Few-Body Systems最新文献

We examine the spatial distribution of electric charges within an extended, non-conductive cylinder featuring an inner radius denoted as (r_{0}). Our investigation unveils the emergence of a distinct modified attractive-inverse square potential, arising from the intricate interplay between the electric field and the induced electric dipole moment of a neutral particle. This modified potential notably departs from the conventional inverse-square potential, showcasing an additional term proportional to (r^{-1}). As a result, we present compelling evidence for the realization of a discrete energy spectrum within this intricate system.

Cold three-body recombination between helium and silver atoms is studied using hyperspherical coordinates. The three-body Schrodinger equation, represented in the slow variable discretization approach at short distances and in the adiabatic method at large distances and using the potential-energy surface represented as the addition of realistic He-He and He-Ag pair interaction potentials, is solved using the R-matrix propagation method, in order to numerically calculate the three-body recombination rates for the He+He+Ag(rightarrow )He(_2)+Ag and He+He+Ag(rightarrow )HeAg+He processes. Not only zero-angular momentum (J=0) states but also (J>0) states are considered in the calculations, allowing for treating the recombination processes at collision energies beyond the threshold regime. The results of our calculations will be presented and discussed.

We consider the (^{3}hbox {H}) nucleus within the AAA model that includes mass identical particles interacting through a phenomenological nuclear potential. We extend the three-nucleon Hamiltonian (beta {widehat{{H}}}_{0}+{V}_{nucl.}) using the parameter (beta =m_{0}/{m^*}) that determines the variations (m^*) of the averaged nucleon mass (m_{0} = (m_{n} + m_{p})/2). It was found that the (^{3}hbox {H}) binding energy is a linear function of the mass ({m^*}/m_0) when it changes within the ranges (0.9{<}{m^*}{/m}_{0}{<}1.25). Thus, the relation between energy and mass is expressed by an analogy to the well-known formula (E=mc^{2}). This effect takes a place in small vicinity around the experimentally motivated value of the nucleon mass due to Taylor expanding the general relation (Esim 1/m). The equivalent mass of a nucleon, defined by using this energy-mass dependence, can phenomenologically describe the effect of the proton/nucleon mass difference on 3N binding energy.

Phenomenological Poincaré invariant quantum mechanical models can provide an efficient description of the dynamics of strongly interacting particles that is frame independent and consistent with spectral and scattering observables. These models are representation dependent and in order to apply them to reactions with electromagnetic probes it is necessary to use a consistent electromagnetic current operator. The purpose of this work is to use local gauge invariance to construct consistent strong current operators. Current operators are constructed from a model Hamiltonian by replacing momentum operators in the Weyl representation by gauge covariant derivatives. The construction provides a systematic method to construct expressions for current operators that are consistent with relativistic models of strong interaction dynamics.

We are reporting here on a series of theoretical investigations with both algebraic models and geometric cluster models of alpha clusters in (^{12})C, focusing on the structure of the ground state, the first excited (0^+) state and the second excited (2^+) state with the purpose, in particular, of establishing if the rotational bands are compatible with rigid structures or rather if they are quantum mixture of different configurations. In a first series of paper (Vitturi et al., Transition densities and form factors in the triangular (alpha )-cluster model of 12C with application to 12C+(alpha ) scattering. Phys Rev C 101:014315, 2020; Casal et al., Alpha-induced inelastic scattering and alpha-transfer reactions in 12C and 16O within the Algebraic Cluster Model. Eur Phys J A 57:33, 2021), we assume a rigid equilateral triangle shape and study in detail several properties that descend from the algebraic framework, such as the energy spectrum, electromagnetic observables and calculate the transition densities in order to extract elastic and inelastic cross-sections for various processes. In a second series of papers (Moriya et al., Three-(alpha ) Configurations in the 0(^+) States of 12C. Few-Body Syst 62:46, 2021; Moriya et al., Three-(alpha ) configurations of the second (J^pi ) = 0(^+) state in 12C. Eur. Phys J A 59:37, 2023), we solve the three-body Schrödinger equation with orthogonality conditions using the stochastic variational method with correlated Gaussian basis functions. The two-body density distributions indicate that the main configurations of both the (0_2^+) and (2_2^+) states are acute iscosceles triangle shapes coming from (^8)Be((0^+))+(alpha ) configurations and find some hints that the second (2^+) state is not an ideal rigid rotational band member of the Hoyle state band.

The three-body nuclear and molecular resonances for (^{135}_{~55})Cs+(^2_1)H+(^2_1)H, and (^{133}_{~55})Cs+(^3_1)H+(^3_1)H systems are calculated in “cuboctahedron (^{135}_{~55})Cs(^2_1)H(_2) (^textrm{A}_{46})Pd(_{12}) and (^{133}_{~55})Cs(^3_1)H(_2) (^textrm{A}_{46})Pd(_{12}) clusters” in a very wide range from 0.01[fm] to several hundreds of nm in “one stretch” with more than “100 significant figures”, where the mass number A of Pd could be 102, 104, 105, 106, 108, 110 but neglected hereafter, because Pd isn’t concerned directly with the nuclear reaction. We obtained several new “three-ion resonance states” between the expected molecular CsH(_2) ground state and the first excited state in cuboctahedron CsH(_2)Pd(_{12}) cluster, where H represents either a (^1_1)H, a (^2_1)H, or a (^3_1)H, respectively. The molecular “ground and the first excited states” in the cluster are derived by the Kohn-Sham equation or the ADF package which could mainly describe many electrons rather than cores of ions. We found that the E2 transition times from some CsH(_2) ((7/2^+)) resonance states (or the IOS states) to the nuclear (^{139}_{~57})La ((7/2^+)) ground state are about (tau =10^{-1}sim 10^{-6})sec for five traditional potentials, and (tau =10^{-2}sim 10^{-8})sec for six potentials with our long range three-body force (3BLF) where the “molecular resonances” can strongly interfere with the “nuclear resonances”. The thermal nuclear “critical reaction value” (or fusion constant) and/or ultra low energy corresponding value: (C_mathrm{high/low})=(duration time)(times )(density)(times )(energy or temperature) are compared. It was found that (C_textrm{low}) is almost the same order as (C_textrm{high}) or more. Finally, an ignition method for the synthesis will be discussed.

A computational method is proposed to calculate bound and resonant states by solving the Klein–Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential is represented in a Coulomb–Sturmian basis. This basis facilitates the exact analytic evaluation of the Coulomb Green’s operator in terms of a continued fraction. In the extension to relativistic problems, we cast the Klein–Gordon and Dirac equations into an effective Schrödinger form. Then the solution method is basically an analytic continuation of non-relativistic quantities like the angular momentum, charge, energy and potential into the effective relativistic counterparts.

Using the effective-range expansion for the two-body amplitudes may generate spurious sub-threshold poles outside of the convergence range of the expansion. In the infinite volume, the emergence of such poles leads to the breakdown of unitarity in the three-body amplitude. We discuss the extension of our alternative subtraction scheme for including effective range corrections in pionless effective field theory for spinless bosons to nucleons. In particular, we consider the neutron-deuteron system in the doublet S-wave channel explicitly.

We investigate the properties of the excited state of (^4textrm{He}), (^4textrm{He}^*), within the framework of Efimov physics and its connection to the unitary point of the nuclear interaction. We explore two different approaches to track the trajectory of (^4textrm{He}^*) as it crosses the (^3textrm{H})+p threshold and potentially becomes a resonant state. The first approach involves an analytical continuation of the energy with respect to the Coulomb coupling, while the second approach introduces an artificial four-body force that it is gradually released. By utilizing Padé approximants and extrapolation techniques, we estimate the energy and width of the resonance. Our results suggest a central energy value of (E_R=0.060(3)) MeV and a width of (Gamma /2=0.036(6)) MeV using the Coulomb analysis, and (E_R=0.068(1)) MeV and (Gamma /2=0.007(5)) MeV with the four-body force analysis. Interestingly, these results are consistent with calculations based on ab-initio nuclear interactions but differ from the accepted values of the (0^+) resonance energy and width. This highlights the challenges in accurately determining the properties of resonant states in light nuclei and calls for further investigations and refinements in theoretical approaches.