The Physics of Warm Nuclei: With Analogies to Mesoscopic by Helmut Hofmann

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Indeed, this force should have important consequences, as one may already guess from the example of the van der Waals gas. There, the interaction is similar, namely attractive at large distances but repulsive at small ones, and this model is capable of treating the phase transition to the liquid. The point is, however, that this feature cannot adequately be treated in Hartree approximation. 2). Eventually, depending on the strength of this repulsive part the integral may even attain a positive value.

Its value, as well as that of κ, the real and imaginary parts of K, can be determined from the two equations 2 (k 2 − κ2 ) = 2mN (E − U ) and 2 kκ = mN W . It is seen that for positive W the κ is positive, too. This means that a wave travelling in 2 the x direction experiences an attenuation according to |φ(x)| ∼ exp(−2κx): The imaginary part of the potential describes a decrease in intensity due to the ”absorption” of particles of given energy. One may thus define a mean free path λ= 2 1 k = . 54) Basic properties of finite nuclei 21 ˆ OM are real reflecting the fact Notice that the eigenvalues E of the Hamiltonian h that we are dealing with elastic scattering.

At this stage it is worthwhile to briefly mention the close analogy with electromagnetic waves. Optical properties of dielectric materials are specified by the dielectric function ε(ω) which may be split into its real and imaginary parts by writing ε(ω) = ε (ω) + iε (ω). Any finite ε (ω) implies loss of energy of the elec√ tromagnetic wave to the medium. In such a case the index of refraction n = ε becomes complex (assuming the magnetic susceptibility µ to be close to unity). As in the case discussed before, the attenuation of the electromagnetic wave can be described by introducing a complex wave vector.