Study of the spin orbit force using a bubble nucleus O. Sorlin (GANIL) Trento Sept 2014 THE PITCH The spin orbit (SO) force plays major role in nuclear structure to create shell gaps that are linked to the r process peaks l,s Shell gap l l s s The SO force has been postulated more than 60 years ago nowadays fundamental descriptions exist but models differ and no experiment is so far was able to test the SO force far from stability. ρ p (r) Si We proprose to use a bubble nucleus to test the properties of this SO force first time
OUTLINE I. Presentation of the topic The SO force and magic nuclei Magic nuclei and the r process SO force in extreme conditions Probing the SO force using a bubble nucleus II. Experimental part -1p knock-out to prove existence of bubble nucleus (NSCL/MSU) Transfer reactions to observe change in SO force (GANIL/France) III. Results/Discussions Density and isospin dependence of the SO force Consequences for r process May the force be with you Obi-Wan Kenobi Star Wars
Magic nuclei and the spin-orbit interaction V(r) 0-50 r n, L J N=4 40 N=3 20 N=2 8 N=1 2d 1g 2p 1f 2s 1d 40 20 8 H.O + L 2 + 50 40 28 20 14 8 L.S 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 SO force leads to shell gaps at 14, 28, 50, 82, 126 M. Goppert-Mayer Nobel prize 1949 l s
Magic nuclei and r process nucleosynthesis s : slow neutron captures r : rapid neutron captures Solar r abundance Solar Strong shell closure Weak shell closure Adapted from Pfeiffer, Kratz et al. Elements in solar system i 13/2 f 5/2 p h 9/2 1/2 3/2 126 126 d 3/2 f 7/2 s 1/2 h 11/2 g 7/2 d 5/2 g 9/2 82 50 82 50 Around 132 Sn Drip line
Atomic mass model predictions p drip line r process n drip line Z=55 KNOWN MASSES WARNING TITAN report Models can be all statisfactory (within 600keV) when masses are known It does not mean they have good predictibility Need to understand the physics process to extrapolate to unknown regions
ρ(r) # V s ρ n (r) = W n (r) % 1 $ r Density dependence The SO force in extreme conditions +W 2 ρ p (r) r & ( s ' j=l-s l,s splitting V ls (r) r Normal nucleus Neutron skin (drip-line) Bubble nucleus or SHE r j=l+s Splitting between j orbits Isospin dependence W 1 2W 2 W 1 W 2 (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- superheavy nuclei -> use the Si bubble nucleus
Using a bubble nucleus to probe SO interaction Si: proton bubble nucleus Change in neutron SO splitting Proton orbits Si 36 S p 1/2 p 3/2 Si x 36 S y=2mev Δ n SO/SO (%) = y-x (x+y)/2 = Diff Mean 100 RMF NL3 Proton depletion in s 1/2 1d 3/2 2s 1/2 1d 5/2 ΔSO(p)/SO (%) 80 60 40 20 RMF DDME2 Gogny D1S SGII Si 20 36 S 20 14 16 0.5 1.5 2 1 Δ(2s 1/2 ) or density depletion
I. Presentation of the topic The SO force and magic nuclei Magic nuclei and astrophysics SO force in extreme conditions SO force in the bubble nuclei Si II. Experimental part -1p knock-out to prove existence of bubble nucleus (NSCL/MSU) Transfer reactions to observe change in SO force (GANIL/France) III. Results/Discussions Density and isospin dependence of the SO force May the force be with you Obi-Wan Kenobi Star Wars
(NSCL/MSU) Si v/c=0.36 105 pps 33Al γ
Proton occupancies in Si using (- 1p) reac=on Gamma-ray spectrum at 90 33 Al BR(%) Si (-1p) 33 Al 1.4(2) L=2 2.4(4) L=0 14±2 L=2 L=0 L=2 Preliminary A. Mutschler E*=3707 kev p // Σoccupancy(L=2)= 5.7(2) Σoccupancy (L=0)=0.15 (2) p // ground state 79±2 33 Al L=2 Very small L p =0 knock-out observed -> in agreement with a bubble nucleus
Si: a bubble nucleus Proton orbits 1d 3/2 2s 1/2 occup 0.2 1.8 ρ p (r) 36 S Rather large central depletion -> look what is the change in SO 1d 5/2 36 S 20 6 36 S(d, 3 He) 35 P Khan et al. PLB 156 (1985) Proton orbits 1d 3/2 2s 1/2 occup 0.15(3) ρ p (r) Si ΔSO(p)/SO (%) 100 80 60 40 20 RMF NL3 RMF DDME2 Determin Gogny D1S SGII 1d 5/2 5.7(2) 0.5 1.5 2 1 Δ(2s 1/2 ) Si 20 Si(-1p) 33 Al Mutschler et al. in prep. J.P. Ebran DDME2 interaction
I. Presentation of the topic The SO force and magic nuclei Magic nuclei and astrophysics SO force in extreme conditions SO force in the bubble nuclei Si II. Experimental part -1p knock-out to prove existence of bubble nucleus Transfer reactions to observe change in SO force III. Results/Discussions Density and isospin dependence of the SO force Consequences Perspectives May the force be with you Obi-Wan Kenobi Star Wars
Change of p 3/2 -p 1/2 and f 7/2 -f 5/2 splittings between 36 S and Si using (d,p) transfer reactions (d,p) transfer reaction used to probe the Energy (E*) Angular momenta (L) Occupancies/vacancies of neutron orbitals d p θ p E p -> binding energy γ f p 5/2 1/2 3/2 f 7/2 θ p -> orbital momentum L=1,3 Probability of transfer-> vacancy of the neutron orbitals Si If excited state, decays by γ ray emmission
Si(d,p) reac=on in inverse kinema=cs at GANIL Si 10 5 pps 20A.MeV GANIL Tracking detectors (CATS) S1 p EXOGAM γ CD 2 target 2.6mg cm - 2 CHIO + plas=c GANIL, IPN Orsay, CEA Saclay IPHC Strasbourg MUST2 EXOGAM Ioniza=on chamber (CHIO) Annular detector (S1)
Spin-orbit splittings in 35 Si using Si(d,p) 35 Si S n 11 E*<1.5 MeV E*>1.5 MeV 910 L assignments from proton angular distributions Accurate energy of states with γ-ray detection G. Burgunder et al., Phys. Rev. Letters 112 (2014)
Evolution of the p 3/2 -p 1/2 SO splitting ρ p (r) N=21 isotones 40 Ca Z=20 ρ p (r) 36 S 4 protons d 3/2 Z=16 ρ p (r) Si 2 protons s 1/2 Z=14 No change in p 3/2 - p 1/2 spliyng between 41 Ca and 37 S Large reduc=on of p 3/2 - p 1/2 spliyng between 37 S and 35 Si, no change of f 7/2 - f 5/2
Density and Isospin dependence of the SO interac=on Evolution of the p SO splitting as a function of central depletion ΔSO(p)/SO (%) 100 80 60 40 20 36 S RMF: iso. indep. MF iso. dep. exp RMF DDME2 Determin 46 Ar RMF NL3 Gogny D1S Si SGII 0.5 1.5 2 1 Δ(2s 1/2 ) 46 Ar: Gaudefroy et al. PRL 99 (2007) Si: Burgunder et al. PRL 112 (2014) Density & Isospin dependences well taken into account by MF calculations RMF does not have the proper isospin dependence of the SO interaction Consequences for shell gaps formed by the SO interaction for r process and SHE Perspectives Estimate the reduction of SO splitting when reaching drip line using appropriate isospin and density dependence Look at the effect of SO reduction on fission barriers of neutron rich nuclei Location of stable Super Heavy Elements to be revisited / better constrained?
Summary The spin orbit (SO) force plays major role in nuclear structure to create shell gaps that are linked to the r process peaks. We used a bubble nucleus Si to constraint the density and isospin dependence of the SO force. We find that a certain category of models can be ruled out to predict the evolution of SO far from stability where the r process takes place. Impacts of the SO on r process nucleosynthesis should be explored in the future. We can anticipate consequences for shell gap evolution as well as fission barrier distributions -> modify r peaks locations /shape?
March 8-14, 2015 Russbach, Austria Directors of the School: K.- L. Kratz (Mainz), O. Sorlin (GANIL), S. Bishop (Munich) ScienJfic CommiNee: A. Banu (Virginia) J. Margueron (Lyon) M. Busso (Perugia) L. I. Mashonkina (Moscow) N. Christlieb (Heidelberg) U. O^ (Mainz/Szombathely) R. Diehl (Munich) A. Parikh (Barcelona) J. Duprat (Orsay) R. Pizzone (Catania) M. El Eid (Beirut) F.- K. Thielemann (Basel) S. Harissopulos (Athens) W.B. Walters (Maryland) Ch. Iliadis (Chapel Hill) A. Zilges (Cologne) T. Kajino (Tokyo)
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