I see where my mistake was now that I read the work of Horrace.
It was in the elastic constant K.  I just used the electrical force on  the 
proton and the lattice spacing
to compute the elastic constant.
 
I did not factor in that total force on a stationary proton is zero.   I 
needed to 
calculate the force on a slightly displaced proton as a subtraction of  
opposing forces.
  You have showed me the way.
 
Now what is the difference between the palladium and the dissolved  
deuterium lattice vibrations?
They are, I believe, similar in frequency.  The phase may be the  big 
difference.  The adjacent
lattice vibrations at the shortest wavelengths are 180 deg out of  phase.
 
The entire dissolved hydrogen lattice my be vibrating in phase as a single  
quantum system.
I believe that cold fusion is an affect of a big difference in the way  
dissolved hydrogen vibrates.
 
What do you think?
 
Horrace, did you go back to school or what?  Your work is orders of  
magnitude better than it was a few short 
years ago.
 
Frank Z

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