Precessors spectral function

Appendix 1. Calculation of Fourier Amplitudes b -i for Librators Appendix 2. Transformation of Integral for Spectral Function of Precessors Appendix 3. Optical Constants of Liquid Water... 

The phase regions occupied by the librators and precessors are depicted in Fig. 27 in coordinates h, l2 for the parameters u = 5.9, p = %/9. We take two values of the form factor/ 0.65 in (a) and 0.85 in (b). When/increases, the / and 2P areas extend to the larger h and l values. The values of Vmin are shown as functions of l in Fig. 21c. In this example (and in the calculations described in Section V.C) the potential well depth U0 is much greater than kBT, that is, u> 1. We see in Fig. 27 that for the J and 2P areas the boundary values for h are still greater than it. This property is used to simplify analytical expressions for the spectral functions. 

APPENDIX 2. TRANSFORMATION OF INTEGRAL FOR SPECTRAL FUNCTION OF PRECESSORS... 

Substituting all variables into integral (A2) and taking into account Eq. (197d), we finally derive Eqs. (174)-(178) for the spectral function of the precessors. 

The regions C and V, to which the spectral functions L(z) and L(z) correspond, are occupied by the particles localized in the well. Any -particle penetrates into the flat part of the well. We may conditionally call it libratorThe P-particle, conditionally called precessor, move only in the parabolic part of the well and has energy h close to that, for which the effective potential V(9) undergoes its minimum, in which... 

Hence, for the transition from the full expression (210) to the simplified (8)-(10) (a) in Eq. (175), containing the normalizing coefficient C, the contributions of precessors and rotators were disregarded. Moreover, we removed a misprint committed in GT2 and inserted additionally in the formula for D the factor d equal to 0.7. One may interpret this factor as that, which accounts for influence of surrounding molecules on the spectral function (8). 

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