Improved treatment of blocking effect at finite temperature

Abstract

The blocking effect caused by the odd particle on the pairing properties of systems with an odd number of fermions at finite temperature interacting via the monopole pairing force is studied within several approximations. The results are compared with the predictions obtained by using the exact solutions of the pairing Hamiltonian. The comparison favors the approximation with the odd particle occupying the top level, which is the closest to the Fermi surface and whose occupation number decreases with increasing temperature.

Pairing in excited nuclei: a review

“…Ω as indicated in figures 3 and 4 of [101]. In particular, the gap obtained within q k -blocked BCS increases slightly with temper ature at low temperature, which qualitatively agrees with the exact gap (figure 35(b)).…”

“…However, the physical nature of the pairing reentrance in odd systems is completely different with that observed in the even ones, namely it is caused by the blocking effect of the odd particle, which is strong at zero temperature but depleted at finite temperature. This effect has been latter confirmed in [101] where a correct treatment of the blocking effect in odd nuclei at finite temperature was proposed. This treatment begins with the analysis of the exact solution of the pairing Hamiltonian (1) at finite temperature (see section 4.3 for the details of exact pairing solutions at finite temperature).…”

“…is the occupation number of the odd particle on the blocked single-particle level k [101]. This occupation number q k of the odd particle automatically satisfies two conditions observed in its above exact solution, namely it equals to 1 at zero temperature and varies with temper ature.…”

“…The Maino's method was popularly used to describe the pairing properties of excited odd nuclei. The second feature is that the occupation number of the odd particle does not remain equal to 1 as its value at zero temperature, but decreases with increasing temperature as discussed in [101]. This feature clearly indicates that the blocking effect caused by the odd particle is weaken due to the effect of temperature.…”

Pairing phase transition in an odd–even hot 69Zn nucleus

“…It is also seen in figure 2(a) that the neutron pairing gap increases at low T, reaches a maximum at T ∼ 0.5 MeV, and strongly decreases after that. This is well-known as the pairing reentrance phenomenon, which is caused by the weakening of the thermal blocking effect due to the odd neutron in 69 Zn [24,34,41]. This phenomenon also results in a stronger variation of the neutron pairing gap with temperature at T > 0.5 MeV than that of the proton one as shown in figures 2(a) and (c).…”