陈融导师：陈列文教授合作者：蔡宝军，许昌，李宝安，李小华

Single-nucleon potential decomposition of

the nuclear symmetry energy

Shanghai Jiao Tong UniversityHuzhou, 2012-4

Symmetry energy and its density slope

Single-nucleon potential decomposition

Discussions

Summary

Also,single-nucleon potential can be expanded as:C. Xu, B.A. Li, L.W. Chen, and C.M. Ko, Nucl. Phys. A (2011)

Yes, we can

HVH theoremWe consider here non-relativistic situation

Right-hand side

Left-hand side

N.M.Hugenholtz and L.Van.Hove, Physica XXIV 363-376 (1958)

plus them we have:

Right-hand side:

minus them we have

Take left-hand side into consideration, that is

and

and

and have:

We have:

So that

So now we write

further into:

For convenience,we write

with

3 non-relativistic phenomenological models (10 sets of parameters) are used here in discussions:

MDI (x=-1,0,1) L.W. Chen, C.M. Ko, and B.A. Li, Phys. Rev. Lett (2005)

B.A. Li and L.W. Chen, Phys. Rev. C (2005)

Skyrme-Hartree-Fock (MSL0,SKM*,SLy4) L.W. Chen, C.M. Ko, B.A. Li, and J. Xu, Phys. Rev. C (2010)

J. Bartel et al., Nucl. Phys. A386, 79 (1982) E. Chabanat et al., Nucl. Phys. A635, 231 (1998

Gogny-Hartree-Fock (D1,D1S,D1N,D1M) J. Decharge and D. Gogny, Phys. Rev. C

21, 1568(1980) J.F. Berger, M. Girod, and D. Gogny, Comp. Phys. Comm. 63, 365 (1991)

F. Chappert, M. Girod, and S. Hilaire, Phys. Lett. B 668, 420 (2008)

S. Goriely, S. Hilaire, M. Girod, and S. Peru, Phys. Rev. Lett. 102, 242501 (2009)

MDIPotential energy density:

Single-nucleon potential:

Skyrme-Hartree-FockSkyrme interaction

Single-nucleon potential:

Gogny-Hartree-FockGogny interaction

Single-nucleon potential:

here

Discussions

Symmetry energydecomposition

Density slopedecomposition

The importance of

Density slopecorrelations

𝑈 𝑠𝑦𝑚 ,2

SummaryWithin the framework of HVH theorem, symmetry energy and its density slope can be decomposed into terms of single-nucleon potential.

term seems to be responsible for different shapes of symmetry energy

term for density slope might not be casually neglected.

Magnitude of and are generally comparable, therefore Lane approximation is not sufficient especially when is close to 1. Namely, the contribution of for single nucleon potential should be included.

is still poorly known, therefore further constraining is of significance for a more precise description of single nucleon potential, and thus symmetry energy and its density slope .

¡Mucho Gracias!