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Analyzing the Interplay of Nuclear Incompressibility and Symmetry Energy to Elaborate on Conclusion

This study examines the conclusion using the interplay of nuclear incompressibility and symmetry energy. It explores the relationship between KA and K∞, and the effects of Kτ and KCoul on K∞.

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Analyzing the Interplay of Nuclear Incompressibility and Symmetry Energy to Elaborate on Conclusion

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  1. Purpose: Elaborate on the conclusion 230 < K < 250 MeV, by exploting the interplay of nuclear incompressibility and symmetry energy.

  2. KA = K + Ksurf A-1/3 + Kτδ2 + KCoul Z2 A-4/3 We do not discuss the old macroscopic approach (unreliable, cf. [1]), but the above expression can be used in connection with the microscopic models, which allow calculating the parameters (no fit !). In many attempts to deduce K from the ISGMR the linear relation between KAand K was assumed. Cf. J.P. Blaizot. [1] M. Pearson, Phys. Lett. B271 (1991) 12; S. Shlomo and D. Youngblood, Phys. Rev. C47 (1993) 529.

  3. Ksurf= cK with c ~ -1 (cf. Ref. [1]). True ?? KA = K(non rel.)(1+cA-1/3) + Kτ(non rel.)δ2 + KCoul(non rel.) Z2 A-4/3 KA = K(rel.)(1+cA-1/3) + Kτ(rel.)δ2 + KCoul(rel.) Z2 A-4/3 KCoul should not vary much from the non-relativistic to the relativistic description. But since both the terms which include K and Kτ contribute, a more negative Kτcanlead to a the extraction of a larger K (and vice-versa). Remember: Kτis negative and depends on the density dependence of the symmetry energy ! [1] M. Centelles et al., Phys. Rev. C65 (2002) 044304

  4. SLy4 protocol, α=1/6 MICROSCOPIC (!) CHF K around 230-240 MeV.

  5. α=0.3563, • neglect of the Coulomb exchange • and center-of-mass corrections in the • HF mean field. The result of B.J. Agrawal et al., is consistent with this plot !

  6. There has been a claim that the different behaviour of relativistic and non-relativistic models has its origin in the different density dependence of the symmetry energy curve S(ρ). Skyrme forces: softer symmetry energy (values at saturation around 26-32 MeV). RMF: stiffer. Constrained by -meson coupling gρ. J. Piekarewicz, PRC 66 (2002) 034305. C: 28 MeV B: 37 MeV ←“softening” (~ 0.5 MeV)

  7. The symmetry energy (Esym or S) All these forces fit finite nuclei: with different values of J and of the derivatives of S

  8. How to experimentally discriminate between models ? E ~ A-1/3 δE/E = δA/3A Even if we take a long isotopic chain of stable, spherical isotopes: Sn → δE/E is of the order of 3%, that is, 0.45 MeV (≈ 2σexp). Calculations should be made at the same level of accuracy.

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