Mean-field and blocking effects on odd-even mass differences and rotational motion of nuclei

Abstract

The odd-even differences of nuclear masses are strongly influenced by mean-field and odd-nucleon blocking effects. When such effects are taken into account, the determination of the pairing interaction strength needs to be modified, resulting in larger pairing gaps. This method leads to an improved description for both moments of inertia and backbending frequencies of rotational bands, with no additional parameters. ͓S0556-2813͑99͒50111-8͔PACS number͑s͒: 21.60. Cs, 21.10.Dr, 27.70.ϩq Since the Bardeen-Cooper-Schrieffer ͑BCS͒ theory was applied to atomic nuclei ͓1,2͔, pairing correlations have been crucial to the understanding of many properties, such as binding energies, collective rotational motion, and quasiparticle excitation energies. The interaction strength, G, of the pairing force is the key parameter that governs the properties of the short-range correlations.The G value is usually determined by fitting the BCS pairing gaps (⌬ϭG ͚ i U i V i ͓2͔͒ of even-even nuclei to experimental odd-even mass differences. However, if one then calculates the corresponding theoretical mass differences ͑i.e., in the same manner as calculating the experimental value, but with theoretical masses͒, it turns out that they are systematically smaller than the experimental mass differences and also smaller than the BCS pairing gaps, at least for the deformed rare-earth nuclei described below. The experimental mass difference should, in principle, be identical to the corresponding theoretical value, but not to the pairing gap, though the gap plays the dominant role in determining the mass difference.The above systematic discrepancies suggest that other significant effects exist. It has been pointed out, in a recent work by Satuła, Dobaczewski, and Nazarewicz ͓3͔, that one of the important effects stems from the deformed mean field. Due to the twofold Kramers degeneracy of single-particle levels, odd-and even-nucleon systems in the deformed field have different energies, which contribute to odd-even mass differences. For light-and medium-mass nuclei, the Kramers effect can be comparable with the pairing contribution ͓3͔. Furthermore, when neighboring nuclei have different deformations, the shape-changing effect also plays a role. These two factors originate from the deformed mean field and, therefore, we will refer to them in the following as the meanfield effect.Moreover, the pairing gaps of even-even nuclei cannot include the odd-nucleon blocking effects of adjacent odd nuclei, while experimental odd-even mass differences of course contain such blocking effects ͓2,4͔. This can become significant when the density of single-particle levels around the Fermi surface is not very high. Simple BCS calculations typically show that the odd-nucleon blockings can reduce pairing gaps by more than 10% for the rare-earth nuclei. Hence, it should be expected that the mean-field and blocking effects influence the determination of pairing strengths.Two very sensitive probes of pairing correlations and, therefore, of the pairing strengths, are...

N=Znuclei: a laboratory for neutron–proton collective mode

“…The five-point formula is also used in Refs. [17,28,29]. ∆ (4) (N ) and ∆ (5) (N ) show quite similar results for most nuclei since ∆…”

“…Above formula indicates that ∆ (3) (N ) measures the additional binding gain by the last neutron in the even-N system relative to the odd system with one more neutron. It should be mentioned that, besides pairing, a number of other mechanisms may contribute to the OES [14,15,16,17]. This includes effects induced by the mean field in deformed nuclei (or the Kramers degeneracy) and the contribution from the diagonal interaction matrix elements of the twobody force.…”

Odd-even staggering of binding energies as a consequence of pairing and mean-field effects

“…According to the analysis of nuclear masses, the meanfield contribution to the OES is significant in light nuclei, but it is reduced to ∼100-200 keV in heavy deformed nuclei [32] due to the relatively close spacing of singleparticle levels.…”

Gamow-Teller strength and the spin-isospin coupling constants of the Skyrme energy functional

“…Such breaking obviously occurs for rotating nuclei, in which the current and spinorbit time-odd channels (linked to time-even channels by the gauge symmetry) play an important role. Timeodd terms also interfere with pairing correlations in the masses of odd-A and odd-odd nuclei [4][5][6] and contribute to single-particle energies [7][8][9] and magnetic moments [10]. Finally, the spin-isospin channel of the effective interaction determines distributions of the Gamow-Teller (GT) strength.…”