^passcce,^ III! Ecole N o r m a l e S u p é r i e u r e de Lyon
L a b o r a t o i r e d'Annecy-Ie-Vieux de Physique des Particules
On the Possible Existence of Magnetic Charges in Nuclear Matter and Finite Nuclei.
Tran Huu Phat * Laboratoire de Physique Théorique ENS L A P P f Chemin de Bellevue, BP 110, F - 74941 Annecy-le-Vieux Cedex, France
Abstract Based on the Walecka-Serot theory of nuclei and the Ginzburg-Landau theory of critical phenomena it is shown that the nucléon pairing correlation of superconductivity type certainly leads to the existence of magnetic charges in nuclear matter and finite nuclei. The neutron pairing correlation yields the topological vortices in neutron matter and neutron stars.
BS&L/APP-A-495/94 October 1994
"On leave of absence from Vietnam Atomic Commission, 59 Ly Thuong Kiet, Hanoi, Vietnam. f URA 14-36 du CNRS, associée à l'E.N.S. de Lyon.
VOL
2 6 te 2 2
Pairing is one of the basic nucleon-nucleon correlations appearing in nuclei. For medium and heavy nuclei there is no proton-neutron pairing correlation of superconductivity type [1], T h e physical consequence of pairing correlation on nuclear properties as well as on nuclear structure have been the fascinating subjects of extensive studies since more than three decades and its relevance for the discovery of many important nuclear phenomena so far can be hardly overestimated. The theory of pairing correlation in nuclei is presented in detail in a lot of monographs and reviews [1-3]. T h e attempt to get more complete understanding of the origin of the pairing correlation on the basis of the bare nucleon-nucleon interaction is recently made by [4]. In this paper the possible existence of magnetic charges a n d topological singularities, related to the nucléon pairing correlation of the BCS type, is considered within the framework of the. Ginzburg-Landau theory [5] and the Walecka-Serot theory of nuclei [6]. It is organized as follows. In Section 1 the generalized Ginzburg-Landau equations for nuclear matter in the "superconducting" state is drived. The Section 2 deals with the possible existence of magnetic charges in nuclear matter and finite nuclei. The Section 3 is devoted to detailed consideration of topological vortices in neutron matter and neutron stars. The discussion and conclusion are given in Section 4.
S 1 . Let us first derive the relativistic Giuzburg-Landau equations for the order parameters describing the nucléon pairing correlation in nuclear matter. Let
*-(S) be the isotopic doublet of nucléons. T h e nucléon pairing correlation of BCS type leads to the occurrence of the order parameters which form a vector
ip =
exp[iY.l3(x)]ip.
where T are generators of the vector representation of 577(2) group and V-hyper charge. So, instead of (1) we have the full Lagrangian C = (Dll ) + ±( 0 to zero as p —* + o o .
T h e n the stokes theorem is applied:
