Transitions between energy states

It is known that the Breit interaction can give contributions in excess of one thousand wave numbers even to energies of transitions between lowest-lying states of very heavy elements (see, e.g., tables 7 and 8). It is also clear that the point nuclear model becomes less appropriate when the nuclear charge is increased. Therefore, the RECPs designed for accurate calculations of actinide and SHE compounds should allow one to take into account the Breit interaction and the finite size of nuclei. The most economic way is to incorporate the corresponding contributions into the RECP operator. 

The underlying basis of NMR is that when nuclei with a nonzero spin quantum number are placed in a magnetic field they take up one of a discrete number of quantized states. The application of radiofrequency (rf) energy produces transitions between these states. The energy changes associated with these transitions are detected as small voltages induced in... 

Oik — wave number corresponding to the energy of transition between states 2 and k. flit = oscillator strength for the transition 2—fk, i.e., probability that transition 2- k will take place given that the probability of all transitions is unity. 

Fluid atoms act as a heath bath for the triatomic molecule, providing activation energy for transitions between states A and B and dissipation to stabilize the molecule following a transition. Three different pathways connect states A and B. In each of them, a different atom of the molecule squeezes its way through the gap formed by the other two atoms. In each of the transition states, the three atoms are collinear with a different atom at the center. 

Here, as usual, ran = Vai — rai, final states of a system, i.e., the total level width is represented as sum of the partial contributions, connected with radiative decay into the concrete final states of a system. These contributions are proportional to the probabilities of the corresponding transitions. Naturally, the form of operator in (10) is determined by a gauge of the photon propagator (look discussion in Ref. [26]). In the zeroth approximation, the dependence f, on the nuclear and electron coordinates (/ n, l e(h)) is factorized ( eN). Therefore, the combined electron (hole)-nuclear one-photon transitions occur as each of the operators Tn and Te in (10) contains the combination of the nuclear and electron variables. After factorization and some transformations, the expression (10) can be presented in the following form ... 

Nuclear magnetic resonance (NMR) experiments subject a sample to a strong, static homogeneous magnetic field B = (0,0, B) that splits the energy levels of degenerate nuclear spin states. Transitions between these Zeeman levels are induced with an oscillating field (radio frequencies around 10 cm i). 

An immediate consequence of the form of H PPP) in (11.13) is that excitation energies for transitions between states of equal number of 7r-electrons involve only differences of the a and 7 parameters. This can be illustrated by the operator... 

Tam and (Tac denote respective surface free energies). The transition between the melt and the amorphous state, described by the hne Tam, occurs for... 

For a two-state transition between a native state, N, and an unfolded state, U, the equilibrium unfolding constant, Kud, partition coefficient, Q, mole fraction of each state, X, and standard free energy change for the unfolding reaction are defined as follows. 

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