abstract

The Bohr hypothesis shows that there are simple rotational energies in the definition of the energies of ground state bands of the even–even rare earths and actinides. These energy levels are arranged as \(0^+\), \(2^+\), \(4^+\), … A sequence of the ratios of energies of the higher excited states to the \(2^+\) state gives rise to a number of integers which clarifies equal interval energy spacing in the formation of the levels in the ground state bands. Such an approximately equal interval energy spacing may also be traced for higher order bands of these nuclei and not only for even–even but also for a number of odd–even, even–odd and odd–odd nuclei. This work attempts to underline the peculiarities in the spectra of rare-earth and actinide elements. Analyses also indicate a physical effect in \(K^{\pi }=2^+\) band of \(^{232}\)Th element.

abstract

In the present work, we have interpreted recently available experimental data for high-spin states of the near-spherical nuclei \(^{91,92}\)Zr, using the shell-model calculations within the full \(f_{5/2}\), \(p_{3/2}\), \(p_{1/2}\), \(g_{9/2}\) model space for protons and valence neutrons in \(g_{9/2}\), \(g_{7/2}\), \(d_{5/2}\) orbits. We have employed a truncation for the neutrons due to huge matrix dimensions, by allowing one neutron excitation from \(g_{9/2}\) orbital to \(d_{5/2}\) and \(g_{7/2}\) orbitals. Results are in a good agreement with the available experimental data. Thus, theoretically, we have identified the structure of many high-spin states, which were tentatively assigned in the recent experimental work. The \(^{91}\)Zr \(21/2^+\) isomer lies at low-energy region due to fully aligned spins of two \(g_{9/2}\) protons and one \(d_{5/2}\) neutron.

abstract

The emergence of regularity and symmetry in the Mirror Energy Differences (MED) have been investigated in the present work. The MED has been calculated between mirror pair using the energies of their excited states generated by the valence protons correlation and valence neutrons correlation, respectively. The similarity in the MED i.e. positive (increasing) trends of the \(A = 47\) and \(A = 49\) mirror pair nuclei was known a test of valence symmetry in mirror nuclei. The analogous similarity in the MED i.e. negative (decreasing) trends in mirror pair nuclei with \(Z\) or \(N\) two units more or less than the closed shell, has been proposed as further evidence of the particle-hole symmetry in MED.

abstract

In this work, we study the Friedmann–Robertson–Walker cosmology in which a Chaplygin gas is coupled to a non-linear scalar field in the framework of the Hořava–Lifshitz theory. In writing the action of the matter part, we use the Schutzs formalism so that the only degree of freedom of the Chaplygin gas plays the role of an evolutionary parameter. In a minisuperspace perspective, we construct the Lagrangian for this model and show that in comparison with the usual Einstein–Hilbert gravity, there are some correction terms coming from the Hořava theory. In such a set-up and by using some approximations, the classical dynamics of the model is investigated and some discussions about their possible singularities are presented. We then deal with the quantization of the model in the context of the Wheeler–DeWitt approach of quantum cosmology to find the cosmological wave function. We use the resulting wave functions to investigate the possibility of the avoidance of classical singularities due to quantum effects.

abstract

The so-called “entropic mechanism” for ordering noise-induced phase transitions has been formerly used to stabilize nanopatterns in a realistic model for a monolayer of laterally interacting adsorbates. Here, we use this mechanism to stabilize pinning states and induce stochastic localized patterns (“dissipative solitons”) on the monolayer. The key to achieve that goal is to displace only one of the stable homogeneous states toward field values at which the lateral interactions can elicit stable nanopatterns. At larger noise intensities, the “soliton” locations fluctuate with larger amplitude. However, since more localized patterns are elicited by the noise, their motion becomes confined when looked at longer timescales.

abstract

An useful approach is investigated in order to analyze a class of a stochastic differential equations that can be encountered in quantum optics problems, especially, in the case of two-photon losses on the driven cavity mode. The passage to the ordinary coupled differential equations is presented and the treatment of the obtained coupled system is explored. Generalization of the problem to stimulate variable coefficients is discussed and the exact solutions are achieved in explicit forms under suitable conditions on the coefficients.