Finite-range pairing in nuclear density functional theory
Facility for Rare Isotope Beams, Michigan State University（稀有同位素束设施，密歇根州立大学）；Institut für Theoretische Physik II, Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学理论物理第二研究所）；Department of Physics and Astronomy, Michigan State University（密歇根州立大学物理与天文学系）
Pairing correlations are ubiquitous in low-energy states of atomic nuclei. To incorporate them within nuclear density functional theory, often used for global computations of nuclear properties, pairing functionals that generate nucleonic pair densities and pairing fields are introduced. Many pairing functionals currently used can be traced back to zero-range nucleon-nucleon interactions. Unfortunately, such functionals are plagued by deficiencies that become apparent in large model spaces that contain unbound single-particle (continuum) states. In particular, the underlying computational schemes diverge as the single-particle space increases, and the results depend on how marginally occupied states are incorporated. These problems become more pronounced for pairing functionals that contain gradient-density dependence, such as in the Fayans functional. To remedy this, finite-range pairing functionals are introduced. In this study, this is done by folding the pair density with Gaussians. We show that a folding radius of about 1\,fm offers the best compromise between quality and stability, and substantially reduces the pathological behavior in different numerical applications.
We discuss the possible manifestation of pairing dynamics in nuclear collisions beyond the standard quasi-static treatment of pairing correlations. These involve solitonic excitations induced by pairing phase difference of colliding nuclei and pairing dynamic enhancement in the di-nuclear system formed by merging nuclei.
The coexistence of neutron-neutron (n-n), proton-proton (p-p), and neutron-proton (n-p) pairings is investigated by adopting an effective density-dependent contact pairing potential. These three types of pairings can coexist only if the n-p pairing is stronger than the n-n and p-p pairings for isospin asymmetric nuclear matter. In addition, the existence of n-n and p-p pairs might enhance n-p pairings in asymmetric nuclear matter when the n-p pairing strength is significantly stronger than the n-n and p-p ones. Conversely, the n-p pairing is reduced by the n-n and p-p pairs when the n-p pairin…
在三维坐标空间中，采用正则基含时Hartree-Fock-Bogoliubov理论（Cb-TDHFB）处理对关联，模拟了重离子碰撞.将Cb-TDHFB应用于22 O +22 O碰撞，并采用接触型对能泛函，比较了Cb-TDHFB和TDHF的结果，研究了对关联在核聚变中的作用.我们的结果似乎表明，配对效应不增加在这个系统中的融合截面。
Nucleon-Nucleon Phase Shifts and Pairing in Neutron Matter and Nuclear Matter
我们考虑了无限中子物质和核物质中的1 S 0配对，并指出在最低阶近似下，当配对相互作用取为1 S 0通道中的裸核子-核子（NN）相互作用时，配对相互作用和能隙可以直接由1 S 0相移确定.这是由于在这个分波中NN相互作用的几乎可分离的特征。由于最近的NN相互作用是电荷相关的，我们必须解决耦合的间隙方程质子，中子，中子和中子质子配对的核物质。结果，然而，被发现是接近与电荷无关的电位所获得的。
Pairing in nuclear systems with effective Gogny and V_low-k interactions
核系统的配对性质是研究核子-核子有效相互作用的灵敏探针。我们比较了从唯象Gogny相互作用和从实际相互作用中提取的重整化群激发的低动量V_low-k相互作用得到的核和中子物质的1 S 0配对能隙。我们发现，这些相互作用预测的配对间隙是在一个很好的协议在很宽的范围内的亚核密度。在中子和核物质中的单粒子谱在Hartree-Fock理论中重整化的情况下，有效力的预测之间的紧密一致性仍然保持不变。
Pairing effects in non-uniform nuclear matter, surrounded by electrons, are studied in the protoneutron star early stage and in other conditions. The so-called nuclear pasta phases at subsaturation densities are solved in a Wigner-Seitz cell, within the Thomas-Fermi approximation. The solution of this problem is important for the understanding of the physics of a newly born neutron star after a supernova explosion. It is shown that the pasta phase is more stable than uniform nuclear matter on some conditions and the pairing force relevance is studied in the determination of these stable phases…
The structure and density dependence of the pairing gap in infinite matter is relevant for astrophysical phenomena and provides a starting point for the discussion of pairing properties in nuclear structure. Short-range correlations can significantly deplete the available single-particle strength around the Fermi surface and thus provide a reduction mechanism of the pairing gap. Here, we study this effect in the singlet and triplet channels of both neutron matter and symmetric nuclear matter. Our calculations use phase-shift equivalent interactions and chiral two-body and three-body interactio…
Effects of pairing with isospin $T=0$ and $T=1$ are systematically studied in a model, which is based on a realistic nucleon-nucleon interaction and allows to describe the transition from infinite nuclear matter to finite nuclei. Special attention is paid to the development of the spin-orbit term in the mean field of nucleons in finite nuclei. The spin-orbit term yields a drastic suppression of $T=0$ proton-neutron pairing but does not lead to a complete disappearance in finite nuclei. Arguments are presented, why no clear evidence of $T=0$ pairing can be observed in the binding energies of fi…
Surface behaviour of the pairing gap in semi-infinite nuclear matter
从Paris NN-势的可分形式出发，利用最近在坐标表象中明确发现的有效对相互作用，对半无限核物质中的$^1S_0$ -对隙进行了微观评价.采用了由V. A. Khodel、V. V. Khodel和J. W. Clark提出的一种新方法，而不是直接迭代求解间隙方程，从而大大简化了计算过程。在我们的计算中得到的间隙$Δ$在表面区域表现出强烈的变化，在表面附近具有明显的最大值。
To describe quantal collective phenomena, it is useful to requantize the time-dependent mean-field dynamics. We study the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for the two-level pairing Hamiltonian, and compare results of different quantization methods. The one constructing microscopic wave functions, using the TDHFB trajectories fulfilling the Einstein-Brillouin-Keller quantization condition, turns out to be the most accurate. The method is based on the stationary-phase approximation to the path integral. We also examine the performance of the collective model which assumes th…
The uncertainty in the nuclear matrix elements (NMEs) of $0νββ$ decay for $^{76}$Ge, $^{82}$Se, $^{128}$Te, $^{130}$Te, and $^{136}$Xe in the self-consistent quasiparticle random phase approximation (QRPA) method is investigated by using eighteen Skyrme interactions supplemented with either a volume- or surface-type of pairing interactions. The NMEs for the isotopes concerned (except $^{136}$Xe) are less sensitive to the particle-hole ($ph$) interactions, while strongly dependent on the employed isovector particle-particle ($pp$) pairing interactions even though the pairing strengths are optim…
The self-energy effect on the neutron-proton (np) pairing gap is investigated up to the third order within the framework of the extend Bruecker-Hartree-Fock (BHF) approach combined with the BCS theory. The self-energy up to the second-order contribution turns out to reduce strongly the effective energy gap, while the \emph{renormalization} term enhances it significantly. In addition, the effect of the three-body force on the np pairing gap is shown to be negligible. To connect the present results with the np pairing in finite nuclei, an effective density-dependent zero-range pairing force is e…
We show that the Nambu-Goldstone formalism of the broken gauge symmetry in the presence of the $T=1$ pairing condensate offers a quantitative description of the binding-energy differences of open-shell superfluid nuclei. We conclude that the pairing-rotational moments of inertia are excellent pairing indicators, which are free from ambiguities attributed to odd-mass systems. We offer a new, unified interpretation of the binding-energy differences traditionally viewed in the shell model picture as signatures of the valence nucleon properties. We present the first systematic analysis of the off-…
