Abstract
Relationships between the coupling constant and the binding energy of threshold bound states are obtained in a simple manner from an iterative algorithm for solving the eigenvalue problem. The absence of threshold bound states in higher dimensions can be easily understood.
Similar content being viewed by others
References
M. Aubert-Frecon et al., Chem. Phys. Lett. 405, 422 (2005).
A.M. Frolov, A.J. Thakker, Phys. Rev. A 46, 4418 (1992).
Y.D. Liu, P.-N. Roy, Chem. Phys. Lett. 121, 6282 (2004).
I. Tanihata, Nucl. Phys. A 520, c411 (1990).
I. Tanihata, J. Phys. G 22, 157 (1996).
B. Jonson, Nucl. Phys. A 690, 151c (2001).
B. Jonson, Nucl. Phys. A 631, 234 (1998).
P.G. Hansen, Nucl. Phys. A 649, 355c (1999).
B.A. Brown, P.G. Hansen, Phys. Lett. B 381, 391 (1996).
RNBT Collaboration, Nucl. Phys. A 616, 426c (1996).
J. Dobaczewski, W. Nazarewicz, Philos. Trans. R. Soc. London, Ser. A 356, 2007 (1998).
E. Hiyama, Few-Body Syst. 34, 79 (2004).
B.M. Young, PhD Thesis, Michigan State University (1994).
I. Hamamoto, Phys. Rev. C 72, 024301 (2005).
B. Simon, Ann. Phys. (N.Y.) 97, 279 (1976).
S. Flügge, Practical Quantum Mechanics, Vol. 1 (Springer-Verlag, Berlin, 1970).
M. Znojil, J. Phys. A 20, 1751 (1987).
N. Dunford, J. Schwartz, Linear Operators, Part II: Spectral Theory (Interscience, New York, 1963).
I.C. Gohberg, M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space, Transl. Math. Monogr., Vol. 18 (American Mathematical Society, 1969).
G. Gat, B. Rosenstein, Phys. Rev. Lett. 70, 5 (1993).
H. Collins, H. Georgi, D. Zeltser, A perturbative expansion for weakly bound states (1995) URL http://www.citebase.org/abstract?id=oai:arXiv.org:hep-ph/9510%398.
D. Waxman, J. Phys. A 31, 1329 (1998).
W.A. Berger, H.G. Miller, J. Phys. A 39, 14075 (2006).
L.I. Schiff, Quantum Mechanics, third edition (McGraw-Hill, New York, 1955).
M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
C. Itzykson, J. Drouffe, Statistical Field Theory, Vol. 1 (Cambridge University Press, Cambridge, 1989).
J. Dobaczewski, W. Nazarewicz, T.R. Werner, J.F. Berger, C.R. Chinn, J. Dechargé, Phys. Rev. C 53, 2809 (1996).
N. Sandulescu, N.V. Giai, R.J. Liotta, Phys. Rev. C. 61, 061301(R) (2000).
H. Terasaki, H. Flocard, P.H. Heenen, P. Bonche, Nucl. Phys. A 621, 706 (1997).
A.T. Kruppa, P.H. Heenen, H. Flocard, R.J. Liotta, Phys. Rev. Lett. 79, 2217 (1997).
N. Michel, W. Nazarewicz, M. Ploszajczak, K. Benneceur, Phys. Rev. Lett. 89, 042502 (2002).
M. Stoitstov, N. Michel, K. Matsuyanagi, Phys. Rev. C 77, 054301 (2008).
J. Dobaczewski, N. Michel, W. Nazarewicz, M. Ploszajczak, J. Rotureau, Prog. Part. Nucl. Phys. 59, 432 (2007).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by W. Nazarewicz
Rights and permissions
About this article
Cite this article
Berger, W.A., Miller, H.G. & Waxman, D. Threshold bound states. Eur. Phys. J. A 37, 357–360 (2008). https://doi.org/10.1140/epja/i2008-10636-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epja/i2008-10636-0