -4 ε p1 ε p 2 j p1, l p1 ε p 2 spherical deformed -6 ε p 1 ε p 1 E( J ) 2 h = J ( J 2I + 1) N core N n1 N n2 When a spherical gap weakens, cross shell excitations can develop Quadrupole energy gain can bring the nucleus to deform If large deformation : low 2 + energy, large B(E2) value

18 From two-body short-range interactions to collective motion

19 II. The N=20 shell closure N=4 40 N=3 20 N=2 8 N=1 2d 1g 2p 1f 2s 1d Role of proton-neutron interaction π -νd 3/2? Collapse of shell closure New magic number g 9/2 p 1/2 f 5/2 p 3/2 f 7/2 d s 3/2 1/2 l 2 l 1 s 1 s 2 H.O + L 2 + L.S

20 ESPE in N=20 isotones and structural changes s 1/2 d 3/2 N=20 1) 28 O unbound? 16 Neutron Island of inversion 0f 7/2 2) N=20 disappears : Enhanced cross shell excitations Low 2 +, high B(E2) 3) Birth of a new magic number at N=16 34 Si T. Otsuka EPJA (2004) Ca Role of V pn d 3/2 to break the N=20 shell closure

21 28 O unbound? Bounderies of the N=20 playground Notami et al., PLB B542 (2002) 49 26,28 O nuclei unbound Drip line reached at N=16 in 24 O -d 3/2 orbit unbound 24 O N=20 F and Ne are bound up to N=22, 24 N=16 Adding one SINGLE proton in enables to bind SIX neutrons!

22 S 2N (MeV) Ca Mg Mg Neutron Number N 45 Ca E(2 + ) [MeV] N=20 magic number Disappears! N=20 20 Ca 12 Mg 14 Si 16 S Neutron Number 40 Ca 36 S 32 Mg B(E2) [e 2 fm 4 ] N=20 no gap gap 40 Ca 38 Ar 36 S 34 Si 32 Mg 30 Ne N/Z

23 Large occupancy of fp shells at N=20! 2p2h mechanism 30,32 Mg (-1n) -> occupancy and L value of neutron orbits Neutron ESPE Occupancy fp orbits fp J. R. Terry et al., PRC 77 (2008) In 32 Mg (N=20), ~2 neutrons occupy the fp shells Cross shell excitations are largely favoured

24 Search for a new magic number N=16 : Use of 22 O(d,p) 23 O to probe the neutron N=16, 20 shell closures 23,22 O Tracking, timing detectors Neutron wall d CD 2 target O 14 f 7/2 d 3/2 s 1/2 22 O CsI θ p p RIKEN (Japan) Elekes et al. PRL98 (2007)

25 The sizes of the N=20 and N=16 gaps in Oxygen Gated on neutrons Gated on 4 MeV neutron peak L=2 N=20 : 1.3 MeV N=16 : 4.0 MeV 23 O Elekes et al. PRL98 (2007) /2 + observed PRL99 (2007)

26 Evolution of Harmonic Oscillator shell closures SPIN FLIP Δl=0 INTERACTION 14 C 8 6 p 3/2 34 Si d3/2 s 1/2 14 π 68 Ni f 7/2 [ ] π [ ] [ ] π ν ν d s 5/2 1/2 8 N~8 Role of p 1/2 the π p 3/2 - ν p 1/2 interaction 6 6 ν p 3/2 p 3/2 f 7/2 g 9/2 p 1/2 f p 5/2 3/2 f 7/2 Z=6 Z=14 Z=28 N~20 N~40 p 3/2 Z=2 Z=8 f 7/2 Z=20 π π π ν d p 5/2 s 1/2 1/2 ν p 3/2 Role of the π - ν d 3/2 interaction Role of the π f 7/2 - ν f 5/2 interaction f p 7/2 3/2 d 3/2 s 1/2 d g 5/2 9/2 f 5/2 p 1/2 p 3/2 ν f 7/2 12 Be O Cr Large N/Z

27 Great similarity between the three cases of HO shell numbers N=8 N=20 N=40 Beta decay studies M. Hannawald, PRL 82 (1999) 1391 O. Sorlin et al. EPJA 16 (2003) 55 Dramatic change of nuclear structure due to spin-flip pn interaction!

28 Take away messages : Monopole term Very powerfull to predict structural evolution, Important role of correlations at mid-shells-> deformation Robust effect of NN forces to change HO shell gaps Too much monopole can cause severe damages!!!