RSS Few-Body Systems
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Study of the Alpha-particle Monopole Transition form Factor
Abstract
The \({{}^4\textrm{He}}\) monopole form factor is studied by computing the transition matrix element of the electromagnetic charge operator between the \({{}^4\textrm{He}}\) ground-state and the \(p+{{}^3\textrm{H}}\) and \(n+{{}^3\textrm{He}}\) scattering states. The nuclear wave functions are calculated using the hyperspherical harmonic method, by starting from Hamiltonians including two- and three-body forces derived in chiral effective field theory. The electromagnetic charge operator retains, beyond the leading order (impulse approximation) term, also higher order contributions, as relativistic corrections and meson-exchange currents. The results for the monopole form factor are in fair agreement with recent MAMI data. Comparison with other theoretical calculations are also provided.
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Effect of Background Scattering on Efimov Scenario for Overlapping Narrow Feshbach Resonances
Abstract
Efimov physics in the vicinity of two overlapping narrow Feshbach resonances can be explored within a framework of a three-channel model where a non-interacting open channel is coupled to two closed molecular channels. Here, we determine how it compares to the extended two-channel model, which includes an open channel with finite background scattering and a single molecular channel. We identify the parameter range in which the three-channel model surpasses the extended two-channel model. Furthermore, the three-channel model is extended to include background scattering, and then both models are applied to the experimentally relevant system of bosonic lithium atoms polarized on two different energy levels, with an isolated and two overlapping narrow Feshbach resonances, respectively. We confirm, in agreement with previous studies, that being small, the background scattering length in lithium has a negligible effect on the Efimov features in the case of isolated resonance. However, in the case of overlapping Feshbach resonances, the inclusion of background scattering improves the performance of the theory with respect to the experimentally measured position of the Efimov resonance.
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Beyond of the Hyperspherical Quantum Mechanic
Abstract
The aim of this work is to explain how, starting from the orthogonality expression of two polynomials, we deduce the Schrödinger equation and the solution of the N-body problem including two-body correlations as well as the existence of shells. Generated by the behaviour of kinetic energy for a two-body interaction. The quantification of matters is obtained by the application of the weight function algorithm to the statement that two states are independents when their product integrated over the whole space is null leading to a two variables second order differential equation. The Nuclear Shell Model is a consequence of the kinetic energy behaviour for increasing number of nucleons in ground state. It leaves the mean field theory useless.
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Resonances in the Quark Model
Abstract
A discussion is presented of the estimates of the energy and width of resonances in constituent models, with focus on the tetraquark states containing heavy quarks.
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The Role of the Effective Range in Strongly-Interacting Few-Body Systems
Abstract
Strongly interacting systems appear in several areas of physics and are characterized by attractive interactions that can almost, or just barely, loosely bind two particles. Although this definition is made at the two-body level, this gives rise to fascinating effects in larger systems, including the so-called Efimov physics. In this context, the zero-range theory aims to describe low-energy properties based only on the scattering length. However, for a broad range of physical applications, the finite range of the interactions plays an important role. In this work, I discuss some aspects of finite-range effects in strongly interacting systems. I present the zero-range and shapeless universalities in two-body systems with applications in atomic and nuclear physics. I derived an analytical expression for the s-wave bound-state spectrum of the modified Pöschl–Teller potential for two particles in three dimensions, which is compared with the approximations to illustrate their usefulness. Concerning three identical bosons, I presented a trimer energy scaling function that explicitly includes the effective range. The implications for larger systems are briefly discussed.