Narrow Results

In this paper, we address the well-known cosmic coincidence problem in the framework of the f(G) gravity. In order to achieve this, an interaction between dark energy and dark matter is considered. A set-up is designed and a constraint equation is obtained, which generates the f(G) models that do not suffer from the coincidence problem. Due to the absence of a universally accepted interaction term introduced by a fundamental theory, the study is conducted over three different forms of logically chosen interaction terms. To illustrate the set-up three widely known models of f(G) gravity are taken into consideration and the problem is studied under the designed set-up. The study reveals that the popular f(G) gravity models do not approve of a satisfactory solution of the long standing coincidence problem, thus proving to be a major setback for them as successful models of universe. Finally, two nonconventional models of f(G) gravity have been proposed and studied in the framework of the designed set-up. It is seen that a complete solution of the coincidence problem is achieved for these models. The study also reveals that the b-interaction term is much more preferable compared to the other interactions, due to its greater compliance with the recent observational data.

The decay of bromine-76 was studied using high resolution HpGe detectors in singles and coincidence mode. Bromine-76 was produced via two reactions: ⁷⁵As(α,3n)⁷⁶Br and ⁷⁶Se(p,n)⁷⁶Br. The results of these experiments verified the previously reported levels of ⁷⁶Se. In addition to the previously described transitions and levels, 37 new γ-rays and 15 new energy levels were found for the first time.

The decay of ⁷²As has been investigated by means of γ-ray spectroscopy. The ⁷²As nuclei were produced through the ⁷²Ge(p, n)⁷²As reaction. The Compton-suppressed spectrometer and high-purity Ge detectors have been used in singles and in coincidence modes respectively to study γ-rays in the β⁺+EC decay of ⁷²As to ⁷²Ge. 79 γ-rays, among which 3 were observed for the first time, were reported. A decay scheme of ⁷²As including 1 new level is proposed that accommodates 77 of these transitions. Tentative spin and parity assignments are suggested for a number of levels according to the log ft values and γ-branching ratios.

The γ-ray spectra of ¹⁸⁸Re decay have been studied by using a Compton-suppressed spectrometer and a three parameters γ-γ-T list coincidence system. Experimental data analysis demonstrated that six γ-rays at 557, 810, 1463, 1867, 1936 and 2022 keV and three levels at 1443, 1936 and 2022 keV are confirmed again. Seven new γ-rays at 309.60±0.04, 826.90±0.02, 979.29±0.08, 1103.7±0.4, 1828.2±0.1, 1842.5±0.2 and 1982.5±0.2 keV have been identified, three new levels at 309.60, 1828.2 and 1982.5 keV are assigned. The β^- decay branching ratio is deduced. In addition, in order to study this γ-unstable nucleus, shape calculations using the Hartree–Fock–Bogoliubov-like formalism were carried out for positive-parity states in ¹⁸⁸Os. The TRS plots reveal that, as the spin increases up the band, the triaxiality parameter γ changes.

We prove that there exists positive even integer $k$ such that $\varphi (n)=\varphi (n+k)$ holds for infinitely many $n$. We also prove various estimates on number of solutions to $\varphi (p-1)=\varphi (q-1)$ for distinct primes $p$ and $q$.

The decay of bromine-76 is studied by means of γ-ray spectroscopy. Bromine-76 is produced via two reactions: ⁷⁵As(α, 3n)⁷⁶Br and ⁷⁶Se(p, n)⁷⁶Br. The results of these experiments verify the previously reported levels of ⁷⁶Se. In addition to the previously described transitions and levels, 37 new γ-rays and 15 new energy levels are found for the first time. In addition, in order to study the deformation of ⁷⁶Se which lies in transitional region between strongly deformed and spherical nuclei, we calculate the total Routhian surfaces (TRS) of positive-parity states by cranking shell model formalism.

The high-spin states in ¹²⁶I have been investigated by using in-beam γ-ray spectroscopy with the ¹²⁴Sn(⁷Li, 5n)¹²⁶I reaction at a beam energy of 48 MeV. The previously known level scheme of ¹²⁶I has been extended and modified considerably by adding about 60 new γ-transitions and establishing 5 new bands. The backbendings in the yrast band 1 and the yrare band 3 are found both due to a pair of h_11/2 neutrons alignment. The configurations for the newly identified bands 2, 4, 5 and 6 have been assigned.