Synopsis The singularities in specific heat C p and expansion coefficient α P occurring at the λ transition of liquid helium can be related directly to the spectrum of elementary excitations by assuming an appropriate variation of the energy gap Δ(P, T) . For this purpose the surface Δ(P, T) near the λ line is approximated by a cylindrical section with generator parallel to the λ line. The observed singularities can then be explained if the second derivatives ( ∂ 2 Δ / ∂T 2 ) P , ( ∂ 2 Δ / ∂T∂P ), and ( ∂ 2 Δ / ∂P 2 ) T have logarithmic singularities along the λ line, the first derivatives ( ∂Δ/∂T ) P and ( ∂Δ/∂T ) T ) remaining finite. The assumed shape of the surface Δ ( P, T ) imposes a relation between C P and α P identical to that obtained by applying a similar “cylindrical approximation” to the surface S ( P, T ). Fitting the above model to the observed values of C P near T λ yields an expression for ( ∂ 2 Δ / ∂T 2 ) P , which can be integrated twice to obtain Δ ( T ). The resulting values of Δ ( T ) agree well with experiment.
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