
\sect{Heat Capcity of He4 system, energy gap}

%Baruch's  B04, revised by dcohen

The specific heat of ${He^{4}}$ at low temperatures has the form

\[ \ C_{v}= A(T) + B(T) e^{-\Delta/T}\]

This is explained by the having a dispersion 
relation that give rise to long wavelength 
phonons ${\omega = c|\bm{k}|}$ and short wavelength  
rotons ${\omega(k)= \Delta + b(|\bm{k}|-k_0)^2}$, 
where $k_0=1/a$ is comparable to the mean 
interparticle separation.

\begin{itemize}
\item [(a)] Find explcity expressions for 
the coeficients $A(T)$ and $B(T)$ 

\item [(b)]
What would be the power in the $T$ dependence
of the coefficients if the the system were two dimensional?

\end{itemize}

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