Volume 251, number 3 PHYSICS LETTERS B 22 November 1990 On the nuclear Meissner effect J.L. Egido Departamento de Fisica Te6rica, Universidad Aut6noma de Madrid, 17-28049 Madrid, Spain and P. Ring Physikdepartment der Technischen Universit?it Mfinchen, W-8046 Garching, FRG Received 29 June 1990; revised manuscript received 10 September 1990 We briefly comment on the nuclear Meissner effect in view of a recent criticism of Sugawara-Tanabe et al. We show that the criticism is unfounded. On the contrary we argue, that the Sugawara-Tanabe interpretation of the effect is misleading. In a recent letter by Sugawara-Tanabe and Tanabe [ 1 ] it is argued that in our publications on particle number projection [2,3 ] we have neglected a phase in the evaluation of certain overlap matrix elements and that, due to this fact their conclusion on the nu- clear Meissner effect is different from ours. The purpose of this letter is twofold. First, to show that the expression in ref. [ 1 ] for the overlap of two Hartree-Fock-Bogoliubov wavefunctions rotated against each other in gauge space reduces to ours after a simple manipulation, i.e. no phase has been ne- glected in the calculations of ref. [ 3 ] and second to indicate that the definition of the pairing energy in ref. [ 1 ] deviates from the usual expression found in the scientific literature. This leads in ref. [ 1 ] to a misinterpretation of the results of the number pro- jected calculation. The overlap in question, which is needed for the evaluation of number projected matrix elements is given by x~= ( q~lexp[i(nl/L ) (~-N) ]1 ~ ) =exp[ -i(nl/L)N] (~1 ~t) • (1) Let the Hartree-Fock-Bogoliubov function I ~b) be defined by the quasiparticle operators tXk, i.e. I ~l 9 ) ~ Ot l . . . OtN I - ) , (2) with a ~ = E UmkC+m "~ VmkCm, (3) m where c,,, c~ are particle operators. The wave function [ ~t) rotated in gauge space is then given by I~t) ~exp[i(nl/L)N]lq)) =c~, ...c~u [ - ), (4) with a ~ ~- E UmkC+m "~ ~'mkCm' (5) m and U=exp[i(nl/L)]U, ~'=exp[-iOd/L)]V. (6) By means of the Bloch-Messiah theorem [4] we can express the wave functions (2) and (4) in the canon- ical basis Iq~)= I-I (uk+vka~a~)l--) (7) k>O and I~)= l-I {uk+vkexp[i(2nl/L)]a~a~}l--). k>O (8) 0370-2693/90/$ 03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland) 3 31