Energy Staggering in the High K Rotational Band

Introducing the staggering index S(I) to describe the energy spectra of the λrigid and λ-soft nuclei, it becomes very clear that there are two kinds of energy staggering for which the S(I) -I plots have opposite zigzag behavior. They can be described using the axially asymmebtric rotor model with vibration-rotation coupling and the interaction boson model O(6) limit with three-body potential or the angular momentum projection deformed Hartree-Fock method (PDHF ), respectively. The theoretical predictions for the characteristics of the staggering in high K rotational band are given. Analyzing the experimental data of high K band spectra of the nuclei in the mass range. 160, it is demoastrated that the energy staggering does exist in the high K band. At the same time, some evidences for the shape transition indicated by zigzag phase change of S(I)-I plots are undoubtedly found.     

Energy Staggering in Ground Bands of 232Th and 236,238U Nuclei Using the Interacting Vector Boson Model

The ΔI=2 and ΔI=4 staggering parameters of transition energies E_γ for normally deformed positive parity ground bands in ²³²Th and ^236,238U nuclei are studied in framework of the symplectic extension of the interacting vector boson model. The model parameters are obtained from the fitting procedure between the calculated excitation energies and the corresponding experimental ones. The staggering parameters represent the finite difference approximations to higher order derivatives dⁿE_γ/d Iⁿ of the γ -ray transition energies in a ΔI=2 and ΔI=4 bands, which yielding multipoint formulae. The first order derivative (two-point formula) provides us with information about the dynamical moment of inertia. The staggering oscillation for the fourth order derivative (five-point formula) is about 0.5 KeV and is even larger than that in superdeformed bands. The quite similarity in dynamical moments of inertia of the isotopes ^236,238U up to high spin states indicate that the phenomenon of identical bands is not restricted to superdeformed bands.     

Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field

We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei ¹⁶O and ²⁰⁸Pb, the deformed nucleus ²⁰Ne. Good agreement is obtained.     

Nuclear Level Density with Non-zero Angular Momentum

The statistical properties of interacting fermions have been studied for various angular momentum with the inclusion of pairing interaction. The dependence of the critical temperature on angular momentum for several nuclei, have been studied. The yrast energy as a function of angular momentum for 28Si and 24 Mg nuclei have been calculated up to 60.0 MeV of excitation energy. The computed limiting angular momenta are compared with the experimental results for ^26Al produced by ^12C＋ 14N reaction. The relevant nuclear level densities for non-zero angular momentum have been computed for ^44Ti and ^136 Ba nuclei. The results are compared with their corresponding values obtained from the approximate formulas.     

190，192Pb原子核的超形变带的带外衰变（英文）

将基于组合方法的角动量投影的位能曲面群用于研究铅同位素原子核190,192Pb 的超形变转动带。位能曲面群计算中采用了Gogny D1S 以及Skyrme SkP SLy4 三种相互作用。如用Gogny D1S 相互作用,190Pb 原子核没有明显的超形变转动带,而192Pb 原子核有非常显著的超形变转动带。用W. K. B. 方法计算了192Pb 原子核的超形变带穿透宽度。该穿透宽度很大与用GW模型（Nucl. Phys. A 660 （1999）197）分析实验数据给出的结果相近。在Gogny D1S 相互作用情形下,就角动量投影对位能曲面群的影响作了讨论,发现角动量投影压低了分隔超形变转动带与正常形变转动带之间的位垒。还用Skyrme SkP 和SLy4 相互作用计算了角动量投影的位能曲面群,发现位垒明显高于Gogny D1S 相互作用给出的位垒。在Skyrme 相互作用情形下,192Pb 原子核的超形变带穿透宽度明显小于Gogny 相互作用给出的宽度,但是较SB方法（Phys. Rev. C,60 （1999） 051305） 分析实验数据得到的结果高出几个数量级。于是,对SB 方法提出了质疑,因为它给出了极其微小的传播宽度。The combined method is applied to calculate the angular momentum projected potential energy surfaces (AMPPES) of 190,192Pb. The Supper-deformed(SD) rotational bands of the two nuclei are studied with the AMPPES computed with the Gogny D1S and Skyrme SkP and SLy4 interactions. It is found that there is no pronounced SD band in 190Pb in the case of the Gogny interaction, which is consistent with the experimental observation. A well developed SD band with the Gogny interaction is found in 192Pb. The tunneling width of 192Pb is comparable to that given by the GW approach (Nucl. Phys. A 660 (1999)197) and orders of magnitude larger than that given by the SB approach (Phys. Rev. C 60 (1999) 051305). The influence of the angular momentum projection on the potential energy surfaces is examined in the case of the Gogny interaction for 190,192Pb. It is shown that the angular momentum projection suppresses the barrier separating the SD and ND rotational bands. Higher barriers of the AMPPESs for the two nuclei computed with the Skyrme SkP and SLy4 interactions are obtained compared with those given by the Gogny force. The tunneling width of 192Pb is also big for the Skyrme interactions. We put the SB approach into question which gives only an extremely small spreading width.     

Structure Evolution in the Even-Even 124-134Xe with IBM2

We have investigated the structure evolution of the ^124-134Xe isotopic chain in the framework of the proton-neutron interacting model IBM2. The positive parity spectra of the ground state, quasi-β and quasi-γ bands are reproduced well. The staggering in ^124-130Xe are almost completely removed and the γ band agree well with the experiment data, even for the high-spin quasi-γ states. The key quantities of the collective structure evolution, including level energies, the B(E2) transition branching ratios, and the M1 excitations to 1₁⁺ mixer-symmetry states are analyzed by comparing with the experimental data. The parameters for representation of the O_πν(6) and SU_πν^*(3) features in isotopes are examined. Both experimental data and theoretical results show that the shape phase transition of ^124-134Xe isotopic chain is from the SU_πν^*(3) (triaxial rotation) to the U_πν(5) (vibration motion) with a considerable constituent of the O_πν(6) symmetry (γ-unstable rotation), where the shape phase transition rapidly takes place between the neutron number N = 76 and N = 78.     

SEEKING FOR THE U(5) LIMITING CASE OF IBA-Ⅱ

In the region of even-even nuclei from A=96 to A=120, only the energy spectrum of ¹¹⁰₄₈Cd₆₂ may be described by IBA-Ⅱ involving the states {N_π +N _L -1,1}. But it can be described by IBA-Ⅰ too. To distinguish these two schemes, more angular momentum measurement is needed.     

稀土区奇A核晕带存在从转动到振动形状演化的直接证据(英文)

原子核的形状演化效应是核结构研究的重要基础问题之一。通常认为,A=160质量区的奇A核位于大形变核区域,它们的激发态能谱将呈现出典型的转动激发特征。然而,基于E-GOS曲线方法,发现随着角动量的增加,该质量区奇A核的晕带具有显著地从转动激发演化成为振动激发的形状演化现象。此外,为深入理解原子核形状演化的微观机制,采用Total-Routhian-Surface（TRS）方法针对稀土区的奇A核进行了理论计算,结果表明,165Yb和157Dy同位素在低激发态时具有稳定的长椭形变,当角动量大于0.50 MeV后,核芯的四极形变显著减小并开始产生三轴形变。The phase transition of nuclei with increasing angular momentum (or spin) and excitation energy is one of the most fundamental topics of nuclear structure research. The odd-N nuclei with A ≈160 are widely considered belonging to the well-deformed region, and their excitation spectra are energetically favored to exhibit the rotational characteristics. In this work, however, the evidence suggesting that the nuclei changes from rotation to vibration along the yrast lines as a function of spin was found. The simple method, named as E-Gamma Over Spin (E-GOS) curves, would be used to discern the evolution from rotational to vibrational structure in nuclei for various spin ranges. Meanwhile, in order to understand the band structure properties of nuclei, theoretical calculations have been performed for the yrast bands of the odd-A rare-earth nuclei within the framework of the total routhian surface (TRS) model. The TRS plots predict that the 165Yb and 157Dy isotopes have large quadrupole shapes at low spin states. At higher rotational frequency (hω~ >0.50 MeV), a clear reduction of the quadrupole deformation is indicated by the present results, and the isotopes become rigid in the γ deformation.     

Studies on the Ne(p, d)Ne and Ne(d, p)Ne reactions

Angular distribution measurements have been performed on the ²¹Ne(p, d)²⁰Ne and ²¹Ne(d, p)²²Ne reactions at E_p = 20 MeV and E_d = 10.2 MeV, respectively. In the ²¹Ne(p, d) ²⁰Ne reaction, the prolific formation of the J^π = 2⁺, 1.63 MeV state was characterized by l_n = 2 pickup, and the distribution associated with the 4⁴, 4.25 MeV state was suggestive of a weak l_n = 2 pickup. All of the observed l_n = 1 pickup strength is associated with formation of the 2⁻, 4.97 MeV ²⁰Ne level. The ²¹Ne(d, p)²²Ne results indicate that l_n = 2 transfer is involved in the formation of the 1.28, 3.36, 5.52, 5.63 and 6.65 MeV ²²Ne states. The angular distribution observed for the 2⁺, 4.46 MeV state and also the unresolved 5.33, 5.36 MeV composite of states required both l_n = 0 and l_n = 2 components in the associated distorted-wave Born approximation fits. The spectroscopic factors extracted from the present results are compared with those predicted by the Nilsson model without mixing: Applications of the angular momentum projection rule to the ²¹Ne(d, p)²²Ne reaction are considered.     

APPROXIMATE ANGULAR MOMENTUM PROJECTION OF THE DEFORMED HARTREE-FOCK STATE FOR K=1

Using our approximate angular momentum projection method with one parameter, the projection spectra of the axially symmetric Hartree-Fock intrinsic states are studied. The approximate and the exact projection matrix elements are obtained and compared each other. The projection integrals for angular momentum J=1 to 11 are given. The energy spectra of the nuclei ⁴⁴Ti and ⁵⁰Ti are calculated, and the results coincide with the observed energy levels fairly well.     

Er，Yb和Hf同位素的基态占有率（英文）

应用严格求解的Nilsson 平均场加推广对力模型,在同时考虑质子-质子和中子-中子间对力相互作用的情况下,对稀土区的152-164Er,154-166Yb 和156-168Hf 核素的结合能、奇偶能差、低激发态转动惯量等基态性质进行系统的统一描述。通过计算结果与实验数值比较分析显示,对力相互作用在阐明以上核素能谱的基态性质中起到了关键的作用。应用拟合上述物理量所确定的模型参数,对156-162Yb 核素基态中价核子配成角动量J = 0,1,… ,12的价核子对占有率的计算结果显示,配成角动量为偶数价核子对的占有率远远高于配成角动量为奇数价核子对的占有率,其数值结果揭示了配成角动量为S,D和G的价核子对在所考虑的核素基态性质中占主导地位。The Nilsson mean-field plus extended-pairing model for deformed nuclei is applied to describe the ground-state properties of selected rare-earth nuclei. Binding energies, even-odd mass differences, moments of inertia for the ground-state band of 152-164Er, 154-166Yb, and 156-168Hf are calculated systematically in the model employing both proton-proton and neutron-neutron pairing interactions. In comparison with the corresponding experimental data, it is shown that for these rare-earth nuclei, pairing interaction is crucial in elucidating the properties of the ground state. With model parameters determined by fitting the energies of these states, ground-state occupation probabilities of valence nucleon pairs with angular momentum J =0,1, …,12 for even-even 156-162Yb are calculated. It is inferred that the occupation probabilities of valence nucleon pairs with even angular momenta are much higher than those of valence nucleon pairs with odd angular momenta. The results clearly indicate that S, D, and G valence nucleon pairs dominate in the ground state of these nuclei.     

利用18O(6Li,d)22Ne反应研究22Ne Eα=470 keV共振态的性质

慢速中子俘获过程（s过程）是合成比铁重元素的重要途径之一。22Ne（α,n）25Mg反应是大质量AGB星中s过程主要的中子源,其中的22Ne主要通过14N（α,γ）18F（β+）18O（α,γ）22Ne反应链合成。该反应链中关键反应18O（α,γ）22Ne在天体物理感兴趣能区的截面非常低,其天体反应率主要来自于22Ne α分离阈附近低能共振态的贡献,但目前相关能级的共振参数严重缺失。在HI-13串列加速器的Q3D磁谱仪上,通过测量18O（6Li,d）22Ne反应的角分布,利用DWBA分析确定了22Ne分离阈附近共振能级E_α=470 keV的自旋宇称为0+,为后续计算18O（α,γ）22Ne的天体反应率打下了基础。About a half of the abundances of elements heavier than iron comes from the so-called slowneutron capture process (s-process) in Asymptotic Giant Branch (AGB) stars, with the 22Ne(α, n)25Mg reaction as one of the main neutron sources. In the beginning phase of AGB thermal pulse, 22Ne is produced by the 14N(α, γ)18F(β+)18O(α, γ)22Ne reaction sequence, in which the 18O(α, γ)22Ne reaction plays a key role. While the reaction rate of the 18O(α, γ)22Ne is mainly affected by several resonant states lying closely to the α threshold in 22Ne, up to now, the relevant 22Ne parameters are fragmentary in the energy region corresponding to the typical temperatures of s-process. The direct measurement of the 18O(α, γ)22Ne reaction rate is extremely difficult due to the very low cross section. In this work, we investigated the 22Ne resonant states via the 18O(6Li, d)22Ne reaction at the Beijing HI-13 tandem accelerator of China Institute of Atomic Energy. Based on the DWBA analysis, preliminary results showed that the spin-parity of 22Ne E_α=470 keV resonant states was assigned as 0+, which would make contributions to subsequent calculation for the reaction rate of the 18O(α, γ)22Ne.     

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions

We explore the tricritical points and the critical lines of both Blume-Emery-Griffiths and Ising model within long-range interactions in the microcanonical ensemble. For K=K_MTP, the tricritical exponents take the values β=1/4, 1=γ^-≠γ⁺=1/2 and 0=α^-≠α⁺=-1/2, which disagree with classical (mean field) values. When K>K_MTP, the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K_CTP), where the values of the critical expoents become β=1/2, 1=γ^-≠γ⁺=2 and 0=α⁺≠α⁺=1.     

Nuclear structure studies in the tellurium isotopes: the Te(d, p)Te reaction

The levels of ¹²⁷Te have been studied with the ¹²⁶Te(d, p)¹²⁷Te reaction at 7.5 MeV bombarding energy using the MIT multiple-gap broad-range magnetic spectrograph. A total number of 154 levels was observed below 5.7 MeV excitation energy. The angular distributions of 47 of the emitted proton groups were compared with DWBA stripping calculations to determine the orbital angular momentum of the captured neutrons. Transition strengths (2J+1)S_{ln, j} were extracted and compared to pairing-theory calculations. The total number of vacancies measured in the and states in the target is 6.0 , which is considerably lower than the expected value of 7.4 from pairing theory. It is suggested that this discrepancy results mainly from failure of the DWBA theory to predict the correct cross section for the l_n = 5 transition.     

95Zr(n,γ)96Zr的间接测量

95Zr（n,γ）96Zr是稳定燃烧的恒星中合成96Zr的唯一途径,对研究恒星演化和重元素合成具有重要的意义。由于95Zr半衰期为64 d,直接测量95Zr（n,γ）96Zr截面极为困难,因此,本工作采用替代比率法间接测量95Zr（n,γ）96Zr截面。本工作测量了94Zr（18O,16Oγ）96Zr和90Zr（18O,16Oγ）92Zr反应,得到了复合核96Zr*和90Zr*衰变到γ道的几率比,并利用截面已知的91Zr（n,γ）92Zr截面乘以实验所测比率,得到了E_n=0~8 MeV能区的95Zr（n,γ）96Zr中子俘获截面。95Zr(n, γ)96Zr cross section is important for the study of stellar evolution and heavy elements nucleosynthesis because the reaction is the only way to produce the 96Zr in Asymptotic giant branch stars. The direct measurement of 95Zr(n, γ)96Zr is very difficult due to the short half-life of 95Zr, 64 days. The surrogate ratio method was carried out to measure 95Zr(n, γ)96Zr cross sections. We measured the 94Zr(18O, 16Oγ)96Zr and 90Zr(18O, 16Oγ)92Zr reactions and obtained the γ-decay probability ratio of compound nuclei 96Zr* and 92Zr*. The 95Zr(n, γ)96Zr cross section is determined by the obtained ratio multiplying the known 91Zr(n, γ)92Zr cross section at E_n=0~8 MeV.     

Rotational Property of~(249)Cm in Particle-Triaxial-Rotor Model

We study the rotational energy spectrum and deformation feature of very heavy nucleus 249Cm in the particle-triaxial-rotor model with variable moment of inertia.Such a nucleus is the unique one involving both multiband structure and high spin states and locating very near the superheavy region.By calculating the energy spectrum,we determine the configurations and quadrupole and triaxial deformation parameters β and γ of the nucleus.The calculated results indicate that the high spin band of 249Cm is built upon the ν[620] 12+configuration with deformation parameters β = 0.296 and γ = 7.5 and the bands based on the ν[622] 32+,ν[613] 72+,ν[750] 12 configuration respectively are also the ones with quite large axial deformation but small triaxial deformation.     

A study of the Ti(He, t) and Ni(He, t) reactions to isobaric analogue states

The (³He, t) reaction populating 0⁺ and 2⁺ states in ^{58, 60}Cu and ^{46, 48}V which are isobaric analogue states (IAS) of the 0⁺ ground states and 2⁺ first excited states in ^{58, 60}Ni and ^{46, 48}Ti have been studied at an incident ³He energy of 24.6 MeV. Triton spectra were measured for the targets ^46,48Ti, ^natNi and ⁵⁸Ni and angular distributions for the 0⁺ and 2⁺ IAS of ^{46, 48}Ti and ^{58, 60}Ni determined. The data were obtained using a magnetic spectrometer and position-sensitive detectors. The results have been analysed using DWBA theory. The 0⁺ → 0⁺ transitions to analogue states are described quite well using a microscopic form factor derived from a nucleon-nucleon interaction. However, with a Gaussian form, the m.s. radius of this interaction is only limited to the region 0–9 fm². Comparisons with data at other incident energies indicate that the strength of the effective interaction is strongly energy dependent. The Coulomb energies and (³He, t) angular distributions of the states assigned as the 2⁺ analogues in ⁴⁸V and ^58,60Cu are not described well by the models investigated. The ⁴⁶V 2⁺ IAS angular distribution is reproduced by a microscopic calculation, however. The ratios of the 0⁺ → 2⁺ IAS to the 0⁺ → 0⁺ IAS transitions are used to deduce a quadrupole deformation for the valence neutrons. The difference in the quadrupole deformations of the matter and proton distributions, as determined by other means, is found to be correlated with those of the valence neutrons. Several transitions to non-analogue states are also investigated.     

A study of the level structure in Fe from the (d, p) reaction on Fe

The reaction ⁵⁶Fe(d, p)⁵⁷Fe is investigated at 12 MeV using the Aldermaston multi-channel magnetic spectrograph. The angular distributions of protons leading to various states in ⁵⁷Fe upto an excitation of 6.7 MeV are measured over an angular range 5°–175°. The data are analysed with the distorted wave Born approximation calculations; a satisfactory agreement is found in most cases upto about 100°. Spin, parity and the spectroscopic factors for various states are obtained and the positions of the single-quasiparticle energies determined. The results are compared with those for the isotonic nuclei ⁵⁵Cr and ⁵⁹Ni and with the pairing theory.     

THE QUARK MASS EFFECT OF THE DISTRIBUTION AMPLITUDES IN γγ-EXCLUSIVE PROCESSES

In this paper we have analyzed the γ^*π°→γ, γγ→ππ and γγ→ρρ processes by using the sum rules of the distribution amplitude ФM(xi,Q²), which are obtained from the π°→γγ and the π→μν decay processes. Since the angular distributions of the γγ→π°π° and γγ→ρ_⊥ρ_⊥ amplitudes are sensitive to the shape of the distribution amplitude ФM(xi,Q²), there is a possibility to investigate the effect of the quark mass from the angular distributions of γγ→MM exclusive processes.     

APPLICATIONS OF THE MODIFIED SURFACE DELTA INTERACTION IN THE ANGULAR MOMENTUM PROJECTION DEFORMED HAREE-FOCK METHOD

In this paper a modified surface delta interaction with an angular momentum correction term is proposed.By using this interaction the deformed Hartree-Fock and the approximate angular momentum projection calculations are performed for even-even nuclei in mass region A=56—74.The single particle energy spectra of the ground state configurations obtained are more reasonable than that calculated with KB matrix elements.The agreement of the calculated binding energies and projection energy spectra with experimental ones is fairly good.