Simultaneous Microscopic Description of Nuclear Level Density and Radiative Strength Function

Abstract

Nuclear level density (NLD) and radiative strength function (RSF) are described simultaneously within a microscopic approach, which takes into account the thermal effects of the exact pairing as well as the giant resonances within the phonon-damping model. The good agreement between the results of calculations and experimental data extracted by the Oslo group for 170,171,172 Yb isotopes shows the importance of exact thermal pairing in the description of NLD at low and intermediate excitation energies and invalidates the assumption based on the Brink-Axel hypothesis in the description of the RSF. The rapid decrease in level spacing between the excited states as the excitation energy increases to several MeV leads to an exponential increase in the level densities and transition probabilities between the excited levels in the medium and heavy nuclei. In this condition it is impractical to deal with an individual state. Instead, it is meaningful and convenient to consider the average properties of nuclear excitations. Two main quantities, which are often employed to describe these properties, are the nuclear level density (NLD) and radiative γ-ray strength function (RSF). The NLD is defined as the number of excited levels per unit of excitation energy E * , whereas the RSF is the average transition probability per γ-ray energy E γ . The NLD provides the information on several properties of an atomic nucleus, namely the pairing correlations and nuclear thermodynamic properties such as temperature, entropy, heat capacity, etc. [1]. The RSF reveals the characteristics of average nuclear electromagnetic properties [2]. These two quantities have important contributions in the study of low-energy nuclear reactions and nuclear astrophysics such as the calculation of the stellar reaction rates and the description of nucleosynthesis in stars [3,4]. The study of NLD and RSF has therefore been one of the most important topics in nuclear structure physics. It became particularly attractive after the recent developments of the experimental technique proposed by Oslo's group (the Oslo method), which is able to extract simultaneously both NLD and RSF from the primary γ-decay spectrum of the residual compound nucleus created in the transfer and/or inelastic scattering reactions [5][6][7]. These experimental data also serve as a good testing ground for all the present theoretical approaches to NLD and RSF.Although the concepts of NLD and RSF are rather old [2,8], a unified theory, which can describe simultaneously and microscopically both the NLD and RSF is still absent so far. The NLD can be described quite well within the finite-temperature shell model quantum Monte-Carlo method [9], but this method is time consuming when it is applied to heavy nuclei. Regarding the γ-strength functions, which involve giant resonances and the related RSF, they are beyond the scope of this method. The Hartree-Fock BCS [10] and Hartree-FockBogolyubov plus combinatorial method (HFBC) [11] have provided a global description of NLD and might be consid...

Bubble nuclei within the self-consistent Hartree-Fock mean field plus pairing approach

“…These experiments confirmed the theoretical predictions [20] that the single-particle strength of the proton-hole configuration 3s 1/2 in 205 Tl amounts to 70%-90%, whereas the remaining strength of 30%-10% is mainly exhausted in the two-neutron hole configuration 2d 3/2 [18]. This indicates that the candidates to the bubble structure must have unoccupied s levels, such as 22 O and 34 Si (unoccupied 2s level) [9,11], 46 Ar (unoccupied 2s level) [8,21], and 206 Hg (unoccupied 3s level) [21]. In these bubble candidates, the shell closure often takes place when the states of low angular momenta are located at or near the top of the Fermi energy.…”

“…Within the FTEP, the particle number is exactly conserved at both zero and finite temperatures. As a result, the exact pairing gap does not vanish at T = T c as the FTBCS gap but monotonically decreases with increasing T and remains finite at T as high as 4 MeV [40,46].…”

“…Based on the SU(2) algebra of angular momentum, the pairing Hamiltonian (11) can be directly diagonalized to obtain the exact eigenstates E S and single-particle occupation numbers f S j at T = 0 and at different values of the total seniority S, which is the total number of unpaired particles [33,34]. Using these eigenvalues, one can construct the exact partition function within the CE as [40,46]…”

“…The levels outside the truncated spectrum are treated within the independent particle model (IPM), whose occupation numbers are expressed in terms of the Fermi-Dirac distribution as in the case of the FTHF [Eq. (9)] [46]. Regarding the FTHF and FTBCS cases, in general, no cutoff is required as the matrix diagonalization is not used in solving them.…”

Finite-Temperature Relativistic Nuclear Field Theory: An Application to the Dipole Response

“…As both of these structures have a very complex nature at the interface of coherent oscillations and pure particle-hole excitations and their microscopic texture is linked to the astrophysical r-process nucleosynthesis, they continuously attract active interest from both experiment and theory [2].An accurate theory for the response of compound nuclei, which is required most often for applications, is extremely challenging. The common practice is to confine the framework by the simplest one-loop approximation, such as thermal random phase approximation (TRPA) [3,4], thermal quasiparticle RPA (TQRPA) [3,5] or its version with exact pairing [6], and one step further is represented by the continuum TQRPA [7][8][9]. A few extensions of T(Q)RPA including damping mechanisms have been formulated, for instance, in Ref.…”