? 3 H and the role of spin-dependent forces in the ?-N interaction

Kolesnikov, N. N.; Тарасов, В. И.

doi:10.1007/bf00893139

Cited by 3 publications

(4 citation statements)

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“…Here E < 0 and are the total energy and the corresponding wavefunction ( = 1) of the beryllium-muonic atom, respectively. The ground-state wavefunctions of the five-body beryllium-muonic atoms in this work are represented in the form [6] …”

mentioning

confidence: 99%

Etching Effect of Hydrogen Plasma on Electron Cyclotron Resonance-Chemical Vapor Deposition and Its Application to Low Temperature Si Selective Epitaxial Growth

Sasaki

Takahashi

1998

Jpn. J. Appl. Phys.

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The bound-state properties and hyperfine structure splitting in the ground S 1 2 (L = 0)-states of the three-electron beryllium-muonic atoms 9 Be 4+ µ − e − 3 and 10 Be 4+ µ − e − 3 are determined numerically with the use of highly accurate variational five-body wavefunctions. All computations of the berylliummuonic atoms are performed with the use of the two independent electron spin functions.The analysis of the hyperfine structure of various muonic atoms is an important method which is often used to determine the magnetic nuclear properties (see, e.g., [1,2]). Recently, we have calculated the hyperfine structure splitting in the ground S 1 2 (L = 0)-states of the berylliummuonic atoms 9 Be 4+ µ − e − 3 and 10 Be 4+ µ − e − 3 [3]. Our goal in this work is to improve the overall accuracy of the method used in [3]. In particular, in our present calculations the two independent spin functions are used for the three-electron subsystem instead of a single basis set. Furthermore, the total numbers of basis functions used in this study are significantly larger than analogous numbers in [3]. By using the new, improved version of our computational method we evaluate the hyperfine splitting in the five-body beryllium-muonic atoms. In addition to the hyperfine splitting we also determine a number of bound-state properties. Such properties are of great interest for better understanding of the internal structure of the beryllium-muonic atoms.Note that each of the beryllium-muonic atoms contains three electrons (e − ), one negatively charged muon (µ − ) and a heavy beryllium nucleus M Be 4+ , where the symbol M designates the mass of the beryllium nucleus. In atomic units, whereh = 1, m e = 1, |e| = 1, the non-relativistic Hamiltonian of an arbitrary beryllium-muonic atom takes the form

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confidence: 99%

Etching Effect of Hydrogen Plasma on Electron Cyclotron Resonance-Chemical Vapor Deposition and Its Application to Low Temperature Si Selective Epitaxial Growth

Sasaki

Takahashi

1998

Jpn. J. Appl. Phys.

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“…( 4), each of which explicitly depends upon the six relative coordinates r 12 , r 13 , r 23 , r 14 , r 24 and r 34 , where r ij =| r i − r j |= r ji and r i (i = 1, 2, 3, 4) are the Cartesian coordinates of all four (point) particles. This variational expansion is well known in few-body physics since the middle of 1970's (see, e.g., [19], [20], [49] and earlier references therein). After many years of successful calculations of different bound states in various nuclear and atomic few-body systems this variational expansion in multi-dimensional gaussoids can be recognized as very effective, fast and sufficiently accurate in 99% cases, including all positronium hydrides HPs discussed in this study.…”

Section: New Methods For Highly Accurate Bound State Computa-tions Of...mentioning

confidence: 99%

“…The variational expansion in multi-dimensional guassoids was proposed, developed and applied to various nuclear and atomic systems by N.N. Kolesnikov and his co-workers in the middle of 1970's (see, e.g., [19], [20] and earlier references therein). The explicit form of this variational expansion in the case of four-body systems is…”

Section: Bound State Wave Functions and Properties Of The Positro-niu...mentioning

confidence: 99%

Bound-state properties, positron annihilation and hyperfine structure of the four-body positronium hydrides

Frolov

2022

Molecular Physics

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Bound state properties of the ground (bound) 1 S(L = 0)−state(s) in the four-body positronium hydrides 1 HPs, 2 HPs (DPs), 3 HPs (TPs) and MuPs are determined and investigated. By using numerical data from our computations of these four-body systems we have determined a number of different annihilation rates for each of these positronium hydrides and evaluated the hyperfine structure splitting. The properties of the ground (bound) states in the four-body exitonic M h + e − 2 e + complexes, where M ≥ 1 and M ≤ 1, have also been evaluated numerically. The

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“…Each of the basis functions in this expansion explicitlty depends upon all six relative coordinates r ij , where r ij = r r r r r , , , , 12 13 14 23 24 and r 34 . For the ground state of the MuPs system the variational expansion in six-dimensional gaussoids takes the form (see, e.g., [14,15]):…”

Section: Four-body Muonium-positronium Systemmentioning

confidence: 99%

Atomic few-body systems with muonium

Frolov

2017

J. Phys. B: At. Mol. Opt. Phys.

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Properties of some few-body systems which include one positively charged muon µ + and two electrons e − are discussed. In particular, we consider the negatively charged muonium ion Mu − (or µ + e − 2 ) and four-body MuPs (or µ + e − 2 e + ) systems each of which has only one stable bound (ground) state. The problem of annihilation of the electron-positron pair(s) in the MuPs system is investigated. The hyperfine structure splitting of the ground state in the MuPs system evaluated with our expectation value of the muon-positron delta-function is ∆ ≈ 23.05758 M Hz. Another group of interesting four-body neutral systems investigated in this study includes the p + µ + e − 2 , d + µ + e − 2 and t + µ + e − 2 'quasi-molecules'. These quasi-molecules are formed in large numbers when positively charged muons slow down in liquid hydrogen, or in liquid deuterium and/or tritium. The properties of these systems are unique, since they occupy an intermediate position between actual two-center molecules and one-center atoms. PACS number(s): 32.10.Fn, 31.15.A-and 31.15.VeIn this communication we report the results of our analysis of some three-and fourbody systems each of which include one positively charged muon µ + and two electron e − .Briefly, we can say that each of these few-body systems contains muonium Mu (or µ + e − ), or muonium ion Mu − (or µ + e − 2 ). Recently, there is an increasing experimental interest to such few-body systems (see discussions and references in [1] - [5]). This can be explained by rapidly growing experimental abilities to detect and isolate similar few-particle systems.Moreover, by using the modern experimental techniques one can investigate some of the bound state properties of these systems. Another reason follows from the fact that the µ + muon has positive electric charge and relatively small particle mass. This means that all atomic and molecular few-body systems which contain one positively charged muon and two electrons have very special electron density distribution which differs substantially from electron density distributions in 'similar' atomic and molecular systems. In reality, such systems can be considered as a separate class of bound systems which are neither atoms, nor molecules. In some cases, the positively charged muon plays a role of central particle which stabilize a few-electron structure, e.g., in the Mu − ion and MuPs system (see below).Formally, all few-body systems with positively charged muon are unstable, but their lifetime τ (≈ 2 · 10 −6 sec) significantly exceeds the mean time(s) of atomic transitions and decay processes τ tr ≤ 1 · 10 −11 sec. In other words, these few-body quasi-atomic systems can be created and stabilized in their bound state(s) substantially faster than the decay of the µ + muon can occur.As follows from the above, it is important to predict the overall stability of the few-body systems which include muonium Mu (or muonium ion Mu − ) and investigate their basic properties. These problems are considered in our study. In particular, below we consid...

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? 3 H and the role of spin-dependent forces in the ?-N interaction

Cited by 3 publications

References 8 publications

Etching Effect of Hydrogen Plasma on Electron Cyclotron Resonance-Chemical Vapor Deposition and Its Application to Low Temperature Si Selective Epitaxial Growth

Etching Effect of Hydrogen Plasma on Electron Cyclotron Resonance-Chemical Vapor Deposition and Its Application to Low Temperature Si Selective Epitaxial Growth

Bound-state properties, positron annihilation and hyperfine structure of the four-body positronium hydrides

Atomic few-body systems with muonium

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