Fermi-Liquid Behavior ofHe3Adsorbed on Liquid Helium

Abstract

= 3.5, y 0 = 2.5, and rc^SxlO 12 cm" 3 (i.e., al.3-MeV, 150-kA beam of 1.4 cm radius) and a hydrogen plasma of density n p~1 0 14 cm" 3 so that n B /n p x0.05.The final temperature is (T e +T { ) f «30 keV by Eq. (7) with/«y 0 /i/. The time required to achieve this temperature falls in the range 30 nsec<^<l jxsec.We thank Dr. R. E. Lee for valuable discussions on the theory of relativistic beams and return currents. ^he notation is v~Nr e ; N is the number of beam electrons per unit beam length, r e is the classical electron radius, and y« y n = (1 -v B 2 /c 2 )' 1^2 . 2 We neglect the beam-plasma two-stream instability. The growth rates are decreasing functions of y and the plasma-beam density ratio, as discussed by Y. B. Fainberg, V. D. Shapiro, and V. I. Shevchenko, Zh. Eksp. Teor. Fiz. 57, 966 (1969) [Sov. Phys. JETP 30, 528 (1970].3 It may be shown that neglect of the displacement current in Eq. (3) is valid for distances longer than cr^ behind the beam front. 4 T. G. Roberts and W. H. Bennett, Plasma Phys. 10, 381 (1968); S. Putnam, Physics International Co. Re-Andreev 1 has shown that the behavior of the surface tension of dilute solutions of 3 He in 4 He at high temperatures (T> 0.5 K) demonstrates that some 3 He is adsorbed on the surface of the liquid. In Andreev's model the adsorbed 3 He is assumed to be in a set of independent quasiparticle states with energy spectrum 2 * = ~ € 0 +p 2 /2M.(1)The surface tension of the solution, a, is then the surface tension of liquid 4 He, a 4 , reduced by the two-dimensional "pressure" of the 3 He quasiparticle gas on the surface. From measurements of Aa=a 4~ a at T>0,5K and assuming that the sur-port No. . 7 Only a small drift of the ions t^{ m e /m i )vv p in the beam direction results from momentum conservation. 8 The factor d in Eq. (7) depends on the geometry and is given by d-\ +21n(b/a), where b is an outer radius where the field energy integral is cut off. 9 H. (to be published).face quasiparticle gas could be treated by Boltzmann statistics, Zinov'eva and Boldarev 3 determined approximate values for the surface binding energy e 0 and the effective mass M.There is considerable interest in studying the many-body properties of adsorbed helium particularly in this case since the substrate (liquid helium) is uniquely perfect and homogeneous. We therefore have made further measurements of a down to low temperatures (0.04 K) and over a wide range of X, the concentration in the bulk phase (30 ppm to saturation). Under these conditions the adsorbed 3 He can be changed from a fraction of an atomic layer, when it behaves like Some properties of 3 He adsorbed on the surface of liquid helium are determined from measurements of the surface and interfacial tension of 3 He-4 He mixtures. As a mixture approaches phase separation, the 3 He adsorbed on the surface grows continuously into the upper, 3 He-rich phase. At all temperatures the limit of low surface density is well described by the Andreev model, although there is some evidence for a weak, attractive quasiparticl...

Measurement of the surface tension of superfluid4He at low temperature by capillary wave resonances

“…2 + 9al2e-4koz + 25a2e-8koz)e-2koz + k~V~c(6aoa I + 30ala2e-4k~ -4k~ cos(2k0x) (2) + k~V2c(lOaoa2)e -6k~ cos(4k0x) +... Irrotational surface excitations of an inviscid incompressible fluid of uniform depth do propagate according to the dispersion relation:…”

Structure and stability of superfluid4Hesystems with cylindrical symmetry

“…which may be identified with the experimental [38][39][40] values of the surface tension exp quoted in Table I; and ͑ii͒ the asymptotic energy per unit length…”

Study on Surface Tension of Fluid Helium Three

“…The internal excitations in 3 He should also be different from 4 He. An experiment by Guo et al [14] on 3 He floating on bulk liquid 4 He has shown a quadratic temperature dependence of the surface tension. They inferred that the surface tension of bulk liquid 3 He has T 2 dependence like the 3 He layer on 4 He, as expected for a Fermi system at low temperatures.…”