Interaction boson

For N identical non-interacting bosons, equation (8.32) needs to be modified in order for to be normalized when some particles are in identical singleparticle states. The modified expression is... 

Although we have explained Bose-Einstein condensation as a characteristic of an ideal or nearly ideal gas, i.e., a system of non-interacting or weakly interacting particles, systems of strongly interacting bosons also undergo similar transitions. Eiquid helium-4, as an example, has a phase transition at 2.18 K and below that temperature exhibits very unusual behavior. The properties of helium-4 at and near this phase transition correlate with those of an ideal Bose-Einstein gas at and near its condensation temperature. Although the actual behavior of helium-4 is due to a combination of the effects of quantum statistics and interparticle forces, its qualitative behavior is related to Bose-Einstein condensation. 

Iachello, F., and Arima, A. (1987), The Interacting Boson Model, Cambridge University Press. 

Kirson, M. W., and Leviatan, A. (1985), Resolution of Any Interacting-Boson-Model Hamiltonian into Intrinsic and Collective Parts, Phys. Rev. Lett. 55, 2846. 

Schaaser, H., and Brink, D. (1984), Calculations away from SU(3) Symmetry by Cranking the Interacting Boson Model, Phys. Lett. B 143, 269. 

In the method of interacting bosons, one introduces boson creation, T t, and annihilation, [ operators satisfying boson commutation relations... 

The remaining important aspect is how to derive these properties from a microscopic theory. In this respect, particularly interesting is the interacting boson-fermion model described at this workshop by Micnas [23]. This model is an extension of the method discussed above to mixed systems of bosons and fermions [24]. A symmetry analysis of this system will be presented elsewhere. 

For a review, see, F. Iachello and P. van Isacker, The Interacting Boson-Fermion Model, Cambridge University Press, Cambridge, England (1991)... 

Y. Wang, J.P. D lncao, C.H. Greene, Efimov effect for three interacting bosonic dipoles, Phys. Rev. Lett. 106 (2011) 233201. 

In the interacting boson model-2, low lying collective states of nuclei are described in terms of 12 dynamical bosons [ARI77,0TS78], six proton and six neutron bosons. The six proton and neutron bosons have angular momentum J=0 (s-boson) and J=2 (d-boson). It is convenient to introduce creation (d, s ) (u = 2, 1, 0) and annihilation (du,s) operators. When proton ( tt ) and neutron (v) degrees of freedom are added, the creation and annihilation operators assume an extra label ( tt, v), d s, ... 

One of the most interesting aspects of the Interacting Boson Model concerns its connections with the underlying fermion space. The understanding of the mechanism through which bosonlike features arise from effective nuclear hamiltonians provides, in fact, a way to relate collective spectra to the fermion motion. 

SAMBATARO Microscopic Theory of the Interacting Boson Model... 

In the following, we discuss mostly the use of our BET for these simple models. We do this because it will help the reader to understand the essence of our BET, and also because these models were studied by Otsuka et. al. [10,11], and by Arima et. al. [12]. (They did this with a stated purpose of justifying the interacting-boson approximation (IBA) [13].) It will be seen below that, in spite of the use of the same models, the conclusions we arrive at differ significantly from those given by these authors. 

The effect of neutron-proton symmetry breaking on the distribution of M1 strength in the SU(3) limit of the Interacting Boson Model (IBA-2) is studied. A possible alternative choice for the Majorana force is investigated, with a structure that resembles more closely that which is calculated in microscopic theories. It is found that the specific choice for the Majorana interaction has important consequences for the magnetic strength distribution function. In addition it allows for an alternative interpretation of the second excited K7T=0+ band in rare earth nuclei, as a mixed-symmetry state. 

C.W. de Jager, in Interacting Boson-Boson and Boson-Fermion Systems, p.225, ed. 0. Scholten, (World Scientific, Singapore 1984) [Die83] A.E.L. Dieperink, Prog. Part. Nucl. Phys. 9, 121 (1983). 

Interacting Boson Model-2 for High-Spin States... 

The N-P Interacting Boson Model is extended to include bosons of spins 4, 6, 8,.. in addition to the usual S and D bosons, in order to treat nuclear states of high spin within the IBM formalism. 

The Importance of an Accurate Determination of Interacting Boson Model-2 Parameters... 

First, a brief description of the neutron-proton Interacting Boson Model (IBM-2) is given. Next, this model is applied to experimental data in order to determine its empirical parameters. Finally, we discuss why an accurate determination of these parameters is so important. 

IAC79] F. Iachello, in Interacting Bosons in Nuclear Physics, ed. F. 

In terms of the three limiting group symmetries used in the interacting boson model (IBM), the shape transition of Ru or Pd nuclei can be explained as a SU(5) to 0(6) transition [STA82]. The transition of Sr or Zr nuclei is characterized instead as SU(5) to SU(3). 

Recent Experimental Investigations and Interacting Boson Model Calculations of Even Te Isotopes... 

The dependence of the transitional moment Q of the gg/2 bands in 75Br and 77Rb is plotted in Fig. 2 and 3 as function of the rotational frequency ho). Wiile Q is essentially constant in 77Rb, it drops in /9Rb and 73>7 Br above spin 17/2 " Several explanations have been proposed to explain this reduction of Qt in the Interacting Boson KFermion) model... 

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