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In this paper, how to compute the eigenfrequencies of the structures composed of a series of inclined cables is shown. The physics of an inclined cable can be complicated, so solving the differential equations even approximately is difficult. However, rather than solving the system of 4 first-order equations governing the dynamics of each cable, the governing equations are instead converted to a set of equations that the exterior matrix satisfies. Therefore, the exterior matrix method (EMM) is used without solving the original governing equations. Even though this produces a system of 6 first-order equations, the simple asymptotic techniques to find the first three terms of the perturbative solution can be used. The solutions can then be assembled to produce a 6 × 6 exterior matrix for a cable section. The matrices for each cable in the structure are multiplied together, along with the exterior matrices for each joint. The roots of the product give us the eigenfrequencies of the system. [ABSTRACT FROM AUTHOR]

The validity of the Brink-Axel hypothesis, which is especially important for numerous astrophysical calculations, is addressed for 116, 120, 124 Sn below the neutron separation energy by means of three independent experimental methods. The-ray strength functions (GSFs) extracted from primary?-decay spectra following charged-particle reactions with the Oslo method and with the shape method demonstrate excellent agreement with those deduced from forward-angle inelastic proton scattering at relativistic beam energies. In addition, the GSFs are shown to be independent of excitation energies and spins of the initial and final states. The results provide a critical test of the generalized Brink-Axel hypothesis in heavy nuclei, demonstrating its applicability in the energy region of the pygmy dipole resonance. [ABSTRACT FROM AUTHOR]

The cascading 3.21 and 4.44 MeV electric quadrupole transitions have been observed from the Hoyle state at 7.65 MeV excitation energy in 12C, excited by the 12C(p,p′) reaction at 10.7 MeV proton energy. From the proton-γ-γ triple coincidence data, a value of Γrad/Γ=6.2(6)×10-4 was obtained for the radiative branching ratio. Using our results, together with ΓE0π/Γ from Eriksen et al. [Phys. Rev. C 102, 024320 (2020)] and the currently adopted Γπ(E0) values, the radiative width of the Hoyle state is determined as Γrad=5.1(6)×10-3  eV. This value is about 34% higher than the currently adopted value and will impact models of stellar evolution and nucleosynthesis. [ABSTRACT FROM AUTHOR]