The role of nuclear fusion reactions are highly important at the low energies (E ∼ 1eV to few keV) for the primordial nucleosynthesis as well as stellar nucleosynthesis of light elements. Mechanism of nuclear fusion reactions in this energy domain can be explained successfully in terms of quantum mechanical tunneling through the mutual Coulomb barrier of interacting nuclei. In this paper, we have studied astrophysical S-factor, fusion cross-section and thermonuclear reaction rate of a few α-induced nuclear fusion reactions-9Be(α,n)12C, 11B(α,p)14C and 12C(α, γ)16O which are investigated adopting the single-step selectiveresonant tunneling model (SRTM). As an improvement over earlierworks, the authors have used here a microscopically derived density dependent double-folding potential model, invoking the M3Y-Reid NN interactions, for the numerical computation of the astrophysical S-factor, S(E); the fusion cross-section, σ(E) and thermonuclear reaction rate, <σv>. The results have been compared with those found in the literature and those are in good agreement.
The relativistic Hartree-Bogoliubov (RHB) approach, is solved in an axially deformed harmonic-oscillator basis, using the DD-ME2 and DD-PC1 functionals with a separable pairing force, scanning the number of oscillator shells Nf up to 24 for eight even-even nuclei from 16O to 294Ds, chosen to sample both light-to-superheavy mass numbers and spherical-to-strongly- deformed shapes. Together with the self-consistent quadrupole deformation, we track the binding energy, the proton, neutron and charge radii, the pairing energies and the Fermi energies, and we judge convergence against explicit tolerances, so that the basis required for each observable can be compared from one nucleus to another. The observables converge at clearly different rates: the radii and the Fermi energies settle first, the energy per nucleon follows, and the pairing energies stabilize last, often non-monotonically and more slowly the heavier the nucleus. The basis needed depends on the observable and on the accuracy required, and it is fixed neither by the mass number nor by the deformation alone: when high precision is demanded, spherical nuclei converge first and deformed nuclei last, while shape instability and a large single-particle space delay the convergence of the radii and the Fermi energies. Finally, we analyse the computational cost, which rises steeply with the basis size because of the block structure of the axially symmetric problem, and we derive practical guidelines for choosing the basis in large-scale calculations.
A recent report on 7Li(e,e′K+) electroproduction runs by the A1 collaboration at the Mainz Microtron (MAMI) assigns a sharp pion-momentum line at pπ−≈113.8±0.1 MeV/c to Λ3H→π−+3He weak decay, resulting in exceptionally large Λ3H binding-energy BΛ(Λ3H)=0.523±0.013±0.075 MeV. Here I discuss an alternative interpretation of the observed sharp line in terms of Λ7Heg.s.→π−+7Li(Ex=478 keV) weak decay and its implications for BΛ(Λ7He).
We present a closed-form construction of the orbital coefficients of fractional parentage (CFP) of three identical particles in the translationally invariant harmonic oscillator (HO) Jacobi basis. These coefficients are usually obtained by numerically diagonalizing a permutation operator in every energy–angular-momentum block. We show that this diagonalization is unnecessary. Dressing the class operator P^13+P^23 with the single unitary W^=H^1Φ^ — a fixed complexification followed by the HO bracket with mass parameter d=1 — turns it into the label swap times an integer, and every CFP is then the single ket |Ki,s〉=2Q^sW^†|i〉 — a 2-scaled, sign-decorated column of the d=1 bracket restricted to one e2-parity of the labels — whose norm, 1+s〈i|J^|i〉, is itself a single matrix element. The same W^ carries label parity into swap symmetry, W^Q^sW^†=R^s, which is what makes the bookkeeping collapse. The eigenvalues are the exact integers ± 2 and ± 1 that label the S(3) symmetry classes. The construction is uniform in E, L and symmetry class, and reduces the CFP-specific work from O(n3) to O(n2) in the block dimension; an eigensolver remains only inside the bracket engine that supplies H^1, and all residual numerical error originates there. We implement it on top of an SU(3)-basis bracket engine and run the full battery of checks over all 1301 blocks up to E=50 (912 366 CFPs, largest block 2907 × 2907): the S(3) class assignment is exact in every block, and the residual numerical error — entirely the bracket engine’s — stays below 10−8 throughout E ≤ 35 and is restored to 10−22 or better by a quadruple-precision build beyond that. We further validate the construction against the independently generated antisymmetrization data of a production three-nucleon code, including the 3He ground-state energy of the full pipeline.
This study examines the photoabsorption cross section (σ) and the electric dipole polarizability (αD) for the closed-shell and closed-subshell nuclei ⁴⁰Ca, ⁴⁸Ca, ⁹⁰Zr, ¹¹⁶Sn, ¹⁴⁴Sm, and ²⁰⁸Pb using the self-consistent Random Phase Approximation (RPA) based on the Skyrme Hartree–Fock (HF) approach. Twenty types of Skyrme interactions are employed, covering a wide range of nuclear matter properties, including the incompressibility modulus KNM, saturation density ρ₀, symmetry energy J, symmetry energy slope parameter L, effective isovector mass mv*/m, TRK enhancement factor (κ). We calculated the centroid energy Ecen and the dipole polarizability αD, and we compared them with experimental data to gain insight into the internal structure of the nuclei under investigation. Furthermore, the sensitivity of the calculated properties to nuclear matter parameters is explored through the evaluation and analysis of the Pearson linear correlation coefficient.
