Strong hyperon-nucleon pairing in neutron stars

We explore the possibilities of hyperon-nucleon pairing, involving lambda or sigma- hyperons, using different Nijmegen hyperon-nucleon potentials. We find possible very large nsigma- gaps and estimate their relevance for neutron star physics.     

Strength distributions and statistical spectroscopy. I. General theory

The strength distribution for an arbitrary excitation is given in terms of a double expansion, and its sum rules by single expansions, in polynomials defined by the initial and final energy spectra. In model spaces which are not too large, a rapid convergence, to within fluctuations, is assured by the action of a central limit theorem, as is shown in particular by considering the response of the system under infinitesimal deformations of the Hamiltonian. When larger spaces are decomposed into subspaces defined by a partitioning of the single-particle space a similar convergence results. At the same time, close contact is made with, and important corrections are found to, intuitive procedures which are often used for approximating strength distributions. The general features of the distribution are often easily understood in termsof a simple geometry made effective in the model space by the central limit theorem, and further features by exploiting the connection of this geometry to the unitary group of transformations in the single-particle space. Extensions are given for multipole strengths and sum rules, appropriate when the angular momenta (and isospins) are specified for the states involved in the transitions. Measures for the RMS fluctuations in the sum-rule quantities, and correlations between them, are given by combining the low-order-polynomial (statistically smoothed) strengths with an assumed Porter-Thomas distribution for the (high-order) strength fluctuations.     

Quantum information entropies for a squared tangent potential well

The particle in a symmetrical squared tangent potential well is studied by examining its Shannon information entropy and standard deviations. The position and momentum information entropy densities _ρs(x)${\rho }_s(x)$, _ρs(p)${\rho }_s(p)$ and probability densities ρ(x)$\rho (x)$, ρ(p)$\rho (p)$ are illustrated with different potential range L and potential depth U  . We present analytical position information entropies _Sx$S_x$ for the lowest two states. We observe that the sum of position and momentum entropies _Sx$S_x$ and _Sp$S_p$ expressed by Bialynicki-Birula–Mycielski (BBM) inequality is satisfied. Some eigenstates exhibit entropy squeezing in the position. The entropy squeezing in position will be compensated by an increase in momentum entropy. We also note that the _Sx$S_x$ increases with the potential range L, while decreases with the potential depth U  . The variation of _Sp$S_p$ is contrary to that of _Sx$S_x$.     

Quantum information entropies for position-dependent mass Schrödinger problem

The Shannon entropy for the position-dependent Schrödinger equation for a particle with a nonuniform solitonic mass density is evaluated in the case of a trivial null potential. The position S_x$S_x$ and momentum S_p$S_p$ information entropies for the three lowest-lying states are calculated. In particular, for these states, we are able to derive analytical solutions for the S_x$S_x$ entropy as well as for the Fourier transformed wave functions, while the S_p$S_p$ quantity is calculated numerically. We notice the behavior of the S_x$S_x$ entropy, namely, it decreases as the mass barrier width narrows and becomes negative beyond a particular width. The negative Shannon entropy exists for the probability densities that are highly localized. The mass barrier determines the stability of the system. The dependence of S_p$S_p$ on the width is contrary to the one for S_x$S_x$. Some interesting features of the information entropy densities ρ_s(x)${\rho }_s\left(x\right)$ and ρ_s(p)${\rho }_s\left(p\right)$ are demonstrated. In addition, the Bialynicki-Birula–Mycielski (BBM) inequality is tested for a number of states and found to hold for all the cases.     

Rare-earth nuclei and the pseudo-SU(3) model

An extended version of the pseudo-SU(3) model is used to describe low-energy positive-parity states of three rare-earth nuclei in a full proton-neutron formalism. Along with other residual interactions, the Hamiltonian includes the pairing which induces mixing between different representations of SU(3). Excitation energies, B(E2) values, B(M1) values, quadrupole moments, andg _R factors of¹³⁶Xe,¹³⁸Ba, and²⁰⁴Hg are calculated in a truncation free environment and the results are compared with the experimental data and other theories.     

球形平均场加四极-四极和对力模型在单j壳内的量子相交叉行为(英文)

介绍了单j壳的球形平均场加几何四极-四极和标准对力模型的量子相交叉行为。在单j=15/2的壳内,计算了随模型控制参数变化的多个物理量如低激发能级、激发态间重叠积分、低激发态间的B（E2）比值和电四极矩比值。结果显示,在类转动到对激发相的演化中,多个物理量在交叉区存在非常明显的变化,如B（E2;4₁ → 2₁）/B（E2;2₁ → 0_g）,B（E2;4₂ → 2₁）/B（E2;2₁ → 0_g）等,并且这些变化在核子数达到半满壳时尤为显著。此外,尽管当j较小时,由几何四极-四极相互作用得到的低激发能级不满足转动谱规律,但当j值足够大时,这些低激发能级满足转动谱规律。The analysis of the quantum phase crossover behavior in the spherical shell model mean-field plus the geometric quadrupole-quadrupole (Q·Q) and standard pairing model within a single-j shell is reported. Several quantities, such as low-lying excitation energies, the overlaps of excited states, ratios of some B(E2) and electric quadrupole moments of some low-lying states as functions of the control parameter of the model in a j=15/2 shell are calculated. The results show that there are noticeable changes in the crossover region of the rotational-like to the pair-excitation phase transition, such as B(E2;4₁ → 2₁)/B(E2;2₁ → 0_g) and B(E2;4₂ → 2₁)/B(E2;2₁ → 0_g), especially in the half-filling case. Though the low-lying excitation energies generated from the geometric quadrupole-quadrupole interaction not satisfy the pattern of a rotational spectrum when j is small, these energies follow the pattern of a rotational spectrum when j is sufficiently large.     

SD配对壳模型对质量数A~130区原子核的形状渡越研究(英文)

利用SD配对壳模型研究了质量数A~130区原子核的低激发态性质。为了减少参数,模型采用了等强度对力,取质子和中子对力强度等同近似,而非同类核子间的四极-四极相互作用强度取为同类核子间四极-四极相互作用强度的两倍。计算结果显示,模型的振动-转动和振动-γ不稳定运动的形状渡越特征与相互作用玻色子模型对应的形状相变特征基本吻合,从而说明SD配对壳模型是壳模型的一种合理近似。The SD-pair shell model is applied to analyze the evolution of low-lying states of even-even nuclei in A~130 mass region. In the model, the pairing and the quadrupole-quadrupole interactions are taken into account. The results show that there are clear signatures of the crossover from vibrational to rotational or from vibrational to the γ-soft shape phase.     

A Class of Quasi-exact Solutions of Rabi Hamiltonian

A class of quasi-exact solutions of the Rabi Hamiltonian, which describes a two-level atom interacting with a single-mode radiation field via a dipole interaction without the rotating-wave approximation, are obtained by using a wavefunction ansatz. Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and the field frequency satisfy certain relations. As an example, the lowest exact energy level and the corresponding atom-field entanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings and counter-rotating cases of the Rabi Hamiltonian.