The Interacting Boson Model for Anomalous Rotational Bands

The interacting boson model for anomalous rotational bands is proposed. In the rotational SU(3) limit,an asymptotic limit is discussed. Within the framework of the model several analytic relations for energies and electro-magnetic transition rates are derived.

PT Symmetric Quantum Models Living in an Auxiliary Pontryagin Space

In the traditional theoretical descriptions of microscopic physical systems （typically, atoms and molecules） people strongly relied upon analogies between the classical mechanics and quantum theory. Naturally, such a methodical framework proved limited as it excluded, up to the recent past, multiple, less intuitively accessible phenomenological models from the serious consideration. For this reason, the classical-quantum parallels were steadily weakened, preserving still the basic and robust abstract version of the key Copenhagen-school concept of treating the states of microscopic systems as elements of a suitable linear Hilbert space. Less than 20 years ago, finally, powerful innovations emerged on mathematical side. Various less standard representations of the Hilbert space entered the game. Pars pro toto, one might recall the Dyson＇s representation of the so-called interacting boson model in nuclear physics, or the steady increase of popularity of certain apparently non-Hermitian interactions in field theory. In the first half of the author＇s present paper the recent heuristic progress as well as phenomenologieal success of the similar use of non-Hermitian Ham iltonians will be reviewed, being characterized by their self-adjoint form in an auxiliary Krein space K. In the second half of the author＇s text a further extension of the scope of such a mathematically innovative approach to the physical quantum theory is proposed. The author＇s key idea lies in the recommendation of the use of the more general versions of the indefinite metrics in the space of states （note that in the Krein-space case the corresponding indefinite metric P is mostly treated as operator of parity）. Thus, the author proposes that the operators P should be admitted to represent, in general, the indefinite metric in a Pontryagin space. A constructive version of such a generalized quantization strategy is outlined and found feasible.

A QCD Model Using Generalized Yang-Mills Theory

Generalized Yang-Mills theory has a covariant derivative, which contains both vector and scalar gauge bosons. Based on this theory, we construct a strong interaction model by using the group U（4）. By using this U（4） generalized Yang-Mills model, we also obtain a gauge potential solution, which can be used to explain the asymptotic behavior and color confinement.

The Interacting Boson Model of Dipole—Octupole Strong Correlations in SU（3） Limit for Positive Parity States

Within the framework of the Usdpf(16) interacting boson model (IBM), the effects of strong correlations of the dipole (p?-boson) and the octupole (f?-boson) degree of freedom on the positive-parity states of even-even nuclei in SU(3) limit are discussed. It is shown that configurations of an even number of many p- and f-bosons can not only be incorporated into the usual low-lying collective rotational bands, such as the ground state band, β- and γ-vibrational bands, but also naturally form the rotational bands, etc. These results are similar to that of Usdg(15)-IBM and in good agreement with the experimental data of the nucleus. Besides, several intraband E2 transition probabilities are given, which are consistent with that of Usd(6)-IBM.

Isospin and symmetry structure in ^(34)S

The interacting boson model-3(IBM-3) has been used to study the energy levels and electromagnetic transitions for the nucleus 34 S.The main components of the wave function,isoscalar and isovector parts in the M1 and E2 transitions for low-lying states have been investigated.According to this study,the theoretical calculations are in agreement with experimental data,and the nucleus 34 S is in transition from U(5) to S U(3).

Relation between the E(5) symmetry and the interacting boson model beyond the mean-field approximation

In a unified algebraic scheme,we investigate the relation between the E(5) symmetry and the interacting boson model beyond the mean-field level.The results indicate that the E(5) symmetry is actually in between the critical point of the U(5)-O(6) transition and the O(6) limit but it is fairly close to the former based on the phase diagram of the interacting boson model at the large boson number limit.In addition,an algebraic Hamiltonian of the E(5)-β2n model is proposed.

Description of the properties of the low-lying energy states in ^(100)Mo with IBM2

The properties of the low-lying energy states for the l00 Mo isotope is investigated within the framework of the proton-neutron interacting model IBM2. By considering the relative energy of the d proton boson to be different from that of the neutron boson and taking into account the dipole interacting among like-boson Lπ·Lπ and Lπ·Lπ, the low-lying energy spectrum is reproduced well. Particularly, the relative position of the energies for 2＋1, 0＋2, 2＋2 and 4＋1 states shifted correctly fit the experimental data. The electromagnetic properties, including the key observable B（E2） reduced transition branching ratios and the E2 reduced matrix elements of the experimental data, are well described. Our calculations show possible shape coexistence in the l00Mo nucleus.

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.