Testing the validity of the Spin-orbit interaction Nuclear forces at the drip-line O. Sorlin (GANIL, Caen, France)

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1 PART 1: Testing the validity of the Spin-orbit interaction Nuclear forces at the drip-line O. Sorlin (GANIL, Caen, France) Introduction to the SO interaction Historical picture -> magic numbers The SO in the Relativistic Mean Field approach Role at drip line and in Superheavy nuclei A bubble nucleus to probe the validity of the SO interaction 34 Si a bubble nucleus PART 2: Predictions Use of transfer reaction Interpretation How are proton neutron interactions changing at drip line? Motivation The d 5/2 d 3/2 proton neutron interaction in 26 F Two experimental techniques Intepretation May the force be with you Obi-Wan Kenobi Star Wars XL workshop Hirschegg, Jan 2012

2 The Spin orbit interaction: definition, effects

3 Spin orbit force and magic numbers 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, Haxel et al. Nobel prize 1949 ( r) ρ ( r = v s r V ) s H.O + L 2 + L.S The SO interaction has been introduced to account for the existence of large shell gaps (magic numbers) which could not be explained otherwise

4 ρ(r) The spin orbit (SO) interaction in Mean Field models ρ ( r) ρ ( r) τ τ τ = W + W 1 2 r r V s ' ( r) τ Density dependence l,s s splitting + ½( l + 1) - l/2 j j V ls (r) Normal nucleus Neutron skin (drip-line) Bubble nucleus (SHE) r r Isospin dependence W W 1 1 / W / W 2 2 Asymmetric splitting of j orbits 2 ( MF) 1 ( RMF) No isospin dependence in RMF - SO force revealed in atomic nuclei as nuclei have finite size -Its density dependence should play a role in extreme systems, not studied so far

5 The spin orbit interaction at the drip line 40 Ne MF and RMF calculations predict different behaviours of the SO interaction when reaching drip lines SO splitting weaker in RMF (comes from isospin dependence) Would affect the evolution of shell gaps differently Consequence for the r process nucleosynthesis G. A. Lalazissis et al. Phys. Lett. B 418 (1998)

6 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 Agrees with Morjean et al. PRL 101 (2008)

7 Superheavy nuclei anticipated with the S3 project at GANIL By coutesy of C. Theisen

8 How to test the validity of the spin-orbit interaction? - Density dependence - L.S - Isospin dependence

9 Probing the SO interaction using a bubble nucleus. 2πs 1/2 empty in 34 Si 1d 3/2 2s 1/2 1d 5/2 34 Si a bubble nucleus, Grasso et al PRC 79 (2009) [ ] 34 Si 20 [ ] 36 S 20 central depletion 34 Si 36 S RMF The 34 Si exhibits a large central depletion compared to 36 S. Orbits probing the interior of nucleus strongly affected Predictions RMF/ NL3 95% MF Skyrme 40% Test of density dependence of the SO force by determining the change of p 3/2 -p 1/2 splitting between 34 Si / 36 S Change of ν(p 1/2 -p 3/2 ) splitting p 1/2 p 3/2 34 Si n SO/SO (%) = n (SO) = y-x Diff Mean n SO/SO (p 3/2 -p 1/2 ) SM 40 % y-x (x+y)/2 VlowK 20-40% cutoff dependent Assuming 2 protons removed from 2s 1/2 x 36 S = y=2mev

10 Experimental set up for 34 Si(d,p) 35 Si Tracking detectors (CATS) EXOGAM 34 Si pps 20A.MeV S1 CD 2 CHIO + plastic ions d p θ p protons γ s f p 5/2 1/2 3/2 f 7/2 35 Si Reaction in inverse kinematics GANIL, IPN Orsay,CEA Saclay, IPHC Strasbourg

11 EXPERIMENTAL RESULTS 34 Si(d,p) 35 Si dσ dω mb/sr g.s. f SF=0.56(11) N p f 7/2 40 p 3/2 106 < θ lab < 115 S n θ CM ~10 35 Si 20 p 1/2 dσ dω 910keV p E* dσ dω 2040keV SF=0.70(14) p N γ / /2-120 SF=0.73(14) Θ p (lab) 35 Si 7/ Eγ [kev] J=3/2 -, agrees with Nummela et al. PRC (2001)

12 INTERPRETATION (1) SF f 7/2 p 3/2 2MeV p 1/2 p 3/2 36 S MeV E(MeV)* 34 Si f 7/2 p 3/2 p 1/2 Reduction of observed SO splitting between 36 S and 34 Si by about 55% Qualitatively agrees with density dependence of the SO Asymmetric shift of the p components Expected from an. s coupling Isospin dependence seems between MF and RMF but depends on change in occupancy! Consider the effect of correlations on the SO splitting value Work in progress using Shell Model calculations (F. Nowacki)

13 Studying proton-neutron interactions at the drip line

14 MOTIVATIONS Z=120 Superheavy nuclei Explosive nucleosynthesis π ν 15MeV

15 Are proton-neutron interactions similar at drip line? d 5/2 p 24 O n 26 F d 3/2 V pn (d 3/2d 5/2) J=1,2,3,4 15MeV d 5/2 π ν d 3/2 -> Study of 26 F 26 F 0.77MeV 26 Ffree 3 S n =800keV J USDA USDB Shell Model, Brown Int (J) (kev) 25 O unbound, Hoffman PRL 100(2008) 26 F g.s. J=1 from beta-decay, Reed et al. PRC 3 + : Frank et al. (NSCL) PRC (2011) Masses: Jurado PLB 649 (2007) Search for J=2, 4 states using different experimental techniques Compare experimental binding energies in 26 F to those predicted by Shell Model using effective forces constrained closer to stability need spectroscopy of 26 F.

16 Search for J=2 excited state in 26 F M. Stanoiu et al. accepted in PRC 2012 wedge GANIL Secondary beams SISSI target N γ BaF J= E(keV) E F Ne O 22 N 19 C 3 A/Q Thick Target: C (112 mg.cm -2 ) + active Plastic 103mg.cm -2 SPEG

17 Searching for a 4 + isomer in 26 F 26 F, others 2.5ms 7ms Delayed γ spectrum up to 10ms Compatible with M3 transition! J=4 1 others N γ F t(ms) A. Lepailleur, O.S. et al. GANIL

18 Proton-neutron interaction d 5/2 d 3/2 in 26 F V pn (d 5/2 d 3/2 ) d 5/2 p 24 O n 26 F d 3/2 EXP USDA Interaction energy (kev) 26 Ffree J USDA Brown exp Spin J ~30% reduced interaction as compared to Shell Model! + Global shrink of levels Use proper treatment of continuum Work in progress (G. Hagen) Int (J) (kev)

19 Conclusions & Perspectives PART 1: Use of a bubble nucleus 34 Si to prove the density-dependence of the spin-orbit interactoion Change of the neutron p 3/2- p 1/2 splitting by ~55% between 36 S and 34 Si. So far exp value fall in between MF and RMF pedictions! Determine the amplitude of the bubble Study the effect of fragmentation of sp states on this splitting (collab. F. Nowaki). Consequences Drip line, Location of the island of stability in SHE PART 2 : Use the spectroscopy of 26 F to infer the change of the proton-interaction close to drip line Reduction of the interaction by 30% Check the atomic mass, confirm energy of unbound state(s) (collab. T. Look at the effect of the continuum to account for this reduced interaction (collab. G. Hagen)

20 END OF TALK, After are extras

21 INTERPRETATION (2) Change of SO interaction with proton occupancy 100 Shell Model RMF SO/SO (%) exp MF Bare 2 body (2s 1/2 ) The use of 2-body V lowk bare forces cannot itself account for the observed SO change The Mean Field (MF) model seems not to be adequate The Relativistic Mean Field model would be adequate if s 1/2 =1 (i.e. the bubble is moderate) Otherwise new ingredients needed in the theory! Determine experimentally the amplitude of the bubble (scheduled in 2012 at NSCL/MSU)

22 EXPERIMENTAL RESULTS (2) SF SF 1 p 3/2 p 1/2 2MeV Ca E* 36 S Taking the major fragment of the s.p. strength the p3-p1 SO splitting is 2MeV in 41 Ca It is 1.7MeV taking the whole strength. Uozumi et al. PRC (1993) f p 1/2 7/2 p 3/2 2MeV MeV f 7/2 p 3/2 p 1/2 E* 34 Si Taking the major fragment of the s.p. strength -> Reduction of the SO splitting by 55% -> Asymmetric shift of p 1/2 and p 3/2 states Role of correlations is being investigated F. Nowacki and A. Poves 1

23 The use of a bubble nucleus to probe the SO interaction 6 36 S Exp /2+ ρ p (r)(fm -3 ) Grasso et al, PRC 79 (2009) 36 S 34 Si RMF calc r(fm) d 3/2 s 1/2 d 5/2 d 3/2 s 1/2 d 5/ S S(d, 3 He) 35 P 1/2 + 5/2 + 3/ (MeV) 2386 EXP 35 P Khan et al. PLB 156 (1985) 3/2+ 1/2+ 16 IDEAL CANDIDATE -Large central proton depletion F~40% -Magic nucleus E(2 + ) > 3.3MeV -Weak mixing between states 34 Si 20 The neutron p orbits probes the interior of the nucleus, while the f probes the surface The neutron p 3/2 -p 1/2 splitting should change between 36 S and 34 Si