Nuclear density functional theory is the only microscopical theory that can be applied throughout the entire nuclear landscape. Its key ingredient is the energy density functional. In this work, we propose a new parameterization UNEDF2 of the Skyrme energy density functional. The functional optimization is carried out using the POUNDerS optimization algorithm within the framework of the Skyrme Hartree-Fock-Bogoliubov theory. Compared to the previous parameterization UNEDF1, restrictions on the tensor term of the energy density have been lifted, yielding a very general form of the energy density functional up to second order in derivatives of the one-body density matrix. In order to impose constraints on all the parameters of the functional, selected data on single-particle splittings in spherical doubly-magic nuclei have been included into the experimental dataset. The agreement with both bulk and spectroscopic nuclear properties achieved by the resulting UNEDF2 parameterization is comparable with UNEDF1. While there is a small improvement on single-particle spectra and binding energies of closed shell nuclei, the reproduction of fission barriers and fission isomer excitation energies has degraded. As compared to previous UNEDF parameterizations, the parameter confidence interval for UNEDF2 is narrower. In particular, our results overlap well with those obtained in previous systematic studies of the spin-orbit and tensor terms. UNEDF2 can be viewed as an all-around Skyrme EDF that performs reasonably well for both global nuclear properties and shell structure. However, after adding new data aiming to better constrain the nuclear functional, its quality has improved only marginally. These results suggest that the standard Skyrme energy density has reached its limits and significant changes to the form of the functional are needed.Comment: 18 pages, 13 figures, 12 tables; resubmitted for publication to Phys. Rev. C after second review by refere

General expressions for transport coefficients of a single-component gas ͑namely, thermal conductivity and shear and bulk viscosities͒ of bosons are derived from a Boltzmann-Uehling-Uhlenbeck transport equation by means of the Chapman-Enskog method to first order. These expressions are then used for the calculation of the associated transport relaxation times and applied to the pion gas produced in ultrarelativistic heavy-ion collisions. The influence of Bose enhancement factors on transport properties can be seen by comparison with previous calculations. ͓S0556-2813͑96͒02306-0͔PACS number͑s͒: 25.75.Ϫq, 05.60.ϩw

Recently, it has been recently shown that the linear response theory in symmetric nuclear matter can be used as a tool to detect finite size instabilities for different Skyrme functionals [1,2]. In particular it has been shown that there is a correlation between the density at which instabilities occur in infinite matter and the instabilities in finite nuclei.In this article we present a new fitting protocol that uses this correlation to add new additional constraint in Symmetric Infinite Nuclear Matter in order to ensure the stability of finite nuclei against matter fluctuation in all spin and isospin channels. As an application, we give the parameters set for a new Skyrme functional which includes central and spin-orbit parts and which is free from instabilities by construction.

It is known that some well-established parametrizations of the EDF do not always provide converged results for nuclei and a qualitative link between this finding and the appearance of finite-size instabilities of SNM near saturation density when computed within the RPA has been pointed out. We seek for a quantitative and systematic connection between the impossibility to converge self-consistent calculations of nuclei and the occurrence of finite-size instabilities in SNM for the example of scalar-isovector (S=0, T=1) instabilities of the standard Skyrme EDF. We aim to establish a stability criterion based on computationally-friendly RPA calculations of SNM that is independent on the functional form of the EDF and that can be utilized during the adjustment of its coupling constants. Tuning the coupling constant $C^{\rho \Delta\rho}_{1}$ of the gradient term that triggers scalar-isovector instabilities of the standard Skyrme EDF, we find that the occurrence of instabilities in finite nuclei depends strongly on the numerical scheme used to solve the self-consistent mean-field equations. The link to instabilities of SNM is made by extracting the lowest density $\rho_{\text{crit}}$ at which a pole appears at zero energy in the RPA response function when employing the critical value of the coupling constant $C^{\rho \Delta\rho}_{1}$ extracted in nuclei. Our analysis suggests a two-fold stability criterion to avoid scalar-isovector instabilities: (i) The density $\rho_{\text{min}}$ corresponding to the lowest pole in the RPA response function should be larger than about 1.2 times the saturation density; (ii) one needs to verify that $\rho_{p}(q_{\text{pq}})$ exhibits a distinct global minimum and is not a decreasing function for large transferred momenta.Comment: 9 pages, 11 figures, submitted to Phys. Rev.

We present the development of the extended Skyrme N2LO pseudo-potential in the case of spherical even-even nuclei calculations. The energy density functional is first presented. Then we derive the mean-field equations and discuss the numerical method used to solve the resulting fourth-order differential equation together with the behaviour of the solutions at the origin. Finally, a fitting procedure for such a N2LO interaction is discussed and we provide a first parametrization. Typical ground-state observables are calculated and compared against experimental data.

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The formalism of linear response theory for Skyrme forces including tensor terms presented in article [1] is generalized for the case of a Skyrme energy density functional in infinite matter. We also present analytical results for the odd-power sum rules, with particular attention to the inverse energy weighted sum rule, M−1, as a tool to detect instabilities in Skyrme functionals.

Due to Pauli blocking of intermediate states, the scattering matrix (or $T$ matrix) of two fermionic atoms in a Fermi gas becomes different from that of two atoms in free space. This effect becomes particularly important near a Feshbach resonance, where the interaction in free space is very strong but becomes effectively suppressed in the medium. We calculate the in-medium $T$ matrix in ladder approximation and study its effects on the properties of collective modes of a trapped gas in the normal-fluid phase. We introduce the in-medium interaction on both sides of the Boltzmann equation, namely in the calculation of the mean field and in the calculation of the collision rate. This allows us to explain the observed upward shift of the frequency of the quadrupole mode in the collisionless regime. By including the mean field, we also improve considerably the agreement with the measured temperature dependence of frequency and damping rate of the scissors mode, whereas the use of the in-medium cross section deteriorates the description, in agreement with previous work.Comment: 17 page