Pairing effect on the giant dipole resonance width at low temperature

Abstract

The width of the giant dipole resonance (GDR) at finite temperature T in Sn-120 is calculated within the Phonon Damping Model including the neutron thermal pairing gap determined from the modified BCS theory. It is shown that the effect of thermal pairing causes a smaller GDR width at T below 2 MeV as compared to the one obtained neglecting pairing. This improves significantly the agreement between theory and experiment including the most recent data point at T = 1 MeV.Comment: 8 pages, 5 figures to be published in Physical Review

Thermal pairing in Richardson model

“…The reason of why this works has been analysed in detail in Section IV.A.1 of Ref. [10], where Fig. 1(f) shows that a symmetric line shape of δN i ultimately leads to a large cancellation of the positive and negative wings in δΔ i (see Fig.…”

“…In the same Ref. [10] it has been also proved that the MHFB theory restores the unitarity relationR 2 (T ) =R(T ) for the modified generalized particle-density matrixR(T ), in which the single-particle density ρ and particle-pairing tensor τ are replaced with their modified partners,ρ andτ .…”

“…In Ref. [10], by generalizing of the secondary Bogoliubov transformation (19), the MHFB equation was derived using the variational principle in the same way as for the derivation of the HFB equation at finite temperature [3]. In the limit of constant pairing interaction G of the obtained MHFB equation one recovers the MBCS equation (22) above.…”

“…A test-example for such case with the Woods-Saxon spectrum for neutrons in 120 Sn was analyzed in Ref. [10]. This sets the criterion of applicability of the MBCS, which requires that the single-particle space used in practical calculations should be sufficiently large so that the line-shape of δN i as a function of the single-particle energies i is symmetric with respect to the Fermi surface.…”

“…In the recently proposed modified-BCS (MBCS) theory [8,9], and its generalization, the modified-HFB (MHFB) theory [10], it has been shown for the first time that it is the fluctuations of quasiparticle number that smooth out the sharp SN phase transition and lead to the non-vanishing thermal pairing in finite systems. These quasiparticle-number fluctuations are ignored in the standard BCS and HFB theories at finite temperature, as has been pointed out by Goodman [4].…”