Specific Heat of He Confined in Cylindrical Micro-Channels and Near the Superfluid Transition

• Published in: Journal of low temperature physics 2007-12, Vol.149 (5-6), p.209-221
• Main Authors: Aouaroun, Tahar, Ahlers, Guenter
• Format: Article
• Language: English
• ISSN: 0022-2291
• DOI: 10.1007/s10909-007-9515-6

We present new measurements of the specific heat C P of He confined in cylindrical micro-channels of diameter L=1.89 mum at saturated vapor pressure and near the bulk superfluid-transition temperature T lambda . The results, when combined with the specific-heat exponent alpha=-0.01264, and with the correlation-length exponent nu=0.6709 obtained from alpha by hyper-scaling, support the departure from a universal, size independent, scaling function reported before by Lipa et al. [J. Low Temp. Phys. 124(3-4): 443, 2001] for L=8.17 mum and 0.26 mum. In agreement with Lipa et al., we found that a size independent effective scaling function can be recovered within experimental resolution when an empirical effective correlation-length exponent {expression} is used. As expected from theory, well away from T lambda the temperature dependence of the suppression of C P by the confining medium is consistent with a power law with an exponent equal to alpha+nu=0.658. The universal ratio of the suppression at equal distances below and above the transition was measured to be R f2=2.3+/-0.2. This result is consistent with the theoretical value R f2=2.06 obtained by Bhattacharyya and Bhattacharjee and is close also to the ratio R &D*x {asymptotically equal to}2.7 of the correlation-length amplitudes.