Radial collective flow and thermalization are studied in gold on gold collisions at 150, 250, and $400A$ MeV bombarding energies with a relativistically covariant formulation of a QMD code. We find that radial flow and “thermal” energies calculated for all the charged fragments agree reasonably with the experimental values. The experimental hardware filter at small angles used in the FOPI experiments at higher energies selects mainly the thermalized particles.

The halo nucleus ${}^{11}\mathrm{Li}$ is treated as a three-body system consisting of an inert core of ${}^9\mathrm{Li}$ plus two valence neutrons. The Faddeev equations are solved using separable potentials to describe the two-body interactions, corresponding in the ${n-}^9\mathrm{Li}$ subsystem to a $p_{1/2}$ resonance plus a virtual s-wave state. The experimental ${}^{11}\mathrm{Li}$ energy is taken as input and the ${}^9\mathrm{Li}$ transverse momentum distribution in ${}^{11}\mathrm{Li}$ is studied.

We show how the stability of the $E2/M1\mathrm{}$ ratio, evaluated at the T-matrix pole, can be understood given a much wider variation at the K-matrix pole.

Elster and Weppner [Phys. Rev. C 57, 189 (1998)], conclude from comparisons of their results with proton elastic scattering data that an optical potential formed from a model based upon the impulse approximation to the scattering is inappropriate below 200 MeV. That is certainly the case with their model, however folded models using $\mathrm{NN}\hspace{0.5em}g$ matrices have been shown to be appropriate. They claim that higher order terms in the spectator expansion are the required corrections and that a Faddeev calculation is needed. We show that the less than satisfactory comparisons of their calculated results with data are due to their use of free $\mathrm{NN}\hspace{0.5em}t$ matrices as the transition operators. Comparison of predictions obtained from the (complex, nonlocal) optical model potentials we find by folding appropriate medium modified $\mathrm{NN}$ interactions with data from the scattering of 65 and 200 MeV protons from ${}^{40}\mathrm{Ca}$ illustrate this.

We reply to the preceding comment.

Pulsed ${}^{238}\mathrm{U}$ and ${}^{208}\mathrm{Pb}$ beams have been used to populate multi-quasiparticle high-$K$ isomers in neutron-rich hafnium isotopes at and beyond the line of β-stability, via inelastic excitation and transfer. Spectroscopic properties and configuration assignments of several new high-$K$ isomers are compared with earlier theoretical predictions. A striking example of the robustness of the $K$ quantum number is demonstrated by the observed competition between $E1\mathrm{}$ and $E3\mathrm{}$ decay modes in ${}^{180}\mathrm{Hf},$ the heaviest stable isotope of the element.

The $R$-parity nonconservation phenomenology within the minimal supersymmetric standard model with gauge mediated supersymmetry breaking has been studied. New constraints on the lepton number violating constant ${\lambda }_{111}^{\prime }$ were imposed by nonobservability of the neutrinoless double β decay. We have found that ${\lambda }_{111}^{\prime }$ depends strongly on the effective supersymmetry breaking scale Λ only and deduced limits which are much stronger than those previously found in literature.

We address the problem of pion production in low-energy $\pi$-nucleus collisions. For the production mechanism, we assume a simple model consisting of a coherent sum of single pion exchange and the excitation—followed by the decay into two pions and a nucleon—of the $N^{*}\mathrm{}\left(1440\right)\mathrm{}$ resonance. The production amplitude is modified by the final state interaction between the pions calculated using the chirally improved Jülich meson exchange model including the polarization of the nuclear medium by the pions. The model reproduces well the experimentally observed $\pi \overrightarrow{A}\pi \pi A$ cross sections, especially the enhancement with increasing A of the ${\pi }^{+}{\pi }^{-}$ mass distribution in the threshold region.

We propose a soluble model of the nonlinear effects in the Coulomb excitation of the multiphonon giant dipole resonances. Analytical expressions for the multiphonon transition probabilities are derived, based on the SU(1,1) algebra. For reasonably small magnitude of nonlinearity $x\simeq 0.1-0.2$ enhancement factor for the double giant resonance excitation probabilities and the cross sections reaches values $1.3-2$ compatible with experimental data. The enhancement factor is found to decrease with increasing bombarding energy in the range 70–700 MeV per nucleon.

Three-nucleon forces have been considered to be one possibility to resolve the well-known discrepancy between experimental values and theoretical calculations of the nucleon analyzing power in low energy nucleon-deuteron scattering. In this Rapid Communication, we investigate the possible effects of two-pion exchange three-nucleon forces on the analyzing power and the differential cross section. We found that the reason for different effects on the analyzing power by different three-nucleon forces found in previous calculations is related to the existence of the contact term. Effects of some variations of two-pion exchange three-nucleon forces are investigated. Also, an expression for the measure of the nucleon analyzing power with quartet $P$-wave phase shifts is presented.

Mesons are made of quark-antiquark pairs held together by the strong force. The one channel spectator, Dirac, and Salpeter equations can each be used to model this pairing. We look at cases where the relativistic kernel of these equations corresponds to a timelike vector exchange, a scalar exchange, or a linear combination of the two. Since the model used in this paper describes mesons which cannot decay physically, the equations must describe stable states. We find that this requirement is not always satisfied, and give a complete discussion of the conditions under which the various equations give unphysical, unstable solutions.

We describe some properties of a relativistic model of confinement and show how that model may be used to construct T matrices for quark-antiquark systems. [In the absence of the confinement model, our Lagrangian reduces to that of the SU(3)-flavor Nambu–Jona-Lasinio model.] If we have absolute confinement, our T matrix is expressed in terms of bound states (or resonances), without the presence of quark scattering states. We find that is a straightforward matter to describe singlet-octet and pseudoscalar-axial-vector mixing in this formalism. We also demonstrate that the construction of the T matrices of the model allows us to obtain expressions for various current correlation functions, once the meson decay constants are calculated. That calculation is readily made starting with knowledge of the T matrix. The most complex situation we consider is that of the $\eta -{\eta }^{\prime }$ system, with both singlet-octet and pseudoscalar-axial-vector mixing, calculated in the presence of a (covariant) confinement model. Values of masses, coupling constants and mixing angles are given for the π, ω, φ, η, and ${\eta }^{\prime }$ mesons and for some of their radial excitations.

We describe the mixing of $q\overline{q}$ pseudoscalar states with longitudinal $q\overline{q}$ axial-vector states, making use of a relativistic quark model that includes a model of confinement. (In the absence of the confinement model, our model reduces to the Nambu–Jona-Lasinio model.) In addition to the pion, we find $J^P{=0\mathrm{}}^{-}$ states at 1.18, 1.36, 1.47, 1.63, and 1.68 GeV. The first two of these states are in the region of the π(1300) that is assigned a mass of $1300\pm 100\mathrm{MeV}$ and a width of 200–600 MeV in the data tables. We provide values of the coupled-channel $q\overline{q}$ T matrix, as well as the mixing angle, which is energy-dependent in our analysis. In addition, we describe a model of confinement for longitudinal axial-vector $q\overline{q}$ states that is used in the calculation of vacuum polarization diagrams. (That analysis supplements our previous study of confinement in the case of pseudoscalar mesons.) We show that our confinement model may be made covariant. We use the covariant model to calculate the decay of the various states, ${\pi }^{\prime },$ to the $\pi +\rho$ and $\pi +\sigma$ channels at one-loop order. At one-loop order, it is found that only the nodeless state at 1.18 GeV and the state at 1.36 GeV have significant widths for ${\pi }^{\prime }\to \pi +\sigma .$ These states have somewhat larger widths for the decay ${\pi }^{\prime }\to \pi +\rho ,$ leading to ${\Gamma }_{\mathrm{tot}}=0.368\mathrm{}\mathrm{GeV}$ for the state at 1.18 GeV and 0.150 GeV for the state at 1.36 GeV. We note that the state 1.18 GeV is a mixed pseudoscalar–axial-vector state, while the state at 1.36 GeV is the $\pi \mathrm{}\left(2S\right)\mathrm{}$ state to a good approximation, since it has a very small admixture of axial-vector components. There is information concerning the decay ${\pi }^{\prime }\to \pi +(\pi +\pi {)}_{L=0\mathrm{}}$ that is extracted from experimental data for three-body final states. Our (nodeless) state at 1.18 GeV has the correct energy and width to fit that data. However, our widths for ${\pi }^{\prime }\to \pi +(\pi +\pi {)}_{L=1\mathrm{}}$ are larger than those for ${\pi }^{\prime }\to \pi +(\pi +\pi {)}_{L=0\mathrm{}}.$ That suggests that final-state interactions are probably quite important in understanding the branching ratios for ${\pi }^{\prime }$ decays to states of three pions. Our results also suggest that, if we were to study the π(1300), and include final-state interactions, it is necessary to include both the 1.18 GeV and the 1.36 GeV states in the analysis. (On the other hand, since the 1.36 GeV state is a $2S$ state, it may be only weakly excited in the reactions used to generate final states of three pions.)

We investigate the model dependence and the importance of choice of database in extracting the physical nucleon-$\Delta \mathrm{}\left(1232\right)\mathrm{}$ electromagnetic transition amplitudes, of interest to QCD and baryon structure, from the pion photoproduction observables. The model dependence is found to be much smaller than the range of values obtained when different datasets are fitted. In addition, some inconsistencies in the current database are discovered, and their affect on the extracted transition amplitudes is discussed.

A new sum rule for ${\gamma }_{\pi },$ the backward spin polarizability of the nucleon, is derived from a backward-angle dispersion relation. Taking into account single-pion and multipion photoproduction in the s channel up to the energy ${\omega }_{\max }=1.5\mathrm{}\hspace{0.5em}\mathrm{GeV}$ and resonances in the t channel with mass below $1.5\hspace{0.5em}\mathrm{GeV},$ it is found for the proton and neutron that $[{\gamma }_{\pi }{]}_p=-39.5\pm 2.4$ and $[{\gamma }_{\pi }{]}_n=52.5\mathrm{}\pm 2.4,$ respectively, in units of ${10}^{-4}\hspace{0.5em}{\mathrm{fm}}^4.$

We present a consistent calculation of half-off-shell form factors in the pion-nucleon vertex and the nucleon self-energy. Numerical results are presented. Near the on-shell point the pion-nucleon vertex is dominated by the pseudovector coupling, while at large nucleon invariant masses we find a sizable pseudoscalar admixture.

Pion-pion scattering is investigated in the framework of the resonating group method. The wave function of an isolated pion, described as a quark-antiquark system interacting through a potential composed of a central and a spin-spin part, is determined using the spinless Salpeter equation. Given these ingredients the kernel of the integrodifferential equation governing the relative motion of the colliding pions is calculated using relativistic kinematics. The corresponding $S-$ and D-wave pion-pion phase shifts are compared with their Galilean counterparts.

Using the generating functional method, the $\sigma$ and $\omega$ meson propagators in nuclear matter have been determined in a relativistic mean-field effective model where a coupling between the nucleon and the scalar meson quadratic in the scalar field has been added to the standard Walecka Lagrangian. As an example of application, the in-medium $\sigma$ and $\omega$ mesonic branches have been considered.

Dynamical breaking of chiral symmetry in effective models of QCD is studied. Introducing a cutoff function or a nonlocal interaction, the Noether current must be modified and thus the Ward-Takahashi identity and the PCAC relation are modified accordingly. We point out that the pion decay constant must be defined consistently with the Noether current so that the low-energy relations are satisfied. We define the proxy of the Noether current for general effective models, which is consistent with loop expansion of the Cornwall-Jackiw-Tomboulis effective action. A general formula for the pion decay constant in terms of the Bethe-Salpeter amplitude is derived. The effective Pagels-Stokar formula is proposed, which is useful to estimate the decay constant without solving the Bethe-Salpeter equation.