The geometric content of the interacting boson model for molecular spectra: A testground for the nuclear IBM

The recently proposed algebraic model for collective spectra of diatomic molecules is analysed in terms of conventional geometrical degrees of freedom. We present a mapping of the algebraic hamiltonian onto an exactly solvable geometrical hamiltonian with the Morse potential. This mapping explains the success of the algebraic model in reproducing the low-lying part of molecular spectra. At the same time the mapping shows that the expression for the dipole transition operators in terms of boson operators differs from the simplest IBM expression and in general must include many-body boson terms. The study also provides an insight into the problem of possible interpretations of the bosons in the nuclear IBM.     

Relationship between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson

The generator coordinate method is used to relate the interacting boson model and the collective model through an isometric transformation. It associated complex parameters to the original boson operators whereas the ultimate collective variables are real. The mapping of operators of the interacting boson model onto those of the collective model turns out to be of Holstein-Primakoff type.     

On the relation between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson. II

The generator coordinate method is used to relate the interacting boson model of Arima and lachello and the collective model of Bohr and Mottelson through an isometric transformation. It associates complex parameters to the original boson operators whereas the ultimate collective variables are real. The absolute squares of the collective wave functions can be given a direct probability interpretation. The lowest order Bohr-Mottelson hamiltonian is obtained in the harmonic approximation to the interacting boson model; unharmonic coupling terms render the collective potential to be velocity dependent. The mapping of operators of the interacting boson model onto those of the Bohr-Mottelson model turns out to be of Holstein-Primakoff type.     

On the relation between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson

The generator coordinate method is used to relate the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson through an isometric transformation. It associates complex parameters to the original boson operators whereas the ultimate collective variables are real. The absolute squares of the collective wave functions can be given a direct probability interpretation. The lowest order Bohr-Mottelson hamiltonian is obtained in the harmonic approximation to the interacting boson model; anharmonic coupling terms render the collective potential to be velocity-dependent.     

原子核代数模型中的F-旋混合态、回弯、电磁跃迁问题的研究

在原子核的代数模型框架下,讨论了集体回弯效应、较高自旋的Ｆ－旋混合对称态以及电磁跃迁几率等问题． The collective backbending effect, F spin mixed symmetry states have been studied for the nuclei with moderate high spins. It is found that there is an additional L(L+3) proportional term in the E2 transition rates in the sdg interacting boson model and solved the long standing problem of reduction of collectivity in the wave function of boson models. The electromagnetic transitions in the spdf interacting boson model have been calculated and compared with existing experimental...     

Rotational states and interacting bosons

Rotational states are investigated in terms of the interacting boson model. A ground-state rotational band is built from a shell-model many-nucleon system. It is shown that the S and D collective nucleon pairs play dominant roles in low-spin states of the band and that this S-D dominance is broken in high-spin states. The intrinsic hamiltonian is constructed from the effective nucleon-nucleon interaction used in the shell model calculation and the intrinsic state of the rotational band is shown to be comprised primarily of S and D pairs. We introduce a λ boson which is a linear combination of s, d and higher angular momentum bosons, and the boson intrinsic state is given by the λ boson condensate state. The s and d bosons constitute approximately 90 % of the λ boson, and the boson intrinsic state reproduces very well the energy and the intrinsic quadrupole moment of the nucleon intrinsic state. The s-d boson hamiltonian is constructed from the S and D pairs, while effects of non S-D pairs are also included by renormalization of the boson hamiltonian. The renormalization is made by using the λ boson. The s-d boson quadrupole operator is derived similarly. The boson hamiltonian and quadrupole operator thus derived reproduce well the exactly calculated values for low-spin states of the rotational band, although the accuracy decreases in high-spin states. It is shown that the IBM possesses the same physical picture of the rotational states as the Nilsson scheme with pairing correlations. It is therefore concluded that the IBM is capable of describing low-lying rotational states.     

Biunitary representation of the selfconsistent collective-coordinate method for large-amplitude collective motion

A reformulation of the selfconsistent collective-coordinate method of Marumori, Maskawa, Sakata and Kuriyama is given in a biunitary representation for the purpose of studying the relation to the generalized Dyson boson mapping. It is shown that, in this reformulation, a special choice of representation gives the c-number version of the generalized Dyson boson mapping. It is also shown that this representation yields a powerful method to estimate the coupling effect between collective and non-collective phonon degrees of freedom in the large-amplitude collective motion.     

Dyson-type boson mapping and SU(6) boson model

The Dyson-type boson mapping is applied to realistic cases to show that it is a very promising method for describing nuclear collective motion. Eigenvectors are obtained in the corresponding hermitian boson theory from the results of right- and left-hand-side eigenvalue problems in the Dyson boson theory. The numerical results are compared with those of the SU(6) boson model and exact quasiparticle shell-model calculations within the multi-phonon subspace.     

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).     

Collective nature of the boson peak and universal transboson dynamics of glasses

Using probe molecules with resonant nuclei and nuclear inelastic scattering, we are able to measure the density of states exclusively for collective motions with a correlation length of more than approximately 20 A. Such spectra exhibit an excess of low-energy modes (boson peak). This peak behaves in the same way as that observed by conventional methods. This shows that a significant part of the modes constituting the boson peak is of collective character. At energies above the boson peak, the reduced density of states of the collective motions universally exhibits an exponential decrease.     

Mean-field approximation and the collective transformation for Dyson boson hamiltonians

Hartree and TDA approximations are derived for non-hermitian boson hamiltonians such as the one obtained with the Dyson boson expansion. It is shown how to construct a collective transformation from the structure of Hartree and TDA bosons. This approach is applied to monopole pairing hamiltonian in the tin region.     

Anharmonic collective excitation in a solvable model

We apply the time-dependent variational principle, the nuclear field theory, and the boson expansion method to the Lipkin model to discuss anharmonicities of collective vibrational excitations. It is shown that all of these approaches lead to the same anharmonicity to leading order in the number of particles. Comparison with the exact solution of the Lipkin model shows that these theories reproduce quite well.     

A calculation of low-lying collective states in even-even nuclei

We present results of a calculation of the low-lying collective quadrupole states in even-even nuclei within the framework of the proton-neutron interacting boson model.     

THE GENERATOR COORDINATE METHOD AND NUCLEAR COLLECTIVE MOTIONS (Ⅷ) THE CHOICE AND REPRESENTATION OF COLLECTIVE DEGREES OF FREEDOM

The choice and representation of degrees of freedom of collective motions are thoroughly discussed. Starting from the dynamical group of a shematic model, it is pointed out that the number of independent collective degrees of freedom is uniquely determined, although there exist different continuous variable or boson representations. If more collective degrees of freedom were involved, there must be accompanied conditions.     

基于微观IBM对电子-核散射及核电磁性质的研究(Ⅱ) ME理论方案

从一种微观作用玻色子模型（IBM）玻色子集体态子空间映射出费米子集体态子空间,通过假定玻色子算符形式以及使物理算符在两集体态子空间中对应归一化基矢间矩阵元相等,给出了从费米子单体算符导出玻色子单体算符的一种微观理论方法（ME方法）,文中以获取玻色子结构函数亦即确定玻色子形式核跃迁电荷／电流密度算符为例对此作出了详细介绍,利用微观IBM提供的波函数可在玻色子态空间中求出核跃迁电荷／电流密度,结合电子－核散射以及核电磁跃迁的形式理论,可建立研究电子－核散射各种形状因子与微分散射截面以及核约化跃迁几率,电磁多极矩,核态g因子等物理量的理论方案,在微观sdgIBM-1下利用该方案初步计算了146Nd核21^ 态到o 1^ 态的跃迁电荷密度以及约化跃迁几率,理论结果与实验值符合较好。