Shannon information entropy for a hyperbolic double‐well potential

We use the ansatz method to obtain the symmetric and antisymmetric solutions of a hyperbolic double‐well potential by solving the Heun differential equation. The Shannon entropy is studied. The position S_x and momentum S_p information entropies for the low‐lying two states N = 1, 2 are calculated. Some interesting features of the information entropy densities ρ_s(x) and ρ_s(p) as well as the probability density ρ(x) are demonstrated. We find that ρ(x) is equal or greater than 1 at positions for the allowed potential‐depth values of U₀ = 595.84 (symmetric case) and U₀ = 1092.8 (antisymmetric case). This arises from the fact that most of the density is less than 1, the curve has to rise higher than 1 to have a total area of 1 as required for all probability distributions. We find that the position information entropy S_x decreases with the potential strength but the momentum entropy S_p is contrary to the S_x. The Bialynicki‐Birula–Mycielski inequality is also tested and found to hold for these cases. © 2015 Wiley Periodicals, Inc.     

Nilsson mean-field plus the extended pairing model description of rare earth nuclei

The Nilsson mean-field plus the extended pairing model for well-deformed nuclei is applied to some representative rare earth examples. The binding energies, some low-lying pair-excited states and even-odd mass differences of Er, Yb and Hf isotopes are calculated systematically within the proton frozen-pair excitation limit. A comparison with experimental data for these nuclei shows that the results of the extended pairing model are better than those for the standard pairing model with the BCS approximation and the nearest-orbit pairing model.     

利用SD对壳模型讨论偶偶Mo核的集体性质(英文)

利用SD对壳模型讨论了偶偶Mo核低激发谱的集体性质。发现当SD对按照如下方法来确定，即对于两核子体系，通过对角化表面δ相互作用哈氏量，将SD对取为01^＋态和21^＋态，该模型可以合理的描述偶偶Mo核低激发态的集体性质。The SD-pair shell model was applied to study the even-even^94 Mo-^100 Mo. It is found that with the SD pair determined as 01^＋ and 21^＋ states of a two-valence-nucleon system with a Hamiltonian, which contains the single particle energy term and the Surface-Delta interaction （SDI） between like nucleons, the collectivity of low-lying states can be described reasonably.     

Shell model calculations for heavy deformed nuclei

The pseudo SU(3) model is shown to be a powerful scheme for describing the excitation spectra as well asB(E2) andB(M1) transition strengths in heavy deformed nuclei. It is also useful for describing double beta decay amplitudes for transitions from the ground state of an even-even nucleus to the ground and excited states of the daughter nucleus, both for the two and zero neutrino emitting modes. The existence of selection rules which strongly restricts the decays is discussed. Anti-correlations between the quadrupole deformation and the Gamow-Teller (GT⁺) strength are found in an extension of the pseudo SU(3) model which explicitly includes pairing, which is also able to describe the fragmentation of the scissors mode. The projected shell model is introduced and proposed as an alternate means for studying single and double beta decay processes. Presented by J.G. Hirsch at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. This work was supported in part by CONACyT (México), CONICET (Argentina), NSF and DOE (U.S.A.).     

Microscopic calculations for upper-fp,g<Subscript>9/2</Subscript> shell nuclei: Ge &; Se

Shell-model calculations for isotopes of Ge and Se are reported where valence nucleons beyond the N = 28 = Z core occupy levels of the normal parity upper-fp shell (f_5/2,p_3/2,p_1/2) and the unique parity g_9/2 intruder configuration. Results are given for realistic interactions of the Kuo-Brown-3 type with various model space truncations that key in on the number of nucleon pairs allowed to occupy the intruder level. Electromagnetic (E2 & M1) rates as well as decay probabilities are calculated, some of which are key in determining the structure of “waiting point” nuclei that regulate certain nucleo-astrosynthesis processes. The role of the intruder level, which is treated on an equal footing with the normal parity levels, is shown to be important for reproducing structural details. The levels of the upper-fp shell are handled within the framework of a normal ls-coupled basis as well as its pseudo-SU(3) counterpart, and respectively, the g_9/2 as a single level and as a member for the complete gds shell. The second of these two approaches, namely, the SU(3) picture, allows one to better probe the effect of deformation.     

Study of structural and electronic transport properties of Ce-doped LaMnO3

The structural and electronic transport properties of La_1−x Ce _x MnO₃ (x=0.0–1.0) have been studied. All the samples exhibit orthorhombic crystal symmetry and the unit cell volume decreases with Ce doping. They also make a metal-insulator transition (MIT) and transition temperature increases with increase in Ce concentration up to 50% doping. The system La_0.5Ce_0.5MnO₃ also exhibits MIT instead of charge-ordered state as observed in the hole doped systems of the same composition.     

Five-dimensional quasispin and the spectra of odd-parity yrast configurations in the Ba region

The 5-dimensional quasispin formalism is used to evaluate the (n, T)-dependent factors of the matrix elements of abnormal parity operators of relevance for yrast-band spectroscopy. The formalism allows the leading pseudo-SU(3) representation of the normal (N) parity part of a shell-model configuration to be coupled to low-seniority states of the abnormal (A) parity high-j intruder part of the configuration. To illustrate the importance of the n_A, T_A dependence of the (A) to (N) space-coupling matrix elements this model is applied to the negative-parity yrast spectra of ¹²⁷La and ¹²⁷Ba, using hamiltonian parameters which give a reasonable fit for ¹²⁶Ba. The ¹²⁷La spectrum is reproduced with a seniority-one truncation of the h_{$\text{11}\text{2}$} configuration; the ¹²⁷Ba spectrum indicates a need for higher-seniority admixtures.     

Dynamical symmetries in contemporary nuclear structure applications

In terms of group theory—the language of symmetries, the concept of spontaneous symmetry breaking is represented in terms of chains of group-subgroup structures that define the dynamical symmetry of the system under consideration. This framework enables exact analytic solutions of the associated eigenvalue problems.     

A close look at the competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei

competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei is analyzed in the framework of the mean-field plus the dynamic quadurpole-quadurpole, pairing and particle-hole interactions, whose Hamiltonian is diagonalized in the basis U(24) ?(U(6) ? S U(3) ? S O(3))■(U(4) ? S US(2)■ S UT(2)) in the L = 0 configuration subspace. Besides the pairing interaction, it is observed that the quadurpole-quadurpole and particlehole interactions also play a significant role in determining the relative positions of low-lying excited 0~+ and 1~+ levels and their energy gaps, which can result in the ground state first-order quantum phase transition from J = 0 to J = 1.The strengths of the isovector and isoscalar pairing interactions in these even-even nuclei are estimated with respect to the energy gap and the total contribution to the binding energy. Most importantly, it is shown that although the mechanism of the particle-hole contribution to the binding energy is different, it is indirectly related to the Wigner term in the binding energy.     

Strength distributions and statistical spectroscopy II. Shell-model comparisons

The theory of the preceding paper is applied to a number of M1, E2, and E4 electro-magnetic excitations in the (ds)⁶ space. Comparisons are made in detail with shell-model results for the pth energy-weighted sum rules, with p = 0, 1, 2 and starting states spanning the entire spectra, as well as with the exothermic-endothermic decomposition of the non-energy weighted sum rule, and the RMS fluctuations in, and correlations between, the sum-rule quantities. Further comparisons are made for the strength distributions themselves. In all cases the agreements are good, for the sum rules remarkably so, so that the statistical theory describes very well the essential features of the strength distribution. The only (partial) exception is with the usual low-lying quadrupole collectivity found microscopically for two of the starting states (for which most of the strength goes to a single final state) and predicted, though not in such detail, via a statistical calculation of the effective number of final states available for the quadrupole transitions. We are seeing here a real coexistence of collective and statistical phenomena. At higher excitations, where concentration of much of the strength into a single state is not to be expected, all the essential features should be statistically describable. As a result of the comparisons, we expect that the statistical theory, supplemented by further methods for the evaluation of the necessary input traces, should give an almost complete account of the essential features of the strength distributions, even in model spaces of arbitrarily large dimensionality.