121929671
Nuclear matter and neutron star properties calculated with the skyrme interaction
The effective Skyrme interaction has been used extensively in mean-field models for several decades and many different parametrizations of the interaction have been proposed. All of these give similar agreement with the experimental observables of nuclear ground states as well as with the properties of infinite symmetric nuclear matter at the saturation density n0. However, when applied over a wider range of densities (up to ∼3n0) they predict widely varying behavior for the observables of both symmetric and asymmetric nuclear matter. A particularly relevant example of naturally occurring asymmetric nuclear matter is the material of which neutron stars are composed. At around nuclear matter density, this can be well represented as a mixture of neutrons, protons, electrons, and muons (n+p+e+μ matter) in β-equilibrium, and these densities turn out to be the key ones for determining the properties of neutron-star models with masses near to the widely used “canonical” value of 1.4M⊙. By constructing equations of state for neutron-star matter using the different Skyrme parametrizations, calculating corresponding neutron-star models and then comparing these with observational data, an additional constraint can be obtained for the values of the Skyrme parameters. Such a constraint is particularly relevant because the parametrizations are initially determined by fitting to the properties of doubly closed-shell nuclei and it is an open question how suitable they then are for nuclei with high values of isospin, such as those at the neutron drip-line and beyond. The neutron-star environment provides an invaluable testing ground for this. We have carried out an investigation of 87 different Skyrme parametrizations in order to examine how successful they are in predicting the expected properties of infinite nuclear matter and generating plausible neutron-star models. This is the first systematic study of the predictions of the various Skyrme parametrizations for the density dependence of the characteristic observables of nuclear matter; the density dependence of the symmetry energy for β-equilibrium matter turns out to be a crucial property for indicating which Skyrme parameter sets will apply equally well for finite nuclei and for neutron-star matter. Only 27 of the 87 parametrizations investigated pass the test of giving satisfactory neutron-star models and we present a list of these.
122193074
The effect of the tensor force on the predicted stability of superheavy nuclei
The effect of the tensor component of the Skyrme effective nucleon-nucleon interaction on the single-particle structure in superheavy elements is studied. A selection of the available Skyrme forces has been chosen and their predictions for the proton and neutron shell closures investigated. The inclusion of the tensor term with realistic coupling strength parameters leads to a small increase in the spin-orbit splitting between the proton 2f7/2 and 2f5/2 partners, opening the Z=114 shell gap over a wide range of nuclei. The Z=126 shell gap, predicted by these models in the absence of the tensor term, is found to be stongly dependent on neutron number with a Z=138 gap opening for large neutron numbers, having a consequent implication for the synthesis of neutron-rich superheavy elements. The predicted neutron shell structures remain largely unchanged by inclusion of the tensor component.
14308528
Mass dispersions from giant dipole resonances using the Balian–Vénéroni variational approach
The Balian–Veneroni variational approach has been implemented using a three-dimensional time-dependent Hartree–Fock (TDHF) code with realistic Skyrme interactions and used to investigate the mass dispersions from giant dipole resonances in 32S and 132Sn decaying through particle emission. The fluctuations obtained are shown to be quantitatively larger than the standard TDHF results.
118393197
Single-particle dissipation in TDHF studied from a phase-space perspective
N. Loebl, A. S. Umar, J.A. Maruhn, P.-G. Reinhard, P.D. Stevenson, and V. E., Oberacker Institut fuer Theoretische Physik, Universitaet Frankfurt, D-60438 Frankfurt, Germany Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA Institut fuer Theoretische Physik II, Universitaet Erlangen-Nuernberg, D-91058 Erlangen, Germany and Department of Physics, University of Surrey, Guildford, GU2 7XH, UK (Dated: August 30, 2012)
16956676
Continuum time-dependent Hartree-Fock method for giant resonances in spherical nuclei
This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied in the case of nuclear giant monopole resonances in the small and large amplitude regimes. The problem is spatially unbounded as the resonance state is in the continuum. The practical requirement to perform the calculation in a finite-sized spatial region results in a difficulty with the spatial boundary conditions. Here we propose an absorbing boundary condition scheme to handle the conflict. The derivation, via a Laplace transform method, and implementation is described. The accuracy and efficiency of the scheme is tested and the results presented to support the case that they are a effective way of handling the artificial boundary. © 2013 American Physical Society.
117963510
Mass distributions in a variational model
The time-dependent Hartree-Fock approach may be derived from a variational principle and a Slater Determinant wavefunction Ansatz. It gives a good description of nuclear processes in which one-body collisions dominate and has been applied with success to giant resonances and collisions around the barrier. It is inherently unable to give a good description of two-body observables. A variational principle, due to Balian and Veneroni has been proposed which can be geared to good reproduction of two-body observables. Keeping the Slater Determinant Ansatz, and restricting the two-body observables to be the squares of one-body observables, the procedure can be implemented as a modification of the time-dependent Hartree-Fock procedure. Applications, using the Skyrme effective interaction, are presented for the mass distributions of fragments following de-excitation of the giant dipole resonance in 32 S. An illustration of the method's use in collisions is given.
2592138
Vacuum Hydrodynamics
The Higgs vacuum – with its constant background field – is not ‘empty’ but is a kind of medium. Any ordinary medium, viewed at sufficiently long length scales, has a hydrodynamic description and can propagate sound waves. The vacuum medium is unusual; the speed of sound is formally infinite and there is no linear sound-wave regime. Instead, long-wavelength disturbances are described by some intrinsically nonlinear hydrodynamic equations. The purpose of this Letter is more to raise questions than to answer them. The premise is that the vacuum of the Standard Model, with its non-zero background field 〈φ〉 6 = 0, is a kind of medium [1]. The only other assumption is that a “mean free path” scale λmfp exists and is finite. (While λmfp must be long compared to particle-physics length scales, whether it is a millimeter or an astronomical or cosmological scale is another question.) My point is that at sufficiently long length scales L ≫ λmfp any fluid medium can be described by hydrodynamics (see, for example, [2, 3, 4]). That is, it can be treated as an ideal fluid up to corrections of order λmfp/L [5]. In the hydrodynamic regime the only relevant modes are those directly linked to conservation laws. In particular, energy-momentum conservation equations lead directly to longitudinal pressure waves — sound waves. Let us briefly review the derivation. The energy-momentum tensor for a perfect fluid has the form [c = 1, gμν = diag(1,−1,−1,−1)] T μν = (E + P )uu − Pg , (1) where E is the energy density, P is the pressure, and uμ is the flow 4-velocity u = (u0, ~u), with u 2 0 − ~u = 1. (2) The energy-momentum conservation equation ∂μT μν = 0 yields ∂ ∂t [ (E + P )u0 ] + ∂ ∂xj [ (E + P )uu0 ] − ∂P ∂t = 0, (3) ∂ ∂t [ (E + P )u0u ] + ∂ ∂xj [ (E + P )uu ] + ∂P ∂xi = 0. (4) Consider a small perturbation about a static, homogeneous equilibrium state E0, P0, ~u = 0. If the pressure variation δP and the energy variation δE are sufficiently small they must be proportional, with their ratio fixed by the thermodynamic derivative ∂P ∂E ∣
18791932
Gaussian effective potential for the U(1) Higgs model
In order to investigate the Higgs mechanism nonperturbatively, we compute the Gaussian effective potential of the U(1) Higgs model (“scalar electrodynamics”). We show that the same simple result is obtained in three different formalisms. A general covariant gauge is used, with Landau gauge proving to be optimal. The renormalization generalizes the “autonomous” renormalization for λϕ4 theory and requires a particular relationship between the bare gauge coupling eB and the bare scalar self-coupling λB. When both couplings are small, then λ is proportional to e4 and the scalar/vector mass-squared ratio is of order e2, as in the classic 1-loop analysis of Coleman and Weinberg. However, as λ increases, e reaches a maximum value and then decreases, and in this “nonperturbative” regime the Higgs scalar can be much heavier than the vector boson. We compare our results to the autonomously renormalized 1-loop effective potential, finding close agreement in the physical predictions. The main phenomenological implication is a Higgs mass of about 2 TeV.
118692296
Applying Optimized Perturbation Theory to QCD at Low Energies
We discuss the use of the optimization procedure based on the Principle of Minimal Sensitivity to the third-order calculation of {\mbox{${R_{e^+e^-}}$}}. The effective coupling constant remains finite allowing us to apply the Poggio-Quinn-Weinberg smearing method down to energies below 1 GeV, where we find good agreement between theory and experiment. The couplant freezes to a value of $\alpha_s/\pi = 0.26$ at zero energy which is in remarkable concordance with values obtained phenomenologically.
118504036
Response to Brodsky and Lu's Letter "On the Self-Consistency of Scale-Setting Methods
The claim that the Principle of Minimal Sensitivity is "disfavored" because it does not satisfy certain "self-consistency requirements" is meaningless, and shows a basic misunderstanding of the renormalization-scheme-dependence problem.
16425949
PHYSICAL MECHANISMS GENERATING SPONTANEOUS SYMMETRY BREAKING AND A HIERARCHY OF SCALES
We discuss the phase transition in (3+1)-dimensional λΦ4 theory from a very physical perspective. The particles of the symmetric phase ("phions") interact via a hard-core repulsion and an induced, long-range -1/r3 attraction. If the phion mass is sufficiently small, the lowest-energy state is not the "empty" state with no phions, but is a state with a nonzero density of phions Bose–Einstein condensed in the zero-momentum mode. The condensate corresponds to the spontaneous-symmetry-breaking vacuum with ≠ 0 and its excitations ("phonons" in atomic physics language) correspond to Higgs particles. The phase transition happens when the phion's physical mass m is still positive; it does not wait until m2 passes through zero and becomes negative. However, at and near the phase transition, m is much, much less than the Higgs mass Mh. This interesting physics coexists with "triviality;" all scattering amplitudes vanish in the continuum limit, but the vacuum condensate becomes infinitely dense. The ratio , which goes to zero in the continuum limit, can be viewed as a measure of nonlocality in the regularized theory. An intricate hierarchy of length scales naturally arises. We speculate about the possible implications of these ideas for gravity and inflation.