Proton-neutron interactions
The key to structural evolution
Paradigm
Detour before starting
6+
690
4+
330
2+
100
0+
0
J
E (keV)
?
Amplifies
structural
Benchmark
differences
700
333
Centrifugal
stretching
100
Without
rotor
0
Rotor J(J + 1)
Deviations
paradigm
Identify additional
degrees of freedom
Microscopic perspective
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.
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
Microscopic mechanism of first order phase
transition (Federman-Pittel, Heyde)
(N ~ 90 )
2-space
1-space
Monopole shift of proton s.p.e. as function of
neutron number
Can we see this experimentally?
A simple signature of phase
transitions
MEDIATED
by sub-shell changes
Bubbles and Crossing patterns
Seeing structural evolution
Different perspectives can yield different insights
3.4
3.4
3.0
R4/2
2.8
2.6
2.4
2.2
3.0
2.6
2.4
1.8
1.8
1.6
1.6
88
90
92
94
N
Onset of deformation
96
magic
2.2
2.0
86
Mid-sh.
2.8
2.0
84
N=84
N=86
N=88
N=90
N=92
N=94
N=96
3.2
R4/2
Ba
Ce
Nd
Sm
Gd
Dy
Er
Yb
3.2
56
58
60
62
64
66
68
70
Z
Onset of deformation
as a phase transition
mediated by a change in shell structure
“Crossing” and “Bubble” plots as indicators of phase
transitional regions mediated by sub-shell changes
A~100
Z=36
Z=38
Z=40
Z=42
Z=44
Z=46
3,2
3,0
2,8
2,4
3,0
2,8
2,6
R4/2
R4/2
2,6
2,4
2,2
2,2
2,0
2,0
1,8
1,8
1,6
1,6
52
54
56
58
60
Neutron Number
62
64
66
N=52
N=54
N=56
N=58
N=60
N=62
N=64
N=66
3,2
36
38
40
42
Proton Number
44
46
B(E2; 2+  0+ )
R4/2
Sudden changes in R4/2
signify changes in
structure, usually from
spherical to deformed
structure
Observable
E2
Nucleon number, Z or N
3.4
R4/2
2.8
2.6
2.4
2.2
0,012
Z=56
Z=58
Z=60
Z=62
Z=64
Z=66
Z=68
1/E2
0,010
+
3.0
0,014
1/E(21 )
Ba
Ce
Nd
Sm
Gd
Dy
Er
Yb
Def.
3.2
0,008
0,006
0,004
2.0
Sph.
1.8
0,002
1.6
84
86
88
90
92
94
N
Onset of deformation
96
0,000
84
86
88
90
92
Neutron Number
94
96
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
Masses and Nucleonic Interactions
Masses:
Total mass/binding energy: Sum of all interactions
Mass differences: Separation energies
shell structure, phase transitions
Double differences of masses: Interaction filters
Macro
Micro
•
•
•
•
Shell structure:
Quantum phase transitions:
Collective effects
Interaction filters
~ 1 MeV
~ 100s keV
~ 100 keV
~ 10-15 keV
25
23
21
S(2n) MeV
19
17
15
13
Sm
11
9
Hf
Ba
Pb
7
Sn
5
52
56
60
64
68
72
76
80
84
88
92
96
Neutron Number
100
104
108
112
116
120
124
128
132
Measurements of p-n Interaction Strengths
dVpn
Average p-n interaction between
last protons and last neutrons
Double Difference of Binding Energies
dVpn (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
Valence p-n interaction: Can we measure it?
dVpn (Z,N) =
¼ [ {B(Z,N)
-
B(Z, N-2)}
p
n
-
{B(Z-2, N)
p
n
Int. of last two n with Z protons,
N-2 neutrons and with each other
p
-
- B(Z-2, N-2)} ]
n
p
n
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
Orbit dependence of p-n
interactions
126
82
Low j, high n
High j, low n
50
82


Z  82 , N < 126
Behavior of p-n interactions
3
3
1
2
82
126
2
1
50
82


Z > 82 , N > 126
Z > 82 , N < 126
208Hg
In terms of proton and neutron orbit
filling, p-n interaction
p-n interaction is short range
similar orbits give largest p-n interaction
126
82
LOW j, HIGH n
HIGH j, LOW n
50
82
Largest p-n interactions if proton and neutron shells are
filling similar orbits
126
Empirical p-n interaction strengths
82
indeed strongest along diagonal.
High j, low n
50
82
Neidherr et al, preliminary
First direct correlation of observed
growth rates of collectivity with
empirical p-n interaction strengths
BEWARE OF FALSE CORRELATIONS!
Realistic Calculations
Microscopic Density Functional
Calculations with Skyrme forces and
different treatments of pairing
W. Nazarewicz, M. Stoitsov, W. Satula
Density Functional Theory
My understanding of DFT:
Would you like to see it again? OK.
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:
http://workshop.turkfizikdernegi.org
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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