Study of the spin orbit force using a bubble nucleus O. Sorlin (GANIL)

Transcription

1 Study of the spin orbit force using a bubble nucleus O. Sorlin (GANIL) I. General introduction to the atomic nucleus Charge density, nuclear orbits Shell gaps-> magic nuclei II. The spin orbit force History Mean field theories Implications to explosive stellar nucleosynthesis super heavy nuclei III. Probing the spin orbit force May the force be with you The use of a bubble nucleus 34 Si Obi-Wan Kenobi Star Wars Production of 34 Si at the GANIL accelerator Determine the neutron SO splitting using 34 Si(d,p) 35 Si Results IV Conclusions/ Perspectives Russbach, March 2014

2 Study of the spin orbit force using a bubble nucleus O. Sorlin (GANIL) I. General introduction to the atomic nucleus Charge density, nuclear orbits Shell gaps-> magic nuclei II. The spin orbit force History Mean field theories Implications to explosive stellar nucleosynthesis super heavy nuclei III. Probing the spin orbit force The use of a bubble nucleus 34 Si Production of 34 Si at the GANIL accelerator Determine the neutron SO splitting using 34 Si(d,p) 35 Si Results IV Conclusions/ Perspectives

3 Charge density of the nucleus : ρ(r) E e = c/λ E e ~200MeV for λ =1fm q = transferred momentum e At small q F(q) ~Ze (1-q 2 /6 <r 2 >) F(q) 0.1 Large q : central density distribution ρ(r) scaling with A 1/ r (fm) Saturation of nuclear forces r

4 Charge density of the nucleus : ρ(r) E e = c/λ E e ~200MeV for λ =1fm q = transferred momentum e- ρ(r) L=0 L=1 L=2 At small q F(q) ~Ze (1-q 2 /6 <r 2 >) F(q) 0.1 Large q : central density distribution r r

5 Charge density depletion in the center of the 205 Tl nucleus Cavendon PRL (1982) Charge density depletion due to the change in 3s 1/2 occupancy by 0.7 proton ρ[fm -3 ] Pb 205 Tl r[fm] Independent particle model works well also in the interior of nucleus Δρ (r) (e fm -3 ) r[fm] MF s 1/ r (fm)

6 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 d 5/2 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 scales with orbit occupancy -> Mixing with collective states at high E* -> Study limited (so far) to STABLE nuclei

7 Study of the spin orbit force using a bubble nucleus O. Sorlin (GANIL) I. General introduction to the atomic nucleus Charge density, nuclear orbits Shell gaps-> magic nuclei II. The spin orbit force History Mean field theories Implications to explosive stellar nucleosynthesis super heavy nuclei III. Probing the spin orbit force The use of a bubble nucleus 34 Si Production of 34 Si at the GANIL accelerator Determine the neutron SO splitting using 34 Si(d,p) 35 Si Results IV Conclusions/ Perspectives

8 Magic nuclei and the spin-orbit interaction V s (r) = W ρ(r) r ρ(r) V ls (r) s r r N=4 40 N=3 20 N=2 8 N=1 2d 1g 2p 1f 2s 1d d 5/2 g 9/2 p 1/2 f 5/2 p 3/2 f 7/2 d s 3/2 1/2 d 5/2 Spin Orbit 6, 14, 28, 50, 82, 126 M. Goppert-Mayer Nobel prize 1949 H.O + L 2 + l L.S s

9 The spin orbit (SO) interaction in Mean Field models # V s ρ n (r) = W n (r) % 1 $ r +W 2 ρ p (r) r & ( s ' ρ(r) Density dependence + ½( l + 1) j l,s splitting r - l/2 j V ls (r) Normal nucleus Neutron skin (drip-line) Bubble nucleus (SHE) r Asymmetric splitting of j orbits Isospin dependence W W 1 1 / W / W ( MF) ( RMF) No isospin dependence in RMF Density and isospin dependence of the SO interaction not yet known/contrained Important for 1- r process 2- bubble nuclei 3- superheavy nuclei

10 Shell closures and neutron captures nucleosynthesis s : slow neutron captures (AGB stars) up to cm - 3 r : rapid neutron captures (NS mergers?) > cm - 3 Elements in solar system Closed shells Drop of n capture cross sec;ons σ n Large (γ,n) rates: (n,γ)- (γ,n) equilibrium Longest half- lives T 1/2 Accumula;on of elements Smoothening of r peak due to neutron emission P n

11 Influence of nuclear structure on the abundance of elements Solar r abundance 132 Sn Solar Strong shell closure Weak shell closure Adapted from Pfeiffer, Kratz et al. Location and shape of r process peaks does depend on the evolution of shell gaps (but not only!) Need new accelerators to produce/study nuclei further from stability Probe the spin-orbit interaction using other data d 3/2 f 7/2 s 1/2 i 13/2 f 5/2 p h 9/2 1/2 3/2 Around 132 Sn 126 h 11/2 g 7/2 d 5/2 g 9/ Drip line

12 Quest for superheavy elements ρ[fm -3 ] W[MeV fm -1 ] neutrons protons neutrons protons total M. Bender et al. PRC 60 (1999) SHE display central density depletions at certain proton and neutron numbers Reduction of the SO splittings depends on isospin dependance of SO Location of island of stability depends on models

13 Study of the spin orbit force using a bubble nucleus O. Sorlin (GANIL) I. General introduction to the atomic nucleus Charge density, nuclear orbits Shell gaps-> magic nuclei II. The spin orbit force History Mean field theories Implications to explosive stellar nucleosynthesis super heavy nuclei III. Probing the spin orbit force A bubble nucleus 34 Si Production of 34 Si at the GANIL accelerator Determine the neutron SO splitting using 34 Si(d,p) 35 Si Results / Perspectives IV Conclusions/ Perspectives

14 Finding a bubble nucleus in nature. E(2 + ) [MeV] N=20 20 Ca Neutron Number 1d 3/2 2s 1/2 1d 5/2 [ ] 40 Ca 20 ρ p (r) 40 Ca

15 Finding a bubble nucleus in nature. E(2 + ) [MeV] N=20 20 Ca 16 S Neutron Number 1d 3/2 2s 1/2 1d 5/2 [ ] 36 S 20 ρ p (r) 40 Ca ρ p (r) 36 S

16 Finding a bubble nucleus in nature. E(2 + ) [MeV] N=20 20 Ca 14 Si 16 S Neutron Number 1d 3/2 2s 1/2 1d 5/2 [ ] 34 Si 20 ρ p (r) ρ p (r) ρ 40 Ca 36 S p (r) 34 Si Calc. J.P Ebran, DDME2 interaction

17 PROBING THE SO INTERACTION WITH A BUBBLE NUCLEUS 34 Si 36 S Change of ν(p 1/2 -p 3/2 ) splitting p 1/2 p 3/2 34 Si x 36 S y=2mev HF/Skyrme RMF n 1 V sα n p r r n 1 V sα ρn( r) + ρ p( r r r [ 2ρ ( r) + ρ ( r ] s ) [ ] s ) Δ n SO/SO (%) = y-x (x+y)/2 = Diff Mean Predictions Δ n (SO) = y-x Δ n SO/SO (%) RMF/ NL3 95 MF Skyrme Shell Model 33 Isospin dependence differs HF/ Skyrme and RMF models

18 Probing the neutron orbits in 34 Si via transfer reaction in inverse kinematics d p θ p E p -> binding energy θ p -> orbital momentum L γ p f 5/2 1/2 f 3/2 7/2 Probability of transfer-> vacancy 34 Si If excited state, decays by γ ray emmission

19 36 S (v/c 0.3) Production and selection of 34 Si at GANIL target degrader Av/Z selection With degrader A 3 /Z 2 selection Energy loss 20 Mg 20 O 35 Si 34 Si Energy loss 34 Si pps Time of flight Time of flight

20 Experimental setup for the 34 Si(d,p) 35 Si reac?on 34Si 34 Si, pps d p θ p f p 5/2 1/2 3/2 f 7/2 35 Si Reaction in inverse kinematics Copyright E. Rindel IPN Orsay

21 Experimental setup for the 34 Si(d,p) 35 Si reac?on 34Si 34 Si, pps Position sensitive gaz detector 0.2 mm resolution Copyright E. Rindel IPN Orsay

22 Experimental setup for the 34 Si(d,p) 35 Si reac?on 34Si 34 Si Copyright E. Rindel IPN Orsay

23 Experimental setup for the 34 Si(d,p) 35 Si reac?on 34Si 34 Si, pps Segmented Ge crisyals N γ 35 Si E γ (kev) Copyright E. Rindel IPN Orsay

24 Experimental setup for the 34 Si(d,p) 35 Si reac?on 34Si 34 Si, pps Ionisation chamber Digitized signal Copyright E. Rindel IPN Orsay

25 EXPERIMENTAL RESULTS 34 Si(d,p) 35 Si S n 1134 E*<1.5MeV E*>1.5MeV L assignments from proton angular distributions Accurate energy of states with γ-ray detection J. Burgunder et al., Phys. Rev. Letters 2014

26 Evolution of the p 3/2 -p 1/2 SO splitting ρ p (r) 40 Ca Z=20 ρ p (r) 36 S Z=16 ρ p (r) 34 Si Z=14 The p 3/2 -p 1/2 splitting changes by almost a factor of 2 between 37 S and 35 Si Density dependence of the SO interaction proven Isospin dependance constrained

27 Modification of the SO splitting in a bubble nucleus ΔSO/SO (%) RMF DDME2 RMF NL3 Gogny D1S No isospin dependance SGII iso. dep. exp Δ(2s 1/2 ) Exp. favors density AND isospin dep. of SO interaction Anticipate consequences for drip line and SHE nuclei

28 Spin orbit interaction and superheavy elements ρ[fm -3 ] W[MeV fm -1 ] neutrons protons neutrons protons total M. Bender et al. PRC 60 (1999) ε n [MeV] ε p [MeV] RMF p 1/2 p 3/2 f 5/2 114 f i 7/2 13/2 h 9/2 large SO 120 weak SO 172 Size of gaps depends on strength of the SO force Island of SHE favoured at Z~120 in RMF

29 Conclusions & Perspec?ves 34 Si Bubble nucleus to probe density and isospin dependence of the SO interac;on Change of the neutron p 3/2- p 1/2 splivng by ~33% è Density dependance of the SO interac;on established è isospin dependence of the SO interac;on è Conseq. on shell gaps far from stability and explosive nucleosynthesis è Conseq. on the Loca;on/existence of island of stability SHE è Determine the amplitude of the density deple;on (in NSCL/MSU with Gre;na)