Two-pion exchange and strong form-factors in covariant field theories

In this work improvements to the application of the Gross equation to nuclear systems are tested. In particular we evaluate the two pion exchange diagrams, including the crossed-box diagram, using models developed within the spectator-on-mass-shell covariant formalism. We found that the form factors used in these models induce spurious contributions that violate the unitary cut requirement. We tested then some alternative form-factors in order to preserve the unitarity condition. With this new choice, the difference between the exact and the spectator-on-mass-shell amplitudes is of the order of the one boson scalar exchange, supporting the idea that this difference may be parameterized by this type of terms.Comment: RevTeX, 21 pages, 19 figures (PostScript

Time-dependent Gross-Pitaevskii equation for composite bosons as the strong-coupling limit of the fermionic BCS-RPA approximation

The linear response to a space- and time-dependent external disturbance of a system of dilute condensed composite bosons at zero temperature, as obtained from the linearized version of the time-dependent Gross-Pitaevskii equation, is shown to result also from the strong-coupling limit of the time-dependent BCS (or broken-symmetry RPA) approximation for the constituent fermions subject to the same external disturbance. In this way, it is possible to connect excited-state properties of the bosonic and fermionic systems by placing the Gross-Pitaevskii equation in perspective with the corresponding fermionic approximationsComment: 4 pages, 1 figur

Conference Discussion of the Nuclear Force

Discussion of the nuclear force, lead by a round table consisting of T. Cohen, E. Epelbaum, R. Machleidt, and F. Gross (chair). After an invited talk by Machleidt, published elsewhere in these proceedings, brief remarks are made by Epelbaum, Cohen, and Gross, followed by discussion from the floor moderated by the chair. The chair asked the round table and the participants to focus on the following issues: (i) What does each approach (chiral effective field theory, large Nc, and relativistic phenomenology) contribute to our knowledge of the nuclear force? Do we need them all? Is any one transcendent? (ii) How important for applications (few body, nuclear structure, EMC effect, for example) are precise fits to the NN data below 350 MeV? How precise do these fits have to be? (iii) Can we learn anything about nonperturbative QCD from these studies of the nuclear force? The discussion presented here is based on a video recording made at the conference and transcribed afterward.Comment: Discussion at the 21st European Conference on Few Body Problems (EFP21) held at Salamanca, Spain, 30 Aug - 3 Sept 201

Relativistic effects and quasipotential equations

We compare the scattering amplitude resulting from the several quasipotential equations for scalar particles. We consider the Blankenbecler-Sugar, Spectator, Thompson, Erkelenz-Holinde and Equal-Time equations, which were solved numerically without decomposition into partial waves. We analyze both negative-energy state components of the propagators and retardation effects. We found that the scattering solutions of the Spectator and the Equal-Time equations are very close to the nonrelativistic solution even at high energies. The overall relativistic effect increases with the energy. The width of the band for the relative uncertainty in the real part of the scattering $T$ matrix, due to different dynamical equations, is largest for backward-scattering angles where it can be as large as 40%.Comment: Accepted for publication in Phys. Rev.

Unitarity and the Bethe-Salpeter Equation

We investigate the relation between different three-dimensional reductions of the Bethe-Salpeter equation and the analytic structure of the resultant amplitudes in the energy plane. This correlation is studied for both the $\phi^2\sigma$ interaction Lagrangian and the $\pi N$ system with $s$-, $u$-, and $t$-channel pole diagrams as driving terms. We observe that the equal-time equation, which includes some of the three-body unitarity cuts, gives the best agreement with the Bethe-Salpeter result. This is followed by other 3-D approximations that have less of the analytic structure.Comment: 17 pages, 8 figures; RevTeX. Version accepted for publication in Phys. Rev.

Anomalous rotational-alignment in N=Z nuclei and residual neutron-proton interaction

Recent experiments have demonstrated that the rotational-alignment for the $N=Z$ nuclei in the mass-80 region is considerably delayed as compared to the neighboring $N \ne Z$ nuclei. We investigate whether this observation can be understood by a known component of nuclear residual interactions. It is shown that the quadrupole-pairing interaction, which explains many of the delays known in rare-earth nuclei, does not produce the substantial delay observed for these $N=Z$ nuclei. However, the residual neutron-proton interaction which is conjectured to be relevant for $N=Z$ nuclei is shown to be quite important in explaining the new experimental data.Comment: 4 pages, 3 figures, final version accepted by Phys. Rev. C as a Rapid Communicatio

Gauge invariant reduction to the light-front

The problem of constructing gauge invariant currents in terms of light-cone bound-state wave functions is solved by utilising the gauging of equations method. In particular, it is shown how to construct perturbative expansions of the electromagnetic current in the light-cone formalism, such that current conservation is satisfied at each order of the perturbation theory.Comment: 12 pages, revtex

Extended gaussian ensemble solution and tricritical points of a system with long-range interactions

The gaussian ensemble and its extended version theoretically play the important role of interpolating ensembles between the microcanonical and the canonical ensembles. Here, the thermodynamic properties yielded by the extended gaussian ensemble (EGE) for the Blume-Capel (BC) model with infinite-range interactions are analyzed. This model presents different predictions for the first-order phase transition line according to the microcanonical and canonical ensembles. From the EGE approach, we explicitly work out the analytical microcanonical solution. Moreover, the general EGE solution allows one to illustrate in details how the stable microcanonical states are continuously recovered as the gaussian parameter $\gamma$ is increased. We found out that it is not necessary to take the theoretically expected limit $\gamma \to \infty$ to recover the microcanonical states in the region between the canonical and microcanonical tricritical points of the phase diagram. By analyzing the entropy as a function of the magnetization we realize the existence of unaccessible magnetic states as the energy is lowered, leading to a treaking of ergodicity.Comment: 8 pages, 5 eps figures. Title modified, sections rewritten, tricritical point calculations added. To appear in EPJ

Asymptotic Freedom for Non-Relativistic Confinement

Some aspects of asymptotic freedom are discussed in the context of a simple two-particle non-relativisitic confining potential model. In this model asymptotic freedom follows from the similarity of the free-particle and bound state radial wave functions at small distances and for the same angular momentum and the same large energy. This similarity, which can be understood using simple quantum mechanical arguments, can be used to show that the exact response function approaches that obtained when final state interactions are ignored. A method of calculating corrections to this limit is given and explicit examples are given for the case of the harmonic oscillator.Comment: 16 pages, 5 figures, RevTex

Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs

We define 2-decompositions of ribbon graphs, which generalise 2-sums and tensor products of graphs. We give formulae for the Bollobas-Riordan polynomial of such a 2-decomposition, and derive the classical Brylawski formula for the Tutte polynomial of a tensor product as a (very) special case. This study was initially motivated from knot theory, and we include an application of our formulae to mutation in knot diagrams.Comment: Version 2 has minor changes. To appear in Annals of Combinatoric