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46. The interaction in the BCS theory of superconductivity
LIQUID HELIUM
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45. V o r t i c i t y i n s u p e r f l o w . S. M. BHAGAT and K. MENDELSSOHN. Clarendon Laboratory, Oxford. Isothermal flow of liquid He II through a capillary of 276 ~ diameter and 150 cm length has been measured. The liquid was first passed through a vycor glass filter in which the flow was a l w a y s subcritical. For low pressure heads the flow through the capillary was completely pressure independent and the critical velocity changed with temperature somewhat like ps/p. At higher pressures, dissipation was observed which, once it had set in, was maintained to low pressures. Shootening of the capillary to 17.6 cm resulted in much ( ~ 5 times) smaller, pressure dependent velocities. Moreover, the pressure dependency of the flow rate became very complicated, fil;st decreasing with falling A p and then suddenly increasing again. A sensative explanaton of the observed phenomena on the basis of vortex formation is suggested.
II. S U P E R C O N D U C T I V I T Y 46. The interaction in the BCS theory of superconductivity. JAMESC. SWIHART. IBM Research Laboratory, Poughkeepsie, New York, U.S.A. If in the BCS interaction 1), e~ and ek" are not set equal to zero, the ground state wave function can be determined without limiting the interaction to a region 2(~a~x)av wide at the Fermi surface. A variation of the total energy with respect to h~ leads to an integral equation for s0(k) which is now a function of k. The e0 thus determined minimizes the energy as long as e0 ~ 0. For k such t h a t the integral equation gives e0 < 0, the energy is minimized by hk('l -- h~) = 0. The strength of the interaction and the size of the region in k-space over which it is effective are n o t independent quantities but both are determined by the critical temperature. 1) Bardeen, Cooper and Schrieffer, Phys. Rev. 108 (1957) 1175. 47. A t h e o r y of s u p e r c o n d u c t i v i t y * ) . RYOICHI KIKUCHI. D e p a r t m e n t of Physics, W a y n e State University, Detroit, Michigan, U.S.A. Applying F e y n m a n's path integral technique to the system of electrons and phonons, one can first integrate over phonon coordinates to derive virtual interaction among electrons. Then if the electron-phonon interaction is strong enough compared with the Coulomb interaction among electrons, a contribution to the partition function becomes large when a pair of electrons located close to each other are permuted with another pair lying side by side. For short we m a y call this a parallel permutation. Permutations form polygons in the coordinate space. Double polygons made of parallel permutations Can be regarded as " B o s e " particles. Superconducting state is interpreted as a Bosecondensed state of these " B o s e " particles. This picture has a close similarity with t h a t of S c h a f r o t h , B u t l e r and B l a t t . This is also related to the recent work on statistical mechanics of M o n t r o 11 and W a r d. *) Supported by the U.S. Department of Defence. 48. Superconductivity. J. A. KOK. N.V. Philips Gloeilampen Fabrieken, Eindhoven, Nederland. A superconductor is supposed to consist of two components of atomic volumes V and V J r / I V ( L a s a r e v ) . The expansion results in an unimportant change in
S 147
45. V o r t i c i t y i n s u p e r f l o w . S. M. BHAGAT and K. MENDELSSOHN. Clarendon Laboratory, Oxford. Isothermal flow of liquid He II through a capillary of 276 ~ diameter and 150 cm length has been measured. The liquid was first passed through a vycor glass filter in which the flow was a l w a y s subcritical. For low pressure heads the flow through the capillary was completely pressure independent and the critical velocity changed with temperature somewhat like ps/p. At higher pressures, dissipation was observed which, once it had set in, was maintained to low pressures. Shootening of the capillary to 17.6 cm resulted in much ( ~ 5 times) smaller, pressure dependent velocities. Moreover, the pressure dependency of the flow rate became very complicated, fil;st decreasing with falling A p and then suddenly increasing again. A sensative explanaton of the observed phenomena on the basis of vortex formation is suggested.
II. S U P E R C O N D U C T I V I T Y 46. The interaction in the BCS theory of superconductivity. JAMESC. SWIHART. IBM Research Laboratory, Poughkeepsie, New York, U.S.A. If in the BCS interaction 1), e~ and ek" are not set equal to zero, the ground state wave function can be determined without limiting the interaction to a region 2(~a~x)av wide at the Fermi surface. A variation of the total energy with respect to h~ leads to an integral equation for s0(k) which is now a function of k. The e0 thus determined minimizes the energy as long as e0 ~ 0. For k such t h a t the integral equation gives e0 < 0, the energy is minimized by hk('l -- h~) = 0. The strength of the interaction and the size of the region in k-space over which it is effective are n o t independent quantities but both are determined by the critical temperature. 1) Bardeen, Cooper and Schrieffer, Phys. Rev. 108 (1957) 1175. 47. A t h e o r y of s u p e r c o n d u c t i v i t y * ) . RYOICHI KIKUCHI. D e p a r t m e n t of Physics, W a y n e State University, Detroit, Michigan, U.S.A. Applying F e y n m a n's path integral technique to the system of electrons and phonons, one can first integrate over phonon coordinates to derive virtual interaction among electrons. Then if the electron-phonon interaction is strong enough compared with the Coulomb interaction among electrons, a contribution to the partition function becomes large when a pair of electrons located close to each other are permuted with another pair lying side by side. For short we m a y call this a parallel permutation. Permutations form polygons in the coordinate space. Double polygons made of parallel permutations Can be regarded as " B o s e " particles. Superconducting state is interpreted as a Bosecondensed state of these " B o s e " particles. This picture has a close similarity with t h a t of S c h a f r o t h , B u t l e r and B l a t t . This is also related to the recent work on statistical mechanics of M o n t r o 11 and W a r d. *) Supported by the U.S. Department of Defence. 48. Superconductivity. J. A. KOK. N.V. Philips Gloeilampen Fabrieken, Eindhoven, Nederland. A superconductor is supposed to consist of two components of atomic volumes V and V J r / I V ( L a s a r e v ) . The expansion results in an unimportant change in