Skip to main content
Log in

Some universal properties of density matrices for finite nuclei (bound systems)

  • Proceedings of the LXV International Conference “Nucleus 2015: New Horizons in Nuclear Physics, Nuclear Engineering, Femto- and Nanotechnologies” (LXV International Conference on Nuclear Spectroscopy and the Structure of Atomic Nuclei)
  • Published:
Bulletin of the Russian Academy of Sciences: Physics Aims and scope

Abstract

The properties of one-body and two-body density matrices of a nucleus as a nonrelativistic system are studied. Unlike the usual procedure applied in the theory of infinite systems, for a nucleus of A nucleons these quantities are determined as the expectation values of A-body multiplicative operators that depend on the relative coordinates and momenta (Jacobi variables) and affect the intrinsic wave functions. The translational invariance of these operators is thus ensured. An algebraic technique based on the Cartesian representation is developed for handling such operators. Within this technique, the coordinate and momentum operators are linear combinations of production and annihilation operators \(\hat \vec a^ + \) and \(\hat \vec a\) with commutation relations for bosons (oscillators). Each of the multiplicative operators reduces to the normally ordered product of two exponents, one of which depends on set \(\left\{ {\hat \vec a^ + } \right\}\) only and is located to the left of the second, which depends on \(\left\{ {\hat \vec a} \right\}\) only. This procedure offers a new view of the origin of the so-called Tassie–Barker factors and other model-independent results. In addition, the proposed method yields a fair description of the available experimental data and can easily be extended to investigate the role of short-range nucleon-nucleon correlations within these translationally invariant calculations of nucleon density and momentum distributions in light nuclei.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Shebeko, A., Papakonstantinou, P., and Mavrommatis, E., Eur. Phys. J. A, 2006, vol. 27, p. 143.

    Article  ADS  Google Scholar 

  2. Shebeko, A.V., Grigorov, P.A., and Iurasov, V.S., Eur. Phys. J. A, 2012, vol. 48, p. 153.

    Article  ADS  Google Scholar 

  3. Ernst, D.J., Shakin, C.M., and Thaler, R.M., Phys. Rev. C, 1973, vol. 7, p. 925.

    Article  ADS  Google Scholar 

  4. Antonov, A., Hodgson, P., and Petkov, I., Nucleon Momentum and Density Distributions in Nuclei, Clarendon, 1988.

    Google Scholar 

  5. Iwamoto, F. and Yamada, M., Prog. Theor. Phys., 1957, vol. 17, p. 543.

    Article  ADS  MathSciNet  Google Scholar 

  6. Frosch, R.F., et al., Phys. Rev., 1967, vol. 160, p. 874; Arnold, R.G., et al., Phys. Rev. Lett., 1978, vol. 40, p. 1429.

    Article  ADS  Google Scholar 

  7. Sick, I. and McCarthy, J.S., Nucl. Phys. A, 1970, vol. 150, p. 631.

    Article  ADS  Google Scholar 

  8. De Vries, H., De Jager, C.W., and De Vries, C., At. Data Nucl. Data Tables, 1987, vol. 36, p. 495.

    Article  ADS  Google Scholar 

  9. Cioft degli Atti, C., Pace, E., and Salme, G., Phys. Rev. C, 1991, vol. 43, p. 1155.

    Article  ADS  Google Scholar 

  10. Pieper, S.C., Wiringa, R.B., and Pandharipande, V.R., Phys. Rev. C, 1992, vol. 46, p. 1741.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. V. Shebeko.

Additional information

Original Russian Text © A.V. Shebeko, 2016, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2016, Vol. 80, No. 5, pp. 620–626.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shebeko, A.V. Some universal properties of density matrices for finite nuclei (bound systems). Bull. Russ. Acad. Sci. Phys. 80, 559–565 (2016). https://doi.org/10.3103/S106287381603028X

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S106287381603028X

Navigation