Testing the validity of the Spin-orbit force Nuclear forces at the drip-line O. Sorlin (GANIL, Caen, France) PART 1:

Transcription

1 Testing the validity of the Spin-orbit force Nuclear forces at the drip-line O. Sorlin (GANIL, Caen, France) PART : The 34 Si a bubble nucleus? Probing the neutron SO interaction using the 34 Si nucleus Experimental results on (d,p) reaction Interpretation, discussion The 34 Si nucleus as a tool to study nuclear matter incompressibility?! PART 2: Are proton neutron interactions changing at drip line? Motivation The d 5/2 d 3/2 proton neutron interaction in F Two experimental techniques Interpretation/perspectives May the force be with you Obi-Wan Kenobi Star Wars Workshop Shell Model Strasbourg, October 202

2 34 Si a bubble nucleus? 4 ρ p (r)(fm -3 ) Grasso et al, PRC 79 (2009) RMF calc S Si r(fm) d 3/2 s /2 d 5/ S 6 20 SUMMED OCCUPANCY S(d, 3 He) 35 P 36 S /2 + Exp 5/2 + 3/ (MeV) Khan et al. PLB 56 (985) EXP 35 P /2+ 3/2+ /2+ In 34 Si, the s /2 orbit should be empty è proton central density depletion Correlations determined from SM lead to Δs /2 =.45 Occupancy of this orbit should be determined using 34 Si(-p) knock out at NSCL This will provide the amplitude of the proton bubble.

3 Probing the spin- orbit interacon using the 34 Si nucleus > the mean field theories > the shell model approach

4 V s τ The spin orbit (SO) interaction in Mean Field models ρ ( r) ρ ( r) τ τ ' τ ( r) = W + W s 2 r r + ½( l + ) Density dependence ρ(r) l,s splitting - l/2 j j V ls (r) r Normal nucleus Bubble nucleus (SHE) r Isospin dependence W W / W / W 2 2 Asymmetric splitting of j orbits 2 ( MF) ( 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 Reduced SO splitting in bubble nucleus for orbits probing the interior of the nucleus! Reduction magnified in RMF approaches

5 Probing the two- body SO interacon N=20 SF(d,p) MAJOR FRAGMENTS 37 S Z=20 40 Ca 39 K f 7/2 p 3/2 p /2 G. Eckle et al. NPA 49 (989) Z=8 38 Ar d 3/ MeV Z=6 37 Cl 36 S Z=4 Z=2 34 Si 32 Mg s /2 d 5/2 Change of SO splizng?!!"!! 2!!2!!!!2!!!!!"!2!!!!2!!!!!"! 35 Si Pure two- body SO force See Nowacki, Smirnova, Otsuka

6 Determination of the p SO splitting in 35 Si

7 Experimental set up to study the 34 Si(d,p) 35 Si reaction Collab. GANIL, IPN Orsay, CEA Saclay, IPHC Strab PHD G. Burgunder 34Si (GANIL) target 34 Si, pps 20A.MeV Beam tracking d p θ p Annular detector Si f p 5/2 /2 3/2 f 7/2 Si strips MUST2 Copyright E. Rindel IPN Orsay

8 Proton time and energy spectra using MUST2 MUST2 ΔE[MeV] Ep[MeV] Ep[MeV]

9 Identification of the Si nuclei Ionization chamber (CHIO) C. Spitaels (GANIL), gated on γ-rays of 35 Si * C induced background CF 4 gas 70 mbar Rise time 250ns, Fall time.5 µs digitized every 0ns

10 EXPERIMENTAL RESULTS 34 Si(d,p) 35 Si f 06 < θ lab < 5 7/2 f 5/2 p 3/2 p / / /2-7/2-30

11 d 3/2 s /2 SF SF 0.75 f 7/2 p / f 7/2.9 MeV p 3/2 2 MeV p 3/2 2 MeV p /2 4 Ca GAP N=28 MAJOR STRENGTH ΔSO(p) Uozumi et al. PRC 50 (994) 37 S G. Eckle et al. NPA 49 (989) f 7/ p /2 p 3/2 0.9.MeV d 3/2 Taking correlaons into account : d 3/2 d 3/2 E*(MeV) E*(MeV) 35 Si G. Burgunder et al. to be submijed !!"!!.45!!2!!!!2!!!!!"!2!!!!2!!!!!" 400!"#! Large change in p SO splizng Two- body SO interacon

12 Evolution of SPE from two-body SO interaction Reducon of νp /2 - p 3/2 splizng between 37 S and 35 Si and aber removal of 2 protons* from πds /2 *.45 according to shell model (F. Nowacki)- > to be confirmed experimentally SPE(MeV) p /2 p 3/2 f 7/2 N=2 2s /2 π ν 2p /2 2p 3/2 +70keV per proton - 85keV per proton Increase of the SO splizng due to the two- body SO interacon Si 37 6 S p /2 p 3/2 35 Si x=.3 37 S y=.7mev Δ n SO/SO (%) = Diff Mean = =%

13 Modification of the SO splitting in a bubble nucleus Change of ν(p /2 -p 3/2 ) splitting p /2 p 3/2 35 Si Δ n SO/SO (%) = x=.3 Diff Mean = 37 S y=.7mev =% for Δs /2 =.45 ) ΔSO/SO (%) iso. indep. RMF NL3 RMF DDME2 SGII exp Gogny DS iso. dep. central depletion 34 Si 36 S Grasso et al. PRC (2009) $ W s ρ τ (r) = W τ (r) % & r W W / W / W ( MF) ( RMF) Δ(2s /2 ) +W 2 ρ τ ' τ (r) r isospin dependence Isospin independence ' ( ) s Exp. favors density AND isospin dep. of SO interaction Anticipate consequences for drip line and SHE nuclei

14 Spin orbit interaction and superheavy elements ρ[fm -3 ] W[MeV fm - ] neutrons protons neutrons protons total M. Bender et al. PRC 60 (999) ε n [MeV] ε p [MeV] RMF p /2 p 3/2 f 5/2 4 f 7/2 i 3/2 h 9/2 large SO 20 weak SO 72 Size of gaps depends on strength of the SO force Island of SHE favoured at Z~20 in RMF

15 Studying proton-neutron interactions at the drip line

16 Nuclear forces at large proton-neutron asymmetry energy Z=20 Superheavy nuclei Rapid neutron capture Explosive nucleosynthesis 7MeV π ν.7mev From 32 Sn to 22 Zn the same proton g 9/2 orbit intervene -> Same pn interactions involved! But change in binding energy asymmetry. Do proton-neutron interactions change at large p-n binding energy asymmetry?

17 Are proton-neutron interactions similar at drip line? d 5/2 p 24 O n F d 3/2 V pn (d 3/2 d 5/2 ) J=,2,3,4 5MeV d 5/2 π ν d 3/2 -> Study of F F 0.77MeV 25 O unbound, Hoffman PRL 00 (2008) F g.s. J= from beta-decay, Reed et al. PRC Ffree S n =800keV J USDA USDB Shell Model, Brown Int (J) (kev) 3 + : Frank et al., PRC (20) Masses: Jurado PLB 649 (2007) Search for J=2, 4 states using different experimental techniques Compare experimental binding energies in F to those predicted by Shell Model using effective forces constrained closer to stability need spectroscopy of F.

18 Search for J=2 excited state in F M. Stanoiu et al. PRC 202 GANIL 36 S 75A.MeV 3µAe MCP Secondary beams SISSI target wedge N γ BaF J= E(keV) ΔE F 2.75 Ne O 22 N 9 C 3 A/Q Thick Target: C (2 mg.cm -2 ) + active Plastic 03mg.cm -2 SPEG

19 Search for the isomeric 4 + state in F F E 500µm E2 500µm Al 500µm DSSSD 000µm E3 500µm veto 5000µm Clovers Ge A. Lepailleur (PhD thesis, GANIL) 28 Ne : 0.4/s F : 5.5/s 24 O : 0.058/s

20 Showing of this isomeric 4 + state in F F E 500µm E2 500µm Al 500µm DSSSD 000µm E3 500µm veto 5000µm Clovers Ge ms 40% isomer feeding! 642 J=4 Gate 642 kev F implantaon 2.2 (2) ms [ 0ms 2ms ] [ 20ms 22ms ]

21 Study of the beta decay of F 642 β- decay selecon rules : J = 0, ± F β unbound β Ne 0 + [ 0ms 30ms ] me F implantaon

22 Study of the beta decay of F 642 β- decay selecon rules : J = 0, ± F β unbound β Gate 673 kev Gate 499 kev Gate 797 kev Ne 0 +

23 . Proton-neutron interaction d 5/2 d 3/2 in F V pn (d 5/2 d 3/2 ) d 5/2 p 24 O n F d 3/2 exp exp USDA Interaction energy (kev) Ffree J USDA Brown exp Int (J) (kev) Spin J Reduced interaction as compared to Shell Model + Global shrink of levels -> reduced residual interaction Use proper treatment of continuum Assuming 40% isomer

24 Conclusions & Perspectives PART 2 : Determine spectroscopy of F to infer the change of the proton-interaction close to drip line Global reduction of the interaction and residual interaction Should be taken into account to model F isotopes Check the atomic mass, confirm energy/spin assignment of the 3 + unbound state Systematics study of N=7 isotones to be carried out. PART : Use of a bubble nucleus 34 Si to probe the spin-orbit interactoion Change of the neutron p 3/2- p /2 splitting by ~25% between 36 S and 34 Si. Unique way to determine the strength of two-body SO interaction Exp value close to MF predictions -> isospin dep. of SO interaction Determine the amplitude of the bubble (exp currently been analyzed) Consequences for SHE?... Use bubble nucleus to study matter incompressibility at low ρ!

25 SF 37 S 0.75 f 7/2 p 3/2 p / MeV d 3/2 p 3/2 p /2 f 5/ MeV L=,3 4 5 L=3 E(MeV)* 0.75 L=3 L=,2 L= 35 Si