The astrophysical S-factor of the 7Li(p,gamma)8Be reaction has been studied at low energies with including an information about asymptotic normalization coefficient for the 7Li+p -> 8Be configuration. In order to do this, the differential cross-section of the proton transfer reaction 7Li(3He,d)8Be at energy of 24.3MeV has been analyzed within the framework of the modified distorted wave Born approximation (MDWBA). The value of ANC for the 7Li+p -> 8Be(0+, E = 0.0MeV) configuration was derived to be 58.43 +/- 1.95 fm-1. The values of ANCs for the 7Li+p -> 8Be(2+, E = 3.04MeV) configuration were extracted to be 16.67 +/- 0.54fm-1 and 9.73 +/- 0.31fm-1 for total angular momentum jp7Li=3/2 and jp7Li=1/2, respectively. These ANC values were used in estimating the astrophysical S(E) factor of proton radiative capture by the 7Li nucleus at astrophysically relevant energies within the framework of the modified R-matrix method. The value of the total astrophysical S factor of the 7Li(p,gamma)8Be reaction at zero energy was found to be S(0) = 1.35keV b. The reaction rate of the7Li(p,gamma)8Be process was calculated over the relevant temperature range of astrophysical interest.
We study three-particle Schrodinger operators on the two-dimensional lattice Z(2) and show that a critical mass ratio gamma(c) approximate to 2.75194 governs the existence of a bound trimer in the fermionic 2 + 1 configuration (two identical fermions and a third particle). For gamma < gamma(c) there is a topological prohibition (Pauli suppression) of a three-body bound state, whereas for gamma > gamma(c) a doubly degenerate eigenvalue emerges below the essential spectrum with the strong-coupling asymptotics z(gamma, lambda) = -lambda+e(0)(gamma)+O(lambda(-1)). Within a unified framework based on the Birman-Schwinger principle and strong-coupling asymptotic analysis, we compare this behaviour with the bosonic case of three identical particles, where two bound states exist below the essential spectrum and the ground-state energy satisfies z(1)(s) (& micro;) = -3 & micro; + C-2 + O(& micro;(-1)). The resulting second-order phase transition with respect to the mass ratio gamma is relevant for the design of experiments on fermionic trimers in optical lattices and for modelling excitonic complexes and defect-bound states in two-dimensional nanomaterials, where the critical value gamma(c) serves as a design guideline for the observability of three-body bound states. We also outline a modified three-particle lattice model with two competing interaction channels, for which the Birman-Schwinger analysis naturally leads to a Landau-type scenario of a first-order phase transition in the space of trimer bound states. In the bosonic case we prove a strong-coupling theorem describing the existence and asymptotics of trimer bound states, while in the fermionic 2+1 case we establish a spectral phase-transition theorem that identifies an explicit critical mass ratio gamma(c) separating the trimer and non-trimer regimes.
This review investigates the multifaceted roles of nitrogen-fixing and phosphate-mobilizing bacteria in natural ecosystems, with a particular focus on their contributions to plant growth and sustainable soil management. These microbial communities contribute substantially to nutrient cycling by converting atmospheric nitrogen into plant-available forms and mobilizing insoluble phosphorus in soil, thereby enhancing soil fertility and promoting sustainable plant productivity. This review synthesizes current knowledge on the mechanisms underlying biological nitrogen fixation, phosphate solubilization and mineralization, and the production of plant growth–promoting metabolites. Particular attention is given to plant–microbe interactions and their role in improving nutrient availability, regulating plant physiological processes, and enhancing tolerance to abiotic stresses such as salinity, drought, and heavy metal contamination. The findings underscore the ecological importance of these plant-associated microbial communities and highlight their potential applications in biofertilizer and biostimulant development for sustainable agriculture and reduced dependence on synthetic fertilizers.
The analysis of the directly measured experimental cross-section for the nuclear-astrophysical 12C(n,gamma)13C reaction leading to the first excited state of the 13C nucleus has been performed within the modified two body potential approach. The peripheral nature of the reaction 12C(n,gamma)13C(1/2+; 3.09MeV) has been demonstrated. New value of the asymptotic normalization coefficient for 12C+n -> 13C(1/2+; 3.09MeV) vertex with their uncertainty has been obtained. The new value of the asymptotic normalization coefficient obtained in this work was used for the extrapolation of the cross-section to low energies within the modified two body potential approach. The Maxwellian-averaged neutron capture cross-section at kT=30 keV has been determined to be 11.07 +/- 0.70 mu barn. The partial astrophysical S factor at zero energy is found to be S(0)=(1.44 +/- 0.09)x1021 fm5/s.
This article studies the expression of spiritual and moral issues in the poems of the great thinker Alisher Navoi and the expression of social, political and educational issues in the poems of Zahiriddin Muhammad Babur. It comprehensively studies the expression of human dignity, its spirituality, its place in political life, its place in social life, the scope of educational issues, and its moral aspects in the poems of Alisher Navoi and Zahiriddin Muhammad Babur on these topics. Alisher Navoi's poetic skills and his poems are works that reflect many issues that are relevant not only for his time, but also for today. It expresses many issues such as human spirituality, its morality, attitude to values, faith and belief, friendship and hard work, promotion of enlightenment and learning, the value of the word and its beauty, attitude to the word, call to good deeds, will and religion. Attention is also paid to the artistic and aesthetic characteristics of the poems of Alisher Navoi and Zahiriddin Muhammad Babur and their analysis
