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Submitted on 1 Jan 1978
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MOBILITY OF NEGATIVE IONS IN LIQUID 3He
R. Bowley
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, suppliment au no 8, Tome 39, aoat 1978, page
C6-79
MOBILITY OF NEGATIVE IONS IN
LIQUID
3 ~ e R. M. BowleyDepartment of Physics, University of Nottingham, University Park, Nottingham N G 7 2RD England
Resume.- Selon la thlorie, la mobilit6 d'ions negatifs dans 11h61ium-3 normal devrait augmenter quand la temperature est abaissbe. Ceci est cependant incoherent avec les rdsultats expdrimentaux de Ahonen et al.
Abstract.- The mobility of negative ions in normal 3 ~ e should increase as the temperature is lowered according to theory. However, this is inconsistent with the experimental results of Ahonen et al.
The mobility of ions in 3 ~ e is governed by the scattering of quasiparticles. If the ion recoils in a scattering event, energy is absorbed, making it less likely that the final state of the quasiparti- cle is unoccupied. A simple calculation /1/ based on the idea that the ion recoils as a free particle predicts that the mobility should increase at low temperatures, T, as T - ~ .
However, the mobility of negative ions appears to be independent of temperature, whereas for posi- tive ions the mobility increases linearly with ln(T) at low temperatures / 2 / .
An explanation for the weak temperature depen- dence of the mobility was given by Josephson and Lekner 1 3 1 . They showed that the ion recoils freely for a very short time ; for times of order 14/kBT the recoil motion is more diffusive.
Josephson and Lekner proposed a form for the recoil function F(k,t), which involves the frequen- cy d,ependent mobility ~ ( w ) . They were then able to estimate the temperature dependence of the mobility of negative ions if they assumed that the scatte- ring cross-section o is constant. The result is for T < T o :
8l4$
u(T)-~ = :I,,
-
ln(To/T> + O( (LI,~~$~~(T~/T>)~I (1 Here u - l = 14%0n3 and T corresponds to the frequen- cy at which Re~(w) decreases to zero. Equation (1) appears to be 'appropriate for negative ions becau-se
Milo$
is small, typically of order 0.1. Thus,provided T is not very much larger than T, the corrections to Equation (1) may be ignored.
This model has been extended to allow Reu(w) to be calculated self-consistently /4/. The theory can then be applied to positive ions, and it is
found that the mobility increases linearly with In(T
IT)
in excellent agreement with experiment /5,6/.The modified theory when applied to negative ions still gives in lowest order equation (1). If one considers ions at pressures of about 28 bar, then Hpk; is about 0.12 171. By reducing the tempe- rature by a factor of ten, the mobility should in- crease by about 25 % according to equation ( I ) . This is inconsistent with the data of Ahonen et al. /7/ as shown in their figure 4 ; the mobility at 28.4 bar is constant between 3 and 30 mK.
Could this discrepancy be caused by measu- ring the mobility using electric fields which are too large ?
Ahonen et al. have measured the non-linear dependence relation of v on E for negative ions in 3 ~ e in strong fields. It is possible to calculate this /8/ using the theory of Fetter and ~urkijzrvi / 9 / together with the recoil function of Josephson and Lekner as modified by the author. The results for both positive ions and negative ions are as follows 181.
1. For high fields such that 2MkFv/kBT>>1 the ratio v/E becomes independent of temperature.
2. The ratio v/E appears to decrease linear- ly with v in this region provided 14kFv
:
k TB 0'
3. At temperature above T the ratio v/E is almost constant, independent of temperature and field.
The data of Ahonen et al. 171 at 28.8 bar and 3 mK are consistent with Point (2), i.e. v/E decreases linearly with v. However, they also found that for a field of 60 V cm-I the ratio v/E is in- dependent of temperature. For such a field
2$kFv/kgT is less than unity, even at 3 mK, so that
C6-80
the ratio v/E is not constant because of Point ( 1 ) . We conclude that a field of 6 0 V c m i is not too large to measure the mobility.
Clearly it is desirable to have further mea- surements of the mobility and of the dependence of
v on E for a wide range of fields in order to test the theory more completly, and to confirm the results of Ahonen et al.
References
/ I / Abe,R. and Aizu,K., Phys. Rev.
123
(1961) 10 /2/ Anderson,A.C., Kuchnir,M. and Wheatley, J.C.,Phys. Rev.
168,
(1968) 261/ 3 / Josephson,B.D. and Lekner,J., Phys. Rev. Lett.
23 ( 1 9 6 9 ) I l l
-
141 Bowley,R.M., J. Phys. C: Solid State Phys.
2
(1978) 75
151
Roach,P.D., Ketterson,J.B. and Roach,P.R., Phys. Lett.63A
(1977) 273161 Kokko, J
.
,
Paalanen,M.A.,
Schoepe, W. and Takano, Y. (preprint)/7/ Ahonen,A.I., Kokko,J., Paalanen,M.A., Richard- son,R.C., Schoepe,W. and Takano,Y., J. Low Temp. Phys.
30
(1978) 205/ 8 / Bowley,R.M., J. Phys. C : Solid State Phys., to be published
/9/ Fetter,A.L. and ~urkijzrvi, Phys. Rev.
