Origin of the neutron skin thickness of 208Pb in nuclear mean-field models

We study whether the neutron skin thickness Δrnp of 208Pb originates from the bulk or from the surface of the nucleon density distributions, according to the mean-field models of nuclear structure, and find that it depends on the stiffness of the nuclear symmetry energy. The bulk contribution to Δrnp arises from an extended sharp radius of neutrons, whereas the surface contribution arises from different widths of the neutron and proton surfaces. Nuclear models where the symmetry energy is stiff, as typical of relativistic models, predict a bulk contribution in Δrnp of 208Pb about twice as large as the surface contribution. In contrast, models with a soft symmetry energy like common nonrelativistic models predict that Δrnp of 208Pb is divided similarly into bulk and surface parts. Indeed, if the symmetry energy is supersoft, the surface contribution becomes dominant. We note that the linear correlation of Δrnp of 208Pb with the density derivative of the nuclear symmetry energy arises from the bulk part of Δrnp. We also note that most models predict a mixed-type (between halo and skin) neutron distribution for 208Pb. Although the halo-type limit is actually found in the models with a supersoft symmetry energy, the skin-type limit is not supported by any mean-field model. Finally, we compute parity-violating electron scattering in the conditions of the 208Pb parity radius experiment (PREX) and obtain a pocket formula for the parity-violating asymmetry in terms of the parameters that characterize the shape of the 208Pb nucleon densities.

Neutron skin thickness in the droplet model with surface width dependence: Indications of softness of the nuclear symmetry energy

We analyze the neutron skin thickness in finite nuclei with the droplet model and effective nuclear interactions. The ratio of the bulk symmetry energy J to the so-called surface stiffness coefficient Q has in the droplet model a prominent role in driving the size of neutron skins. We present a correlation between the density derivative of the nuclear symmetry energy at saturation and the J/Q ratio. We emphasize the role of the surface widths of the neutron and proton density profiles in the calculation of the neutron skin thickness when one uses realistic mean-field effective interactions. Next, taking as experimental baseline the neutron skin sizes measured in 26 antiprotonic atoms along the mass table, we explore constraints arising from neutron skins on the value of the J/Q ratio. The results favor a relatively soft symmetry energy at subsaturation densities. Our predictions are compared with the recent constraints derived from other experimental observables. Though the various extractions predict different ranges of values, one finds a narrow window L∼45-75 MeV for the coefficient L that characterizes the density derivative of the symmetry energy that is compatible with all the different empirical indications.

Nuclear Symmetry Energy Probed by Neutron Skin Thickness of Nuclei

We describe a relation between the symmetry energy coefficients csym(ρ) of nuclear matter and asym(A) of finite nuclei that accommodates other correlations of nuclear properties with the low-density behavior of csym(ρ). Here, we take advantage of this relation to explore the prospects for constraining csym(ρ) of systematic measurements of neutron skin sizes across the mass table, using as example present data from antiprotonic atoms. The found constraints from neutron skins are in harmony with the recent determinations from reactions and giant resonances.

Neutron skin of 208Pb, nuclear symmetry energy, and the parity radius experiment

A precise determination of the neutron skin thickness of a heavy nucleus sets a basic constraint on the nuclear symmetry energy (the neutron skin thickness is the difference of the neutron and proton rms radii of the nucleus). The parity radius experiment (PREX) may achieve it by electroweak parity-violating electron scattering (PVES) on 208Pb. We investigate PVES in nuclear mean field approach to allow the accurate extraction of the neutron skin thickness of 208Pb from the parity-violating asymmetry probed in the experiment. We demonstrate a high linear correlation between the parity-violating asymmetry and the neutron skin thickness in successful mean field forces as the best means to constrain the neutron skin of 208Pb from PREX, without assumptions on the neutron density shape. Continuation of the experiment with higher precision in the parity-violating asymmetry is motivated since the present method can support it to constrain the density slope of the nuclear symmetry energy to new accuracy.

Effects of medium on nuclear properties in multifragmentation

In multifragmentation of hot nuclear matter, properties of fragments embedded in a soup of nucleonic gas and other fragments should be modified as compared with isolated nuclei. Such modifications are studied within a simple model where only nucleons and one kind of heavy nuclei are considered. The interaction between different species is described with a momentum-dependent two-body potential whose parameters are fitted to reproduce properties of cold isolated nuclei. The internal energy of heavy fragments is parametrized according to a liquid-drop model with density- and temperature-dependent parameters. Calculations are carried out for several subnuclear densities and moderate temperatures, for isospin-symmetric and asymmetric systems. We find that the fragments get stretched due to interactions with the medium and their binding energies decrease with increasing temperature and density of nuclear matter.

Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested

Nuclear sizes and the isotope shift

Darwin-Foldy nuclear-size corrections in electronic atoms and nuclear radii are discussed from the nuclear-physics perspective. The interpretation of precise isotope-shift measurements is formalism dependent, and care must be exercised in interpreting these results and those obtained from relativistic electron scattering from nuclei. We strongly advocate that the entire nuclear-charge operator be used in calculating nuclear-size corrections in atoms rather than relegating portions of it to the nonradiative recoil corrections. A preliminary examination of the intrinsic deuteron radius obtained from isotope-shift measurements suggests the presence of small meson-exchange currents (exotic binding contributions of relativistic order) in the nuclear charge operator, which contribute approximately 1/2%.

Sum rules and short-range correlations in nuclear matter at finite temperature

The nucleon spectral function in nuclear matter fulfills an energy weighted sum rule. Comparing two different realistic potentials, these sum rules are studied for Greens functions that are derived self-consistently within the T matrix approximation at finite temperature.

Nuclear pairing: surface or bulk?

We analyze how the spatial localization properties of pairing correlations are changing in a major neutron shell of heavy nuclei. It is shown that the radial distribution of the pairing density depends strongly on whether the chemical potential is close to a low or a high angular momentum level and has little sensitivity to whether the pairing force acts at the surface or in the bulk. The pairing density averaged over one major shell is, however, rather flat, exhibiting little dependence on the pairing force. Hartree-Fock-Bogoliubov calculations for the isotopic chain 100-132Sn are presented for demonstration purposes.

Sum rules and correlations in asymmetric nuclear matter

The neutron and proton single-particle spectral functions in asymmetric nuclear matter fulfill energy-weighted sum rules. The validity of these sum rules within the self-consistent Green's function approach is investigated. The various contributions to these sum rules and their convergence as a function of energy provide information about correlations induced by the realistic interaction between the nucleons. The study of the sum rules in asymmetric nuclear matter exhibits the isospin dependence of the nucleon-nucleon correlations.