International Journal of Modern Physics E

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler–Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the form of the field equations than the usual Lagrangian description. It is proven that Poisson brackets, Lagrange brackets, and canonical 2-forms exist that are invariant under canonical transformations of the fields. The technique to derive transformation rules for the fields from generating functions is demonstrated by means of various examples. In particular, it is shown that the infinitesimal canonical transformation furnishes the most general form of Noether's theorem. Furthermore, we specify the generating function of an infinitesimal space-time step that conforms to the field equations.

We study the effect of the variation of fundamental constants, extracted from cosmological models, upon double beta decay rates. It is found that, by assuming the variations of the fundamental constants with time, one may obtain corrections to the calculated values of the double beta decay rates, but only at earlier times. This effect is notorious for the case of a power-law time dependence of the fine structure constant α and of the Fermi constant G_F. However, since these models do not predict any effect on today's decay rates, it is concluded that no significant new information may be extracted about them from current values of double beta decay observables.

This paper describes the lessons we have to draw after the observation of neutrinoless ββ decay by the enriched ⁷⁶Ge experiment, for present and future experiments so as (a) to fulfill the task to confirm the present result (b) to deliver additional information on the main contributions of effective neutrino mass and right-handed weak currents etc. to the 0νββ amplitude. It is shown that presently running and planned experiments are probably not sensitive enough to check the evidence on a reasonable time scale. It is further demonstrated that, the only way to get more information on the individual contributions of m, η, λ etc. to the 0νββ amplitude is to go to completely different types of experiments, rather than those under construction and preparation at present, e.g. to mixed-mode β⁺/EC decay experiments, such as ¹²⁴Xe decay. It is pointed out that the sometimes observed "tension" between the result of 0νββ decay and cosmological experiments like WMAP, SDSS etc. does not exist and is an artificial product of improper analysis of the latter.

Two photon decays of pion are studied in the framework of the Bethe–Salpeter equation under Covariant Instantaneous Ansatz where the structure of hadron-quark vertex function Γ is generalized to include various Dirac covariants (other than γ₅) from their complete set. These covariants are incorporated in accordance with a power counting rule (which was recently employed to calculate leptonic decays constants of pseudoscalar mesons and vector mesons) order by order in powers of the inverse of the meson mass. Pion-photon coupling constant F_π is calculated with the incorporation of leading order covariants.

We show that the conservation and the non-additivity of information, together with the additivity of entropy makes entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the information non-additivity. Nevertheless, the later is also true in other fields, in which the interaction information is important. Examples are classical statistical mechanics, social statistics and financial processes. The second law of thermodynamics is thus proven in its most general form. It is exactly true, not only in quantum and classical physics but also in other processes in which the information is conservative and non-additive.

Relativistic mean field theory is used to produce potential energy surfaces (PESs) for Ti isotopes. The relatively flat PESs suggest that ^{48, 52, 60}Ti, being on the way from vibrations to γ-unstable behavior, are the possible examples with the transitional dynamical symmetry E(5). Especially for ⁴⁸Ti, PES shows that it is a better candidate with E(5) symmetry. These conclusions are supported by the experimental data via the observed ratios of excitation energies.

With a view to study heavy-ion induced fission after complete and/or incomplete fusion reactions, experiments have been performed at the Inter-University Accelerator Center (IUAC), New Delhi, India. The production cross-sections for more than 40 fission-like events (25 ≤ Z ≤ 45) produced in ¹⁶O+¹⁵⁹Tb and ¹⁶O+¹⁶⁹Tm systems, respectively, at E/A = 5.6 and 5.9 MeV have been measured using the recoil-catcher technique followed by off-line γ-spectroscopy. The analysis of the data indicates that fission is one of the competing modes of de-excitation of excited composite system formed via complete and/or incomplete fusion processes, where the evaporation of light nuclear particle(s) are more likely to be expected. Attempts have also been made to study isotopic yield distributions of Yttrium (^{83, 84m, 85, 87m}Y) and Strontium (^{80, 81, 83, 85m}Sr) isotopes in ¹⁶O+¹⁵⁹Tb system, and Indium (^{105, 107, 108, 110}In) and Technetium (^{99m, 101, 104, 105}Tc) isotopes in ¹⁶O+¹⁶⁹Tm system. The statistical analysis of the isotopic yield distribution has also been carried out to determine the most probable values of mass and charge of fission-like events in two systems.

In this study we propose new semi-empirical formulas by modifying the formula of Levkovskii with the new parameters for (n, 2n) and (n, α) reactions cross-sections at 14–15 MeV neutron incident energy. The cross sections have been calculated using the asymmetry parameter depending on empirical formulas for the incoming energies of 14–15 MeV neutrons. The parameters obtained by modifying the original formula of Levkovskii and Konno et al. have been determined by applying the least squares fitting method to the experimental cross sections, and the systematics of the (n, 2n) and (n, α) reactions have been studied. We have also suggested different parameters for the empirical formula to reproduce the cross sections of the (n, 2n) and (n, α) reactions for the neutron incident energy of 14–15 MeV. The modified formulas yielded cross sections representing markedly smaller chi-square (χ²) deviations from experimental values, and values much closer to units as compared with those calculated using Levkovskii's and Konno et al. original formulas. The results obtained have been discussed and compared with the other empirical formulas, and found to be well in agreement when used to correlate the available experimental σ(n, 2n) and σ(n, σ) data of different nuclei.