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“…Out of this domain, matter is predicted to be in its normal phase where pairing is quenched. Notice that the high-temperature boundary T c2 is below or about the same as the single critical temperature in ordinary nuclei ∼ 1 MeV [19,32,33,41,42]. Other Skyrme forces considered here do not predict the re-entrance phenomenons for reasons that we detail hereafter.…”

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“…Out of this domain, matter is predicted to be in its normal phase where pairing is quenched. Notice that the high-temperature boundary T c2 is below or about the same as the single critical temperature in ordinary nuclei ∼ 1 MeV [19,32,33,41,42]. Other Skyrme forces considered here do not predict the re-entrance phenomenons for reasons that we detail hereafter.…”

“…The more complex FT-RHFB equations can be found in our recent work [33]. Denoting h T (r) the thermal averaged mean field Hamiltonian and ∆ T (r) the thermal averaged pairing field, the radial FT-HFB equations read [19,[41][42][43],…”

“…We have performed microscopic calculations of these centroids using the finite-temperature quasiparticle random phase approximation [6] and for temperatures (T) below critical values related with the collapse of pairing gaps (T≤1 MeV ) [7]. These temperatures are near the values characteristic of the pre-supernova core [4].…”

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“…The thermal average procedure of [7] accounts for the inclusion of excited states in taking expectation values at finite temperature. It has also been used to describe two-quasiparticle excitations and QRPA states at finite temperature [6].…”

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