proton-neutron interactions
Post on 14-Jan-2016
52 Views
Preview:
DESCRIPTION
TRANSCRIPT
Proton-neutron interactions
The key to structural evolution
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
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
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)
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?
A simple signature of phase transitions
MEDIATED
by sub-shell changes
Bubbles and Crossing patterns
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
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
B(E2; 2+ 0+ )
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
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
• 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
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
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
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?
Orbit dependence of p-n interactions
82
50 82
126
High j, low n
Low j, high n
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
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
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
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
BEWARE OF FALSE BEWARE OF FALSE CORRELATIONS!CORRELATIONS!
BEWARE OF FALSE BEWARE OF FALSE CORRELATIONS!CORRELATIONS!
W. Nazarewicz, M. Stoitsov, W. Satula
Microscopic Density Functional Calculations with Skyrme forces and
different treatments of pairing
Realistic Calculations
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:
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
Backups
top related