abstract

To investigate the role of surface energy coefficients, we perform a comparative study of heavy-ion fusion and quasi-elastic scattering reactions simultaneously. The results show that the surface energy coefficient significantly influences both fusion and quasi-elastic reactions. Our findings reveal that proximity potential based on the 1977 version, with parameters \(\gamma _{0}=1.08948~\mathrm {MeV}/\mathrm {fm}^{2}\) and \(k_\mathrm {s}=1.9830\), successfully reproduces the experimental measurements of fusion and quasi-elastic scattering. The average relative errors for the fusion cross section and quasi-elastic scattering data for selected reactions are 0.0558 and 0.0826, respectively.

abstract

Gamow–Teller (GT) transitions play a fundamental role in exploring nuclear structure and weak-interaction-mediated decay modes. In this study, a detailed investigation of the GT strength distributions for the neutron-deficient nucleus \(^{74}\)Kr is presented. The theoretical framework is based on the Quasiparticle Random Phase Approximation (QRPA), incorporating both particle–hole (\(ph\)) and particle–particle (\(pp\)) residual interactions. To examine the influence of different interactions, comparative analyses are performed using a schematic model and the Pyatov method. The resulting GT strength distributions are systematically compared with available experimental data to evaluate the predictive capacity of the employed models. This work contributes to a deeper understanding of spin–isospin excitations in nuclei near the \(N\approx Z\) line and provides valuable insights for future studies on weak-interaction processes in exotic nuclei.

abstract

The possible anomalous New Physics contributions to dipole and weak dipole moments of the \(\tau \) lepton bring renewed interest in development and revisiting charge-parity violating signatures in \(\tau \)-pair production in \(Z\)-boson decay at energies of the LHC. In this paper, we discuss effects of anomalous contributions to polarisation and spin correlations in the \(\bar q q \to \tau ^+ \tau ^-\) production processes, with \(\tau \) decays included. Due to the complex nature of the resulting distributions, Monte Carlo techniques are useful, in particular for event reweighing with studied New Physics phenomena. Extensions of the Standard Model spin amplitudes, within the Improved Born Approximation used for the matrix element, are implemented in the TauSpinner program. This is mainly with \(\tau \) dipole and weak dipole moments in mind, but is applicable to arbitrary New Physics interactions, provided they can be encapsulated into the Standard Model \(2 \to 2\) structure of matrix element extensions. The implementation allows one also to introduce an arbitrary phase-shift between vector and axial-vector couplings of \(Z\) boson to \(\tau \) leptons, which would have impact on the observed transverse spin correlations. Basic formulas and algorithm principles are presented, together with distributions for the spin-correlation matrix. Numerical examples of impact on experimental signatures are shown in the case of \(\tau ^\pm \to \rho ^\pm \nu _\tau \to \pi ^\pm \pi ^0 \nu _\tau \) decays. Information on how to use and configure the TauSpinner program is given in Appendix B.

abstract

The analysis of the differential cross section of the \(^{13}\mathrm {C}(t,d)^{14}\)C reaction measured at an incident energy of 38 MeV was performed within the framework of the Modified Distorted Wave Born Approximation. The peripheral character of the reaction was tested. It was shown that the considered reaction is peripheral at the main maximum of the angular distribution of the reaction under consideration. The squared ANC value for the \(^{13}\mathrm {C}+n\to {}^{14}\)C configuration was found to be \(15.50\pm 0.55\) \({\rm {fm}^{-1}}\).