我们分析了观察到的壳层间隙N=Z核确定的结合能差。结果表明，壳层能隙可以用单粒子能级间距、类核子配对和质子-中子配对相互作用的综合贡献来描述。这一结论与Chasman在Phys. Rev. Lett. 99（2007）082501。对于双闭壳层N=Z核，用Woods-Saxon势计算的单粒子能级间距与从观察到的壳层能隙中减去nn对相互作用得到的结果非常接近.对于亚封闭或非封闭壳层N=Z核，pn配对相互作用被证明是重要的观察到的壳层间隙。
英文摘要：
We analyze the observed shell gaps in N=Z nuclei determined from the binding energy differences. It is found that the shell gaps can be described by the combined contributions from the single-particle level spacing, the like-nucleon pairing, and the proton-neutron pairing interaction. This conclusion is consistent with that of Chasman in Phys. Rev. Lett. 99 (2007) 082501. For the double-closed shell N=Z nuclei, the single-particle level spacings calculated with Woods-Saxon potential are very close to those obtained by subtracting the nn pairing interaction from the observed shell gap. For the sub-closed or non-closed shell N=Z nuclei, the pn pairing interaction is shown to be important for the observed shell gaps.
We build and train the artificial neural network model (ANN) based on the experimental $α$-decay energy ($Q_α$) data. Besides decays between the ground states of parent and daughter nuclei, decays from the ground state of parent nuclei to the excited state of daughter nuclei are also included. By this way, the number of samples are increased dramatically. The results calculated by ANN model reproduce the experimental data with a good accuracy. The root-mean-square (rms) relative to the experiment data is 0.105 MeV. The influence of different input is investigated. It is found that either the s…
We study the cooling of isolated neutron stars with particular regard to the importance of nuclear pairing gaps. A microscopic nuclear equation of state derived in the Brueckner-Hartree-Fock approach is used together with compatible neutron and proton pairing gaps. We then study the effect of modifying the gaps on the final deduced neutron star mass distributions. We find that a consistent description of all current cooling data can be achieved and a reasonable neutron star mass distribution can be predicted employing the (slightly reduced by about 40\%) proton 1S0 Bardeen-Cooper-Schrieffer (B…
Various estimates of the even-odd effect of the mass shell of atomic nuclei are considered. Based on the experimental mass values of the Ca, Sn, and Pb isotopes, the dependence of the energy gap on the neutrons number is traced and the relationship of this characteristic to the properties of external neutron subshells is shown. In nuclei with closed proton shells, effects directly related to neutron pairing and effects of nucleon shells are discussed.
Interplay between Nuclear Shell Structure and Pairing around Doubly Magic $^{132}$Sn
TRIUMF；University of British Columbia（不列颠哥伦比亚大学）；University of Manitoba（曼尼托巴大学）；University of Victoria（维多利亚大学）；Justus-Liebig-Universität（吉森大学）；Helmholtz Forschungsakademie Hessen für FAIR (HFHF)（黑森FAIR赫尔姆霍茨研究学院）；University of Western Ontario（韦仕敦大学）
We present results of the Hartree-Fock-Bogolyubov calculations performed using nuclear energy density functionals based on regularized functional generators at next-to-leading and next-to-next-to-leading order. We discuss properties of binding energies and pairing gaps determined in semi-magic spherical nuclei. The results are compared with benchmark calculations performed for the functional generator SLyMR0 and functional UNEDF0.
The shell-model-like approach (SLAP) based on cranking covariant density functional theory (CDFT) with a separable pairing force is developed. The developed cranking CDFT-SLAP with separable pairing force is applied to investigate the rotational spectra in $^{60}$Fe, including the positive-parity yrast band and two negative-parity signature partner bands, in comparison with the cranking CDFT-SLAP with monopole pairing force calculations. Excellent agreement with the available data is achieved.
We perform a systematic study of Gamow-Teller (GT) transitions in the 2p1f shell, using the nuclear shell model with two schematic Hamiltonians. The use of the shell model provides flexibility to analyze the role of different proton-neutron pairing modes in the presence of nuclear deformation. The schematic Hamiltonians that are used contain a quadrupole-quadrupole interaction as well as isoscalar (T=0) and isovector (T=1) pairing interactions, but differ in the single particle energies. The objective of the work is to observe the behavior of GT transitions in different isoscalar and isovector…
Survival of Pairing Correlations and Shell Effects at Scission in Finite-Temperature Nuclear Fission: Implications for Odd-Even Staggering
National Centre for Nuclear Research（国家核研究中心）；China Institute of Atomic Energy, Nuclear Data Center（中国原子能科学研究院核数据中心）；Department of Theoretical Physics, Maria Curie-Skłodowska University（玛丽亚·居里-斯克沃多夫斯卡大学理论物理系）；Department of Physics, Tsinghua University（清华大学物理系）
The spin magnetic dipole transitions and the neutron-proton spin-spin correlations in $sd-$shell even-even nuclei with $N=Z$ are investigated using shell model wave functions. The isoscalar spin-triplet pairing correlation provides a substantial quenching effect on the spin magnetic dipole transitions, especially the isovector (IV) ones. Consequently, an enhanced isoscalar spin-triplet pairing interaction influences the proton-neutron spin-spin correlation deduced from the difference between the isoscalar (IS) and the IV sum rule strengths. The effect of the $Δ$ ($Δ_{33}$ resonance)-hole coupl…
The ground-state bands (GSBs) in the even-even hafnium isotopes $^{170-184}$Hf are investigated by using the cranked shell model (CSM) with pairing correlations treated by the particle-number conserving (PNC) method. The experimental kinematic moments of inertia are reproduced very well by theoretical calculations. The second upbending of the GSB at high frequency $\hbarω\approx0.5$ MeV observed (predicted) in $^{172}$Hf ($^{170,174-178}$Hf) attributes to the sudden alignments of the proton high-$j$ orbitals $\pi1i_{13/2}$ $(1/2^{+}[660])$, $\pi1h_{9/2}$ $(1/2^{-}[541])$ and orbital $\pi1h_{11…
The long standing problem of neutron-proton pairing correlations is revisited by employing the Hartree-Fock-Bogoliubov formalism with neutron-proton mixing in both the particle-hole and particle-hole channels. We compare numerical calculations performed within this method with an exact pairing model based on the $SO(8)$ algebra. The neutron-proton mixing is included in our calculations by performing rotations in the isospin space using the isocranking technique.
Pairing rotations are the low-energy excitations of finite superfluid systems, connecting systems that differ in their number of Cooper pairs. This paper presents a model-independent derivation of pairing rotations within an effective theory that exploits the emergent breaking of U(1) phase symmetries. The symmetries are realized nonlinearly and the Nambu-Goldstone modes depend only on time because the system is finite. Semi-magic nuclei exhibit pairing rotational bands while the pairing spectrum becomes an elliptical paraboloid for open-shell nuclei. Model-independent relations between double…
We utilize a nuclear shell model Hamiltonian with only two adjustable parameters to generate, for the first time, exact solutions for pairing correlations for light to medium-mass nuclei, including the challenging proton-neutron pairs, while also identifying the primary physics involved. In addition to single-particle energy and Coulomb potential terms, the shell model Hamiltonian consists of an isovector $T=1$ pairing interaction and an average proton-neutron isoscalar $T=0$ interaction, where the $T=0$ term describes the average interaction between non-paired protons and neutrons. This Hamil…
Singlet pairing gaps of neutrons and protons in hyperonic neutron stars
在相对论平均场模型和Bardeen-Cooper-Schrieffer理论下研究了超声波中子星中的$^{1}S_{0}$核超流体。以Reid软核相互作用为核子-核子相互作用，计算了中子和质子的$^{1}S_{0}$配对能隙。我们详细研究了超子自由度对中子星物质中$^{1}S_{0}$核子对能隙的影响。结果表明，超子的出现对$^{1}S_{0}$中子配对能隙的重子密度范围和大小几乎没有影响，质子配对能隙在该区域$ρ_B=0.0-0.393$ fm $^{-3}$也略有减小.然而，如果重子密度变得大于0.393 fm ${^{-3}}$，则$^{1}S_{0}$质子配对间隙明显增大。此外，超子的存在还使质子超流的范围明显扩大。在我们的结果中，超子改变了$^{1}S_{0}$质子配对间隙，这必然改变了中子星的冷却性质。
Bayesian neural network (BNN) approach is employed to improve the nuclear mass predictions of various models. It is found that the noise error in the likelihood function plays an important role in the predictive performance of the BNN approach. By including a distribution for the noise error, an appropriate value can be found automatically in the sampling process, which optimizes the nuclear mass predictions. Furthermore, two quantities related to nuclear pairing and shell effects are added to the input layer in addition to the proton and mass numbers. As a result, the theoretical accuracies a…
Pairing gaps in neutron matter need to be computed in a wide range of densities to address open questions in neutron star phenomenology. Traditionally, the Bardeen-Cooper-Schrieffer approach has been used to compute gaps from bare nucleon-nucleon interactions. Here, we incorporate the influence of short- and long-range correlations in the pairing gaps. Short-range correlations are treated including the appropriate fragmentation of single-particle states, and substantially suppress the gaps. Long-range correlations dress the pairing interaction via density and spin modes, and provide a relative…
The multi-particle states and rotational properties of two-particle bands in $^{254}$No are investigated by the cranked shell model (CSM) with pairing correlations treated by a particle-number conserving (PNC) method. For the first time, the rotational bands on top of two-particle $K^π=3^+,8^-$ and $10^+$ states and the pairing reduction are studied theoretically in $^{254}$No. The experimental excitation energies and moments of inertia for the multi-particle state are reproduced well by the calculation. Better agreement with the data are achieved by including the high-order deformation $\vare…
The antisymmetrized quasi-cluster model (AQCM) was proposed to describe α-cluster and $jj$-coupling shell models on the same footing. In this model, the cluster-shell transition is characterized by two parameters; $R$ representing the distance between α clusters and α describing the breaking of α clusters, and the contribution of the spin-orbit interaction, very important in the $jj$-coupling shell model, can be taken into account starting with the α cluster model wave function. Not only the closure configurations of the major shells, but also the subclosure configurations of the $jj$-coupling…
The pairing gap plays a fundamental role in the nuclear many-body problem and many large scale and accurate mass formula fits suggest the smooth nuclear mass dependence $Δ\sim 6(1)~ A^{-1/3}~{\rm MeV}$ in the liquid drop model which lacks a theoretical motivation. Within the BCS theory we analyze the impact of phase equivalent interactions on the pairing gap for a translational invariant many-fermion system such as nuclear and neutron matter. To that end we use explicitly the Similarity Renormalization Group (SRG) transformations. We show that in the on-shell and continuum limits the pairing g…
