PL EN


Preferences help
enabled [disable] Abstract
Number of results
Journal
2014 | 12 | 4 | 221-232
Article title

A relativistic wave equation with a local kinetic operator and an energy-dependent effective interaction for the study of hadronic systems

Content
Title variants
Languages of publication
EN
Abstracts
EN
We study a fully relativistic, two-body, quadratic wave equation for equal mass interacting particles. With this equation the difficulties related to the use of the square roots in the kinetic energy operators are avoided. An energy-dependent effective interaction, also containing quadratic potential operators, is introduced. For pedagogical reasons, it is previously shown that a similar procedure can be also applied to the well-known case of a one-particle Dirac equation. The relationships of our model with other relativistic approaches are briefly discussed. We show that it is possible to write our equation in a covariant form in any reference frame. A generalization is performed to the case of two particles with different mass. We consider some cases of potentials for which analytic solutions can be obtained. We also study a general numerical procedure for solving our equation taking into account the energy-dependent character of the effective interaction. Hadronic physics represents the most relevant field of application of the present model. For this reason we perform, as an example, specific calculations to study the charmonium spectrum. The results show that the adopted equation is able to reproduce with good accuracy the experimental data.
Publisher

Journal
Year
Volume
12
Issue
4
Pages
221-232
Physical description
Dates
published
1 - 4 - 2014
online
23 - 4 - 2014
Contributors
References
  • [1] U. D. Jentschura, Eur. Phys. J. D 61, 7 (2011) http://dx.doi.org/10.1140/epjd/e2010-10414-6[Crossref]
  • [2] N. G. Kelkar, F. Garcia Daza, M. Nowakowski, Nucl. Phys. B 864, 382 (2012) http://dx.doi.org/10.1016/j.nuclphysb.2012.06.015[Crossref]
  • [3] P. M. A. Dirac, Rev. Mod. Phys. 21, 392 (1949) http://dx.doi.org/10.1103/RevModPhys.21.392[Crossref]
  • [4] R. Blankenbecler, R. Sugar, Phys. Rev. 142, 1051 (1966) http://dx.doi.org/10.1103/PhysRev.142.1051[Crossref]
  • [5] L. Cao, Y.-Ch. Yang, H. Chen, Few-Body Syst. 53, 327 (2012) http://dx.doi.org/10.1007/s00601-012-0478-z[Crossref]
  • [6] S. F. Radford, W. W. Repko, Phys. Rev. D 75, 074031 (2007) http://dx.doi.org/10.1103/PhysRevD.75.074031[Crossref]
  • [7] D. Ebert, R. N. Faustov, V. O. Galkin, Eur. Phys. J. C66, 197 (2010) http://dx.doi.org/10.1140/epjc/s10052-010-1233-6[Crossref]
  • [8] M. De Sanctis, P. Quintero, Eur. Phys. J. A 46, 213 (2010) http://dx.doi.org/10.1140/epja/i2010-11032-y[Crossref]
  • [9] G. Y. Leung, N. Mobed, Xiquan Zhu, Rhada Gourishankar, F. C. Kanna, Phys. Rev. C 45, 959 (1992) http://dx.doi.org/10.1103/PhysRevC.45.959[Crossref]
  • [10] F. Gross, Phys. Rev. C 26, 2203 (1982) http://dx.doi.org/10.1103/PhysRevC.26.2203[Crossref]
  • [11] V. B. Mandelzweig, S. J. Wallace, Phys. Lett. B 197, 469 (1997) http://dx.doi.org/10.1016/0370-2693(87)91035-5[Crossref]
  • [12] C. Itzykson, J. B. Zuber, Quantum Field Theory (Mc Graw-Hill, New York, 1988) chapt. X
  • [13] D. R. Phillips, S. J. Wallace, Nucl. Phys A 503, 673 (1989) http://dx.doi.org/10.1016/0375-9474(89)90435-1[Crossref]
  • [14] M. De Sanctis, Eur. Phys. J. A 33, 71 (2007) http://dx.doi.org/10.1140/epja/i2007-10424-4[Crossref]
  • [15] H. W. Crater, J. Schiermeyer, Phys. Rev. D82, 094020 (2010)
  • [16] J. Ferretti, A. Vassallo, E. Santopinto, Phys. Rev. C 83, 065204 (2011) http://dx.doi.org/10.1103/PhysRevC.83.065204[Crossref]
  • [17] M. De Sanctis, J. Ferretti, E. Santopinto, A. Vassallo, Phys. Rev. C 84, 055201 (2011) http://dx.doi.org/10.1103/PhysRevC.84.055201[Crossref]
  • [18] D. Ebert, R. N. Faustov, V. O. Galkin, Phys. Rev. D84, 014025 (2011)
  • [19] A. D. Alhaidari, Int. J. Mod. Phys. A 18, 4955 (2003) http://dx.doi.org/10.1142/S0217751X03015751[Crossref]
  • [20] M. Hamzavi, S. M. Ikhdair, B. I. Ita, Phys. Scr. 85, 045009 (2012) http://dx.doi.org/10.1088/0031-8949/85/04/045009[Crossref]
  • [21] A. S. de Castro, P. Alberto, arXiv:1207.3324v1 [quantph]
  • [22] S. M. Ikhdair, Cent. Eur. J. Phys. 10, 361 (2012) http://dx.doi.org/10.2478/s11534-011-0121-5[Crossref]
  • [23] L. D. Landau, E. M. Lifshits, Quantum Mechanics (Non-relativistic Theory), Vol. 3, 3rd edition (Elsevier Butterworth-Heinemann, Oxford, 1977), chapt. V, par. 36, Problem 3
  • [24] W. Greiner, Relativistic quantum mechanics: wave equations, 3rd edition (Springer-Verlag, Berlin Heidelberg New York, 2000), Exercise 1.11 http://dx.doi.org/10.1007/978-3-662-04275-5[Crossref]
  • [25] J. L. Rosner, J. Phys. G: Nucl. Part. Phys. 34, S127 (2007) http://dx.doi.org/10.1088/0954-3899/34/7/S07[Crossref]
  • [26] J. Beringer et al. (Particle Data Group), Phys. Rev. D 86, 010001 (2012) http://dx.doi.org/10.1103/PhysRevD.86.010001[Crossref]
  • [27] M. De Sanctis, Electr. J. Theor. Phys. 7, 137 (2010)
  • [28] M. De Sanctis, P. Quintero, Eur. Phys. J. A 39, 145 (2009) http://dx.doi.org/10.1140/epja/i2008-10720-5[Crossref]
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-014-0444-0
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.