SLIDE 1
Take a walk on the wild side: the drip-line
By courtesy of A. Bonnaccorso Forewords Part I. Nuclear forces towards the drip line Part II. Proton neutron forces in mirror nuclei.
Take a walk on the wild side: the drip-line Forewords Part I. - - PowerPoint PPT Presentation
Take a walk on the wild side: the drip-line Forewords Part I. - - PowerPoint PPT Presentation
Take a walk on the wild side: the drip-line Forewords Part I. Nuclear forces towards the drip line By courtesy of A. Bonnaccorso Part II. Proton neutron forces in mirror nuclei. Forewords Broad resonance Narrow resonance t = ! E* E*
SLIDE 2
SLIDE 3
In case of a broad resonance, a large part of the wave function lies in the continuum
unbound bound
Γ ⋅t = !
Width of the resonance proportional to the probability to tunnel through centrifugal barrier When the barrier is large or/and E* small Longer time to tunnel through the barrier
- > small Γ -> behave as quasi bound state
Bℓ = ℓ(ℓ+1)"2 2µR2
ν
Large ℓ Narrow resonance
Γ(ℓ, E*,SF)
E*
ν
ℓ
Low
Broad resonance E*
SLIDE 4
Part I: Nuclear forces towards the drip line Γ ⋅t = !
ν
Width of the resonance proportional to the probability to tunnel through centrifugal barrier When it takes longer time to tunnel through the barrier
- > width is small > quasi bound state
In case of a resonance, part of the wave function lies in the continuum
Bℓ = ℓ(ℓ+1)"2 2µR2
ν
Large ℓ
ℓ
Low
Broad resonance Narrow resonance
π ν
In the case of proton orbits, the Coulomb potential leads to an additional barrier. States may behave as quasi-bound states when much lower than the barriers.
SLIDE 5
Part I. Nuclear forces towards the drip-line
SLIDE 6
Nuclear forces towards the drip-line viewed from the study of neutron-rich F isotopes
d5/2 s1/2 d3/2
24F 25F 26F 22O 23O 24O 25O 21N 22N 23N 24N 20C 21C 22C 23C 23F 20O 21O 19N 20N 18C
19C
19O 18N
17C
22F 21F 20F
14 16 Vancouver July 2015
Motivation / Scientific context Study of 26,24F using various experimental techniques at GANIL and GSI
29F 27F
20
31F 27O 28O 26O 25N 26N 24C 30F 28F 27N
d5/2 p1/2
SLIDE 7
Motivations / Scientific context
24F 25F 26F 22O 23O 24O 25O 21N 22N 23N 24N 20C 21C 22C 23C 23F
14 16
29F 27F
20
31F 27O 28O 26O 25N 26N 24C 30F 28F 27N
5
E(2+) (MeV)
22O
14
Neutron Number
20C
8 16
24O
Structural change at N=14
16O 14C 22O and 24O viewed as magic nuclei (used as cores to model neigbouring nuclei)
- C. R. Hofmann et al. PLB 672 (2009)
- M. Stanoiu et al. PRC 78 (2008)
- M. Stanoiu et al. PRC 69 (2004)
SLIDE 8
Motivations / Scientific context
24F 25F 26F 22O 23O 24O 25O 21N 22N 23N 24N 20C 21C 22C 23C 23F
14 16
29F 27F
20
31F 27O 28O 26O 25N 26N 24C 30F 28F 27N
5
E(2+) (MeV)
22O
14
Neutron Number
20C
8 16
24O
Structural change at N=14
16O 14C 22O and 24O viewed as magic nuclei (used as cores to model neigbouring nuclei)
Extension of the valley of stability much further in the F than in O isotopic chain
(challenging theoretical models in general for drip-line prediction)
SLIDE 9
Motivations / Scientific context
24F 25F 26F 22O 23O 24O 25O 21N 22N 23N 24N 20C 21C 22C 23C 23F
14 16
29F 27F
20
31F 27O 28O 26O 25N 26N 24C 30F 28F 27N 22O and 24O viewed as magic nuclei (used as cores to model neigbouring nuclei)
Extension of the valley of stability much further in the F than in O isotopic chain
O F Ne
Reduction of pairing interaction at the drip-line ?
Constraints on models used to describe neutron stars: rotation, cooling … ??
- E. Lunderberg PRL 108 (2012)
- B. Jurado PLB 649 (2007)
SLIDE 10
Motivations / Scientific context
24F 25F 26F 22O 23O 24O 25O 21N 22N 23N 24N 20C 21C 22C 23C 23F
14 16
29F 27F
20
31F 27O 28O 26O 25N 26N 24C 30F 28F 27N 22O and 24O viewed as magic nuclei
Extension of the valley of stability much further in the F than in O isotopic chain Evolution of pairing interaction at the drip line
Constraints on models used to describe neutron stars: rotation, cooling … ??
24O core
π ν
Evolution of proton neutron forces when reaching the drip-line
consequences for r-process nucleosynthesis, shell evolution towards the drip-line
8 8 14
d5/2 d3/2
15MeV
0.77MeV 26F
16
J=1-4+
- C. R. Hofmann PRL 100 (2008)
SLIDE 11
Motivations / Scientific context
22O and 24O viewed as magic nuclei
Extension of the valley of stability much further in the F than in O isotopic chain Evolution of pairing interaction at the drip line
Constraints on models used to describe neutron stars: rotation, cooling … ??
Evolution of proton neutron forces when reaching the drip-line
consequences for r-process nucleosynthesis, shell evolution towards the drip-line
Sn
- 2
- 1.5
- 1
- 0.5
1 2 3 4 J Int(J) (MeV)
26F
Normal pn <Int>
24F 25F 26F 22O 23O 24O 25O 21N 22N 23N 24N 20C 21C 22C 23C 23F
14 16
29F 27F
20
31F 27O 28O 26O 25N 26N 24C 30F 28F 27N
Quenched pn <Int>
26F g.s.: J=1+ / J=4+ isomer / J=2+ prompt γ-decay / J=3+ neutron unbound
SLIDE 12
Discovery ¡of ¡a ¡4+ ¡isomer ¡in ¡26F ¡
26F ¡
- thers ¡
β-‑gated ¡
<2ms ¡
Time ¡(ms) ¡ Nγ ¡
2 ¡ 4 ¡ 6 ¡ 8 ¡ 10 ¡12 ¡14 ¡16 ¡ 103 ¡ 2 ¡103 ¡
4+ ¡ 1+ ¡
2.2(1)ms ¡
643 ¡keV ¡ ¡ M3 ¡
26F ¡
Time ¡of ¡flight ¡ Energy ¡Loss ¡
26F ¡
∆E1 ¡ ∆E2 ¡ ∆E3 ¡ DSSSD ¡ Si(Li) ¡ degrader ¡ 10pps ¡
β- ¡ β- ¡
7.7 ¡(2)ms ¡
SLIDE 13
Beta-‑Decay ¡of ¡26F ¡
26F ¡
∆E1 ¡ ∆E2 ¡ ∆E3 ¡ DSSSD ¡ Si(Li) ¡ degrader ¡ Ge ¡
Unexpected ¡decay ¡curve ¡! ¡ Different ¡lifeUmes ¡! ¡
β-‑gated ¡
10pps ¡
SLIDE 14
Lepailleur ¡et ¡al. ¡Phys. ¡Rev. ¡Le2. ¡110 ¡(2013) ¡
GROUND ¡STATE ¡ ISOMER ¡
SLIDE 15
Discovery of a J=2+ excited state in 26F
SISSI
target Thick Target:
C (112 mg.cm-2) + ‘active’ Plastic 103mg.cm-2 MCP
36S
7 5 A . M e V 3 µ A e , v / c = . 3 4
wedge Secondary beams 3
A/Q
2.75 2.5 200 600 800 400
26Ne9+ 24O 22N 19C
ΔE
SPEG
26F
- M. Stanoiu et al. PRC 85 (2012)
70 BaF2 1000 2000 3000 4000 5 10 15 20
Nγ E(keV)
660 (2+ →1+) Sn
26F
SLIDE 16
Proton neutrons
2s1/2 1d5/2 1d3/2
27Ne17 26F17 25F16
J=3+ unbound states in 26F studied at GSI/LAND
1 2 3 4 5
Counts/200keV
5 10 15 20
J=3+
26F->25F+n
Excellent J=3+ candidate at 260 keV
- M. Vandebrouck, preliminary
Agrees with work of Franck et al. PRC 84 (2011)
J=2,3+
SLIDE 17
3+ ¡
2,3+ ¡
Sn ¡ Sn
- 2
- 1.5
- 1
- 0.5
1 2 3 4 J Int(J) (MeV)
26F
exp
Comparision ¡to ¡theory: ¡effect ¡of ¡conUnuum ¡in ¡26F ¡ ¡ ¡
Excellent ¡agreement ¡for ¡the ¡J=2,4+ ¡energies ¡ ¡ Models ¡not ¡able ¡yet ¡to ¡calculate ¡accurate ¡g.s. ¡binding ¡energy ¡ SystemaUc ¡shi` ¡in ¡energy ¡of ¡unbound ¡states ¡-‑> ¡Treatment ¡of ¡the ¡conUnuum ¡is ¡needed ¡
theory ¡
Calcula;ons ¡J. ¡Holt ¡et ¡al. ¡ S.K ¡Bogner ¡et ¡al. ¡113 ¡(2014) ¡ ¡ ¡
SLIDE 18
MBPT USDb IM-SRG NN+3N-full Expt.
0.5 1 1.5 2 2.5 3 3.5
Energy (MeV)
4
+ +
2
+ + +
2
+
2
+
4
+
3
+
1
+
1
+
1
+
3
+
3
+
3
+
1
+
1
+
2
+
(4
+)
(3
+)
(4
+)
3
+
4
+
1
+
2
+
3
+
2
+
4
+
24F
(4+) ¡ (3+) ¡ (2+,4+) ¡ (1+,2+) ¡
- L. ¡Caceres, ¡…, ¡J. ¡Holt ¡et ¡al. ¡accepted ¡in ¡PRC ¡ ¡
22O ¡core ¡ ¡
π ν
d5/2 ¡ d3/2 ¡ 24F ¡
8 ¡ 8 ¡ 14 ¡
J=2-‑3+ ¡
s1/2 ¡ s1/2 ¡
Comparision ¡to ¡theory: ¡24F ¡ ¡ ¡
Very ¡good ¡agreement ¡for ¡all ¡states ¡
SLIDE 19
Conclusions
Study of the 26F states (J=1-4)+ using several experimental techniques at GANIL and GSI (isomer and in-beam decay, neutron spectroscopy) Textbook case: parabola Int(J) for odd-odd nucleus on top of magic core 24O
(the further from stability including unbound state)
Agreement with theory using realistic interactions for the J=2,4+ Strong shift in energy for the state in the continuum J=3+ Constraint on models aiming at studying pn interactions toward drip-line
(shell evolution for r -process nucleosynthesis)
Future: Study of the same interaction in 28F (all unbound states)
- > What are the mean and residual pn interactions there ?
SLIDE 20
Part ¡II: ¡Proton ¡neutron ¡forces ¡in ¡mirror ¡nuclei ¡
SLIDE 21
p1/2 s1/2
16N 15C 15N 14C 15O 14O 16F 15F
s1/2 p1/2
Change of pn interaction between mirror nuclei : effect of drip line ?
ν
~14MeV ~1.3MeV
2 6
p1/2 s1/2
π ν
~11.4MeV ~2.4MeV
2 6
p1/2
π π ν
s1/2
2 6 8
E*(14O) = 5.173 MeV , E*(14C)= 6.093 MeV Bcoul~4.3MeV
d5/2 d5/2
The coupling of s1/2 and p1/2 nucleons leads to J=0-, 1- states d5/2 and p1/2 nucleons leads to J=3-, 4- states
2- 0- 3- 1- 16N 7 9 397 298 120
16F 16N
How does the 16F level scheme looks like ?
SLIDE 22
Study of unbound states in 16 F using resonant elastic scattering
Si detector
Beam
AXN+p A+1Y 1.01 MeV
proton target (CH2)
Ep dσ dΩ
p
1 1 1
- Thick ‘proton’ target in which the beam is eventually stopped
- Use of inverse kinematics since 15O is radioactive (method -> Gol’dberg 1993)
p + 15O → 16F* → p + 15O
- Rutherford elastic scattering :
2 2 2 '
) 2 / sin( E 4 d d ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = Ω θ σ e Z Z
- Elastic scattering through a resonant state:
p + 15O → p + 15O
3 3 3 2 2 2
Position ⇒ Ex Width of the peak ⇒ Γ Shape ⇒ Jπ
SLIDE 23
2- 0- 3- 1- 16N 7 9 16F 397 298 120 1- 0- 2- 3- 9 7 721 424 193
BOUND UNBOUND
Significant change between mirror nuclei
H(15O,p)15O Resonant elastic scattering
(SPIRAL/GANIL)
0- 1- g.s.
536keV
2-
Search for unbound states in 16F
Ex(keV) Γp (keV) Jπ 25 ± 10 0- 193 (10) 70 ± 5 1- 424 (2) 6 ± 3 2- 721 (4) (15± 5) 3- 7 16 9F
- I. Stefan, F. de Oliveira et al. PRC (2014)
SLIDE 24
15O
Sn= 13.22MeV
15F
Sp = -1.31MeV Sp +Sn
16Ffree 14O
BE(MeV)
Int (0)
16F
1- 0-
Int (0) = -0.775MeV Int (1) = -0.577MeV
14O
p n
16F
Vpn (s1/2p1/2)
s1/2 p1/2
MeV J j j Int J V
J J n p J pn pn p s
621 . ) 1 2 ( ) , ( ) 1 2 (
2 / 1 2 / 1
− = + × + =
∑ ∑
Nuclear forces in 16F
SLIDE 25
ν
~14MeV ~1.5MeV
2 6
p1/2 s1/2 π
Bcoul~4.3MeV
No centrifugal barrier
16F 16N
Diff Vpn(s1/2 p1/2) = -0.621 MeV Vpn(p1/2 s1/2) = -0.943 MeV 40% Vpn(s1/2 p1/2)
ν
~14MeV ~2.78MeV
2 6
p1/2 d5/2
π
Bcoul~4.3MeV Bcent ~13.4MeV Vpn(d5/2 p1/2) A significant reduction of the pn forces is found between the mirror systems for Vpn(s1/2 p1/2)
- > Effect of continuum
A minor change is found for Vpn(d5/2 p1/2)
16F 16N
Diff Vpn(d5/2 p1/2) = -1.66 MeV Vpn(p1/2 d5/2) = -1.83 MeV 10%
- > The centrifugal and Coulomb barriers prevent the proton to move out of the potential well.
SLIDE 26
ν
~14MeV ~1.5MeV
2 6
p1/2 s1/2 π
Bcoul~4.3MeV
No centrifugal barrier
Vpn(s1/2 p1/2)
ν
~14MeV ~2.78MeV
2 6
p1/2 d5/2
π
Bcoul~4.3MeV Bcent ~13.4MeV Vpn(d5/2 p1/2)
int pn(J) = aJ 4π 1 r2
∞
∫
up(r, J)un(r, J) # $ % &
2 dr
The ¡observed ¡difference ¡between ¡16N ¡and ¡16F ¡comes ¡ from ¡the ¡spread ¡of ¡the ¡2s1/2 ¡wave ¡funcUon ¡ ¡ Poorer ¡overlap ¡with ¡the ¡bound ¡proton ¡wave ¡funcUon ¡
- ‑> ¡Weaker ¡effecUve ¡pn ¡interacUon ¡
¡ Overlap ¡of ¡proton ¡and ¡neutron ¡wave ¡funcUons ¡
SLIDE 27
Take away messages
Study of the 16F states (J=1-4)- using resonant elastic scattering technique (use of a low-energy 15O radioactive ion beam in inverse kinematics) Significant deviation of the mirror nuclei spectra 16N/16F Change in effective two-body proton neutron interaction p1/2s1/2 by 40% ! Poor radial proton neutron wave function oeverlap for unbound L=0 protons Treatment of continuum required for light nuclei with extreme large N/Z ratios