Comparison between formulas of rotational band for axially symmetric deformed nuclei

The experimental rotational spectra of the deformed nuclei available in even-even and odd-A nuclei in the rare-earth and actinide regions are systematically analyzed with several rotational spectra formulas,including Bohr-Mottelson's I(I+l)-expansion,Harris'w2-expansion,ab and abc formulas.It is shown that the simple 2-parameter ab formula is much better than the widely used 2-parameter Bohr-Mottelson's AB formula and Harris'αβ formula.The available data of the rotational spectra of both ground-state band in even-even nuclei and one-quaasiparticle band in odd-A nuclei can be conveniently and rather accurately reproduced by ab formula and abc formula.The moment of inertia and the variation with rotational frequency of angular momentum can be satisfactorily reproduced by ab and abc formulas.     

Analytical description of the coherent state model for near vibrational and well deformed nuclei

Analytical formulas for the excitation energies as well as for the electric quadrupole reduced transition probabilities in the ground, beta and gamma bands were derived within the coherent state model for the near vibrational and well deformed nuclei. Numerical calculations were performed for 42 nuclei exhibiting various symmetries and therefore with specific properties. Comparison of the calculation results with the corresponding experimental data shows a good agreement. The parameters involved in the proposed model satisfy evident regularities being interpolated by smooth curves. Few of them, which fall out of the curves, are interpreted as signatures for a critical point in a specific phase transition. This is actually supported also by the figures showing the excitation energy dependence on the angular momentum. The formulas provided for energies and $B\left(E2\right)$ values are very simple, being written in a compact form, and therefore easy to be handled to explain the new experimental data.     

IBA calculations on the even-even Pt isotopes

By performing least-squares-fit calculations on the energy spectra of the even-even ^186–196Pt isotopes, the IBA model I and the IBA model II are compared on an equal footing. It is found that both model I and model II can fit energy spectra and absolute B(E2) transition rates reasonably well. Model II shows a distinct improvement in the energy spectra of β-bands of heavier nuclei in the isotope series. It is suggested that for regions far from the closed shells model I may be used to simulate model II as a useful phenomenological probing tool.     

Empirical pairing gaps and neutron-proton correlations

Analysis of various mass formulas related to neutron-proton correlations in atomic nuclei is carried out.Using the example of the N =Z chain it is shown that for self-adjoint nuclei various formulas proposed in literature for estimating the np pairing energy lead to similar results. Significant differences between the calculation methods arise when nuclei with N = Z are considered, which allows to reveal the complexity of neutron-proton correlations in different types of atomic nuclei and to make assumptions on the correspondence of the mass relation to the real effect of np pairing. The Shell Model parametrization of the binding energy makes it possible to draw additional conclusions on the structure of mass formulas and their relationship.     

Empirical formulas for proton decay half-lives:Role of nuclear deformation and Q-value

Two empirical formulas for the proton decay half-lives including nuclear deformation are proposed. The formula with parameter set I gives the logarithm of the proton decay half-lives as an explicit function of the orbital angular momentum with eight adjustable parameters, whereas that with set II represents the logarithm of the reduced half-lives as an implicit function of the angular momentum with seven adjustable parameters. Experimental data for the half-lives of 44 proton emitters in the ground state or isomeric state were used to obtain the parameters. The experimental and calculated Q values were used. Different sets of parameters were obtained for the ground state transition, isomeric state transition, and all transitions for both deformed and spherical nuclei. The best agreement with experimental data was observed for set I for deformed proton emitters with experimental Q values.     

Diffraction scattering of Λ 3 H and Λ 6 He hypernuclei on nuclei with allowance for edge diffuseness, the structure of hypernuclei, and multiple-scattering effects

General formulas for the amplitudes of the diffraction scattering of two-and three-cluster loosely bound nuclei on spherical nuclei for an arbitrary dependence of the profile functions on the impact parameter are represented in a form that is convenient for calculations. The differential cross sections for the elastic scattering of _Λ ³ H and _Λ ⁶ He hypernuclei and the total cross sections are obtained with allowance for the diffuseness of the target-nucleus edge, the binding energy of incident hypernuclei, the ranges of nuclear forces between the clusters in the hypernuclei, and multiple (double and triple) scattering. Changes in the behavior of the cross sections in response to a transition from the two-cluster to the three-cluster model of the aforementioned nuclei are revealed.     

A simple model of superheavy nuclei

I present a simple algebraic model of superheavy and superdeformed nuclei, produced through heavy-ion collisions, based on a microscopic evaluation of the effective boson numbers in the actinide and superheavy regions. The relevant calculations have been performed within the framework of a deformed shell model, including the pairing interaction between like-particles. As far as the actinide isotopes are concerned, the theoretical boson numbers are compared with the corresponding empirical estimates, obtaining a good agreement. The calculated boson numbers are used to predict collective spectra and electromagnetic transition intensities for actinide — including fission isomers — and superheavy nuclei, by using the interacting boson model (IBM).     

Formation kinetics of brittle phase nuclei in hydrogenated metals under loading

It is shown that the formation of the brittle phase in hydrogenated metal under external loading is a first-order phase transition. The basic equation of the evolution of elastic stress in a uniform and isotropic hydrogenated metal during the formation of a brittle hydride phase is derived and its solution is found. Based on this data, the time dependences of all characteristics of the phase transition into a brittle phase are found; namely, the densities of nuclei of the hydride phase, the size distribution, and the formation rates of the hydride phase nuclei are found. The characteristic time of the transition into the brittle phase is found.     

The effect of surface and Coulomb interaction on the liquid–gas phase transition of finite nuclei

By means of the Furnstahl, Serot and Tang's model, the effects of surface tension and Coulomb interaction on the liquid–gas phase transition for finite nuclei are investigated. A limit pressure p_lim above which the liquid–gas phase transition cannot take place has been found. It is found that comparing to the Coulomb interaction, the contribution of surface tension is dominate in low temperature regions. The binodal surface is also addressed.     

Pair Excitations in Even-Even Nuclei

A charge exchange term is added to the n-p effective interaction in treating eveneven nuclei with shape coexistence. The energy spectra and some of the E2 transition rates are calculated for ^112,114Cd, ^114,116Sn and ^118,120Te nuclei. The inclusion of this new term helps to improve an agreement with experimental data.     

Theoretical investigation of the Gamow-Teller transition across N=40 shell

The Gamow-Teller transitions for pf shell nuclei with proton number less than 40 and neutron number larger than 40 were believed to be blocked, due to the full filling of the neutron orbit. However, recent experimental research shows that the Gamow-Teller transitions for these kinds of nuclei are not blocked. In this paper, we systematically calculate the GT transition of pf shell nuclei ⁷⁶Se in different truncations, and the results are compared with experimental results. It is shown that, due to correlations, the believed blocked GT transition occurs, and the shell model calculations reproduce the experimental GT strength. In addition, the electron capture rates in a stellar environment are calculated and discussed.     

Two-phonon states in doubly even nuclei with 30 ≦ Z ≦ 52

Results of a survey of energies of two-phonon states are presented. Systematic trends are extracted and parametrized with the anharmonic vibrator model. The doubly even nuclei with anomalous 0⁺ first excited states are fitted into a general pattern indicating profound influence of both proton and neutron shell closure on the lowering of the 0^+' state energies. A sharp transition from anharmonic vibrational to almost pure rotational motion in this nuclear region is suggested for nuclei with first excited 2⁺ state energy ≈ 130 keV. Such a possible transition and similar ones already well known in the rare earth and heavy element regions are well described by the model.     

U(6/4) supersymmetry in nuclei

We suggest that supergroups and superalgebras may be useful in classifying the spectra of certain even-even and even-odd nuclei. We show, in particular, that properties of many states in several nuclei, including excitation energies, electromagnetic transition rates and transfer reaction intensities, can be described by a U(6/4) supersymmetry. Our analysis provides the first evidence for the occurrence of supersymmetry in nature.     

Alternative interpretation of sharply rising E0 strengths in transitional regions

It is shown that strong 0(+)(2)-->0(+)(1) E0 transitions provide a clear signature of phase transitional behavior in finite nuclei. Calculations using the interacting-boson approximation (IBA) show that these transition strengths exhibit a dramatic and robust increase in spherical-deformed shape transition regions, that this rise matches well the existing data, that the predictions of these E0 transitions remain large in deformed nuclei, that they arise from the specific d-boson coherence in the wave functions, and do not necessarily require the explicit mixing of normal and intruder configurations from different IBA spaces.     

Observables for the even type of nucleon in the ground states of odd-mass nuclei

Existing data for lighter nuclei on observables, including magnetic moments and single particle multiple moments, are explained if the even nucleons are predominantly coupled to spin zero but with a substantial spin-2 wave function component. Strong predictions can be made on the basis of such wave functions regarding spectroscopic sum rules and the behaviour of general observables such as B(EL) transition rates.     

Binding energies of nuclei

A new theoretical method is proposed to describe known properties of nuclei. The method is based on the theory of nuclear forces given in an earlier paper and results in formulas for the binding energies and dimensions of nuclei which accord with experimental data.     

超越平均场模型对Ba同位素链八极形状演化研究

本文采用超越平均场模型研究了缺中子Ba同位素链114-124Ba的八极形变及其演化规律。计算了Ba链的位能曲面、低能激发谱、电四极跃迁几率、电八极跃迁几率及集体波函数的几率密度分布,并与实验相比较。理论计算较好地再现了Ba核的低能激发结构。位能曲面、低能的负宇称带、较大的B（E3;3₁- → 0₁+）和展宽的几率密度分布表明,114Ba中存在较强的八极关联。116,118Ba具有过渡核特征,而120-124Ba则为典型的四极形变原子核。     

Models of fragmentation with composite power laws

Some models for binary fragmentation are introduced in which a time dependent transition size produces two regions of fragment sizes above and below the transition size. In the first model we assume a fixed rate of fragmentation for the largest fragment and two different rates of fragmentation in the two regions of sizes above and below the transition size. The model is solved exactly in the long time limit to reveal stable time-invariant solutions for the fragment size and mass distributions. These solutions exhibit composite power law behaviours; power laws with two different exponents for fragments in smaller and larger regions. A special case of the model with no fragmentation in the smaller size region is also examined. Another model is also introduced which have three regions of fragment sizes with different rates of fragmentation. The similarities between the stable distributions in our models and composite power law distributions from experimental work on shock fragmentation of long thin glass rods and thick clay plates are discussed.     

Dynamic electron screening in nuclear and mesonic atom E1 transitions

Atomic electrons can influence the electromagnetic transition rates of nuclei and mesonic atoms. We examine this dynamic electron screening effect for E1 transitions. The screening factor is expressed in terms of the forward Rayleigh scattering amplitude, and, for easy computation, the photoelectric cross section. We find that the effect can be large for low-energy transitions, but such transitions are rare for nuclei. The effect on mesonic atom cascades is usually small, but can be quite significant for high-precision experiments and those which look at transitions from high initial n.