Origin of prolate dominance of nuclear deformation - an analysis with Woods-Saxon potential -

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Origin of prolate dominance of nuclear
deformation- an analysis with Woods-Saxon
potential -

• S. Takahara1, N. Tajima2, Y. R. Shimizu3
• 1Kyorin Univ., 2Fukui Univ., 3Kyushu Univ.

RIKEN Symposium 2006 Methods of many-body
systems mean field theories and beyond March 21,
2006
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Contents

• Introduction
• Nilsson Strutinsky method
• Woods-Saxon Strutinsky method
• Summary

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Basic question prolate dominance

• Most of nuclei are deformed into prolate shapes
• Why nuclei prefer prolate shapes?
• Deformation shell structure of single particle
  spectrum
• Relation between Hamiltonians and prolate shapes?
• Only consider mean single-particle potential

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Principal features of single particle potential

• Spin-orbit coupling
• Radial profile (H.O. ? square-well) Frisk
  classical periodic orbits (1990)
• square-well wo LS prolate dominance
• Pairing
• What happens if these features are changed?
• Strutinsky method with Nilsson and Woods-Saxon
  potential

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pseudospin symmetry at µN0.5 e.g. p3/2, d3/2 are
degenerate exactly
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Nilsson LL / LS
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Nilsson pairing
0
0.7
1
1.2
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Nilsson potential results

• PES(e2, e4) over the nuclear chart (1834
  even-even nuclei)
• Proportion of prolate nuclei
• of prolate / ( of prolate of oblate)
• Standard potential 86 are prolate
• Potential profile
• Rp(fll) along fls0 increasing trend, support
  Frisk theory
• Spin-orbit
• Does not favor prolate or oblate oscillating
• Strong interference with l2 term
• Relation with pseudospin symmetry
• Pairing
• Enhances both prolate and oblate dominances

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Calculation with W. S. Strutinsky method

• Easier than HF but costs 10 times longer than
  Nilsson
• Construct a cluster of ten PCs
• Job control with scripts
• PES(ß2, ß4) over the nuclear chart (8ltZlt126,
  8ltNlt184, 1834 even-even nuclei)
• As a function of spin-orbit, pairing,
  (diffuseness) strength, calculate the proportion
  of prolate nuclei

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Woods-Saxon spin-orbit / pairing
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optimized
Ramon-Wyss 1
universal
Ramon-Wyss 2
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Woods-Saxon results

• 6 types of parameter set (global properties on
  the nuclear chart are different. E.g. driplines)
• Essentially the same results
• Spin-orbit / pairing
• Similar results with Nilsson
• Oscillates with spin-orbit strength
• Pairing enhances prolate/oblate dominances
• f_SO1,0 prolate dominance
• f_SO1/2 Nilsson, oblate dominance
• W.S., more than 50 prolate

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Woods-Saxon in progress

• Effect of diffuseness
• Some difficulties
• Existence of continuum
• Restriction on the combination of diffuseness and
  depth
• Arita, ra-potential
• Diffuseness and spin-orbit
• Pseudospin symmetry

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spin-orbit/diffuseness
Preliminary result
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Summary

• approach to explain the origin of prolate
  dominace
• Nilsson Strutinsky published PRC64,037301(2001)
• Interference between spin-orbit and radial
  profile
• Woods-Saxon Strutinsky
• Same as Nilsson qualitatively
• Effect of diffuseness in progress