Skip to main content
SpringerLink
Log in

Stark broadening of hydrogenic spectral lines by two-dimensional multimode quasimonochromatic electric fields

  • Regular Article - Atomic Physics
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We studied the profile of the hydrogenic Ly-alpha line under the two-dimensional multimode quasimonochromatic electric field. We obtained the Stark profile of the main line and of the satellites in the form of the onefold integral. We demonstrated analytically and by numerical calculations that the Stark profile of the main line and of its satellites has a cusp in its center. This unusual shape of the Stark profile is a counterintuitive result.

Graphic abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All data is included in the paper.]

Notes

  1. First, as noted in Sect. 4.1.5 of book [1], the problem involving a three-dimensional multimode QEF can be always reduced to the corresponding two-dimensional problem—see the transition from Eq. (4.1.34) to Eq. (4.1.35) in book [1]. Therefore, the three-dimensional setup in paper [8] is equivalent to the corresponding two-dimensional setup. Second, Kim and Wilhelm [8] obtained zero quasienergies for any ratio of the components of the multimode QEF, including the case where one of the QEF components is much smaller than the other one. Therefore, for proving that the result from paper [8] is erroneous, it was sufficient to show that the quasienergies are nonzeros for the case where one of the QEF components is much smaller than the other one.

  2. Here are some details. The argument f(w) of the exponential in Eq. (9) is: f(w) \(=\) - w\(^{\mathrm {2}}\) - [2D/(abw)]\(^{\mathrm {2}} \quad =\) - w\(^{\mathrm {2}}\) - w\(_{\mathrm {0}}^{\mathrm {4}}\)/w\(^{\mathrm {2}}\). We seek w \(=\) w\(_{\mathrm {0}}\)(1 \(+\) c), where \(| \mathrm{c} |< < 1\). This substitution, upon expanding up to the terms \(\sim \mathrm{c}^{\mathrm {2}}\), yields: f = - w\(_{\mathrm {0}}^{\mathrm {2}}\) - 4c\(^{\mathrm {2}}\)w\(_{\mathrm {0}}^{\mathrm {2}}\). Since c \(=\) (w - w\(_{\mathrm {0}})\)/w\(_{\mathrm {0}}\) and \(\mathrm{w}_{\mathrm {0}} \quad = [2 | D | /\mathrm{(ab)}]^{\mathrm {1/2}}\), we obtain f for expression (13).

References

  1. E. Oks, Plasma Spectroscopy: The Influence of Microwave and Laser Fields, Springer Series on Atoms and Plasmas, vol. 9 (Springer, New York), 1995)

    Book  Google Scholar 

  2. E. Oks, E. Dalimier, A. Faenov, O. Renner, Review of the phenomenon of dips in spectral lines emitted from plasmas and their applications. J. Phys. Conf. Ser. 548, 012030 (2014)

    Article  Google Scholar 

  3. E. Dalimier, E. Oks, O. Renner, Review of langmuir-wave-caused dips and charge-exchange-caused dips in spectral lines from plasmas and their applications. Atoms 2, 178 (2014)

    Article  ADS  Google Scholar 

  4. E. Dalimier, T.A. Pikuz, P. Angelo, Atoms 6, 45 (2018)

    Article  ADS  Google Scholar 

  5. E.V. Lifshitz, Sov. Phys. JETP 26, 570 (1968)

    ADS  Google Scholar 

  6. Ja.B. Zel’dovich, Sov. Phys. JETP 24, 1006 (1967)

  7. V.I. Ritus, Sov. Phys. JETP 24, 1041 (1967)

    ADS  Google Scholar 

  8. S.H. Kim, H.E. Wilhelm, J. Appl. Phys. 44, 802 (1973)

    Article  ADS  Google Scholar 

  9. E. Oks, Diagnostics of Laboratory and Astrophysical Plasmas Using Spectral Lineshapes of One-, Two-, and Three-Electron Systems (World Scientific: Singapore) Chapter 5 (2017)

Download references

Author information

Authors and Affiliations

  1. Physics Department, Auburn University, 380 Duncan Drive, Auburn, AL, 36849, USA

    E. Oks

Authors
  1. E. Oks
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Oks.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Oks, E. Stark broadening of hydrogenic spectral lines by two-dimensional multimode quasimonochromatic electric fields. Eur. Phys. J. D 75, 185 (2021). https://doi.org/10.1140/epjd/s10053-021-00194-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-021-00194-5

Search

Navigation