Born term

If the species is charged then an appropriate Born term must also be added. The react field model can be incorporated into quantum mechanics, where it is commonly refer to as the self-consistent reaction field (SCRF) method, by considering the reaction field to a perturbation of the Hamiltonian for an isolated molecule. The modified Hamiltoniar the system is then given by ... 

Activity Coefficients of Uni-Univalent Chlorides. The second application is to the activity coefficients of electrolytes as a function of the dielectric constant of the media. Returning to Equation 32, for electrolytes at infinite dilution only the Born term remains, that is,... 

This is a generalization of the Onsager reaction field model for a point dipole inside a spherical cavity. For charged solutes, one should also include an ionic Born term, derived by... 

The MUIBED model, through its parent siBED [53], replaces the Bethe part of the BED model with a two-parameter Born term through Eq. (25) leading to ultimately two shell-dependent fitting parameters m and X in Eq. (21), noted in Table 6.4 after both the parameters d2 and d2 are set to zero. 

This derivation recovers significant insufficiencies of the SCA approach, not recognized previously. First, the contribution of the Born term A is totally absent in the SCA cross-section. This is contrary to the common view that, for a heavy projectile, the SCA and Born approaches are equivalent in the description of the total cross-section of excitation. The second (natural) conclusion is that SCA can be used only if A = Eif E = kj/2Mi. This condition follows from the condition of applicability of the quasiclassical approach [28]. The condition is rather critical, its violation results in an exponential decrease of the amplitude A g. 

The on-shell T-matrix is related to the observables that are measured in experiment. Thus, potentials which fit the same NN scattering data produce the same on-shell T-matrices. However, this does not imply that the potentials are the same. As seen in Eqs. (1) and (2), the T-matrix is the sum of two terms, the Born term and an integral term. When this sum is the same, the individual terms may still be quite different. 

Let us consider an example. The T-matrix in the Si state is attractive below 300 MeV lab. energy. If a potential has a strong (weak) tensor force, then the integral term in Eq. (5) is large (small), and the negative Born term will be small (large) to yield the correct on-shell T-matrix element. 

MeV ( ,ab = 2q /M). The abscissa, k, is the variable over which the integration in Eq. (5) is performed. It is seen that, particularly for large off-shell momenta, the Bonn B potential is smaller than the Paris potential. However, notice also that at the on-shell point (q = k, solid dot in Fig. 12) both potentials are identical (both potentials predict the same Ei parameter). Thus, the Bonn B potential has a weaker off-shell tensor force than the Paris potential. Since the Bonn B and the Paris potential predict almost identical phase shifts, the Born term (central force) in the Si state will be more attractive for the Bonn B potential than for the Paris potential. 

However, the influence of long-range interactions has to be taken into account by a term describing the Debye-Hiickel theory. For this term, in the general case the density and the dielectric constant of the mixed solvent have to be determined (see Eq. (7.49)). As the reference state of the electrolyte components refers to the infinitely diluted solution in pure water, the Debye-Hiickel term must be corrected by the so-called Born term, which takes into account the difference between the dielectric constants of water and the solvent mixture [14] ... 

The Born term is no more necessary, as the reference state for the ions is not the pure aqueous solution but the infinite dilution of ions in the solvent mixture. Thus, the MSA-NRTL has only two terms ... 

Born term for regarding the dielectricity constant of the solvent... 

The ionic model was tested by using an extended Born equation to calculate the free-energy change of interaction of lanthanide ions with acetate ligands (Miinze 1972). The equation, in addition to the Born term, includes a cratic term to account for the change in the number of species upon complexation and an activity coefficient term to account for the experimental ionic strength ... 

However it also follows that if there were only dipole forces all the even terms in Zp would be zero for the dipole-allowed transitions. Each term in the Bom series progresses from the initial state to the final by a series of transitions between virtual intermediate states. There are as many transitions as there are orders in the Born term. Each transition changes the parity of the state. Thus an odd number of transitions are required for a dipole-allowed state and therefore only the odd order Born terms contribute. In reality though we only have dipole dominance, not a pure selection rule. Also, first order Born terms are usually not negligible even when forbidden. In any case in the example shown in fig. 5.3, when the sign of Zp is reversed, the cross section 1S-2P remains the same but this is not true of the forbidden transition 1S-2S. 

We begin our consideration of charge transfer by studying the symmetric case, for which Zp = Zrp e Z. In the first Born term, the main contribution originates in components of the target and final bound state wave functions for which the velocity of the electron is comparable with v, and those amplitudes are very small for v large --- more precisely, for v >> Ze /tl, a characteristic electron velocity in the initial and final state ---- even if, as we do for sim-... 

The change in the solvation energy of an ion may be considered to be composed of two terms a purely electrostatic Born term, and a specific term associated with short-range interactions. For an ion lying close to the surface, the electrostatic term may be described by using the model of a globule of practically infinite... 

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