masses and structure in exotic nuclei r. f. casten wnsl, yale eurorib’10, june, 2010
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Masses and Structure in Exotic Nuclei
R. F. CastenWNSL, Yale
Eurorib’10, June, 2010
1 12 4 2( ; )B E
1000 4+
2+
0
400
0+
E (keV) Jπ
Structural Evolution: Simple Observables - Even-Even Nuclei
1 12 2 0( ; )B E
)2(
)4(
1
12/4
E
ER
Masses
1300 2+
0+
2+
6+. . .
8+. . .
Vibrator (H.O.)
E(I) = n ( 0 )
R4/2= 2.0
n = 0
n = 1
n = 2
Rotor
E(I) ( ħ2/2I )I(I+1)
R4/2= 3.33
Doubly magic plus 2 nucleons
R4/2< 2.0
10 20 30 40 50 60 70 80 90 100110120130140150
10
20
30
40
50
60
70
80
90
100
Pro
ton
Num
ber
Neutron Number
80.00
474.7
869.5
1264
1600
E(21+)
10 20 30 40 50 60 70 80 90 100110120130140150
10
20
30
40
50
60
70
80
90
100
Pro
ton
Num
ber
Neutron Number
1.400
1.776
2.152
2.529
2.905
3.200
R4/2
Broad perspective on structural evolution
The remarkable regularity of these patterns is one of the beauties of nuclear structural evolution and one of the challenges to nuclear theory.
Whether they persist far off stability is one of the fascinating questions for the future
R. B. Cakirli
Structural evolution – rapid structural change
Spherical-deformed trans.
Near N ~ 90
Cakirli
Often, esp. in exotic nuclei, R4/2 is not available.
E(21+) is easier to measure, works as well !!!
R4/2 across this region
84 86 88 90 92 94 961.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
Ba Ce Nd Sm Gd Dy Er Yb
R4/
2
N
Better to use in
the form
1/ E(21+)
Vibrator
Rotor
!
56 58 60 62 64 66 68 701.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
N=84 N=86 N=88 N=90 N=92 N=94 N=96R
4/2
Z84 86 88 90 92 94 96
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
Ba Ce Nd Sm Gd Dy Er Yb
R4/
2
N
Physics from different perspectives
Onset of deformation Onset of deformation as a phase transition
mediated by a change in shell structure
Mid-sh.
magic
“Crossing” and “Bubble” plots as indicators of phase transitional regions mediated by sub-shell changes
Cakirli and Casten, PRC 78, 041301(R) (2008)
Sn – Magic: no valence p-n interactions
Both valence protons and
neutrons
The importance of the p-n interaction
Microscopic origins of
phase transitional
behavior
Potentials involved In
Phase transitions
Valence pn interactions
Can we Measure p-n Interaction Strengths?
dVpn
Average p-n interaction between last protons and last neutrons
Double Difference of Binding Energies
Vpn (Z,N) = ¼ [ {B(Z,N) - B(Z, N-2)} - {B(Z-2, N) - B(Z-2, N-2)} ]
Ref: J.-y. Zhang and J. D. Garrett
Vpn (Z,N) =
¼ [ {B(Z,N) - B(Z, N-2)} - {B(Z-2, N) - B(Z-2, N-2)} ]
p n p n p n p n
Int. of last two n with Z protons, N-2 neutrons and with each other
Int. of last two n with Z-2 protons, N-2 neutrons and with each other
Empirical average interaction of last two neutrons with last two protons
-- -
-
Valence p-n interaction: Can we measure it?
Cakirli based on Zhang and Garrett
Empirical interactions of the last proton with the last neutron
Vpn (Z, N) = ¼{[B(Z, N ) – B(Z, N - 2)]
- [B(Z - 2, N) – B(Z - 2, N -2)]}
dVpn has singularities for N = Z in light nuclei• Wigner energy, related to SU(4),
supermultiplet theory, spin-isospin symmetry.
• Physics is high overlaps of the last proton and neutron wave functions when they fill identical orbits.
• Expected to vanish in heavy nuclei due to: Coulomb force for protons; spin-orbit force which brings UPOs into different positions in each shell; protons and neutrons occupy different major shells.
8 10 12 14 16 18 20 22 24 26 28
1000
2000
3000
4000
Vpn (
keV
)
Neutron Number
Ne Mg Si S Ar Ca
This effect should not persist in heavy nuclei.
Does it? In a way, yes!
Rare-earth region
128 130 132 134 136 138 140
200
300
400
UThRaRnPo
Vpn
(ke
V)
Neutron Number
92 94 96 98 100 102 104 106 108 110
200
300
400
Hf
WYbErDyGd
Vpn
(ke
V)
Neutron Number
Sm
62Sm: dVpn(max) at N=94: 12 valence protons, 12 valence neutronsGd 14-14 (?) , Dy 16-16 (?), Er 18-18, Yb 20-20,
Hf, W 22,24, and 24,24
dVpn has peaks for Nval ~ Zval !!!!considering only the number of valence particles,
a possible mini-valence Wigner energy !!R. B. Cakirli, R. F. Casten and K. Blaum, to be published
Agreement is remarkable. Especially so since these DFT calculations reproduce known masses
only to ~ 1 MeV – yet the double difference embodied in dVpn allows one to focus on
sensitive aspects of the wave functions that reflect specific correlations
M. Stoitsov, R. B. Cakirli, R. F. Casten, W. Nazarewicz, and W. Satula PRL 98, 132502 (2007)
Exp.
Models
Masses, Separation energies
A “de-linearization” approach
Two-neutron separation energies
Sn
Ba
Sm Hf
Pb
5
7
9
11
13
15
17
19
21
23
25
52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120 124 128 132
S(2
n)
MeV
Neutron Number
Normal behavior: ~ drops after closed shells with linear segments in betweenDiscontinuities at first order phase transitions
Note that the range of values in S2n is ~ 18 MeV
Binding Energies
Many Methods to estimate
• Mass models – semi-empirical
• Microscopic calculations – many approaches including RMFT, DFT, etc
• Collective models – e.g., IBA, for the collective contribution to binding
• A new approach – pattern recognition techniques, aided by a linear subtraction method
Collective contributions to masses can vary significantly for small parameter changes in collective models, especially for well-deformed
nuclei where collective binding can be quite large.
S2n(Coll.) for alternate fits to Er with N = 100
Gd – Garcia Ramos et al, 2001
Masses: a new opportunity – complementary observable to spectroscopic data in pinning down structure. Strategies for best doing that are still being worked out. Particularly important far off stability where data will be sparse.
Sn
Ba
Sm Hf
Pb
5
7
9
11
13
15
17
19
21
23
25
52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120 124 128 132
S(2n
) MeV
Neutron Number
Cakirli, Casten, Winkler, Blaum, and Kowalska, PRL 102, 082501(2009)
Pattern Recognition “Physics-free” (therefore not biased) – can it tell us any physics???
Analyse the 2-D “surface” of an observable by Fourier transforms
Extrapolate to predict observables in unknown regions
How good is it? To date and longer term prospects
84 90 96 102 108 114 120 1268
10
12
14
16
18
20
22
Nd Hf
S2n
(MeV
)
Neutron Number
Pb
Try on separation energies. Test case: mask portion of data
Pattern recognition for separation energies – Not so good. Rapidly accumulate errors of a few MeV . Can we do better?
More sensitive tests of nuclear models
Remove the linear dependence
isolate and amplify collective effects
S2n-TOTAL = S2n-Linear + S2n-coll.
84 90 96 102 108 114 120 1268
10
12
14
16
18
20
22
Nd Hf
S 2n(M
eV)
Neutron Number
Pb
S2n-coll. (Z=50-82, N=82-126)
Subtract linear function, A + BN, from S2n plot
84 90 96 102 108 114 120 1260
2500
5000
S
2n-c
olle
ctiv
e (ke
V)
Neutron Number
Te Xe Ba Ce Nd Sm Gd Dy Er Yb Hf W Os Pt Hg Pb
The range of S2n is now ~ 2-3 MeV
84 90 96 102 108 114 120 1268
10
12
14
16
18
20
22
Nd Hf
S2n
(MeV
)
Neutron Number
Pb
Cakirli, Casten and Blaum, in progress
84 90 96 102 108 114 120 126
54
58
62
66
70
74
78
82
Z
N
0
1.2
2.4
3.6
4.2
S2n-collective
84 90 96 102 108 114 120 12652
56
60
64
68
72
76
80
Z
N
8.20
13.2
18.2
22.0
S2n
(MeV)
S2n-total
Greatly enhanced sensitivity of S2n-coll.
Now use pattern recognition to fit the S2n-coll values. Then add back the linear function
Work is in progress. Where will it lead? We don‘t have a clue. We will see. Work just beginning.
7000
12000
17000
22000
84 88 92 96 100 104 108 112 116 120 124
N
S2n
WEr
Pb
Nd
Very good agreement. Extrapolating ~ 12 mass units
Frank, Morales, Cakirli, Casten and Blaum, in progress
Principal Collaborators
• R. Burcu Cakirli• Klaus Blaum• Magda Kowalska• Alejandro Frank• Irving Morales
Backups
Correlations of Collective Observables
4+
2+
0+
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