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[en] Essentials of relativistic mean field (RMF) theory and some of its recent applications are presented. The explicit calculations are carried out for a few selected isotopic, isotonic, and isobaric chains of nuclei covering the entire periodic table. The calculated ground-state properties are found to be in good agreement with the corresponding experiment: the binding energies are reproduced, on the average, within 0.25%, and the charge radii differ only in the second decimal place of fermi. The relativistic origin of the pseudospin symmetry is briefly discussed. The density distributions obtained are found to be in good agreement with the experiment (where available). The peripheral factor - the ratio of the neutron and the proton densities at the nuclear periphery, extracted in the antiproton annihilation experiments - is well reproduced. The RMF densities are used to calculate the reaction (σR) and charge-changing (σcc) cross sections in the Glauber model as well as the α (cluster)-daughter interaction energy. The energy in turn is employed to estimate the decay half-lives of superheavy (transactinide) nuclei in the WKB approximation. The calculations are found to agree well with the experiment. This success of the RMF in accurately describing the nuclear properties with only a few fixed parameters is indeed remarkable
[ru]Изложена суть теории релятивистского среднего поля (РСП) и представлены некоторые из ее недавних применений. Проведены точные расчеты для нескольких выбранных изотопических, изотонических и изобарических каналов ядер, полностью охватывающие таблицу периодических элементов. Результаты вычислений свойств основного состояния находятся в хорошем согласии с соответствующим экспериментом: энергии связи воспроизводятся, в среднем, в пределах 0.25 %, а зарядовые радиусы отличаются только во втором знаке после запятой в единицах ферми. Коротко обсуждается релятивистское происхождение псевдоспиновой симметрии. Полученные распределения плотностей находятся в хорошем согласии с экспериментом (где возможен их расчет). Хорошо воспроизводится периферийный фактор - отношение плотности нейтронов к плотности протонов на периферии ядра, извлекаемое в экспериментах по протон-антипротонной аннигиляции. Плотности РСП используются для вычисления сечений реакции (σR) и перезарядки (σcc) в модели Глаубера, а также энергии α (кластерного)-дочернего взаимодействия. Энергия, в свою очередь, может быть использована для оценки периодов полураспада сверхтяжелых (трансактинидных) ядер в рамках ВКБ-приближения. Расчеты находятся в хорошем согласии с экспериментом. Теория РСП успешно описывает свойства ядер при использовании всего нескольких фиксированных параметров
[en] The sensitivity of inflationary spectra to initial conditions is addressed in the context of a phenomenological model that breaks Lorentz invariance by dissipative effects above some threshold energy Λ. These effects are obtained dynamically by coupling the fluctuation modes to extra degrees of freedom which are unobservable below Λ. Because of the strong dissipative effects in the early propagation, only the state of the extra degrees of freedom is relevant for the power spectrum. If this state is the ground state, and if Λ is much larger than the Hubble scale H, the standard spectrum is recovered. Using analytical and numerical methods, we calculate the modifications for a large class of dissipative models. For all of these, we show that the leading modification (in an expansion in H/Λ) is linear in the decay rate evaluated at horizon exit, and that high frequency superimposed oscillations are not generated. The modification is negative when the decay rate decreases slower than the cube of H, which means that there is a loss of power on the largest scales.
[en] Some aspects of lightlike dimensional reduction in flat spacetime are studied with emphasis to classical applications. Among them the Galilean transformation of shadows induced by inertial frame changes is studied in detail by proving that (i) the shadow of an object has the same shape in every orthogonal-to-light screen (ii) if two shadows are simultaneous in an orthogonal-to-light screen then they are simultaneous in any such screen. In particular, the Galilean group in 2 + 1 dimensions is recognized as an exact symmetry of nature which acts on the shadows of the events instead that on the events themselves. The group theoretical approach to lightlike dimensional reduction is used to solve the reconstruction problem of a trajectory starting from its acceleration history or from its projected (shadow) trajectory. The possibility of obtaining Galilean projected physics starting from Poincare invariant physics is stressed through the example of relativistic collisions. In particular, it is shown that the projection of a relativistic collision between massless particles gives a non-relativistic collision in which the kinetic energy is conserved
[en] A class of continuous renormalization group flows with a dynamical adjustment of the propagator is introduced and studied theoretically for fermionic and bosonic quantum field theories. The adjustment allows to include self-energy effects nontrivially in the denominator of the propagator and to adapt the scale decomposition to a moving singularity, and hence to define flows of Fermi surfaces in a natural way. These flows require no counterterms, but the counterterms used in earlier treatments can be constructed using them. The influence of propagator adjustment on the strong-coupling behaviour of flows is examined for a simple example, and some conclusions about the strong coupling behaviour of renormalization group flows are drawn. (Abstract Copyright , Wiley Periodicals, Inc.)
[en] Lindhard proposed his classical equation for the critical channeling angle from consideration of conservation of transverse energy. We generalize those ideas via consideration of conservation of transverse momentum, and propose an improved equation. A dimensional analysis of the problem is also presented, and that analysis puts our arguments and results on a firm footing.
[en] We provide a class of QFTs which exhibit dissipation above a threshold energy, thereby breaking Lorentz invariance. Unitarity is preserved by coupling the fields to additional degrees of freedom (heavy fields) which introduce the rest frame. Using the equivalence principle, we define these theories in arbitrary curved spacetime. We then confront the trans-Planckian question of inflationary cosmology. When dissipation increases with the energy, the quantum field describing adiabatic perturbations is completely damped at the onset of inflation. However it still exists as a composite operator made with the additional fields. And when these are in their ground state, the standard power spectrum obtains if the threshold energy is much larger that the Hubble parameter. In fact, as the energy redshifts below the threshold, the composite operator behaves as if it were a free field endowed with standard vacuum fluctuations. The relationship between our models and the braneworld scenarios studied by Libanov and Rubakov displaying similar effects is discussed. The signatures of dissipation will be studied in a forthcoming paper
[en] We summarize our main findings in deriving the Boltzmann collision term from the Kadanoff-Baym relativistic transport equation and the multiple scattering expansion of the self-energy within a quasi-particle approximation. Our collision term is valid to all orders in perturbation theory and contains processes with any number of participating particles. This work completes a program initiated by Carrington and Mrowczynski and developed further by present authors and Weinstock in recent literature
[en] We study what might be called fractional vortices, vortex configurations with the minimum winding from the viewpoint of their topological stability, but which are characterized by various notable substructures in the transverse energy distribution. The fractional vortices occur in diverse Abelian or non-Abelian generalizations of the Higgs model. The global and local features characterizing these are studied, and we identify the two crucial ingredients for their occurrence--the vacuum degeneracy leading to nontrivial vacuum moduli M, and the BPS nature of the vortices. Fractional vortices are further classified into two kinds. The first type of such vortices appear when M has orbifold Zn singularities; the second type occurs in systems in which the vacuum moduli space M possesses either a deformed geometry or some singularity. These general features are illustrated with several concrete models.