Constraints on neutron skin thickness inPb208and density-dependent symmetry energy

Abstract

Accurate knowledge about the neutron skin thickness ∆R np in 208 Pb has far-reaching implications for different communities of nuclear physics and astrophysics. Yet, the novel Lead Radius Experiment (PREX) did not yield stringent constraint on the ∆R np recently. We employ a more practicable strategy currently to probe the neutron skin thickness of 208 Pb based on a high linear correlation between the ∆R np and J −a sym , where J and a sym are the symmetry energy (coefficient) of nuclear matter at saturation density and of 208 Pb. An accurate J − a sym thus places a strong constraint on the ∆R np . Compared with the parity-violating asymmetry A PV in the PREX, the reliably experimental information on the J − a sym is much more easily available attributed to a wealth of measured data on nuclear masses and on decay energies. The density dependence of the symmetry energy is also well constrained with the J − a sym . Finally, with a 'tomoscan' method, we find that one just needs to measure the nucleon densities in 208 Pb starting from R m = 7.61 ± 0.04 fm to obtain the ∆R np in hadron scattering experiments, regardless of its interior profile that is hampered by the strong absorption.Here we adopt the union of the two values, i.e. J = 32.4 ± 0.6 MeV, and hence the central issue is to determine the symmetry energy a sym of 208 Pb accurately. We extract the mass dependent symmetry energy a sym (A) = J/(1 + κA 1/3 ) [40,41] with β − -decay energies Q β − of heavy odd-A nuclei and with mass differences ∆B between A (Z − 1) and A (Z + 1) as our previous calculations [42,43] but with a new input quantity J, and then derive the a sym of 208 Pb. The merit of these two approaches is that only the well known Coulomb energy survives in Q β − and in ∆B when determining the unknown a sym , where the Q β − and ∆B are all taken from experimental data. Consequently, the a sym is extracted to be 22.4 ± 0.4MeV accurately, which is quite insensitive to the input quantity J. As a result, the derived J − a sym is 10.0 ± 1.0 MeV (solid circle in Fig. 1), which allows us to constrain the neutron skin thickness as well as the slope L in our subsequent calculations.The neutron skin thickness in 208 Pb is predicted to be ∆R np = 0.176 ± 0.021 fm (solid square in Fig. 1), where the estimated error stems from the uncertainties of the J − a sym as well as Eq. (2). To reach such an error level, the A PV in the PREX should be measured at least up to 2% accuracy, which is hardly implemented at present. This fact indicates the J − a sym is much more effective to probe the ∆R np currently. The precise information about the ∆R np is of fundamental importance and has far-reaching implications in neutron star physics, such as the structure, composition and cooling. As an example, a relation of ρ c ≈ 0.16 − 0.39∆R np was put forward to describe the relation between the ∆R np of 208 Pb and the transition density ρ c from a solid neutron star crust to the liquid interior [44], where the ρ c is estimated to be 0.091 ± 0.008 fm −3 . The properties of the cru...

Self-consistent methods for structure and production of heavy and superheavy nuclei

“…The underlying GEDF interactions together with the results of several RMF models were used in [185,186] to study dipole modes of the nuclear skin and their influence on the reaction rates of stellar nucleosynthesis. The results are in a good agreement with earlier studies of symmetry energy effects in the neutron skin of finite nuclei [187].…”

“…A vast amount of work is being devoted to extracting those values from various kinds of data. The major sources of information are heavy-ion collision, low-energy nuclear reactions, nuclear-structure data on neutron skins, dipole skin modes and giant resonance excitations, and, of course, nuclear mass formulas; see, e.g., [185][186][187][188][189][190]. Combining the results of various sources, we conclude that nuclear matter saturates at ρ sat = 0.16 fm −3 with binding energy per nucleons of about E B −16 MeV.…”

“…L sym and K sym are less known. The value L sym = 30 ± 16 MeV [185][186][187][188] is found and estimates mainly from heavyion collisions indicate the rather uncertain range of values K sym = −30 . .…”

Beyond Wigner's isobaric multiplet mass equation: Effect of charge-symmetry-breaking interaction and Coulomb polarization

“…( 4) for T = 3/2 isobaric quartets. The SLy4 interaction [32] that satisfies specific constraints defined in our previous work [33] is employed to compute the nucleonic density distributions. Remarkably, the results for the d coefficients exhibit a clear A-dependence.…”

Generalized isobaric multiplet mass equation and its application to the Nolen-Schiffer anomaly

“…We now briefly discuss the calculated a (CSB) sym,1 (A, T z ) and a (CIB) sym,2 (A, T z ) for finite nuclei. The Skyrme-Hartree-Fock-BCS approach with three interactions studied in our previous work [37], i.e., the SLy4, SLy5 and KDE interactions [38], are employed to calculate the quantities of Eqs. (11,12), in which the empirical gaps from Ref.…”