Study of the spin orbit force using a bubble nucleus O. Sorlin - - PowerPoint PPT Presentation

A Foreword : some open questions in nuclear physics …

α

6He

n n α

8He

n n

How to explain the existence of halo, clusters, quasi-molecular structures ?

Modeled from ab-initio approaches ? Role of nuclear force and symmetries ? Role of coupling to continuum ?

clusters haloes

0 40

6C 14Si 28Ni 16S 20Ca

2000 4000 6000 E(2+) (keV) 4 6 8 10 12 Neutron Number 500 1500 2500 2000 1000 3000 3500 12 16 20 24 Neutron Number 500 1000 1500 2000 32 36 40 44 Neutron Number

8O

A Foreword : some open questions in nuclear physics …

Do magic nuclei persist far off stab.?

• > pillars of nuclear structure
• > remarkable properties due to shell gaps

(i.e. large first excited state energy) 40

2000 4000 6000 E(2+) (keV) 4 6 8 10 12 Neutron Number 500 1500 2500 2000 1000 3000 3500 12 16 20 24 Neutron Number 500 1000 1500 2000 32 36 40 44 Neutron Number

A Foreword : some open questions in nuclear physics …

12Mg 10Ne 4Be 26Fe 24Cr

40 If our world were more neutron-rich ….

• >No sign of energy increase
• > No magic number far from stability !
• > Change of paradigm ….

6C 14Si 28Ni 16S 20Ca

2000 4000 6000 E(2+) (keV) 4 6 8 10 12 Neutron Number 500 1500 2500 2000 1000 3000 3500 12 16 20 24 Neutron Number 500 1000 1500 2000 32 36 40 44 Neutron Number

8O

A Foreword : some open questions in nuclear physics …

12Mg 10Ne 4Be 26Fe 24Cr

Why ? Which part(s) of nuclear force ? Are there new magic nuclei ? What happens to heavier nuclei ? 40

8O

If our world would be more neutron-rich ….

• >No sign of energy increase
• > No magic number far from stability !
• > Change of paradigm ….

Does an island of extra-stability exist for superheavy nuclei ?

Could we predict its location ? Could we synthesize new elements on earth ? Which chemical properties ? Z=120

A Foreword : some open questions in nuclear physics …

A Foreword : some open questions in nuclear physics …

r process

Solar observation Shell closure

r-abundance curve

A

Shell quenching

Which stellar environment(s) produce elements Z>26?

Neutron star mergers ? Likely but …. Link between closed shells and abundance peaks

• > A real impact of shell structure far from stability
• > Determine mass, lifetime, n-capture rates of nuclei
• D. Price & S. Rosswog Science 2006

Study of the spin orbit force using a bubble nucleus

• O. Sorlin (GANIL, presently at CERN)

The spin orbit (SO) force plays major role in nuclear structure to create shell gaps that give rise to magic nuclei. SO force: postulated more than 60 years ago. Theoretical descriptions now exist but predictions differ for ab-normal nuclei No experiment was yet able to test the SO force in ‘extreme’ conditions (superheavy elements, nuclear drip-line -> astrophysics) We propose to use a ‘bubble’ nucleus to test the properties of this SO force

ℓ,s

Shell gap

s

ℓ

s

ℓ

34Si

ρp(r)

THE PITCH

Mardi 26 avril 2016 – LAL Orsay

Introduction on the atomic nucleus

• > Charge density, orbital occupancies

Probe charge density in 36S and 34Si:knockout reactions at NSCL

• > Central proton density depletion in 34Si (i.e. bubble)

Introduction to the spin orbit (SO) force

• > Properties and expectations
• > Use a bubble nucleus to constrain unknown properties

Reduced SO interaction between 36S & 34Si: (d,p) reaction at GANIL

Conclusions / consequences

Layout of the talk

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

Charge density of the nucleus : ρ(r)

e- r

Te≈hc/λ

Large transferred momentum

• > details of the density distribution

208Pb

ρ(r)

A B

Charge density of the nucleus : ρ(r)

208Pb 142Nb 124Sn 92Mo 96Zr 58Ni 52Cr 40Ca 16O

(5/3<r2>)1/2

7 6 5 4 4 5 6 3

A1/3 R=r0A1/3

Halo nucleus

ρ(r)

scaling with A1/3

58Ni 12C 4He

Saturation of nuclear forces

ρ(r)

Z

Hofstader Rev. Mod. Phys. 28 (1956)

Charge density depletion in the center of the 205Tl nucleus

2 4 6 8 0.04 0.08 Δρ (r) (e fm-3) r (fm) MF 3s1/2 Cavedon PRL (1982)

Charge density depletion due to the change in 3s1/2 occupancy by 0.7 proton Independent particle model works rather well also in the interior of nucleus

ρ[fm-3] r[fm]

0.04 0.02 0.06 0.08

206Pb 205Tl

r[fm] 2 4 6 8

ρ(r) r

L=0,1,2,3 n=0,1… Nuclear density = superposition of radial vave funtions with n,L values

Probing nuclear orbits with (e,e’p) reaction

Orbital labelling n,L,J n nodes (n=0,1,2) L angular momentum (s,p,d,f,g,h…) (-1)L parity |L-s|<J<|L+s| (2J+1) per shell example : h11/2: L=5, J=11/2, L and s aligned contains 12 nucleons

• > Quenching factor of occupancy by about 70%
• > Mixing with collective states at high E*
• > Study limited (so far) to STABLE nuclei

s1/2 d3/2 h11/2 d5/2 g7/2

82 50

82 Pb

Np

E * [MeV]

Nuclear orbits

Ep [MeV]

• >Nucleons are arranged on shells
• > Gaps are present for certain nucleon numbers
• > Np detected follows orbit occupancy

Proton density deple6on in 34Si as compared to 36S?

Proton orbits occup.

2s1/2 1d5/2 1d3/2

36S20

2

6

Proton orbits occup.

2s1/2 1d5/2 1d3/2

34Si20 6

36S

ρp(r)

34Si

ρp(r)

J.P. Ebran DDME2 interaction

1

E

1

E

u2 u2 ? ? Amplitude of the central depletion depends on the change in 2s1/2 occupancy But correlations can reduce the amplitude of this depletion 14 14

9Be 36S 35P

p γ

d5/2 s1/2 d3/2 p1/2

u2 36S

p3/2 s1/2

1

E

Probing proton density in36S

reaction theory

σ(n,L) = C2S (j,n,L) σsp(j,Sp) RS

• ccupancy

Knock-out reactions at β≈0.4

d5/2 s1/2 d3/2 p1/2

35P

p3/2 s1/2

n,L,j

γ

p//

L=0 L=2

35P

∆E TOF

35P 35P

36S

target

S800 spectrograph

9Be 36S 35P

p γ

d5/2 s1/2 d3/2 p1/2

u2 36S

p3/2 s1/2 d5/2 s1/2 d3/2 p1/2

35P

p3/2 s1/2

1

E

Probing proton densi6es in 36S

Gretina array: segmented Ge detectors In-flight γ-ray detection-> Doppler corrections Segmented Ge cristals -> Interaction position reaction theory

σ(n,L) = C2S(j,n,L) σsp(j,Sp) RS

• ccupancy

Knock-out reactions at β≈0.4

9Be 36S 35P

p γ

d5/2 s1/2 d3/2 p1/2

u2 36S

p3/2 s1/2 d5/2 s1/2 d3/2 p1/2

35P

p3/2 s1/2

1

E

Probing proton densi6es in 36S

Single γ spectrum

γ γ coincidences

35P

reaction theory

σ(n,L) = C2S(j,n,L) σsp(j,Sp) RS

• ccupancy

Knock-out reactions at β≈0.4

9Be 36S 35P

p γ

d5/2 s1/2 d3/2 p1/2

u2 36S

p3/2 s1/2 d5/2 s1/2 d3/2 p1/2

35P

p3/2 s1/2

1

E

Probing proton densi6es in 36S

35P

33 C2S b(%) 8 29 1.5 2 2.7 2 0.4 2 2 0 L Energy spectrum 15 10 3 1.5 1 2 0.3 2 dσ/dΩ

L=0 L=2

Momentum distrib.

ΣC2S 2

5.5

Quasi full filling of s1/2 and d5/2 orbits (within errors) Only few scattering to the upper d3/2 orbital.

reaction theory

σ(n,L) = C2S(j,n,L) σsp(j,Sp) RS

• ccupancy

Knock-out reactions at β≈0.4

• A. Mutschler et al. PRC (2016)

Proton density of 36S

Proton orbits C2S(±20%)

2s1/2 1d5/2 1d3/2

36S20 0.4 2 5.5

36S

ρp(r)

1

E

u2 14

9Be 34Si 33Al

p γ

d5/2 s1/2 d3/2 p1/2

u2 34Si

p3/2 s1/2 d5/2 s1/2 d3/2 p1/2

33Al

p3/2 s1/2

1

E

Probing proton densi6es in 34Si

Single γ spectrum γ γ coincidences reaction theory

σ(n,L) = C2S(j,n,L) σsp(j,Sp) RS

• ccupancy

Knock-out reactions at β≈0.4

9Be 34Si 33Al

p γ

d5/2 s1/2 d3/2 p1/2

u2 34Si

p3/2 s1/2 d5/2 s1/2 d3/2 p1/2

33Al

p3/2 s1/2

1

E 33Al

77 C2S b(%) 14 3 1.4 1.4 1.5 0.1 2 0.9 2 0.2 2 4.7 2 L 5.8 0.1 0 0.1 0 0.2 dσ/dΩ

L=0 L=2

Probing proton densi6es in 34Si

Energy spectrum Momentum distrib. Very weak 2s1/2 occupancy -> large central density depletion reaction theory

σ(n,L) = C2S(j,n,L) σsp(j,Sp) RS

• ccupancy

Knock-out reactions at β≈0.4

• A. Mutschler et al. to be sumi;ed to Nature

Proton density deple6on in 34Si

Proton orbits C2S (±20%)

2s1/2 1d5/2 1d3/2

36S20 0.4

2

5.5

Proton orbits C2S(±20%)

2s1/2 1d5/2 1d3/2

34Si20

0.2

5.8

36S

ρp(r)

34Si

ρp(r)

J.P. Ebran DDME2 interaction

1

E

1

E

u2 u2 ? Large change in 2s1/2 occupancy (1.8) -> central proton depletion in 34Si -> ‘bubble’ nucleus But same neutron density profiles for the two N=20 nuclei 14 14

Simplified description of atomic nuclei

U(r) r

) ( ' )] ' ( [ ) ' ( ' ) ' , ( ) ' ( ) (

3 3

r v r d r r v r r d r r v r r U

vol vol

ρ ρ ρ − = − ∂ − = =

∫ ∫

Harmonic Oscillator 8, 20, 40

d3/2

20

d5/2 p1/2 s1/2 p3/2

28 40

g9/2

50 14

d5/2

Spin Orbit 6, 14, 28, 50, 82, 126 8

g7/2

δρ/dr L.S

• f7/2

f5/2

δρ/dr

r ρ(r) r

U(r) = H.O L2

+

1d 1f 2s 2p

20

N=2 N=3 1g N=4 2d

40 20

N=1

8 8 40

ℓ,s

• ℓ/2

2εSO= 2ℓ +1

+ ½(ℓ + 1) Asymmetric spliEng of j orbits

s ℓ ℓ s

Density dependence Vℓs(r)

r

ρ(r)

r Normal

Vτ

s(r) = − W 1

∂ρτ (r) ∂r +W2 ∂ρτ '≠τ (r) ∂r $ % & ' ( )  ⋅s 

The spin-orbit (SO) interac6on

Bubble (SHE)

W2 ≈1 2 W

1

(MF) W2 ≈ W

1

(RMF)

Isospin dependence

No isospin dependence in RMF R(r) ℓ=3 ℓ=1 r Halo/ skin

PROPOSED GOAL Determine ρ and τ SO dependence

34Si: proton central deple6on but not neutron

• Red. of neutron SO due to proton deple6on

Reduced SO for bubble and diffuse nuclei

Proton density deple6on in 34Si

Proton orbits C2S (±20%)

2s1/2 1d5/2 1d3/2

36S20 0.4

2

5.5

Proton orbits C2S(±20%)

2s1/2 1d5/2 1d3/2

34Si20

0.2

5.8

36S

ρp(r)

34Si

ρp(r)

J.P. Ebran DDME2 interaction

1

E

1

E

u2 u2 ? Large change in 2s1/2 occupancy (1.8) -> central proton depletion in 34Si -> ‘bubble’ nucleus But same neutron density profiles for the two N=20 nuclei 14 14

d

34Si 35Si

p γ

d3/2 f7/2 p3/2 s1/2

u2 34Si

1

E

dσ(n,L,θ) vacancy reaction theory Transfer reaction (d,p) at β≈0.15

p1/2 d5/2

35Si

d3/2 f7/2 p3/2 s1/2 p1/2 d5/2

n

34Si(d,p) reac6on in inverse kinema6cs

θp

dσ dΩ E*(35Si) Np 3/2- C2S+= 0.84 L=1 1/2-

2+

5/2-

E= C2S⋅Ex

∑

C2S

∑

dΩ =(2j+1) C2S+ dσAWBA(n,L,θ) dΩ Proton energy -> (binding) energy of orbit Proton angle -> orbital momentum L Cross section -> vacancy of the orbit Appropriate momentum matching required n

7/2- L=3

σ(n,L) = C2S(j,n,L) σsp(j,Sp)

vacancy reaction theory Transfer reaction (d,p) at β≈0.15

34Si

105pps 20A.MeV GANIL Tracking detectors CD2 target

p γ

CHIO

plas6c

EXOGAM

34Si

S1

dσ(n,L,θ) vacancy reaction theory Transfer reaction (d,p) at β≈0.15 dΩ =(2j+1) C2S+ dσAWBA(n,L,θ) dΩ

34Si(d,p) reac6on in inverse kinema6cs

35Si

p γ

35Si

d3/2 f7/2 p3/2 s1/2 p1/2 d5/2

σ(n,L) = C2S(j,n,L) σsp(j,Sp)

vacancy reaction theory Transfer reaction (d,p) at β≈0.15 MUST2 dσ(n,L,θ) vacancy reaction theory Transfer reaction (d,p) at β≈0.15 dΩ =(2j+1) C2S+ dσAWBA(n,L,θ) dΩ

34Si(d,p) reac6on in inverse kinema6cs

34Si

105pps 20A.MeV GANIL Tracking detectors CD2 target

p γ

CHIO

plas6c

EXOGAM S1

35Si

p γ

35Si

d3/2 f7/2 p3/2 s1/2 p1/2 d5/2

σ(n,L) = C2S(j,n,L) σsp(j,Sp)

vacancy reaction theory Transfer reaction (d,p) at β≈0.15

34Si

105pps 20A.MeV GANIL Tracking detectors CD2 target

p γ

CHIO

plas6c

EXOGAM Annular detector (S1) S1 EXOGAM Ioniza6on chamber (CHIO)

dσ(n,L,θ) vacancy reaction theory Transfer reaction (d,p) at β≈0.15 dΩ =(2j+1) C2S+ dσAWBA(n,L,θ) dΩ

34Si(d,p) reac6on in inverse kinema6cs at GANIL

35Si

p γ

35Si

d3/2 f7/2 p3/2 s1/2 p1/2 d5/2

σ(n,L) = C2S(j,n,L) σsp(j,Sp)

vacancy reaction theory Transfer reaction (d,p) at β≈0.15 dσ(n,L,θ) vacancy reaction theory Transfer reaction (d,p) at β≈0.15 dΩ =(2j+1) C2S+ dσAWBA(n,L,θ) dΩ

34Si(d,p) reac6on in inverse kinema6cs

Sn

1134

E*<1.5 MeV E*>1.5 MeV

910

35Si

d3/2 f7/2 p3/2 s1/2 p1/2 d5/2

Ep-> (binding) energy of orbit θp-> orbital momentum L σ-> vacancy of the orbit

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

No change in p3/2-p1/2 spliEng between 41Ca and 37S Large reduc6on of p3/2-p1/2 spliEng 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

N=21 isotones

7/2- <5/2-> 3/2- 1/2- 5/2-

• G. Burgunder et al. PRL 112 (2014) 042502

C2S+ C2S+ C2S+

Density and Isospin dependence of the SO interac6on

Knockout reactions from 36S and 34Si beams at NSCL / MSU

• > First ‘evidence’ of a significant central depletion in the atomic nucleus 34Si
• > Asymmetry between proton and neutron density depletions in 34Si
• > unique candidate to probe the spin-orbit interaction in ‘unusual ’ condition

34Si(d,p)35Si transfer reaction at GANIL

• > Show a drastic reduction of SO interaction as compared to N=20 isotones

Better constraints on the models -> choose the correct one(s) Evaluate the reduction of SO splitting when reaching the neutron drip-line Consequence for the r-process nucleosynthesis -> neutron-star mergers Location of ‘stable’ Super Heavy Elements to be revisited / better constrained ?