ABSTRACT
In expression (7.12) and subsequent ones, the coefficients e and m appear. These designations were of course chosen by analogy with the quantum-mechanical expression for the Hamiltonian of a particle with chargee and mass m. Our IJ!-function is, however, not the wavefunction of electrons. The coefficient m can be taken arbitrarily [29] because the IJ!-function is not an observed quantity: an observed quantity is the penetration depth 80 of a weak magnetic field (see equations (7.12), (7.13), and (7.16)):
(7.17)
Since the IJ!-theory in a weak field (7.11) transforms to the Londons theory (though, a number of problems cannot be stated in Londons theory even in this case), the penetration depth 80 is frequently called the London penetration depth and is denoted by 8L orAL· If we assume [29] e and m to correspond to a free electron (eo= 4.8 x 10-10 CGS, m0 = 9.1 x 10-28 g), then I1J!ool 2 = n 8 , where n8 is the 'superconducting electron' concentration thus defined. In fact, one can choose any arbitrary value of m [29, 37] which will only affect the normalization of the observed quantity I1J!ool 2 • In the literature, m = 2m0 occasionally occurs, which corresponds to the mass of a 'pair' of two electrons. As to the chargee in equation (7.12) and subsequent expressions, it is an observed quantity (see later). It seemed to me from the very beginning that one should regard the chargee in equation (7.12) as a certain 'effective charge' eeff and take it as a free parameter. But Landau objected and, in paper [29], it is stated as a compromise that "there is no reason to assume the charge e to be other than the electron charge" . Running ahead I shall note that I still went on thinking of the question of the role of the charge e = eeff as open and pointed out the possibility of clarifying the situation by comparing the theory with experiment (see [14, p 107]) . The point is that the essential parameter involved in the IJ!-theory is the quantity
(7.18)
In paper [29], we set e = e0 and could, therefore, determine re from experimental data on Hem and 80 . At the same time, the parameter re enters the expressions for the surface energy O"ns, for the penetration depth in a strong field (H ~ Hem) and the expressions for superheating and su-
percooling limits. Using the approximate data of measurements available at the time, I came to the conclusion [55] (this paper was submitted for publication on 12 August, 1954) that the chargee= eeff in equation (7.18) is two to three times greater than e0 . When I discussed this result with Landau, he put forward a serious objection to the possibility of introducing an effective charge (he had apparently had this argument in mind before, when we discussed paper [29] but did not then advance it). Specifically, the effective charge might depend on the composition of a substance, its temperature and pressure and, therefore, might appear to be a function of coordinates. But, in that case, the gradient invariance of the theory would be broken, which is inadmissible. I could not find arguments against this remark and, with the consent of Landau, I included it in paper [55]. The explanation seems now to be quite simple. No, an effective charge eeff, which might appear to be coordinate-dependent, should not have been introduced. But it might well be supposed that, say, eeff = 2e0 . And this was exactly the case but it became obvious only after the creation of BCS theory [18] in 1957 and the appearance of the paper by Gorkov [31] who showed that the \11-theory near Tc follows from the BCS theory. More precisely, the \11-theory near Tc is certainly wider than the BCS theory in the sense that it is independent of some particular assumptions used in the BCS theory. But this is a different subject. The formation of pairs with charge 2eo is a very general phenomenon, too. I have already emphasized that the idea of pairing and, what is important, the realistic character of such pairing was far from trivial.
