Protonneutron interactions, collectivity, and density functional theory

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Proton-neutron interactions, collectivity, and
density functional theory

• Linking the forest and the trees
• R.F.Casten
• WNSL, Yale

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Fundamental Questions for the Science of Nuclei

• What binds protons and neutrons into stable
  nuclei and rare isotopes?
• Complexity Microscopic Trees
• What is the origin of simple patterns in complex
  nuclei?
• Collective modes Macroscopic Forest

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Valence Proton-Neutron Interaction

• Development of configuration mixing, collectivity
  and deformation
• Changes in single particle energies and magic
  numbers
• Partial history Goldhaber and de Shalit
  (1953) Talmi (1962) Federman and Pittel ( late
  1970s) Casten et al (1981) Heyde et al
  (1980s) Nararewicz, Dobacewski et al (1980s)
  Otsuka et al( 2000s) and many others.

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Sn Magic no valence p-n interactions
Both valence protons and neutrons
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Potentials involved In Phase transitions
Microscopic origins of phase transitional behavior
Valence pn interactions
Direct experimental evidence
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Can we measure the valence p-n interaction? Empir
ical average p-n interaction of the last proton
and neutron - ?Vpn 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)
This is a slight misnomer because there are two
contributions A real p-n interaction and a
smooth contribution from the symmetry energy
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low j, high n high j, low n
Generic sequencing of shell model orbits
Hence, if the protons and neutrons are filling
similarly (similar fractional filling), the p-n
interaction should be largest.
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Behavior of p-n interactions
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First direct correlation of observed growth rates
of collectivity with empirical p-n interaction
strengths
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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
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Comparisons of DFT calculations with empirical
p-n interaction strengths
What works and what doesnt
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Collaborators
Early work on this subject Jing-ye Zhang, Jerry
Garrett, Daeg Brenner

• R. Burcu Cakirli
• Daeg Brenner
• Eleanor Millman
• Witek Nazarewicz
• Mario Stoitsov
• Wojek Satula

Refs PRL, 94, 092501(2005) 96,
132501(2006) 98, 132502(2007)
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Backups
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Masses Physics
Total mass/binding energy Sum of all
interactions Mass differences Separation
energies shell structure, phase
transitions Double differences of masses
Interaction filters PRECISION REQUIRED

• Shell structure 100-300
  keV
• Quantum phase transitions 100 keV
• Interaction filters (e.g., p-n) 10-15 keV
• Fundamental symmetries lt 1 keV
• (e.g., unitarity of CKM matrix)

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Different perspectives can yield different
insights
Onset of deformation as a phase transition and
change in shell structure
Onset of deformation
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Nuclear collective motion individual nuclei
What is the origin of ordered motion of complex
nuclei? Complex systems often display
astonishing simplicities. Nuclei are no
exception. How is it that a heavy nucleus, with
hundreds of rapidly moving nucleons, can exhibit
collective motion.
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This is a slight misnomer because there are two
contributions A real p-n interaction and a
smooth contribution from the symmetry energy
We will focus mostly on the former, which are
sensitive to the spatial overlaps of the proton
and neutron wave functions