16386160
Extension of the continuum time-dependent Hartree-Fock method to proton states.
This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied to nuclear giant monopole resonances in the small amplitude regime. 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 yields an artificial boundary, which is not present physically. The question of how to ensure the boundary does not interfere with the internal solution, while keeping the overall calculation time low is studied. Here we propose an absorbing boundary condition scheme to handle the conflict. The derivation, via a Laplace transform method, and implementation is described. An inverse Laplace transform required by the absorbing boundaries is calculated using a method of nonlinear least squares. The accuracy and efficiency of the scheme is tested and results presented to support the case that they are an effective way of handling the artificial boundary.
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.
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)
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.
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.
119042764
Resolution of the lambda phi**4 puzzle and a 2-TeV Higgs boson
We argue that massless (lambda Phi^4)_4 is "trivial" without being entirely trivial. It has a non-trivial effective potential which leads to spontaneous symmetry breaking, but the particle excitations above the broken vacuum are non-interacting. The key to this picture is the realization that the constant background field (the mode with zero 4-momentum) renormalizes differently from the fluctuation field (the finite-momentum modes). This picture reconciles rigorous results and lattice calculations with one-loop and Gaussian-approximation analyses. Because of "triviality", these latter two methods should be effectively exact. Indeed, they yield the same renormalized effective potential and the same relation m_h^2 = 8 pi^2 v^2 between the particle mass and the physical vacuum expectation value. This relation predicts a Higgs mass m_h about 2 TeV in the standard model. The non-interacting nature of the scalar sector implies, by the equivalence theorem, that Higgs and gauge bosons interact only weakly, through their gauge and Yukawa couplings.
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.
119407227
Optimization and the Ultimate Convergence of QCD Perturbation Theory
Abstract I suggest that QCD perturbation theory can be convergent, and that “optimization” of the renormalization scheme choice is essential in achieving this. Arguing that higher orders probe shorter distances, I suggest that the effective expansion parameter (the “optimized” couplant) decreases at high orders, leading to an induced convergence. The mechanism is illustrated by a simple mathematical example. The point is that, even if the perturbation series is divergent in all fixed renormalization schemes, the sequence of “optimized” approximations may still converge. It is emphasized that the limit approached by perturbation theory, if any, will not be the exact result of the full theory. Allegations that QCD series are not Borel-summable are critically re-examined in this light.
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.