arXiv subjects

Mantile L. Lekala

Publications and source records attributed to Mantile L. Lekala.

3 recordsLinked to original sources

arXiv2026

4-momentum conservation as the principal framework for mesonic decay: The case of helium-5-lambda

Negative-pion and neutral-pion mesonic decays of the hypernucleus $ _Λ^5$He are investigated within two-body and three-body relativistic kinematics in the rest-frame of the hypernucleus. 4-momentum conservation fully constrains the two-body decay, giving rise to a monochromatic pion momentum that is determined through the Newton-Raphson root-finding algorithm. In the case of three-body decay, where 4-momentum conservation is insufficient, the final-state momenta are parametrised by variables whose variations account for all kinematically allowed momenta. A Monte Carlo sampling method is then employed to generate 50 000 decay events per channel that simultaneously satisfy both energy and momentum conservation. The resulting pion momentum distributions exhibit clear peaks at 103.0 MeV/c for neutral pion decay and 97.3 MeV/c for negative pion decay. In addition, only 0.27\% of neutral pion decay events and 0.03\% of negative pion decay events produce nucleons with momenta exceeding the Fermi momentum of $ ^4$He, and are therefore allowed by the Pauli exclusion principle.

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arXiv2026

Explicit asymptotics of coupling matrix elements for central potentials in the hyperspherical harmonics expansion method

The analytic structure and asymptotic behavior of channel-coupling potentials in three-body systems are investigated within the framework of the hyperspherical harmonics expansion method. The coupling between different Jacobi partitions is expressed using Raynal--Revai transformation coefficients and a reduced hyperangular integral that contains the two-body interaction. For central potentials, this integral is factorised into geometric and dynamical components. Explicit asymptotic scaling laws are derived for the hyperradial coupling strength in the limit of large hyperradius $ρ\to \infty$ for representative nuclear potentials: Gaussian, Yukawa, and Woods--Saxon potentials (short-range), and Coulomb potential (long-range). These short-range potentials are found to exhibit an algebraic decay $\propto ρ^{-(2\ell_{η_i}+3)}$, where $\ell_{η_i}$ is the orbital angular momentum of the interacting pair. This decay is shown to lead to efficient asymptotic decoupling of hyperspherical channels. In contrast, the Coulomb interaction yields couplings that decay only as $1/ρ$, indicating persistent channel coupling at large distances and explaining the slow convergence of hyperspherical expansions for charged systems. These results provide a quantitative basis for truncating the hyperradial domain, for example, in choosing a matching radius for scattering calculations or an upper integration limit in bound-state problems.

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arXiv2019

Theoretical analysis of $^8$Li + $^{208}$Pb reaction and the critical angular momentum for complete fusion

In a theoretical approach, the complete and incomplete fusions are investigated by considering the $^8$Li+$^{208}$Pb reaction. By decreasing the projectile ground-state binding energy $\varepsilon_b$ from its known experimental value, the complete fusion is shown to have insignificant dependence on such variations, whereas the incomplete fusion strongly depends on that. The complete and incomplete fusion cross sections are calculated by using a combination of both continuum-discretized coupled-channel and sum-rule models. To this end, an incident-energy dependent cut-off angular momentum $L_c$ is first obtained by using the available complete fusion experimental data, within an approach which is extended to model results obtained for other incident-energies. An approximated fitted expression linking $L_c$ to the well-known critical value $L_{\rm crit}$ derived by Wilczyński [Nucl. Phys. A 216 (1973) 386] suggests a generalization of the corresponding sum-rule model to energies around and below the Coulomb barrier.

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