Probing properties of the nuclear forcein ‘extreme’ conditions
O. Sorlin (GANIL, Caen, France)
PART 1:

Testing the spin-orbit force with a ‘bubble’ nucleus
PART 2:

Proton-neutron forces at the drip-line‘May the force be with you’
Obi-Wan Kenobi ‘Star Wars’

ARIS, Tokyo, June 2014

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	

1d3/2

0.2

2s1/2

1.8

1d5/2

6∆(2s1/2) between 36S and 34Si
using (-1p) reaction

ρp(r)
36S

36S

2036S(d,3He)35P
Khan et al. PLB 156 (1985)

C2S	

Proton orbits	

ρp(r)

1d3/2
2s1/2

0.17(3)1d5/2

5.76(7)34Si
2034Si(-1p)33Al
Mutschler et al. in prep.

34Si

J.P. Ebran DDME2 interaction

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

Proton	  occupancies	  in	  34Si	  using	  (-­‐1p)	  reac4on	  	  34Si (-1p) 33Al

Gamma-ray spectrum at 90°
33Al

3.7+0.7
13±2
1±0.9

L=2
L=0p//
g.s. 1649, 4037

1/2+, L=0
L=22.5±.436

L=2

L=2p//
g.s. 1649, 3922

ΣC2S(L=2)= 5.76(6)ΣC2S(L=0)=0.17 (3)73±2

5/2+, L=233Al

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

The	  spin-­‐orbit	  (SO)	  interac4on	  $ ∂ρτ (r)∂ρτ '≠τ (r) '  V (r) = −&W1+W2⋅ s)%∂r∂r (sτρ(r) Density	  dependence	  + ½( ℓ + 1) jℓ,ssplitting- ℓ/2rNormal nucleus

Vℓs(r)

Bubble nucleus (SHE)rj

Asymmetric	  spliHng	  of	  j	  orbits	  Isospin	  dependence	  W1 ≈ 2W2 (MF)W1 ≈ W2 (RMF)

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(d,p)	  reac4on	  in	  inverse	  kinema4cs	  at	  GANIL	  EXOGAM	  Tracking	  detectors	  	  (CATS)	  p	  34Si	  105pps	  20A.MeV	  GANIL	  MUST2	  	  CD2	  target	  2.6mg	  cm-­‐2	  γ	 CHIO	  +	  plas4c	  S1	  GANIL,	  IPN	  Orsay,	  CEA	  Saclay	  IPHC	  Strasbourg	  EXOGAM	  Annular	  detector	  (S1)	  Ioniza4on	  chamber	  (CHIO)	  Spin-orbit splittings in 35Si using 34Si(d,p)35Si

Sn1134

E*<1.5 MeV
E*>1.5 MeV

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 p3/2-p1/2 SO splitting
ρp(r)

ρp(r)

40Ca

Z=204 protons d3/2
36S

Z=16

ρp(r)

34Si

2 protons s1/2

Z=14No	  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	  	  Density	  and	  Isospin	  dependence	  of	  the	  SO	  interac4on	  	  Evolution of the p SO splitting as afunction of central depletion100

iso. indep.
iso. dep.
exp

Density dependence
Isospin dependenceof the SO inter.

RMF does not have the proper
isospin dependence of the SO interaction

ΔSO(p)/SO (%)

RMF NL3806040

Determin
Preliminary…

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

34Si

2036S

Consequences for predicting shell gaps
formed by the SO interaction in SHE

RMF DDME2

46Ar

0.5

Gogny D1S

11.5

2

Δ(2s1/2 )46Ar: Gaudefroy et al. PRL 99 (2007)
34Si: Burgunder et al. PRL 112 (2014)

8 6 4 2 0 2 4 6 8 r(fm)Part II:
Proton-neutron interactions at the drip-line

Proton-neutron interactions at the drip-line
d5/2

π	

26F

25F

pInt(J)(MeV)

24O

Vpn ≈n25O(2J+1)
J=1,2,3,4

d3/2

15MeV

d3/2

0.77MeV

d5/2 -> Study of 26F

26FDetermine	  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	  0Sn-0.5
-1
-1.5
-2

Σ (2J+1) int(J)ν	26F4	  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)	  exp

1 2 3 4 J

24,25O	  Hoﬀman	  et	  al.	  PLB	  672(2009),	  PRL	  100(2008)	  Discovery	  of	  a	  4+	  isomer	  in	  26F	  <2ms	  26F	  26F	  Energy	  Loss	  others	  β-­‐gated	  Nγ	  2	  103	  665	  643	  M3	  2+	  4+	  2.2(1)ms	  1+	  103	  Time	  of	  ﬂight	  2	   4	   6	   8	   10	   12	   14	   16	  Time	  (ms)	  Lepailleur	  et	  al.	  Phys.	  Rev.	  LeU.	  110	  (2013)	  Unbound	  states	  in	  26F	  studied	  at	  GSI/LAND	  LAND	  40Ar	  beam	  27Ne	  Proton1n	  neutrons	

1d3/2//	  2s1/2

FRS	  @GSI	  Dipole	  magnet	  ALADIN	  

1d5/2
2625F
27
Ne17161725F	  TFW	  Counts/	  250	  keV	  Gﬁ	  J=3+	  26F	  J=2,3+	  From	  the	  widths	  of	  p//	  and	  neutron	  peak	  	  -­‐>	  Excellent	  candidate	  for	  J=3+	  state	  at	  550	  keV	  	  M.	  Vandebrouck,	  preliminary	  Proton-neutron interaction d5/2-d3/2 in 26F

d5/226Fp24Ond3/2

Excellent	  agreement	  with	  coupled	  cluster	  calcula4ons	  (con4nuum	  not	  yet	  implemented)	  pn	  interac4on	  slightly	  reduced	  as	  compared	  to	  Shell	  Model	  	  	  Weak	  change	  energies	  of	  states	  in	  con4nuum	  	  Centrifugal	  barrier	  ?	  Fit	  with	  data	  into	  con4nuum	  ?	  

.
Shell model
3+2+exp(2,3+)
3+2+

Lepailleur et al., PRL 110 (2013)
Vandebrouck, preliminaryFrank et al., PRC 84 (2011) – previous
Coupled cluster

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….

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