To the modification of methods of nuclear chronometry in astrophysics and geophysics

In practically all known till now methods of nuclear chronometry there were usually taken into account the life-times of only fundamental states of $\alpha$-radioactive nuclei. But in the processes of nuclear synthesis in stars and under the influence of the constant cosmic radiation on surfaces of planets the excitations of the $\alpha$-radioactive nuclei are going on. Between them there are the states with the excited $\alpha$-particles inside the parent nuclei and so with much smaller life-times. And inside the large masses of stellar, terrestrial and meteoric substances the transitions between different internal conditions of radioactive nuclei are accompanied by infinite chains of the $\gamma$-radiations with the subsequent $\gamma$-absorptions, the further $\gamma$-radiations etc. For the description of the $\alpha$-decay evolution with considering of such excited states and multiple $\gamma$-radiations and $\gamma$-absorptions inside stars and under the influence of the cosmic radiation on the earth surface we present the quantum-mechanical approach, which is based on the generalized Krylov-Fock theorem. Some simple estimations are also presented. They bring to the conclusion that the usual (non-corrected) "nuclear clocks" do really indicate not to realistic values but to the \emph{upper limits} of the durations of the $\alpha$-decay stellar and planet processes.Comment: 6 pages, Standard LaTeX v.2

On scattering cross sections and durations near an isolated compound-resonance, distorted by the non-resonant background, in the center-of-mass and laboratory systems

During last 20 years there was revealed and published the phenomenon of the appearing of the time advance instead of the time delay at the region of a compound-nucleus resonance, distorted by the non-resonant background (in the center-of-mass (C-) system). This phenomenon is usually accompanied by a minimum in the cross section near the same energy. Here we analyze the cross section and the time delay of the nucleon-nucleus scattering in the laboratory (L-) system. In the L-system the delay-advance phenomenon does not appear. We use and concretize the non-standard analytical transformations of the cross section from the C-system to the L-system, obtained in our previous papers. They are illustrated by the calculations of energy dependences of cross sections in the L-system for several cases of nucleon elastic scattering by nuclei 12C, 16O, 28Si, 52Cr, 56Fe and 64Ni at the range of distorted resonances in comparison with the experimental data.Comment: 11 pages, 7 figure

On Superluminal motions in photon and particle tunnelings

It is shown that the Hartman-Fletcher effect is valid for all the known expressions of the mean tunnelling time, in various nonrelativistic approaches, for the case of finite width barriers without absorption. Then, we show that the same effect is not valid for the tunnelling time mean-square fluctuations. On the basis of the Hartman-Fletcher effect and the known analogy between photon and nonrelativistic-particle tunnelling, one can explain the Superluminal group-velocities observed in various photon tunnelling experiments (without violation of the so-called "Einstein causality").Comment: standard LaTeX file; accepted for publication in Phys. Lett.

Resonant and non-resonant Tunneling through a double barrier

An explicit expression is obtained for the phase-time corresponding to tunneling of a (non-relativistic) particle through two rectangular barriers, both in the case of resonant and in the case of non-resonant tunneling. It is shown that the behavior of the transmission coefficient and of the tunneling phase-time near a resonance is given by expressions with "Breit-Wigner type" denominators. By contrast, it is shown that, when the tunneling probability is low (but not negligible), the non-resonant tunneling time depends on the barrier width and on the distance between the barriers only in a very weak (exponentially decreasing) way: This can imply in various cases, as well-known, the highly Superluminal tunneling associated with the so-called "generalized Hartman Effect"; but we are now able to improve and modify the mathematical description of such an effect, and to compare more in detail our results with the experimental data for non-resonant tunneling of photons. Finally, as a second example, the tunneling phase-time is calculated, and compared with the available experimental results, in the case of the quantum-mechanical tunneling of neutrons through two barrier-filters at the resonance energy of the set-up.Comment: replaced with some improvements in the text and in the references: pdf (11 pages) produced from a source-file in Word; including one Figur

Time operator in QFT with Virasoro constraints

Time operator is studied on the basis of field quantization, where the difficulty stemming from Pauli's theorem is circumvented by borrowing ideas from the covariant quantization of the bosonic string, i.e., one can remove the negative energy states by imposing Virasoro constraints. Applying the index theorem, one can show that in a different subspace of a Fock space, there is a different self-adjoint time operator. However, the self-adjoint time operator in the maximal subspace of the Fock space can also represent the self-adjoint time operator in the other subspaces, such that it can be taken as the single, universal time operator. Furthermore, a new insight on Pauli's theorem is presented.Comment: 13 pages, No figure, to be published in Physics Letters

Reflectionless Tunnelling of Light in Gradient Optics

We analyse the optical (or microwave) tunnelling properties of electromagnetic waves passing through thin films presenting a specific index profile providing a cut-off frequency, when they are used below this frequency. We show that contrary to the usual case of a square index profile, where tunnelling is accompanied with a strong attenuation of the wave due to reflection, such films present the possibility of a reflectionless tunnelling, where the incoming intensity is totally transmitted