Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-27T22:18:24.288Z Has data issue: false hasContentIssue false
  • English
  • Français

Calculation of Resonance S-Matrix Poles by Means of Analytic Continuation in the Coupling Constant

Published online by Cambridge University Press:  08 March 2017

Jiří Horáček  and
Lukáš Pichl
Jiří Horáček*
Affiliation:
Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic
Lukáš Pichl*
Affiliation:
International Christian University, 3-10-2 Osawa, Mitaka, Tokyo 181-8585, Japan
*
*Corresponding author. Email addresses:[email protected] (J. Horáček), [email protected] (L. Pichl)
*Corresponding author. Email addresses:[email protected] (J. Horáček), [email protected] (L. Pichl)
Get access

Abstract

The method of analytic continuation in the coupling constant in combination with the use of statistical Padé approximation is applied to the determination of complex S-matrix poles, i.e. to the determination of resonance energy and widths. These parameters are of vital importance in many physical, chemical and biological processes. It is shown that an alternative to the method of analytic continuation in the coupling constant exists which in principle makes it possible to locate several resonances at once, in contrast to the original method which yields parameters of only one resonance. In addition the new approach appears to be less sensitive to the choice of the perturbation interaction used for the analytical continuation than the original method. In this paper both approaches are compared and tested for model analytic separable potential. It is shown that the new variant of the method of analytic continuation in the coupling constant is more robust and efficient than the original method and yields reasonable results even for data of limited accuracy.

Keywords

Analytical continuation in the coupling constantresonance parameterscomplex energystatistical Padé approximation
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 4 , April 2017 , pp. 1154 - 1172
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Kukulin, V. I., Krasnopolsky, V. M., and Horáček, J., Theory of resonances: Principles and Applications. Kluwer Academic Publishers, Dordrecht/Boston/London 1988.Google Scholar
[2] Kreckel, H., Bruhns, H., Čížek, M., Glover, S.C.O., Miller, K.A., Urbain, X., Savin, D.W., Science 328 (2010) 69.Google Scholar
[3] Sanche, L., Eur. Phys. J. D 35 (2005) 367–390.Google Scholar
[4] Golser, R., Gnaser, H., Kutschera, W., Priller, A., Steier, P., Wallner, A., Čížek, M., Horáček, J., and Domcke, W., Phys. Rev. Letters 94 (2005) 223003.Google Scholar
[5] Taylor, H. S., Hazi, A. U., Phys. Rev. A 14 (1976) 2071–2074.Google Scholar
[6] Hazi, A. U., Rescigno, T. N., and Kurilla, M., Phys. Rev. A 23 (1981) 1089.CrossRefGoogle Scholar
[7] Hazi, A. U., Taylor, H. S., Phys. Rev. A 1 (1970) 1109–1120.Google Scholar
[8] Moiseyev, N., Physics Reports 302 (1998) 211–293.Google Scholar
[9] Donelly, R. A., Int. J. Quantum. Chem. Symp. 16 (1982) 653.Google Scholar
[10] Riss, U. V., and Meyer, H.-D., J. Phys. B: At. Mol. Opt. Phys. 26 (1993) 4503.Google Scholar
[11] Feuerbacher, S., Sommerfeld, T., Santra, R., and Cederbaum, L. S., J. Chem. Phys. 118 (2003) 6188–6199.Google Scholar
[12] Kukulin, V. I., and Krasnopolsky, V. M., J. Phys. A: Math. Gen. 10 (1977) L33-37.Google Scholar
[13] Krasnopolsky, V. M., and Kukulin, V. I., Phys. Lett. A 69 (1978) 251–254.Google Scholar
[14] Tanaka, N., Suzuki, Y., Varga, K., Phys. Rev. C 56 (1997) 562–565.Google Scholar
[15] Aoyama, S., Phys. Rev. Lett. 89 (2002) 052501.Google Scholar
[16] Funaki, Y., Horiuchi, H., Tohsaki, A., Progress of Theor. Phys. 115 (2006) 115–127.Google Scholar
[17] Si-Chun, Yang, Jie, Meng, and Shan-Gui, Zhou, Chin. Phys. Lett. 18 (2001) 196–198.Google Scholar
[18] Cattapan, G., and Maglione, E., Phys. Rev. C 61 (2000) 067301.Google Scholar
[19] Horáček, J., Mach, P., J. Urban, Phys. Rev. A 82 (2010) 032713.Google Scholar
[20] Papp, P., Matejčik, Š., Mach, P., Urban, J., Paidarová, I., and Horáček, J., Chem. Phys. 418 (2013) 067301.Google Scholar
[21] Horáček, J., Paidarová, I., and Čurík, R., J. Phys. Chem. A 118, 33 (2014) 6536–6541.Google Scholar
[22] Horáček, J., Paidarová, I., and Čurík, R., J. Chem. Phys. 143 (2015) 184102.Google Scholar
[23] Nestmann, B. and Peyerimhoff, S. D., J. Phys. B:At. Mol. Phys. 18 (1985) 615–626.Google Scholar
[24] Mongan, T. R., Phys. Rev. 175 (1968) 1260.CrossRefGoogle Scholar
[25] Klarsfeld, S., Martorell, J., Oteo, J. A., Nishimura, N., and Sprung, D. W. L., Nucl. Phys. A 456 (1986) 373.Google Scholar
[26] Maghari, A., and Tahmasbi, N., J. Phys. A: Math. Gen. 38 (2005) 4469; Tahmasbi, N., and Maghari, A., Physica A 382 (2007) 537.Google Scholar
[27] Siegert, A. J. F., Phys. Rev. 56 (1939) 750.Google Scholar
[28] Kok, L. P., and van Haeringen, H., Annals of Physics 131 (1981) 426–450.Google Scholar
[29] Baker, G. A., and Graves-Morris, P., Padé approximants. Addison-Wesley Publishing Co., 1981.Google Scholar
[30] Krasnopolsky, V. M., Kukulin, V. I. and Horáček, J.: Czech. J. Phys. B 35 (1985) 805–819.Google Scholar
[31] Krasnopolsky, V. M., Kukulin, V. I. and Horáček, J.: Czech. J. Phys. B 40 (1990) 945–1064.Google Scholar
[32] Horáček, J., Zejda, L. and Queen, N. M.: Comp. Phys. Comm. 74 (1993) 187. Comparative Study of Methods for the Construction of Padé Approximants of Type III.Google Scholar
[33] Rakityanski, S. A., Sofianos, S. A., and Elander, N., J. Phys. A: Math. Theor. 40 (2007) 14857–14869.Google Scholar
[34] Krasnopolsky, V. M., Kukulin, V. I. and Horáček, J.: Czech. J. Phys. B 39 (1989) 593–613.Google Scholar
[35] Krasnopolsky, V.M., Kukulin, V. I., Kuznetsova, E. V., Horáček, J., and Queen, N.M., Phys. Rev. C 43 (1991) 822–834.Google Scholar
[36] Chao, J. S.-Y., Falcetta, M. F., Jordan, K. D., J. Chem. Phys. 93 (1990) 1125–1135.Google Scholar
[37] Krylstedt, P., Rittby, M., Elander, N., and Brändas, E., J. Phys. B: At. Mol. Opt. Phys. 20 (1987) 1295–1327.Google Scholar
[38] Rittby, M., Elander, N. and Brändas, E., Lecture Notes in Physics 325 (1989) 129–151.Google Scholar
[39] Simon, B., Ann. Math. 97 (1973) 247–274.Google Scholar
[40] Balslev, E. and Combes, J. M., Commun. Math. Phys. 22 (1971) 280–294.CrossRefGoogle Scholar
[41] Klaus, M. and Simon, B., Annals of Physics 13 (1980) 251–281.Google Scholar
[42] Hehenberger, M., McIntosh, H. and Brändas, E., Phys. Rev. A 10 (1974) 1494–1506.Google Scholar
[43] Hehenberger, M., Froelich, P. and Brändas, , J. Chem. Phys. 65 (1976) 4571.Google Scholar
[44] Čurík, R., Paidarová, I. and Horáček, Jiří, Eur. Phys. J. D 70 (2016) 146.Google Scholar