ARIS, Tokyo, June 2014

Probing properties of the nuclear force in ‘extreme’ conditions

O. Sorlin (GANIL, Caen, France)

‘May the force be with you’ Obi-Wan Kenobi ‘Star Wars’

PART 1: Testing the spin-orbit force with a ‘bubble’ nucleus PART 2: Proton-neutron forces at the drip-line

Part  I:    Test  of  the  spin-­‐orbit  interac4on  by  using  the  

doubly-­‐magic  ‘bubble’  nucleus  34Si  

34Si  doubly  magic:  High  2+  energy,  low  B(E2),  weak ρ(E0)…  Ibbotson  et  al.  PRL  80  (1998)  2081,  Rotaru  et  al.  PRL  109  (2012)  092503  Enders  et  al.  PRC  65  (2002)  034318  +  talk  S.  Grévy    

Proton  density  deple4on  in  34Si  ?    

Proton orbits C2S

2s1/2

1d5/2

1d3/2

36S20 36S(d,3He)35P

Khan et al. PLB 156 (1985)

0.2

1.8

6

36S ρp(r)

Proton orbits C2S

2s1/2

1d5/2

1d3/2

34Si20

0.17(3)

5.76(7)

34Si(-1p)33Al Mutschler et al. in prep.

34Si ρp(r)

J.P. Ebran DDME2 interaction

∆(2s1/2) between 36S and 34Si using (-1p) reaction

NSCL/S800 with Gretina Gamma-gated p// of fragments

Proton  occupancies  in  34Si  using  (-­‐1p)  reac4on    

Gamma-ray spectrum at 90°

36

33Al

34Si (-1p) 33Al

L=2 1/2+, L=0

5/2+, L=2

33Al

L=2

73±2

3.7+0.7 13±2 1±0.9

2.5±.4

p// g.s. 1649, 3922

p// g.s. 1649, 4037

L=2 L=2 L=0

So far very small Lp=0 knock-out observed -> in agreement with a ‘bubble’ nucleus

ΣC2S(L=2)= 5.76(6) ΣC2S(L=0)=0.17 (3)

Density  dependence  

Vℓs(r)

r

ρ(r)

r

Normal nucleus

Vτs (r) = − W1

∂ρτ (r)∂r

+W2∂ρτ '≠τ (r)

∂r$

%&'

()⋅ s

The  spin-­‐orbit  (SO)  interac4on  

ℓ,s

- ℓ/2 j

j

splitting

+ ½( ℓ + 1)

Asymmetric  spliHng  of  j  orbits  

Bubble nucleus (SHE) W1 ≈ 2W2 (MF)W1 ≈W2 (RMF)

Isospin  dependence   No  isospin  dependence  in  RMF  

Reduced  SO  spliHng  in  bubble  nucleus    for  orbits  probing  the  interior  of  the  nucleus  such  as  L=1    

Looking  at  neutron  p3/2-­‐p1/2  SO  evolu4on  when  deple4ng  the  proton  central  density  -­‐>  test  density  and  isospin  dep.  of  SO  

34Si  105pps  20A.MeV  GANIL  

Tracking  detectors    (CATS)  

34Si(d,p)  reac4on  in  inverse  kinema4cs  at  GANIL  

GANIL,  IPN  Orsay,  CEA  Saclay  IPHC  Strasbourg  

MUST2    

CHIO  +  plas4c  

Ioniza4on  chamber  (CHIO)  

S1  

Annular  detector  (S1)  

EXOGAM  

EXOGAM   CD2  target  2.6mg  cm-­‐2  

p  γ

Spin-orbit splittings in 35Si using 34Si(d,p)35Si

Sn

L assignments from proton angular distributions Accurate energy of states with γ-ray detection

G. Burgunder et al., Phys. Rev. Letters 112 (2014)

1134 E*<1.5 MeV E*>1.5 MeV

Evolution of the p3/2-p1/2 SO splitting

No  change  in  p3/2-­‐p1/2    spliHng    between  41Ca  and  37S      Large  reduc4on  of    p3/2-­‐p1/2    spliHng  between  37S  and  35Si,  no  change  of    f7/2-­‐f5/2    

ρp(r) 40Ca

36S ρp(r)

34Si ρp(r)

Z=20

Z=16

Z=14

4 protons d3/2

2 protons s1/2

Determin

20

40

60

80

100

ΔS

O(p

)/SO

(%)

0.5 1.5 2 1 Δ(2s1/2 )

Density  and  Isospin  dependence  of  the  SO  interac4on    

Evolution of the p SO splitting as a function of central depletion

46Ar: Gaudefroy et al. PRL 99 (2007) 34Si: Burgunder et al. PRL 112 (2014)

Gogny D1S

SGII

iso. dep. iso. indep.

RMF DDME2

RMF NL3

34Si

46Ar 36S

exp

Density dependence Isospin dependence RMF does not have the proper isospin dependence of the SO interaction Consequences for predicting shell gaps formed by the SO interaction in SHE

of the SO inter.

ρp(r)

2 4 6 8 2 4 6 8

M. Bender et al. PRC 60 (1999)034304

0 r(fm)

Preliminary…

Part II: Proton-neutron interactions at the drip-line

Proton-neutron interactions at the drip-line

-> Study of 26F

26F

π ν

d5/2

d3/2

15MeV

0.77MeV

24O

p

n

26F d5/2

d3/2

25O

25F Σ (2J+1) int(J) (2J+1)

Vpn ≈

J=1,2,3,4

Determine  the  d5/2-­‐  d3/2  proton-­‐neutron  force  in  26F  Compare  to  Shell  Model  calcula4ons    constrained  closer  to  stability  Compare  to  models  using  realis4c  interac4ons  

24,25O  Hoffman  et  al.  PLB  672(2009),  PRL  100(2008)  

Sn

-2

-1.5

-1

-0.5

1 2 3 4 J

Int(J

) (M

eV)

26F exp

0

4  experiments  to  determine  the  energy  of  the  J=1-­‐4  states  !  J=1,  Mass  g.s.:  Jurado  et  al.,    PLB  649  (2007) J=2,  excited  state  ‘in  beam’  Stanoiu  et  al.  PRC  85  (2012)  J=3,  unbound  state  Frank  et  al.,  PRC    84  (2011)  +  a  new  one  J=4,  M3  isomer  Lepailleur  et  al.  PRL  110  (2013)  

Discovery  of  a  4+  isomer  in  26F  

Time  (ms)  

Nγ  

2   4   6   8   10  12  14  16  

103  

2  103  

26F  

others  β-­‐gated  

Time  of  flight  

Energy  Loss  

26F  

<2ms  

2+  4+  

1+  

2.2(1)ms  643  665  

M3  

Lepailleur  et  al.  Phys.  Rev.  LeU.  110  (2013)  

40Ar  beam  

Dipole  magnet  ALADIN  

Gfi  

TFW  

LAND  

//  FRS  @GSI  

1n  

Unbound  states  in  26F  studied  at  GSI/LAND  

27Ne  

25F  

Coun

ts/  2

50  keV

  26F  

M.  Vandebrouck,  preliminary  

J=3+  

From  the  widths  of  p//  and  neutron  peak    -­‐>  Excellent  candidate  for  J=3+  state  at  550  keV      

J=2,3+  

Proton neutrons

2s1/2

1d5/2

1d3/2

27Ne17 26F17 25F16

Proton-neutron interaction d5/2-d3/2 in 26F

26F p d5/2

24O n d3/2

.

Coupled cluster

Shell model exp

Excellent  agreement  with  coupled  cluster  calcula4ons  (con4nuum  not  yet  implemented)  

Lepailleur et al., PRL 110 (2013) Vandebrouck, preliminary Frank et al., PRC 84 (2011) – previous

3+

2+

(2,3+)

pn  interac4on  slightly  reduced  as  compared  to  Shell  Model      Weak  change  energies  of  states  in  con4nuum    Centrifugal  barrier  ?  Fit  with  data  into  con4nuum  ?  

3+

2+

Special thank’s to: GANIL/IPNO: G. Burgunder, A. Lepailleur, A. Mutschler, M. Vandebrouck, A. Lemasson … The LAND team: T. Aumann, C. Caesar, F. Wamers. D. Rossi …. The NSCL/S800/Gretina teams: D. Weisshar, F. Recchia, D. Bazin, A. Gade, K Wimmer… Theory: F. Nowacki, T. Otsuka, J. P. Ebran, G. Hagen, G. Jansen, A. Brown

Conclusions/ Outlooks PART I: 34Si good candidate for proton ‘bubble’, normal neutron density Reduction of neutron p3/2-p1/2 splitting with proton s1/2 depletion Points to density and isospin dependence of SO interaction PART II: Spectroscopy of bound and unbound states in 26F No drastic change with SM calculations Benchmark for testing realistic forces up to continuum But …Atomic mass of 26F to be confirmed….