Transcript Slides - Agenda INFN

Shell evolution and nuclear forces
O. Sorlin (GANIL, France)
1- Introduction, motivations
2- Illustrative examples of shell evolution
3- Shell evolution vs ‘hierarchy’ of nuclear forces
4- Consequences / perspectives
‘May the force be with you’
Obi-Wan Kenobi ‘Star Wars’
Basic features of the atomic nucleus
Nucleons generate their own potential
Quantum effects -> shell gaps, magic numbers
Early version of Mean field potential V= HO + L2 + LS
(Haxel, Goppert Mayer 1949)
One-body LS term may be a caricature of a more
complicated force (Elliott 1954)
82
40
2d
1g
50
40
N=3
2p
1f
20
N=2
8
28
20
2s
1d
N=1
H.O +
40
f7/2
20
14
8
g9/2
p1/2
f5/2
p3/2
8
L2 + L.S
d3/2
s1/2
d5/2
Shell evolution and nuclear forces
Evolution of the ‘SO’ shell gap, partly due to proton-neutron or
neutron-neutron forces -> N=28 gap increased by 3 MeV
Similar effects in other regions
Interplay mean field - correlations
Open quantum systems at
the drip-line
Drip line
132Sn
p n
78Ni
48Ca
22O
J. D. Holt et al. JPG (2012)
K. Sieja et al. PRC 85 (2012)
-> Study of
Neutron Binding energy (MeV)
Probe never studied combination of orbits far from stability
Unexplored components of the Nuclear Force
(central, tensor, two-body spin-orbit, three body)
->shell evolutions
exp
p3/2
-5
-7 2MeV
-9
28
5MeV
40Ca
f7/2
48Ca
2 body
- 11 vlowK
f7/2
20 22 24 26 28
Neutron
Harmonic oscillator magic numbers
Increase of 2+ energy at N=8, 20, 40 shell gaps
If our universe was more neutron-rich
HO magic numbers would have not been present
N=14, 16 new local closed shells
e.g. Stanoiu PRC 69 (2004), Hoffmann PLB 672(2009)
Which mechanisms -> dramatic changes ?
64Cr
40
8O
32Mg
12Be
E(2+) (keV)
6000
e.g. Sorlin, Porquet PPNP 61 (2008), Phys. Scr T 152 (2013)
Otsuka Phys. Scr T152 (2013)
3500
2500
4000
2000
6C
4Be
2000
3000
2000
1500
8O
20Ca
14Si
1500
1000
500
10Ne
16S
12Mg
1000
500
28Ni
24Cr
26Fe
0
0 12 16
32 36 40 44
20 24
4 6 8 10 12
Neutron Number
Neutron Number
Neutron Number
N=40
Hannawald PRL 82 (1999), Sorlin, EPJA16 (2003), Aoi, PRL 102 (2009)
Gade PRC 81 (2010), Ljungvall PRC81 (2010), Lenzi PRC82 (2010), W. Rother PRL106 (2011)
0
Development of collectivity through npnh excitations
across the N=20 shell gap
pf
20
d3/2
2+
30+2
NEW
NEW
pf
20
d3/2
0+1
40Ca
38Ar
36S
34Si
0+
2+
32Mg
0+
-> Deformation due to combined shell gap reduction and correlations
through ph excitations Poves, Retamosa Phys. Lett. B184 (1987) 311.
> Inversion between 0+inert and 0+2p2h at 32Mg Wimmer et al. PRL 105 (2010)
-> Abrupt transition: 0+2p2h in 34Si is weakly mixed Rotaru et al. PRL 109 (2012)
Discovery of the 0+2 state in 34Si
4-
b-
d3/2
2+
e+
e34Si
E(02+)=2719 ± 3 keV
pf
0+2
2719
34Al
E(keV)
20
34Al m
21 d5/2
34Al
ee+
pf
1+
20
d5/2
d3/2
0+1 ρ2(E0)=13 ± 1mu
Weak mixing
T1/2=19.4(7) ns
0+2
1.5
1
0.5
0.5
1
1.5 E(MeV)
E(0+2) = (Ee- +Ee+)+ 1022keV
0.5 1
1.5 E(MeV)
Rotaru et al. PRL 109 (2012)
Evolution of the N=20 gap below Z=14
Mechanism leading to onset of collectivity well understood
But : Not a proof of N=20 shell gap reduction
Which underlying nuclear forces ?
Spherical
deformed
Study evolution of N=20 gap from outside of the deformed regions,
N=16 rather good shell gap far from stability -> study of N=17 isotones
S.M. Brown et al.PR C 85, 011302(R) (2012), A. Obertelli, et al., PLB 633 (2006) 33
J. Terry, et al., PLB B640 (2006) 86., Z. Elekes, et al., PRL 98 (2007) 102502
Study of nuclear structure at the drip line using 26Ne(d,p) 27Ne
TIARA
qp
d
16
f7/2
p3/2
d3/2
s1/2
d5/2
26Ne
16
26Ne
26Ne
2500pps,
10A.MeV ->SPIRAL
Protons -> TIARA
Gammas -> 4 Exogam
Nuclei -> Vamos
EXOGAM
VAMOS
26Ne(d,p) 27Ne
reaction
BOUND
7/2-
Energy loss
UNBOUND
3/2VAMOS ID
A/Q
7/2L=3
q (deg)
E(keV)
Eg(MeV)
0.35 7/2-
1740
L=1
Sn
1430
0.17 1/2+
0.64 3/2-
885
765
0.42 3/2+
0
SF
J
27Ne
ds/dW
ds/dW
E*(MeV)
q (deg)
Shell evolution viewed from N=17 systematics
E( MeV)
5
N=17
Sn
4
3
(3/2-)
3/27/2-
3/2-
7/2-
Sn
1
(3/2+)
25O
3/23/2+
3/2mirror
(7/2-)
7/2-
7/2-
2
0
3/2-
N=28
Sp
N=20
(7/2-)
(3/2-)
3/2+
27Ne 29Mg
3/2+
3/2+
31Si
33S
d5/2
s1/2
3/2+
3/2+
35Ar 37Ca
d3/2
Protons orbits
Large N=20 gap between Z=14 and Z=20 -> collapses below Z=14 (Si)
Swaping between the f7/2 and p3/2 orbits (N=28) below Z=14
Also found in the N=15 isotones
-> role of specific proton-neutron forces
Shell evolution and the hierarchy of nuclear forces
Large N=20
2p3/2
1f7/2
d5/2
1d3/2
2s1/2
40
42Si
1d5/2 [
]
p
28O
17
1d5/2
Collapse N= 20
& N=28 gaps
1f7/2
2p3/2
1d3/2
28
16
20
n
14
2s1/2
1d5/2
n
p
d5/2
Drip line
Proton-neutron interaction Vpn depends on n, l, j
Hierarchy Vpn1d5/21d3/2 >> Vpn1d5/21f7/2 > Vpn1d5/22p3/2
P(r)
1d
2p
l1
1f
s1
r
l2
s2
Nowacki, Poves PRC 79 (2009)
What happens at the drip line ? e.g. Forssén et al. Phys. Scr. T 2152 (2013)
Which effective forces there ?
Calculations using realistic interactions ?
Trick: Find a benchmarking case to be compared to models
Are proton-neutron interactions similar at drip line ?
p
d5/2
26F
25F
Vpn ≈
p
24O
n
25O
d3/2
S (2J+1) int(J)
(2J+1)
J=1,2,3,4
n
15MeV
0.77MeV
d5/2 -> Study of 26F
26F
Int(J)
(MeV)
d3/2
Sn
-0.5
-1
-1.5
-2
26F
USDA
1 2 3 4 J
Compare experimental binding energies in 26F to those
predicted by Shell Model using effective forces constrained
closer to stability
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)
J=4, M3 isomer Lepailleur et al. PRL (2013)
24,25O
Hoffman et al. PLB 672(2009), PRL 100(2008)
Discovery of a 4+ isomer in 26F
<2ms
26F
26F
others
b-gated
Energy Loss
Ng
2 103
After 26F implantation
T1/2=2.2(1)ms
M3 isomer
103
2 4 6 8 10 12 14 16
Time of flight
Time (ms)
Proton-neutron interaction d5/2d3/2 in 26F
26F
d5/2
p
24O
n
d3/2
Reduced interaction as compared to Shell Model
Compression in energy -> reduced residual
interaction
Excellent agreement with coupled cluster calculations
‘Unexpected behaviour’ of the J=3 state
(to be confirmed soon from GSI/LAND data)
.
Lepailleur et al., PRL (2013)
Shell model
exp
Coupled cluster
Generalization of the hierarchy of nuclear forces
Reduced N=82 gap below 132Sn
g9/2
1h11/2
1g7/2
f7/2
1g9/
L+1
40
d5/2
2
[
p
]
82
50
n
L+1
2d5/2
50
1g9/2
2p1/2 40
1f5/2
2p3/2
Collapse of N=20 gap below 34Si
Reduced N=28 gap below 42Si
1d3/2
2s1/2
1d5/2 [
p
]
1d5/2
28
20
14
n
1f7/2
2p3/2
1d3/2
1f7/2 [
16
n
n
50
p
Collapse of N=40 gap below 68Ni
Collapse N=50 gap around 60Ca
L+1
2p3/2
1f7/2
3p3/2
2f
7/2
82
1h11/2
1g7/2
3p3/2
2f7/2
2s1/2
1d5/2
p
]
n
34
32
n
2d5/2
1g9/2
1f5/2
2p1/2
2p3/2
p
1f7/2
Similar effect with realistic interactions
p
d5/2
G.Hagen et al. PRL 109 (2012) 032502
1g9/
2
Hierarchy of nuclear forces and the r-process
g9/2
r-process
Reduced N=82 gap below 132Sn
Change of ng7/2 energy
3p3/2
2f
3p3/2
82
7/2
1h11/2
2f7/2
1g7/2
82
1h11/2
50
1g7/2
1g9/2
[
p
]
50
n
n
p
1g9/2
r-abundance curve
r –process
Neutron-rich closed shell nuclei survivors
Genitors of stable nuclei -> A=130 peak
Hierarchy of proton-neutron nuclear forces:
- Reduction of the N=82 gap
- Enhanced ng7/2-> p g9/2 transition rate
- Shorter half-lives Cuenca-Garcia EPJA (2007)
- Speed up the r-pocess
Observations
Strong shell closure
Shell quenching
A
B. Pfeiffer, et al., NPA 693 (2001) 282
Few conclusions/perspectives
Recent experimental results obtained worldwide confirm
that the view of immutable closed shell is unappropriate
Universal change of HO shell gaps
Correlations and shell reduction leads to deformation
Shell evolution takes root in identified properties of nuclear forces fewly studied until
recently in nuclear medium
Which properties of the bare forces ‘survive’ inside the medium ?
What is the role of continuum ? What is the role of 3 body forces ?
Which consequences of nuclear force ‘herarchy’ on the r-process nucleosynthesis ?
Special thanks to A. Lepailleur, F. Rotaru, S. Grévy, F. Nowacki, G. Hagen, T. Otsuka,
M. Hjorth-Jensen, W. Catford… & advisory and organizing committees.
The role of three body n-n forces to create SO shell gaps
N=20
Z=20
40Ca
42Ca 43
Ca 44Ca
Theory: J.D. Holt et al. JPG 39 (2012)
G. Hagen et al. PRL 109 (2012)
N=28
f7/2
46Ca
48Ca
Vnn derived from 88,90Zr
Sorlin, Porquet PPNP 2008
exp (d,p),(p,d) from Uozumi et al. NPA 1994, PRC 1994
E*(170)
Sn(230)
s1/2
-4
-6
N=14
Sn(170)
Binding energy (MeV)
Binding energy (MeV)
-2
d5/2
-8
Sn(220)
16O
22O
8 10 12 14
Neutron
p3/2
-5
-2
d5/2
-4
-7
2.5MeV
?
N=28
N=50
-6
-9
f7/2
- 11
40Ca
48Ca
20 22 24 26 28
Neutron
-8
g9/2
See talk Moukadam
68Ni
78Ni
40 42 44 46 48 50
Neutron
Increase of SO shell gaps from n-n interactions
The same trend is observed in the O chain and predicted in the Ni chain (see Moukadam)
Nuclear physics of the r-process [dn~1024cm-3, T~109K]
2- Weak interactions to produce heavy elements :
82
Gamow Teller transition DJ=0, ±1,
[
DL=0
1/T1/2  SGT (Qb-E*)5
Nuclei accumulated at waiting points according to T1/2 -> peak height, duration of r process
T1/2 scales with energy of the transition, and strength of force
Pn values : probability to emit a neutron during b decay -> smoothens the r peaks
b-
] nh11/2
50
82
g9/2
h11/2
g7/2
g7/2 E*
g7/2
protons
neutrons
T1/2 (ms)
1000
Shorter half life due to p-n
interactions
100
10
40
50
N
Evolution of the proton-neutron interaction d5/2d3/2 in the N=17 isotones
30Al
28Na
26F
SM overbinds
SM underbinds
Spin Orbit magic numbers
208Pb
They become progressively
proeminent for heavier nuclei
42
132
78
14Si28≠ 50 Sn82 why ? How is Sn50 ?
164Gd
132Sn
28
20
78Ni
E(2+)
(keV)
4000
48Ca
3500
24
8O
22
90Zr
3000
2500
8O
1500
6C
1000
8 10 1214 16
Neutron Number
0
20Ca
16S
14Si
22 24 26 28 30
Neutron Number
Sn
1500
3000
3000
2000
2000
500
28Ni
50Zr
?
78
Ni
50Sn
1000
64G
Pb
4000
2000
1000
42Si
208
132
4000
2000
8O
500
0
Which mechanisms at play ?
What happens further from stability ?
42Si 48
Ca
6000
2000
28
90Zr
14
4000
SO magic numbers don’t exist for
neutron-rich light nuclei
1000
82Pb
d
0
44 4648 50 52
Neutron Number
0
70 74 78 82
Neutron Number
0
120 126
Neutron Number
S2N (MeV)
36Ca
20
20
30
20
20
45Ca
27Mg
10
S2N (MeV)
40
20
28
15
50Ca
10
35Mg
5
16
20
24
Neutron Number N
42Ca
45S
42Si
22 24 26 28 30
Neutron Number N
Harmonic oscillator magic numbers
Same hint of disappearance of N=20
magic numbers from atomic masses
Key proton-neutronr nuclear forces bring
16O and 40Ca to be doubly magic nuclei
Identify these forces … universal mechanism
40
S2N (MeV)
40
3500
36Ca
3000
30
20
2500
45Ca
27Mg
2000
1500
10
1000
35Mg
16
20
24
Neutron Number
500
0
14Si
10Ne
12Mg
12 16 20 24
Neutron Number
Persistent mechanism to destroy SO magic numbers
The one we discussed
SPIN –FLIP Dl=0 INTERACTION
Universal evolution of HO and SO shell closures
14 1d5/2
2s1/2
8
1p3/2 [ ]
p
6
p1/2
p3/2
n
Role
of the
3/2
28 2p
1f7/2
20
14
1d5/2
[ ]
p
n
p
]
N~8
6
p3/2
p3/2
n
p Z=6
p3/2- n
p1/2pinteraction
Z=2
N~20
d3/2
s1/2
d5/2
16
d5/2
28
N~40
p
1f7/2
Large N/Z
s1/2
d5/2
1g9/2
2d5/2
f5/2
34
p1/2
32
p3/2
28
p
n
n
Role of the p fZ=28
7/2- n fZ=20
5/2 interaction ?
f7/2
1f7/2
2p3/2
d3/2
14
n
Role of the pZ=14
d5/2- nZ=8
d3/2 interaction
2d
50 1g5/2
9/2
40
p1/2
f5/2
p3/2
1f7/2 [
1d
p1/25/2
f7/2
2s1/2
Evolution of the 0+2 states in the N=20 isotones -> island of inversion
2+
30+2
pf
20
d3/2
CD
30Mg
?
NEW
0 +1
40Ca
38Ar
36S
34Si
0+
2+
32Mg
0+
target
30Mg(t,p)32Mg
neutron pair transfer @ISOLDE
Wimmer et al. PRL 105 (2010)
0+1
0+
2
1058
886
172
0+2
2+
0+
32Mg
using g-rays
886
Evolution of the energy of neutron orbits (ESPE) at N=20
2s1/2 1d3/2
1d5/2
28O
40Ca
36S
34Si
32Mg
N=20
Neutron ESPE (MeV)
32Mg
34Si
0
4040
Ca
Ca
28O
16
20
2828
1f7/2
2s1/2
2s1/2
-20
Adapted from T. Utsuno
et al. PRC (1999)
8 10 12 14 16 18 20
Z
N=20 reduced
N=28 collapsed
2p3/2
2p3/2
Proton-neutron interaction Vpn depends on n, l, j
Hierarchy Vpn1d5/21d3/2 >> Vpn1d5/21f7/2 > Vpn1d5/22p3/2
1f7/2
20
1d3/2
16
1d3/2P(r)
-10
N=20 gap constant
N=28 slightly reduced
1d
2p
l1
1f
s1
l2
s2
r
1- Onset of deformation below Z=14
2- Crossing between p and f shell close to drip line ?
3- Is the effective Vpnd5/2d3/2 nuclear force modified there ?
Study of the beta decay of 26F
β-decay selection rules :
∆J = 0 , ±1
3+
unbound
2+
4+
642
660
β
1+
26F
1797
β
0++
2
4+
1499 1673
2018
1673
1499
1507
1797
1701
1797
2+
2018
[ 0ms – 30ms ]
0+
26Ne
26F
implantation
time
PART II: Spin orbit interaction far from stabilityZ=120
Around 132Sn
i13/2
f5/2
h9/2
p
1/2
p3/2
f7/2
h11/2 – h9/2
1.5 MeV
DSO
(MeV)
N/Z
d3/2
h11/2
s1/2 g7/2
d5/2
Drip line
126
126
82
82
50
50
g9/2
How does the spin-orbit interaction changes far from stability
when the surface diffuseness is increased ?
From two-body short-range interactions to collective motion
… seems like the movements of fishes in the sea