Hyperspherical three-body calculation for muonic atoms
TL;DR: In this paper, the ground state energies of exotic three-body atomic systems consisting two muons and a positively charged nucleus have been calculated using hyperspherical harmonics expansion (HHE) method.
Abstract: Ground state energies of exotic three-body atomic systems consisting two muons and a positively charged nucleus like: 1H+μ−μ−, 4He2+μ−μ−, 3He2+μ−μ−, 7Li3+μ−μ−, 6Li3+μ−μ−, 9Be4+μ−μ−, 12C6+μ−μ−, 16O8+μ−μ−, 20Ne10+μ−μ−, 28Si14+μ−μ− and 40Ar18+μ−μ− have been calculated using hyperspherical harmonics expansion (HHE) method. Calculation of matrix elements of two body interactions involved in the HHE method for a three body system is greatly simplified by expanding the bra- and ket- vector states in the hyperspherical harmonics basis states appropriate for the partition corresponding to the interacting pair. This involves the Raynal-Revai coefficients (RRC), which are the transformation coefficients between the hyperspherical harmonics bases corresponding to the two partitions. Use of these coefficients found to be very useful for the numerical solution of three-body Schrodinger equation where the two-body potentials are other than Coulomb or harmonic oscillator type. However, in this work the interaction potentials involved are purely Coulomb. The calculated energies have been compared with (i) those obtained by straight forward manner; and (ii) with those found in the literature (wherever available). The calculated binding energies agree within the computational error.
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TL;DR: A simple Mathematica (versions 7–9) code for computing S-state energies and wave functions of three-particles systems is presented, which enables calculation of expectation values of arbitrary physical operators without any difficulties.
15 citations
TL;DR: In this paper, the energies of the low-lying bound S-states (L = 0) of exotic three-body systems, consisting of a nuclear core of charge +Ze (Z being atomic number of the core) and two negatively charged valence muons, have been calculated by hyperspherical harmonics expansion method (HHEM).
Abstract: In this paper, energies of the low-lying bound S-states (L = 0) of exotic three-body systems, consisting a nuclear core of charge +Ze (Z being atomic number of the core) and two negatively charged valence muons, have been calculated by hyperspherical harmonics expansion method (HHEM). The three-body Schrodinger equation is solved assuming purely Coulomb interaction among the binary pairs of the three-body systems XZ+μ-μ- for Z = 1 to 54. Convergence pattern of the energies have been checked with respect to the increasing number of partial waves Λmax. For available computer facilities, calculations are feasible up to Λmax = 28 partial waves, however, calculation for still higher partial waves have been achieved through an appropriate extrapolation scheme. The dependence of bound state energies has been checked against increasing nuclear charge Z and finally, the calculated energies have been compared with the ones of the literature.
5 citations
TL;DR: In this paper, the energies of three-body Schr\H{o}dinger equations were calculated by hyperspherical harmonics expansion method (HHEM) and the dependence of bound state energies has been checked against increasing nuclear charge Z and finally, the calculated energies have been compared with the ones of the literature.
Abstract: Energies of the low-lying bound S-states (L=0) of exotic three-body systems, consisting a nuclear core of charge +Ze (Z being atomic number of the core) and two negatively charged valence muons, have been calculated by hyperspherical harmonics expansion method (HHEM). The three-body Schr\H{o}dinger equation is solved assuming purely Coulomb interaction among the binary pairs of the three-body systems X$^{Z+}\mu^-\mu^-$ for Z=1 to 54. Convergence pattern of the energies have been checked with respect to the increasing number of partial waves $\Lambda_{max}$. For available computer facilities, calculations are feasible up to $\Lambda_{max}=28$ partial waves, however, calculation for still higher partial waves have been achieved through an appropriate extrapolation scheme. The dependence of bound state energies has been checked against increasing nuclear charge Z and finally, the calculated energies have been compared with the ones of the literature.
2 citations
01 Oct 2019
TL;DR: In this paper, a theoretical scheme is presented to investigate resonant levels in weakly bound nuclear systems by the use of isospectral potentials, and the first 0+ resonance in the neutron-rich 22C is calculated assuming a three-body (20C+n+n +n) cluster model.
Abstract: In this paper, a novel theoretical scheme is presented to investigate resonant levels in weakly bound nuclear systems by the use of isospectral potentials. In this scheme, a new potential is constructed which is strictly isospectral with the original shallow-well potential and has properties which are desirable to make the calculation of resonances more accurate and easier. To demonstrate the effectiveness of the method, the first 0+ resonance in the neutron-rich 22C is calculated assuming a three-body (20C+n+n) cluster model.
2 citations
TL;DR: In this article , the authors discussed the production of more exotic triple baryons including triple-baryons and their decay channels, as well as their bound states and binding energies.
Abstract: Even though lots of $\Lambda$-hypernuclei have been found and measured, multi-strangeness hypernuclei consisting of $\Omega$ are not yet discovered. The studies of multi-strangeness hypernuclei help us further understand the interaction between hyperons and nucleons. Recently the $\Omega N$ and $\Omega\Omega$ interactions as well as binding energies were calculated by the HAL-QCD's lattice Quantum Chromo-Dynamics (LQCD) simulations and production rates of $\Omega$-dibaryon in Au + Au collisions at RHIC and Pb + Pb collisions at LHC energies were estimated by a coalescence model. The present work discusses the production of more exotic triple-baryons including $\Omega$, namely $\Omega NN$ and $\Omega\Omega N$ as well as their decay channels. A variation method is used in calculations of bound states and binding energy of $\Omega NN$ and $\Omega\Omega N$ with the potentials from the HAL-QCD's results. The productions of $\Omega NN$ and $\Omega\Omega N$ are predicted by using a blast-wave model plus coalescence model in ultra-relativistic heavy-ion collisions at $\sqrt{s_{NN}} = 200$ GeV and $2.76$ TeV. Furthermore, plots for baryon number dependent yields of different baryons ($N$ and $\Omega$), their dibaryons and hypernuclei are made and the production rate of a more exotic tetra-baryon ($\Omega\Omega NN$) is extrapolated.
1 citations
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TL;DR: In this article, the renormalized numerov method has been generalized to bound states of the coupled-channel Schroedinger equation and a method for detecting wave function nodes is presented.
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382 citations
TL;DR: In this paper, the authors presented a self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology ~CODATA! for international use.
Abstract: This paper gives the 1998 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology ~CODATA! for international use. Further, it describes in detail the adjustment of the values of the subset of constants on which the complete 1998 set of recommended values is based. The 1998 set replaces its immediate predecessor recommended by CODATA in 1986. The new adjustment, which takes into account all of the data available through 31 December 1998, is a significant advance over its 1986 counterpart. The standard uncertainties ~i.e., estimated standard deviations ! of the new recommended values are in most cases about 1/5 to 1/12 and in some cases 1/160 times the standard uncertainties of the corresponding 1986 values. Moreover, in almost all cases the absolute values of the differences between the 1998 values and the corresponding 1986 values are less than twice the standard uncertainties of the 1986 values. The new set of recommended values is available on the World Wide Web at physics.nist.gov/ constants. ©1999 American Institute of Physics and American Chemical Society. @S0047-2689 ~00!00301-9#
377 citations
TL;DR: In this article, the application of hyperspherical coordinates in a unified treatment of bound states and resonances of two-electron atomic systems and other general Coulomb three-body systems is reviewed.
261 citations
TL;DR: In this paper, a method for solving the Schrodinger equation for the ground state of any number of bosons or for the trinucleon system or α-particle is formulated in the framework of the hyperspherical harmonic expansion method.
242 citations
TL;DR: In this paper, the values of the basic constants and conversion factors of physics and chemistry resulting from the 1986 least squares adjustment of the fundamental physical constants as published by the CODATA (Committee on Data for Science and Technology) Task Group on Fundamental Constants and recommended for international use by CODTA were presented.
Abstract: Presented here are the values of the basic constants and conversion factors of physics and chemistry resulting from the 1986 least‐squares adjustment of the fundamental physical constants as published by the CODATA (Committee on Data for Science and Technology) Task Group on Fundamental Constants and recommended for international use by CODATA. The 1986 CODATA set of values replaces its predecessor published by the Task Group and recommended for international use by CODATA in 1973.
221 citations