Doorway Vibrations in Up-pumping

In Fig. 13, the continuous energy levels on the right hand side represent the phonon states of a solid. In a liquid such as NM there are no true phonons, but there is a band of collective excitations of the lower energy continuum that 

Dlott and Payer s doorway model of phonon pumping [50] suggested two essentially equivalent methods for determining the rate of phonon pumping of doorway vibrations for large polyatomic molecules where only two phonons are needed to pump a doorway vibration. The anharmonic term in the Hamiltonian responsible for two-phonon doorway mode pumping is a cubic anharmonic term of the form [21,50], 

In the high-temperature limit, the Planck occupation factors ri(J,T) can be approximated as na(T) o k TMo). Therefore the up-pumping rate is proportional to the difference in quasitemperatures, that is rtph(T) - rivMT) oc [50]. 

Then the time dependence of the phonon and vibrational quasitemperatures can be described by the differential equations [50] 

The calculation of up-pumping parameters for naphthalene relies on the determination of t(0) from low temperature Raman measurements of doorway vibration transitions. Quite recently Ye et al., used this experimental method to study RDX and y HMX single crystals [140]. Generally speaking, their lineshapes gave values of r(0) that were quite similar to was seen by Hess and Prasad with naphthalene. Thus the naphthalene model for up-pumping appears quite reasonable for RDX and HMX as well. The principle differences are that HMX and RDX have floppy NO2 groups that naphthalene does not, so in Eq. 

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