Forces for extensions of meanfield Extensions of meanfield
















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Forces for extensions of meanfield § Extensions of mean-field ? § Why a new force ? and which forces ? § Some results § Perspectives Ph. D Thesis Marlène Assié Denis Lacroix (LPC Caen), Jean-Antoine Scarpaci (IPN Orsay)

Beyond the mean-field E/A=5 Me. V/u E/A=150 Me. V/u LOW ENERGY INTERMEDIATE ENERGY Extended TDHF mean-field Boltzmann term static : HF dynamical : TDHF Skyrme Forces collisions important + mean-field Skyrme Forces which force ? Bonche et al PRC 13 (1976) 1226

Zero range force versus finite range force • Time Dependent Density Matrix : • With a finite range force : function used : v=v 0 3 (r 1 –r 2) M. Tohyama Prog. Theor. Phys. 94(1995) S. Wang, W. Cassing, Nucl. Phys. A 652 (1999) • Extended TDHF : <ij|v|kl>=<ij|vs|kl> C(|<ij|q²|kl>) D. Lacroix, S. Ayik, Ph. Chomaz, Prog. in Part. Nucl. Phys. 52(2004) cut off k~range

The collision term • In the semi-classical limit p 1 p 3 k k’ p 2 loss p 4 gain interaction dependence Forces in the collision term might be fitted to the nucleon cross-section

Total Cross Section (mb) Cross Section for various Skyrme forces and the Gogny force Li & Machleidt parametrization Energy (Me. V) Li & Machleidt Phys. Rev. C 48 (1993); Phys. Rev. C 49 (1994)

Cross Section for various Skyrme forces and the Gogny force Total Cross Section (mb) Li & Machleidt SGII Sk. M* Sk. P SLy 4 SLy 7 Energy (Me. V) Yildirim et al, Eur. Phys. J. A 10 (2001) ; Yilmaz et al, Phys. Lett. B 472

Cross Section for various Skyrme forces and the Gogny force Total Cross Section (mb) Li & Machleidt SGII Sk. M* Sk. P SLy 4 SLy 7 Gogny None of these forces reproduce nucleon-nucleon in medium crosssection new force energy (Me. V)

Fitted force • Force of finite-range and separable § Gaussian (G) Ä finite-range § Gaussian +constant (G+C) Total cross section (mb) Ä already used for pairing correlations Duguet PRC 69 (2004) 0=0, 18 fm-3 Ä separable : simpler numerically Fit with Gaussian 0=0, 18 fm-3 Fit with Gaussian + c = -655 Me. V fm 3 = -137 Me. V fm 3 ² = 0. 279 fm 2 1²= 1. 54 fm 2 Li & Machleidt c=1. 34 fit (G) energy (Me. V)

Density dependence Parameterization of Li & Machleidt E=50 Me. V Total cross section (mb) Li & Machleidt Phys. Rev. C 48 (1993); Phys. Rev. C 49 (1994) Li & Machleidt parameterization density (fm-3)

Density dependence Parameterization of Li & Machleidt E=50 Me. V Total cross section (mb) Li & Machleidt Phys. Rev. C 48 , 1702; Phys. Rev. C 49, 566 Li & Machleidt parameterization • Density dependence (DDG) Gaussian similar as Skyrme Gaussian + constant introduced to reproduce a density dependence density (fm-3)

Fit with the density dependent function • Fit method : 2 dimensions fit on the energy and the density with 4 parameters Total cross section (mb) =0. 05 fm-3 Li & Machleidt E=50 Me. V fit with the density dependent force (DDG) E=100 Me. V =0. 15 fm-3 energy (Me. V) density (fm-3)

Fit with a sum of Gaussian and density dependence • Fit method : Total cross-section (mb) 2 dimensions fit on the density and the energy with 5 parameters =0. 05 fm-3 Li & Machleidt E=50 Me. V fit with the density dependent force (DDGC) E=100 Me. V =0. 15 fm-3 energy (Me. V) density (fm-3)

Summary • 2 forces which reproduce density and energy dependence of the nucleon-nucleon cross section Case of pairing • particle-hole channel • particle-particle channel • hole-hole channel Skyrme force independent pairing force Case of 2 body correlations • particle-hole channel Skyrme force • 2 particle- 2 hole channel separable finite-range force should use the same force

Comparison with the Skyrme force when k 0 and =0 • Skyrme Force t 0 • Gaussian t 1 -2 ² • Gaussian density dependent t 0 t 1 -2 ² t 3 c 3 Skyrme forces Gaussian (G) Gaussian+ constant (GC) Gaussian density dependent Gaussian+ constant density dependent Up to 10 parameters 2 parameters 3 parameters 4 parameters 5 parameters t 0=-2931 to -1057 Me. V. fm 3 - 655 Me. V. fm 3 - 748 Me. V. fm 3 - 2416 Me. V. fm 3 -2572 Me. V. fm 3 t 1=235 to 970 Me. V. fm 5 183 Me. V. fm 5 491 Me. V. fm 5 1038 Me. V. fm 5 1896 Me. V. fm 5 t 2=-556 to 107 Me. V. fm 5 Neglected t 3=8000 to 18708 Me. V. fm(3+3 ) 13107 Me. V. fm 3+3 13891 Me. V. fm 3+3 =1/6 to 1 0. 17

t 0=-2645 Me. V. fm 3 t 0= -2416 Me. V. fm 3 t 0=-2572 Me. V. fm 3 t 1= 410 Me. V. fm 3 t 1= 1038 Me. V. fm 3 t 1= 1896 Me. V. fm 3 Skyrme Gaussian density Gaussian + c + density Li & Machleidt

Perspectives • Time Dependent Density Matrix (TDDM) W. Cassing, S. J. Wang, Z. Phys. A, 328 (1987) § truncation of the BBGKY hierarchy § takes into account all the two body correlations (extension of HF) Skyrme force separable finite- range force • Perspectives : study of correlations between two neutrons in borromean nuclei Experiment planned for July 2006 at GANIL
Erosion is a destructive force that
Example for like parallel forces
Covalent bond intermolecular forces
The forces shown above are
What is contact force
Intra vs intermolecular forces
Force examples in everyday life
Intra vs intermolecular
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