In the present paper a number conserving random phase approximation is derived as a special case of the recently developed random phase approximation in general symmetry projected quasiparticle mean fields. All the occurring integrals induced by the number projection are performed analytically after writing the various overlap and energy matrices in the random phase approximation equation as polynomials in the gauge angle. In the limit of a large number of particles the well-known pairing vibration matrix elements are recovered. We also present a new analytically number projected variational equation for the number conserving pairing problem.
In the context of a relativistic mean field theory the delta-resonance matter formation in a highly compressed nuclear medium is investigated. For a given set of nucleonmeson coupling constants, the delta-resonance formation is studied by changing the delta-meson coupling constants. The effect on the equation of state and on the deltaresonance population with respect to changes in the delta-resonance coupling constants values is discussed for very asymmetric and quasi-symmetric nuclear matter, as an extension of works restricted to the symmetric nuclear matter treatment. 5,6The occurrence of highly dense baryon-rich resonant matter in relativistic heavy ion collisions 1-3 leads to a great interest in the investigation of the effects of delta matter transition in nuclear matter. These results of heavy ion collisions require a re-investigation of the transition to delta-matter in a model which could properly deal with the nuclear matter properties. * E-mail: sbd@cbpf.br 1529 Mod. Phys. Lett. A 2000.15:1529-1537. Downloaded from www.worldscientific.com by UNIVERSITY OF CALIFORNIA @ SAN DIEGO on 04/13/15. For personal use only.
Isovector pairing collective motion is treated by means of the generator coordinate method. In this scheme, the isospin and number projection is performed analytically by the recognition of symmetry properties in the generalized Bardeen-Cooper-Schrieffer wave functions. Among the results obtained, our generator-coordinate-method values of energy and spectroscopic amplitude are shown to be comparable to those of shell model calculations. This is indeed encouraging, especially in view of the fact that they were reached using a simple approximation. The great simplicity of the present method, as compared with earlier complicated versions, suggests that they might prove useful in the study of isovector pairing collective states which are strongly populated by pair transfer reactions in medium weight nuclei. 0 rr 1 v2 u vl rr2 vv= &~1 V v2 V v1& n2P
Several BCS-type approximations encountered in the literarature were correlated using a 1/N expansion over a set of dispersion type energy equations, which are the exact solution of a system of fermions interacting through a pure pairing force. One of the interesting results obtained is that the BCSϩQRPA approximation coincides with the first order term of the 1/N expansion.
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