Collective states

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Alhassid, Y., Novoselsky, A., and Whelan, N. (1990), Chaos in the Low-Lying Collective States of Even-Even Nuclei, Phys. Rev. Lett. 65,2971. 

M. Rosina, Large eigenvalues of the G-matrix and collective states, in Report of the Density Matrix Seminar (A. J. Coleman and R. M. Erdahl, eds.), Queen s Press, Kingston, Ontario, 1968, p. 51. 

M. Bouten, P. Van Leuven, M. V. Mihailovic, and M. Rosina, A new particle-hole approach to collective states. Nucl. Phys. A202, 127—144 (1973). 

Martin, J.A., W. Greiner Potential Energy Surface Model of Collective States, in High-Angular Momentum Property of Nuclei (N.R Johnson, Ed.) Harwood Academic Publishers, New York, NJ, 1983. 

The energy losses are maximum at maxima of e2(q, to), which corresponds to discrete transitions in isolated molecules, as well as at zeros of the denominator, that is, for solutions of Eq. (3.12), which corresponds to excitation of collective states. In order to find the frequencies of the latter we must know the explicit form of e(q, to). 

In atomic-molecular media the damping of plasmon states is due to the interaction of plasmon waves with electrons, lattice vibrations, and impurities. The electron-plasmon interaction is a long-range one. With absorption of a plasmon, the momentum q is transferred to the electron, resulting in a decay of the collective state into a single-particle one. The latter process is identical with absorption of a photon with the same energy. Wolff102 (see also Ref. 103) has shown that in this case the lifetime can be expressed in terms of two optical constants the absorption coefficient k and the refractive index nT, namely,... 

In condensed media, the transition with the largest value of F0n usually does not correspond to the transitions of an individual molecule into an excited state. For a number of substances the largest F0n corresponds to excitation of collective states of the plasmon type, such as the h[Pg.315]

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, ... 

In the IBA-2 model [Ari83] the structure of the collective states in even-even nuclei is calculated by considering a system of interacting neutron and proton s and d bosons. We will focus attention on the Majorana force,... 

Here N/, x N ( is a direct vector product in the basis of collective states of the donor-acceptor pair. The latter is a direct product of the three-state D basis with... 

The principal difference is in the initial conditions to Eq. (3.541) and Eq. (3.539). The initial condition to Eq. (3.539) is much more convenient because it automatically reveals the zero elements of the kernel, thus allowing us to decrease the rank of the matrix equations. The reaction under consideration illustrates this point looking at the matrix form of main operators in the basis of the four collective states of reacting pairs (D B, DB, D B, DB). They are... 

Here H is the spin Hamiltonian and R is the relaxation superoperator, accounting for the population and phase relaxation in the collective states basis of the RIP ... 

In the collective state basis a direct product of the population vectors is... 

I have been a professional chemist since that time and have worked on my own projects through the years. Being employed as a research and analytical chemist has allowed me to collect state-of-the-art analytical data on many products from alchemical experiments, and so begin to answer some of the questions modern science would ask concerning these materials. 

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