RSS Few-Body Systems
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Reliability of the Born-Oppenheimer Approximation in Noninteger Dimensions
Abstract
We address the question of the reliability of the Born-Oppenheimer (BO) approximation for a mass-imbalanced resonant three-body system embedded in noninteger dimensions. We address this question within the problem of a system of currently experimental interest, namely \(^7\) Li \(-^{87}\) Rb \(_2\) . We compare the Efimov scale parameter as well as the wave functions obtained using the BO approximation with those obtained using the Bethe-Peierls boundary condition.
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On the Lorentz Symmetry Violation Effects on a Particle Subject to a Trigonometric Potential and a Periodic Potential
Abstract
We study the nonrelativistic effects of the Lorentz symmetry violation determined by the coupling between the fixed vector field \(f^{\mu }\gamma ^{5}\) and the derivative of the fermionic field on the squared cotangent potential and a periodic potential in \(\left( 1+1\right) \) -dimensions. Our analysis focusses on how the energy eigenvalues can be influenced by the Lorentz symmetry violation background. From the energy eigenvalues, we extend our discussion to the revival time.
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Explicitly Correlated Gaussians with Tensor Pre-factors: Analytic Matrix Elements
Abstract
We consider a specific form of explicitly correlated Gaussians—with tensor pre-factors—which appear naturally when dealing with certain few-body systems in nuclear and particle physics. We derive analytic matrix elements with these Gaussians—overlap, kinetic energy, and Coulomb potential—to be used in variational calculations of those systems. We also perform a quick test of the derived formulae by applying them to p- and d-waves of the hydrogen atom.
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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.