Download - Proton-neutron interactions
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Proton-neutron interactions
The key to structural evolution
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6+ 690
4+ 330
0+ 0
2+ 100
J E (keV)
?Without
rotor
paradigm
Paradigm
Benchmark
700
333
100
0
Rotor J(J + 1)
Amplifies structural
differences
Centrifugal stretching
Deviations
Identify additional
degrees of freedom
Detour before starting
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Valence Proton-Neutron Interaction
Development of configuration mixing, collectivity and deformation –
competition with pairing
Changes in single particle energies and magic numbers
Partial history: Goldhaber and de Shalit (1953); Talmi (1962); Federman and Pittel ( late 1970’s); Casten et al (1981); Heyde et al (1980’s); Nazarewicz, Dobacewski et al (1980’s); Otsuka et al( 2000’s) and many others.
Microscopic perspective
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Sn – Magic: no valence p-n interactions
Both valence protons and
neutrons
Two effects
Configuration mixing, collectivity
Changes in single particle energies and shell structure
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Microscopic mechanism of first order phase transition (Federman-Pittel, Heyde)
Monopole shift of proton s.p.e. as function of neutron number
Gap obliteration
2-space 1-space
(N ~ 90 )
Can we see this experimentally?
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A simple signature of phase transitions
MEDIATED
by sub-shell changes
Bubbles and Crossing patterns
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Seeing structural evolution Different perspectives can yield different insights
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
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A~100
52 54 56 58 60 62 64 66
1,6
1,8
2,0
2,2
2,4
2,6
2,8
3,0
3,2
Z=36 Z=38 Z=40 Z=42 Z=44 Z=46
R4/
2
Neutron Number
36 38 40 42 44 46
1,6
1,8
2,0
2,2
2,4
2,6
2,8
3,0
3,2
N=52 N=54 N=56 N=58 N=60 N=62 N=64 N=66
R4/
2
Proton Number
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B(E2; 2+ 0+ )
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Sudden changes in R4/2
signify changes in structure, usually from spherical to deformed
structure
Onset of deformation
Sph.
Def.
Observable
Nucleon number, Z or N
R4/2
E2
1/E2
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Often, esp. in exotic nuclei, R4/2 is not available. A easier-to-obtain observable, E(21
+), in the form of 1/ E(21
+), can substitute equally well
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• Shell structure: ~ 1 MeV• Quantum phase transitions: ~ 100s keV• Collective effects ~ 100 keV• Interaction filters ~ 10-15 keV
Total mass/binding energy: Sum of all interactions
Mass differences: Separation energies shell structure, phase transitions
Double differences of masses: Interaction filters
Masses:
Macro
Micro
Masses and Nucleonic Interactions
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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
Neutron Number
S(2
n)
MeV
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Measurements of p-n Interaction Strengths
Vpn
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
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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?
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Orbit dependence of p-n interactions
82
50 82
126
High j, low n
Low j, high n
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82
50 82
126
Z 82 , N < 126
11
3
Z > 82 , N > 126
3
Z > 82 , N < 126
2
2
Behavior of p-n interactions
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208Hg
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In terms of proton and neutron orbit filling, p-n interaction
p-n interaction is short range similar orbits give largest p-n interaction
HIGH j, LOW n
LOW j, HIGH n
50
82
82
126
Largest p-n interactions if proton and neutron shells are filling similar orbits
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First direct correlation of observed growth rates of collectivity with empirical p-n interaction strengths
Empirical p-n interaction strengths indeed strongest along diagonal.
82
50 82
126
High j, low n
Low j, high n
Neidherr et al, preliminary
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BEWARE OF FALSE BEWARE OF FALSE CORRELATIONS!CORRELATIONS!
BEWARE OF FALSE BEWARE OF FALSE CORRELATIONS!CORRELATIONS!
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W. Nazarewicz, M. Stoitsov, W. Satula
Microscopic Density Functional Calculations with Skyrme forces and
different treatments of pairing
Realistic Calculations
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Density Functional Theory
Would you like to see it again? OK.
My understanding of DFT:
So, I hope all this is clear.
Anyway, Nazarewicz, Stoitsov and Satula calculated masses for over 1000 nuclei across the nuclear chart with several interactions, and, from these masses, computed the p-n interactions using the same double difference expression. Lots of results. A few examples:
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http://workshop.turkfizikdernegi.org
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Principal Collaborators
• Burcu Cakirli (Istanbul) dVpn, Bubbles, Masses
• Klaus Blaum (MPI – Heidelberg) Masses
• Magda Kowalska (CERN – ISOLDE) Masses
• And the GSI Schottky and CERN-ISOLDE mass groups for their measurements of Hg, Rn and Xe masses
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