Attractive state

Newton s law of attraction states that the force of interaction of particles is inversely proportional to the square of the distance between them. However, in a general case of arbitrary bodies the behavior of the force as a function of a distance can be completely different. 

Fig. XXII-9.—Interaction energy of two hydrogen atoms, as a function of the distance of separation, (a) repulsive state, (6) attractive state, with molecular formation.

Also with the older formulation of the Pauli principle we can understand that a penetration of the electron orbits, as in the attractive state, whereby the two electrons can, as it were, meet at one place, is only possible when there is also a difference in spin orientation. 

The degeneracy would be removed in a magnetic field and three levels would result according as the projection of the spin moment in the direction of the field is +1, —1, or o, corresponding to the above three spin functions. The attractive state is thus a singlet, the repulsive state a triplet state, and the probabilities of the two states are in the ratio of the statistical weights (2S +1), that is as 1 3. 

Systems with more than two independent variables can be analyzed in a similar way. The stable points in the phase diagram for such systems also are classified on the basis of characteristic solutions of the relevant eigen value equation. Lately, the positions of stable and attracting states of the dynamic system have been referred to as attractors. ... 

The phenomenon of valency saturation is, explained by PanWs exclusion principle. Just as in the case of atoms, so also in that of molecules the atoms, in consequence of this principle, become arranged in shells round the two nuclei. In the hydrogen molecule, the two electrons are in the ground state in the innermost shell they must therefore, like the two electrons of a shell, have opposite spins. Thus, in the attraction-state E- the spins of the two electrons are antiparallel on the contrary, it may be shown that in the state f phis would... 

There are hence three repulsive states A for one attractive state S the chance is i that two normal hydrogen atoms... 

Figure 6. Electron distributions in the repulsive state (upper figure) and attractive state (lower figure) of the hydrogen molecule. Each line represents a contour of constant electronic density increasing with the numbers (after...

Mechanism B includes direct electronic excitation of a molecule from the ground state to an attractive state with energy exceeding the dissociation threshold. Excitation of the state then results in dissociation. As one can see from Fig. 2-24, the energies of the dissociation fragments are lower in this case. 

Mechanism C consists of direct electronic excitation from the ground state to an attractive state corresponding to electronically excited dissociation products. Excitation of this... 

The Ar2 potential curve is shown in Fig. 21. Considering for the present only the attractive state, the Hartree-Fock interaction energy only becomes comparable to that of the polarization potential when the interaction energy is of the order of 0.1 eV. Once again, such considerations restrict the use of the Langevin model to thermal energies. Here, there is no possible ion-quadrupole contribution and in both these cases, dispersion forces are negligible. 

In addition to excitability, the FHN model can also possess oscillatory solutions. Figure 5 a) shows the configuration of the nullclines for a different choice of parameters. Now the system has an imstable fixed point or steady state and the stable attracting state is a limit cycle oscillation shown as the closed loop surrounding the unstable fixed point in the (Mt )-plane of the figure. Chemical patterns such as spiral waves can form in oscillatory as well as excitable systems and we shall have occasion to discuss some aspects of patterns in oscillatory media below. 

This chapter describes in detail how users of the Wassermann philosophy have achieved this lucrative and attractive state with only three measures. 

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