Phenomenological<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>quasiparticle scattering amplitude in dilute solutions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>in superfluid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

From measurements of the spin diffusion, thermal conductivity, and viscosity coefficients in dilute solutions of $^{3}\mathrm{He}$ in superfluid $^{4}\mathrm{He}$, we have phenomenologically determined the amplitude for $^{3}\mathrm{He}$-$^{3}\mathrm{He}$ quasiparticle scattering. Two different parametrizations of the amplitude have been used; one form depends only on the momentum transferred in the scattering event while the other depends on the initial momenta of the quasiparticles as well. The amplitudes are fitted to measurements at temperatures in both the degenerate Fermi-liquid regime ($T\ensuremath{\ll}{T}_{\mathrm{F}}$) and the classical regime ($T\ensuremath{\gtrsim}2{T}_{\mathrm{F}}$), whereas most previously determined amplitudes are valid only in the low-temperature regime. Finally, the possibility that the scattering amplitude is $^{3}\mathrm{He}$-concentration dependent is investigated by fitting measurements at each concentration independently. This procedure indicates that there is an enhancement of the amplitude at small momentum transfer as the concentration increases.

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