*S. Takahara1,　N. Tajima2,　Y. R. Shimizu3

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Presentation transcript:

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

Contents Introduction Nilsson Strutinsky method Woods-Saxon Strutinsky method Summary

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

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

pseudospin symmetry at μN=0.5 e.g. p3/2, d3/2 are degenerate exactly

Nilsson LL / LS Results with Nilsson

Nilsson pairing 0.7 1 1.2

Nilsson potential : results PES(ε2, ε4) 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 fls=0: 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

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(β2, β4) over the nuclear chart (8<Z<126, 8<N<184, 1834 even-even nuclei) As a function of spin-orbit, pairing, (diffuseness) strength, calculate the proportion of prolate nuclei

Woods-Saxon: spin-orbit / pairing

optimized Ramon-Wyss 1 universal Ramon-Wyss 2

Woods-Saxon : results Spin-orbit / pairing 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_SO=±1,0: prolate dominance f_SO=±1/2: Nilsson, oblate dominance W.S., more than 50% prolate

Woods-Saxon : in progress Effect of diffuseness Some difficulties Existence of continuum Restriction on the combination of diffuseness and depth Arita, rα-potential Diffuseness and spin-orbit Pseudospin symmetry

spin-orbit/diffuseness Preliminary　result

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