Benchmark Calculation of Radial Expectation Value $$\varvec{\langle r^{-2} \rangle }$$ ⟨ r - 2 ⟩ for Confined Hydrogen-Like Atoms and Isotropic Harmonic Oscillators

Benchmark Calculation of Radial Expectation Value $$\varvec{\langle r^{-2} \rangle }$$ ⟨... Spatially confined atoms have been extensively investigated to model atomic systems in extreme pressures. For the simplest hydrogen-like atoms and isotropic harmonic oscillators, numerous physical quantities have been established with very high accuracy. However, the expectation value of $$\langle r^{-2} \rangle $$ ⟨ r - 2 ⟩ which is of practical importance in many applications has significant discrepancies among calculations by different methods. In this work we employed the basis expansion method with cut-off Slater-type orbitals to investigate these two confined systems. Accurate values for several low-lying bound states were obtained by carefully examining the convergence with respect to the size of basis. A scaling law for $$\langle r^{n} \rangle $$ ⟨ r n ⟩ was derived and it is used to verify the accuracy of numerical results. Comparison with other calculations show that the present results establish benchmark values for this quantity, which may be useful in future studies. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Few-Body Systems Springer Journals

Benchmark Calculation of Radial Expectation Value $$\varvec{\langle r^{-2} \rangle }$$ ⟨ r - 2 ⟩ for Confined Hydrogen-Like Atoms and Isotropic Harmonic Oscillators

Loading next page...
 
/lp/springer_journal/benchmark-calculation-of-radial-expectation-value-varvec-langle-r-2-U2bPFt1msj
Publisher
Springer Vienna
Copyright
Copyright © 2017 by Springer-Verlag GmbH Austria
Subject
Physics; Particle and Nuclear Physics; Nuclear Physics, Heavy Ions, Hadrons; Atomic, Molecular, Optical and Plasma Physics
ISSN
0177-7963
eISSN
1432-5411
D.O.I.
10.1007/s00601-017-1314-2
Publisher site
See Article on Publisher Site

Abstract

Spatially confined atoms have been extensively investigated to model atomic systems in extreme pressures. For the simplest hydrogen-like atoms and isotropic harmonic oscillators, numerous physical quantities have been established with very high accuracy. However, the expectation value of $$\langle r^{-2} \rangle $$ ⟨ r - 2 ⟩ which is of practical importance in many applications has significant discrepancies among calculations by different methods. In this work we employed the basis expansion method with cut-off Slater-type orbitals to investigate these two confined systems. Accurate values for several low-lying bound states were obtained by carefully examining the convergence with respect to the size of basis. A scaling law for $$\langle r^{n} \rangle $$ ⟨ r n ⟩ was derived and it is used to verify the accuracy of numerical results. Comparison with other calculations show that the present results establish benchmark values for this quantity, which may be useful in future studies.

Journal

Few-Body SystemsSpringer Journals

Published: Aug 8, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off