R' F' Casten

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Masses, Bubbles and Two Nucleon Transfer A New
Perspective on Nuclear Collectivity
Microscopic Drivers of Structural Evolution
R. F. Casten The Yale Elderly Professor of
Physics WNSL, Yale June 18, 2009
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• Themes and challenges of Modern Science
• Complexity out of simplicity -- Microscopic
• How the world, with all its apparent complexity
  and diversity can be constructed out of a few
  elementary building blocks and their interactions
• Simplicity out of complexity Macroscopic
• How the world of complex systems can display such
  remarkable regularity and simplicity

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Broad perspective on structural evolution
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Microscopic origins of collectivity
correlations, configuration mixing and
deformation Residual interactions
Crucial for structure
Crucial for masses
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Sn Magic no valence p-n interactions
Critical role of the valence p-n interaction
Both valence protons and neutrons
NpNn Scheme
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Getting at the p-n interactionsMasses Reflect
Nucleonic Interactions
Total mass/binding energy Sum of all
interactions Mass differences Separation
energies shell structure, phase transitions,
collectivity Double differences of masses
Interaction filters

• Shell structure
  1 MeV
• Quantum phase transitions 100s keV
• Collective effects
  100s keV
• Interaction filters
  10-15 keV

Macro
Micro
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Measurements of 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
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Valence p-n interaction Can we measure it?
?Vpn (Z,N)     ¼ B(Z,N) - B(Z,
N-2) -  B(Z-2, N) - B(Z-2, N-2)
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-
-
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
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Orbit dependence of p-n interactions simple
ideas
Low j, high n
High j, low n
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Can we extend these ideas beyond magic regions?
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Away from closed shells, these simple arguments
are too crude. But some general predictions can
be made
p-n interaction is short range similar orbits
give largest p-n interaction
Largest p-n interactions if proton and neutron
shells are filling similar orbits
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Empirical p-n interaction strengths indeed
strongest along diagonal.
Empirical p-n interaction strengths stronger in
like regions than unlike regions.
Low j, high n
High j, low n
New mass data on Xe isotopes at ISOLTRAP ISOLDE
CERN Neidherr et al, preliminary
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p-n interactions and the evolution of structure
Direct correlation of observed growth rates of
collectivity with empirical p-n interaction
strengths
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BEWARE OF FALSE CORRELATIONS!
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W. Nazarewicz, M. Stoitsov, W. Satula
Realistic Calculations

• Microscopic Density Functional Calculations
  with Skyrme forces and different treatments of
  pairing

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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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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
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The new Xe mass measurements at ISOLDE give a new
test of the DFT
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One last thing
Two regions of parabolic anomalies. Two
regions of octupole correlations Possible
signature?
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http//workshop.turkfizikdernegi.org
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Summary

• p-n interactions and the evolution of
  collectivity
• Mass filters dVpn available far from
  stability
• Crossing pattern around doubly magic nuclei --
  orbit overlaps
• Maximum for similar shell filling along
  diagonal in N-Z plot
• Maximum in like quadrants (p-p or h-h vs p-h or
  h-p)
• Correlation with growth rates of collectivity
• Comparison with DFT calculations
• Possible signature of octupole correlations

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Principal Collaborators

• Burcu Cakirli (Istanbul)
• Daeg Brenner, Jing-ye Zhang
• Dennis Neidherr, Klaus Blaum, Magda Kowalska and
  the entire ISOLTRAP collaboration
• Yuri Litvinov and the GSI Schottky mass group
• Witek Nazarewicz, Mario Stoitsov, and Wojtek
  Satula
• (Lee for secretly editing my first slide)