Isospin dependence ofHe6+poptical potential and the symmetry energy

Abstract

A consistent folding analysis of the elastic p( 6 He, 6 He)p scattering and charge exchange p( 6 He, 6 Li * )n reaction data measured at E lab = 41.6A MeV has been performed within the coupled channels formalism. We have used the isovector coupling to link the isospin dependence of 6 He+p optical potential to the cross section of p( 6 He, 6 Li * )n reaction exciting the 0 + isobaric analog state (IAS) at 3.563 MeV in 6 Li. Based on these results and the Hartree-Fock calculation of asymmetric nuclear matter using the same isospin-dependent effective nucleon-nucleon interaction, we were able to confirm that the most realistic value of the symmetry energy Esym is around 31 MeV. Our analysis has also shown that the measured charge exchange p( 6 He, 6 Li * )n data are quite sensitive to the halo tail of the 6 He density used in the folding calculation and the IAS of 6 Li is likely to have a halo structure similar to that established for the ground state of 6 He. The knowledge about the symmetry part of the nuclear equation of state (EOS) is vital for the understanding of the dynamics of supernovae explosion and the formation of neutron stars [1,2]. The symmetry part of the nuclear EOS is actually determined by the nuclear matter (NM) symmetry energy S(ρ) defined in terms of a Taylor series expansion of the NM binding energy B(ρ, δ) aswhere δ = (ρ n − ρ p )/ρ is the neutron-proton asymmetry parameter. The contribution of O(δ 4 ) and higher-order terms in Eq. (1), i.e., the deviation from the parabolic law was proven to be negligible [3,4]. The NM symmetry energy determined at the NM saturation density, E sym = S(ρ 0 ) with ρ 0 ≈ 0.17 fm −3 , is widely known in the literature as the symmetry energy or symmetry coefficient. Although numerous nuclear many-body calculations have predicted E sym to be around 30 MeV (see, e.g., Refs. [3,4,5,6,10]), a direct experimental determination of E sym still remains a challenging task. One needs, therefore, to relate E sym to some experimentally inferrable quantity like the neutron skin in neutron-rich nuclei [7,8,9,10] or the fragmentation data of heavy-ion (HI) collisions involving N = Z nuclei [11,12,13]. An accurate estimate of the E sym value is also very important for the nuclear astrophysics. For example, a small variation of E sym , used as input for the hydrodynamic simulation of supernovae, affects significantly the electron capture rate in the "prompt" phase of type II supernovae [2]. Another example is a calculation of NM and masses of finite nuclei using Skyrme forces [6] which shows that the neutron-rich NM does not collapse only if the corresponding E sym value is within the range 28 − 31 MeV. E sym is also an important input for the study of the density dependence S(ρ) based on transport-model simulation of the HI collisions (see Ref.[11] and references * Electronic address: khoa@vaec.gov.vn therein), and the most recent transport-model results favor E sym ≈ 31 − 32 MeV [13].Within the frame of any microscopic model for asymmetric NM, the symmetry energy depends stro...

Recent progress and new challenges in isospin physics with heavy-ion reactions

“…115 CDM3Y6 interaction [159]. Khoa also deduced a symmetry energy of about 30 MeV at ρ ≈ ρ 0 from the coupled-channel analysis of the (p,n) charge-exchange reaction [517,518]. This result is consistent with earlier conclusions of several other studies using different approaches.…”

Constraining the density dependence of the symmetry energy in the nuclear equation of state using heavy ion beams

“…The dotted curve correspond to the parameterization adopted by Heiselberg et al [14] in their studies on neutron stars, and obtained by fitting the 5 predictions of the variational calculations of Akmal et al [15]. Finally, the solid square point in the figure correspond to the value of symmetry energy obtained by fitting the experimental differential cross-section data in a charge exchange reaction using the isospin dependent optical potential by Khoa et al [16]. The parameterized forms of the density dependence of the symmetry energy obtained from all these studies are as shown in table I.…”

Nuclear symmetry energy: An experimental overview

“…The blue solid point in the figure correspond to the symmetry energy obtained by constraining the experimental energy of giant dipole resonance (GDR) in 208 Pb by Trippa et al [35]. The square solid point in the figure correspond to the symmetry energy obtained by fitting the experimental differential cross-section data in a charge exchange reaction using the isospin dependent interaction of the optical potential by Khoa et al [36,37]. The green solid curve in the figure is the one obtained from the dynamical AMD model comparison of the experimental isoscaling data assuming the sequential decay effect to be small [3,6].…”

“…Trippa et al [35], have studied the symmetry energy from the correlation between the symmetry energy and the experimental centroid energy of the Giant Dipole Resonance (GDR) in 208 Pb nuclei. Khoa et al [36,37], have studied the symmetry energy from the folding model analysis of the charge exchange p( 6 He, 6 Li)n reaction measured at 41.6 MeV/A. Danielewicz [38] have studied the symmetry energy by constraining the binding energy, neutron skin and the isospin analogue state of finite nuclei.…”