Hyperfine structure S state of muonic helium atom

In this work the nonrelativistic ionization energies 3He2+μ−e− and 4He2+μ−e− of helium-muonic atoms are calculated for S states.The estimates are based on the variational principle of exponential expansion. Convergence of the numerical values of variational energies is studied by increasing a number of the basis functions N. That allows to claim that the obtained energy values have 30-33 significant digits for S states

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The Surface Variational Principle: A Different Perspective for Structural Acoustic Modeling

Volume 1A: 16th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc97/vib-3920 ◽

1997 ◽

Author(s):

J. H. Ginsberg

Keyword(s):

Fourier Series ◽

Variational Principle ◽

Vibration Analysis ◽

Basis Functions ◽

Acoustic Modeling ◽

Normal Velocity ◽

Convergence Properties ◽

Variational Functional ◽

Acoustic Interaction ◽

System Equations

Abstract This paper surveys the development and application of the surface variational principle (SVP) governing the acoustic interaction between surface pressure and normal velocity. SVP is analogous to the method of assumed modes for vibration analysis, in that it represents the response in terms of a sequence of basis functions that are globally defined. The system equations governing the series coefficients are obtained by requiring that the value of the variational functional be stationary. In the wavenumber-based version of SVP, the pressure and velocity are represented by dual range Fourier series. A brief description of the steps entailed in formulating the SVP equations and coupling them to the equations for an elastic structure is provided. Then the computational requirements of an SVP analysis relative to conventional boundary element and finite element techniques are discussed. This is followed by an example illustrating the convergence properties of SVP. Another example is used to highlight the physical interpretation of the SVP representation of surface response. The evolution of the present version of SVP is surveyed, along with some of its applications. The paper closes with a brief discussion of possible future applications of the method.

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Energy spectra of muonic atoms in quantum electrodynamics

EPJ Web of Conferences ◽

10.1051/epjconf/201920405007 ◽

2019 ◽

Vol 204 ◽

pp. 05007 ◽

Cited By ~ 1

Author(s):

A. E. Dorokhov ◽

A. A. Krutov ◽

A. P. Martynenko ◽

F. A. Martynenko ◽

O. S. Sukhorukova

Keyword(s):

Experimental Data ◽

Perturbation Theory ◽

Energy Spectrum ◽

Hyperfine Structure ◽

Nuclear Structure ◽

Quantum Electrodynamics ◽

Vacuum Polarization ◽

Energy Spectra ◽

Hyperfine Splittings ◽

S States

Vacuum polarization, nuclear structure and recoil, radiative corrections to the hyperfine structure of S-states in muonic ions of lithium, beryllium and boron are calculated on the basis of quasipotential method in quantum electrodynamics. We consider contributions in first and second orders of perturbation theory which have the order α5 and α6 in the energy spectrum. Total values of hyperfine splittings are obtained which can be used for a comparison with future experimental data.

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Anomalous magnetic hyperfine structure of theTh229ground-state doublet in muonic atoms

Physical Review A ◽

10.1103/physreva.94.012510 ◽

2016 ◽

Vol 94 (1) ◽

Cited By ~ 7

Author(s):

E. V. Tkalya

Keyword(s):

Hyperfine Structure ◽

Magnetic Hyperfine ◽

Muonic Atoms ◽

Magnetic Hyperfine Structure

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Variational energies for highly excited states of the helium atom

Canadian Journal of Chemistry ◽

10.1139/v78-147 ◽

1978 ◽

Vol 56 (6) ◽

pp. 884-889 ◽

Cited By ~ 1

Author(s):

Wai-Tak Ma ◽

Mary Kuriyan ◽

Huw O. Pritchard

Keyword(s):

Helium Atom ◽

Excited States ◽

Wave Functions ◽

Experimental Results ◽

New States ◽

Variational Wave Functions ◽

Variational Wave ◽

S States

The efficient correlated variational wave functions used previously to study the higher 1 sns states of helium have been extended to other states of the helium atom, 1 snp (n ≤ 23), 2pnp1P (n ≤ 25), and 2pnp3P (n ≤ 25); similar uncorrelated wave functions were used for 1snd (n ≤ 21), 2pnp1D (n ≤ 10), and 2pnp3D (n ≤ 10). Attempts to use the same techniques for the 2pnp1,3S states appear to converge variationally to the energies of the 2s21S and 2s3s3S states respectively. Comparison is made with experimental results where appropriate, and agreement is excellent except in the case of the 1snd states above n = 13.A search was made for excited states of H− in each of these configurations, but no new states were found.

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Ground-state hyperfine structure of the muonic helium atom

Physical Review A ◽

10.1103/physreva.78.032513 ◽

2008 ◽

Vol 78 (3) ◽

Cited By ~ 14

Author(s):

A. A. Krutov ◽

A. P. Martynenko

Keyword(s):

Hyperfine Structure ◽

Helium Atom ◽

Ground State

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Correlated Atomic Pair Functions by the e-ϱ-Method. I. Ground State 11S and Lowest Excited States n1S (n > 1) and n3S of Helium

Zeitschrift für Naturforschung A ◽

10.1515/zna-1999-1209 ◽

1999 ◽

Vol 54 (12) ◽

pp. 711-717

Author(s):

F. F. Seelig ◽

G. A. Becker

Keyword(s):

Integral Equation ◽

Wave Function ◽

Helium Atom ◽

Excited States ◽

Ground State ◽

Single Parent ◽

Hartree Fock ◽

Atomic Pair ◽

Electronic Wave Function ◽

S States

Abstract Some low n1S and n3S states of the helium atom are computed with the aid of the e-e method which formulates the electronic wave function of the 2 electrons ψ = e-e F, where ϱ=Z(r1+r2)–½r12 and here Z = 2. Both the differential and the integral equation for F contain a pseudopotential Ṽ instead of the true potential V that contrary to V is finite. For the ground state, F = 1 yields nearly the Hartree-Fock SCF accuracy, whereas a multinomial expansion in r1, r2 , r2 yields a relative error of about 10-7 . All integrals can be computed analytically and are derived from one single “parent” integral.

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