Isovector and spin-isospin nuclear matter symmetry energy (Skyrme forces):

F.L.Braghin, IWND SE-09, Shanghai, August, 2009

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Isovector and spin-isospin nuclear matter symmetry energy (Skyrme forces): dependences on density and temperature

Fábio L. Braghin

Int. Centr Cond Matter Physics-University of Brasilia, Brasilia, Brasil(and IF-USP, São Paulo, Brasil)

Financial Support:

IBEM/Ministry Scie.-Tech-Brazil

FAP-DF (Brasilia) - Brazil

FAPESP (São Paulo)


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NUCLEAR FORCE dependences on isospin in Drop liquid (macroscopic) models

A() => (spin, isospin) = (s,t)


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Spin-Isospin symmetry energy

Related to an eventual instability of pion condensation (early 70, 80’s), higher

Eventually to DCC

Essentially restoring force of Gamow Teller (GT) resonances

Probe for pionic degree of freedom, eg. in relativistic models Lagrangian

(pseudo-scalar coupling):


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For a small externalperturbation in binding energy:

Standard form:

Relating the symmetry energy coefficient GENERAL AND response function (static) IDEA


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Dynamical Polarizabilities with Skyrme forces

Linear response on time dependent Hartree Fock for Skyrme forces such as:

Behavior of small density fluctuations induced by small amplitude external perturbationthat separates densities of neutrons and protons (s,t= 0,1) neutrons/protons spin up/down (s,t=1,1)


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Writing only the static limit for any densities of protons and neutrons

Form factors for

Densities of states

Particle densities

Densities of momentA

Same standard form of polarizability

Temperature dependence of A

v = b, c, dAsymmetry parameters

NPA(2000); PRC(2005)


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Each of the densities (form factors) for p = n


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Density dependence of the spin-isospin symmetry energy:

FLB,IJMPE(2003)

N Kaiser,PT, (2006)(strongly dependent on each d.o.f./effectMesons exchanges /

Very different predictions


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Temperature dependence of n –p symmetry energy: A 0,1


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Samaddar et al: down triangles (2007)Lie-Wen Chen et al: up triangles (2007)

Moustakidis: dashed (2008)

0 (NN09)

SLyb,b=0.5 (x)SLyb,b=0 ___SGII,b=0.5 (+)SGII,b=0 .....

Different momentum Dependent interactions,Clusters,..

Exp (diff and T*)Shetty et al 2006;Le Fevre et al (2005)Trautmann et al (2006)(INDRA; ALADIN)Kowalski et al(2006) .05


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Full solid symbols , x: 1.33 0 , b = 0

Empty symbols , +: 1.33 0 , b = 0.25

-Onsi et al (a) SkSC4

- Lyon group SLy4- Onsi et al (b)SkSC6

-Sagawa/GiaiSGII

FLB, PRC(2009)


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Spin-isospin: 0

++ SGII (b=.5)

... SGII (b=0)

xx SLy4 (b=.5)

___ SLy4 (b=0)


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0

SGII

SkSC4 SLy4

Smoother variation athigher densities


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Limit of equal densities protons-neutrons

Depending on the Skyrme force

Momentum dependence of the polarizability


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Momentum dependence 0.1 0

Instability forn-matter

2 0


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T=0,1,2,4Spin-isospin:

Momentum dependence at 0

Momentum dependence does not favor spin-isospin instabilities for several Skyrme forces (but yes for neutron-matter instabilities)(not yet extensive)


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Considering always:

In static (or ~ dynamical) framework

Eventually assuming: A = A (b, T,q,..)


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Standard expression

Variation of

Or More generally:

Simultaneous dependence of symmetry energy on different variables

Looking for datato plug with e.o.s.

For finite nuclei ；Densities-> N,Z/Vn Vp

PRC(2005)


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Summary

Calculating symmetry energies from nuclear polarizabilities

Dependences on T, n-p, momentum exchanged depend strongly on density

Ｈｏｗ　ｃ an spin-isospin sym.energ interaction 　（ｔｏｇｅｔｈｅr with(0,1)) ｂｅ　ｐｒｏｂｅｄ　 by pions in 　ｈｉｃ ?

Differential equation available ：ｇｉｖｅ　ｍｅ　 eos 　ａｎｄ　ｋｎｏｗｗｗｈｉｃｈ symmetry ｅｎｅｒｇｙ is ｃｏｍｐａｔｉｂｌｅ．．

- So far no surface or finite size effect taken into account.

Thank you. 謝謝


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For

The same Variation of A with (or b)

Example of ~ opposite behavior:De-Samaddar-nucl-th/0708.2183


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For:

Differential equationbecomes:

Heiselberg, Hjorth Jensen

and

For the eos Stable Density As functionOf n-p


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Neutron matter:

No assumption or consideration on dynamical and nuclear microscopical effects (forces, processes)

- These will provide more precise expressions


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Based on F.L.B.,Phys. Rev. C (2009);Phys. Rev. C 71, 064303 (2005);Int. Journ. Mod. Phys. E12, 755 (2003);Nucl. Phys. A 665, 13 (2000);Nucl. Phys. A 696, 413 (2001)+ A 709, 487 (2002).Proceedings Brazilian Meetings on Nuc Phys 2007, 2008.


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Scalar channel:incompressibility

K and A00 have nearly the same behavior with b,

Mostly quadratic terms in

Isovector and spin-isospin nuclear matter symmetry energy (Skyrme forces):

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