Orateur
Prof.
Edward A. G. Armour
(School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK)
Description
The field generated by a fixed proton and antiproton a distance R apart is a particular example of a dipole field. The existence or otherwise of bound states of an electron (or a positron) in such a field was originally studied by Fermi and Teller and Wightman [1-3] in the late forties. They showed that if R > 0.639 a_0, a bound state of the system existed but if R < 0.639 a_0, no bound states existed. This result was confirmed in the mid-sixties by several authors, including Mittleman and Myerscough [4], Coulson and Walmsley [5] and Byers Brown and Roberts [6]. Crawford [7] obtained the interesting result that if R > 0.639 a_0, a countable infinity of bound states exists.
It is of interest to consider what happens if an electron and a positron are both present in the dipole field. This system corresponds to H + Hbar with the positions of the nuclei fixed, as in the Born-Oppenheimer approximation. Armour et al. [8] were able to show that an upper bound to the R value below which no bound state of this system exists is 0.8 a_0. They did this using the Rayleigh-Ritz variational method and a basis set in prolate spheroidal coordinates similar to Kolos et al. [9], but with the addition of a function to represent very weakly bound positronium. More recently, Strasburger [10] has reduced this upper bound to 0.744 a_0, using a basis set made up of explicitly correlated Gaussian functions.
As far as I am aware, no lower bound has been obtained for the above R value. A question of interest is whether a bound state of the the system containing the electron and the positron exists for R < 0.639 a_0, the critical value for each particle on its own in the presence of the nuclei.
.................
More details in the latex-generated version.
...............
If time permits, I will describe results of a preliminary investigation of the increase in the mass of the positron that would be necessary for it to form a bound state with a hydrogen molecule. The aim is to simulate conditions under which very large positron annihilation rates have been observed in low-energy positron scattering by some larger molecules. These very high rates are thought to be due to positron capture into vibrational Feshbach resonances of infrared-active modes [13].
References
[1] E. Fermi and E. Teller, Phys. Rev. 72, 399 (1947).
[2] A. J. Wightman, Phys. Rev. 77, 521 (1950).
[3] J. E. Turner, J. Am. Phys. Soc. 45, 758 (1977).
[4] M. H. Mittleman and V. P. Myerscough, Phys. Letts. 23, 545 (1966).
[5] C. A. Coulson and M. Walmsley, Proc. Phys. Soc. (London) 91, 31 (1967).
[6] W. Byers-Brown and R. E. Roberts, J. Chem. Phys. 46, 2006 (1967).
[7] O. H. Crawford, Proc. Phys. Soc. (London) 91, 279 (1967).
[8] E. A. G. Armour, V. Zeman and J. M. Carr, J. Phys. B 31, L679 (1998).
[9] W. Kolos, D. L. Morgan, D. M. Schrader and L. Wolniewicz, Phys. Rev. A 11, 1792 (1975).
[10] K. Strasburger, J. Phys. B 35, L435 (2002).
[11] R. F. Wallis, R. Herman and H. W. Milnes, J. Molec. Spectroscopy 4, 51 (1960).
[12] S. Jonsell, Private communication, 2005.
[13] G. F. Gribakin and C. M. R. Lee, Phys. Rev. Lett. 97, 193201 (2006).
Auteur principal
Prof.
Edward A. G. Armour
(School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK)
