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 16 ---------------------------------------------------------------------------- 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
I. General introduction to the atomic nucleus, shell closures, nuclear forces
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
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
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 7/2 82 50 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
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 40 20 8 50 40 28 20 14 8 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
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 50 28 82 20 50 8 20 28 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
How can magic numbers (or shell gaps) be modified by nuclear forces?
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
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 )
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!
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 d3/2-4 16-6 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 20 28 neutrons pn pn Δ( Z = 16) = 8 ( V d 3/ 2 f 7 / 2 Vs 1/ 2 f 7 / 2)
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 14 28 3/2 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
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)
Evolution of the Z=14 shell gap A way to constraint tensor interaction occupancy occupancy 6 4 2 4 2 36 S 44 S 1/2 + 5/2 + 0 Exp+Utsuno 2 4(MeV) 3/2 + Exp 3/2 + 5/2 + 1/2 + 0 2 4 E* strength d 3/2 s 1/2 14 d 3/2 s 1/2 14 16 36 S 20 44 S 28 νf 7/2 3857 2386 1100 845 EXP 35 P 15 20 From N=20 to N=28, the proton is shifted at lower E* and is more fragmented Consistent picture with proton-neutron tensor forces 184 43 15P28 5/2+ 3/2+ 1/2+ 2035 (5/2 + ) EXP Riley + Bastin (5/2 + ) 3/2 + 1/2 + 36 S(d, 3 He) 35 P 44 S 43 P
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
From two-body short-range interactions to collective motion
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 40 20 8 50 40 28 20 14 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
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) 69 40 Ca Role of V pn d 3/2 to break the N=20 shell closure
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!
S 2N (MeV) 40 30 20 10 36 Ca 20 27 Mg 20 35 Mg 16 20 24 Neutron Number N 45 Ca E(2 + ) [MeV] N=20 magic number Disappears! 4 3 2 1 0 N=20 20 Ca 12 Mg 14 Si 16 S 12 16 20 24 Neutron Number 40 Ca 36 S 32 Mg B(E2) [e 2 fm 4 ] 400 200 N=20 no gap gap 40 Ca 38 Ar 36 S 34 Si 32 Mg 30 Ne N/Z
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) 014316. In 32 Mg (N=20), ~2 neutrons occupy the fp shells Cross shell excitations are largely favoured
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 16 14 22 O 14 f 7/2 d 3/2 s 1/2 22 O CsI θ p p RIKEN (Japan) Elekes et al. PRL98 (2007) 102502
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) 102502 5/2 + observed PRL99 (2007)
Evolution of Harmonic Oscillator shell closures SPIN FLIP Δl=0 INTERACTION 14 C 8 6 p 3/2 34 Si 14 20 20 d3/2 s 1/2 14 π 68 Ni 40 28 f 7/2 [ ] π [ ] [ ] π ν 40 28 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 16 14 ν 34 32 28 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 8 4 28 O 20 8 64 Cr 40 24 Large N/Z
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!
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!!!