原子核的形状相变

简要回顾原子核形状相变研究的现状，并将相干态理论与角动量投影方法相结合，在不区分质子玻色子和中子玻色子的相互作用玻色子模型（IBM-1）框架下，对角动量驱动的轴对称情况下的具有U（5）、SU（3）对称性以及两种对称性之间过渡区的原子核的形状相变进行了具体研究。We review the status of the research of nuclear shape phase transitions in this paper. Meanwhile, by taking the coherent state theory and angular momentum projection method, we study the shape phase transitions of axially symmetric even-even nuclei with U（5） symmetry, SU（3） symmetry and those in the transitional region of the two symmetries in the framework of Interacting Boson Model-1 （IBM-1）, which does not distinguish the proton bosons from neutron bosons.     

有限玻色子系统中的激发态量子相变

为了探讨原子核系统中存在激发态量子相变的可能性,在相互作用玻色子模型框架下对有限玻色子系统中的激发态量子相变现象进行唯象分析,特别是针对角动量和有限N效应如何影响U（5）-SU（3）和SU（3）-O（6）过渡区中的激发态量子相变行为进行了系统研究。结果表明,低角动量振动谱中的激发态量子相变特征在现实玻色子数情况下可以很好地保持,但随着角动量增加相变特征逐渐消失。In this work, a phenomenological analysis of the excited-state quantum phase transitions (ESQPTs) in the finite-N boson system has been carried out within the interacting boson model in order to reveal the possibility of finding ESQPTs in nuclear systems. Particularly, the angular momentum and finite-N effects on the ESQPTs in the U(5)-SU(3) and SU(3)-O(6) transitional regions have been systematically investigated. The results indicate that the main features of ESQPTs can be well preserved even at a realistic boson number for small angular momentum but will gradually disappear as the angular momentum increases.     

SD对壳模型下原子核形状相变（英文）

在SD 对壳模型的理论框架下讨论了原子核形状相变模式。研究结果表明,该理论模型可以把相互作用玻色子模型中U（5）-SU（3）以及U（5）-SO（6） 形状相变模式再现出来,相互作用玻色子模型中有关临界点对称性的特征也可以很好地描述。本文同时也发现原子核从振动到转动的形状相变可以通过改变相互作用强度来实现。The nuclear shape phase transitional patterns were studied in the SD-pair shell model. The results show that the transitional patterns similar to the U(5)-SU(3) and U(5)-SO(6) transitions in the interacting boson model can be produced. The signatures of the critical point symmetry in the interacting boson model are also produced approximately. It is also found that the shape phase transitional pattern between vibration and rotation can also be produced by changing the interactional strength.     

相互作用玻色子模型中振转过渡区的特征研究

详细研究了相互作用玻色子模型中U(5)振动极限到SU(3)转动极限的相变行为.通过对能谱和E2跃迁强度等的分析,说明了在临界点的核具有最大的非刚性. Transitional patterns from the U(5) vibrational limit to the SU(3) rotational limit in the interacting Boson model are studied in detail. The transitional behavior of low-lying energy levels, isomer shifts, E2 transition rates, and some other related quantities across the entire region are investigated. The results show that nuclei in the critical region are most non-rigid.     

Two simple schemes for implementing Toffoli gate via atom--cavity field interaction in cavity quantum electrodynamics

This paper proposes two schemes for implementing three-qubit Toffoli gate with an atom (as target qubit) sent through a two-mode cavity (as control qubits). The first scheme is based on the large-detuning atom--cavity field interaction and the second scheme is based on the resonant atom-field interaction. Both the situations with and without cavity decay and atomic spontaneous emission are considered. The advantages and the experimental feasibility of these two schemes are discussed.     

Shape co-existence and structural evolution of the Vi13/2 band in 157Yb

The high-spin states of 157Yb have been studied via the reaction of 144Sm(16O, 3n) at 16O energy of 90 MeV using techniques of in-beam γ-ray spectroscopy. Measurement of γ-γ-t coincidences was performed with 11 BGO(AC)HPGe detectors. Based on the γ-γ coincidence relationships and the measured results of γ-ray anisotropies and DCO ratios, the level scheme for 157Yb was established. The shape co-existence and structural evolution of the Vi13/2 band with increasing angular momentum in 157Yb have been discussed. The systematics of the Vi13/2 bands in the N = 87 odd-A isotones have been compared.     

Rare Decay Process K→πvv^- in Three-Site Higgsless Model]

Rare decay processes K→πvv^- and KL→π^0vv^- are considered in the framework of three-site Higgsless model. The contributions of this new physics model to these two decay processes come from the new heavy gauge bosons and the correction terms for the couplings of the ordinary gauge bosons with fermions. Our numerical results show that the branching ratios of these two decay processes can be enhanced by 40% and 50% relative to those predicted by the standard model.     

Critical behaviour in nuclear structure from spherical to axially symmetric deformed shape in IBM

To compare with the predictions of the transitional dynamical symmetry X(5) proposed by Iachello (2001 Phys. Rev. Lett. 87 052502), the critical behaviours of U(5)--SU(3) are studied in the space of two control parameters in the interacting boson model (IBM). A simple-shaped phased diagram has been presented. It is found that X(5) predictions cannot be exactly reproduced by our calculations and that the best agreement is close to the calculations with boson numbers N = 11 and 12. By comparing with experimental data on X(5)-like nuclei, we find that X(5) predictions and IBM calculations can reproduce the energy ratios and E2 transition ones.     

Analysis of High Accuracy Conservation-Element and Solution-Element Schemes

We propose a technique to construct higher accuracy conservation element and solution element (CE/SE) schemes.A second-order CE/SE scheme is established and its stability condition is examined on the basis of the von Neumann necessary condition. From the viewpoints of accuracy and efficiency, the applied range of the one-order CE/SE scheme and the high-order ones is discussed through some numerical examples.     

Critical Behavior in Nuclear Structure from Spherical to γ-Soft Deformed Shape in IBM

Comparing with the predictions of the transitional dynamical symmetry E（5） proposed by Iachello [Phys. Rev. Lett. 85 （2000） 3580], the critical behaviors from U（5）-0（6） are studied in the space of two control parameters in the interacting boson model. A simple shape phase diagram has been presented. It is found that E（5） predictions cannot be exactly reproduced by our calculations and that the best agreement is close to the calculations with boson number N = 9. By comparing with experimental data on E（5）-like nuclei, we find that E（5） predictions and IBM calculations can reproduce the energy ratios and E2 transition ones.     

Nuclear Structure and Electromagnetic Transitions Investigation in Er Isotopes within Framework of Interacting Boson Model

Interacting Boson Model-2 (IBM-2) is used to determine the Hamiltonian for Er nuclei. Fit values of parameters are used to construct the Hamiltonian, energy levels and electromagnetic transitions (B(E2), B(M1)) multipole mixing ratios (δ(E2/M1)) for some even-even Er nuclei and monopole transition probability are estimated. New ideas are used for counting bosons number at N = 64 and results are compared with previous works.     

An IBM2 Description of the E(5) Symmetry in 134Ba and 108pd

With the low-lying energy levels, E2 transition branching ratios and absolute transition rates of the 134Ba and 108Pd, are investigated in the neutron-proton interacting boson model (IBM2) which includes the quadrupole quadrupole interaction between like bosons and the E(5) symmetry, it shows that the IBM2 can describe the nuclei at critical point of a phase transition well.     

An IBM2 Description of the E(5) Symmetry in 134Ba and 108Pd

With the low-lying energy levels, E2 transition branching ratios and absolute transition rates of the ¹³⁴Ba and ¹⁰⁸Pd, are investigated in the neutron-proton interacting boson model (IBM2) which includes the quadrupole-quadrupole interaction between like bosons and the E(5) symmetry, it shows that the IBM2 can describe the nuclei at critical point of a phase transition well.     

U(5)-SU(3) nuclear shape transition within the interacting boson model applied to dysprosium isotopes

In the framework of the interacting boson model (IBM) with intrinsic coherent state, the shape Hamiltonian from spherical vibrator U(5) to axially symmetric prolate deformed rotator SU(3) are examined. The Hamiltonian used is composed of a single boson energy term and quadrupole term. The potential energy surfaces (PES’ s) corresponding to the U(5)-SU(3) transition are calculated with variation of a scaling and control parameters. The model is applied to ^150–162Dy chain of isotopes. In this chain a change from spherical to well deformed nuclei is observed when moving from the lighter to heavier isotopes. ¹⁵⁶Dy is a good candidate for the critical point symmetry X(5). The parameters of the model are determined by using a computer simulated search program in order to minimize the deviation between our calculated and some selected experimental energy levels, B(E2) transition rates and the two neutron separation energies S_2n. We have also studied the energy ratios and the B(E2) values for the yrast state of the critical nucleus. The nucleon pair transfer intensities between ground-ground and ground-beta states are examined within IBM and boson intrinsic coherent framework.     

Microscopic mean-field boson approach to the shape transition in Sm isotopes

The phase transition from spherical to deformed shape in nuclei ^146–156Sm is analyzed within the mean-field approximation applied to the Dyson boson image of the shell-model hamiltonian. No quasiparticle transformation is involved in the present approach and the Pauli principle in the physical boson subspace is approximately taken into account. The low-energy spectra, B(E2; 0₁⁺→ 2₁⁺) values and the corresponding transition densities are calculated. The results provide a reasonable explanation of the shape transition in the Sm isotopes. The role of bosons with different angular momenta is investigated and it is found that the g-bosons (J = 4) cannot be neglected in the transitional region. Comparison of the present results with those of other approaches is given as well.     

Particle number scale invariant feature of the states around the critical point of the first order nuclear shape phase transition

We study systematically the evolutive behaviors of some energy ratios,E2 transition rate ratios and isomer shift in the nuclear shape phase transitions.We find that the quantities sensitive to the phase transition and independent of free parameter(s) are approximately particle number N scale invariant around the critical point of the first order phase transition,similar to that in the second order phase transition.     

Well-Known Distinctive Signatures of Quantum Phase Transition in Shape Coexistence Configuration of Nuclei

It is interesting that a change of nuclear shape may be described in terms of a phase transition. This paper studies the quantum phase transition of the U(5) to SO(6) in the interacting boson model (IBM) on the finite number N of bosons. This paper explores the well-known distinctive signatures of transition from spherical vibrational to γ-soft shape phase in the IBM with the variation of a control parameter. Quantum phase transitions occur as a result of properties of ground and excited states levels. We apply an affine \(\widehat {SU(1,1)}\) approach to numerically solve non-linear Bethe Ansatz equation and point out what observables are particularly sensitive to the transition. The main aim of this work is to describe the most prominent observables of QPT by using IBM in shape coexistence configuration. We calculate energies of excited states and signatures of QPT as energy surface, energy ratio, energy differences, quadrupole electric transition rates and expectation values of boson number operators and show their behavior in QPT. These observables are calculated and examined for ^{98 ? 102}Mo isotopes.     

Shape phase transition in the odd Sm nuclei: effective order parameter and odd–even effect

Some binding energy related quantities serving as effective order parameters have been used to analyze the shape phase transition in the odd Sm nuclei. It is found that the signals of phase transition in the odd Sm nuclei are greatly enhanced in contrast to the even Sm nuclei. A further analysis shows that the transitional behaviors related to pairing in the Sm nuclei can be well described by the mean field plus pairing interaction model, with a monotonic decrease in the pairing strength G.