He³ Isotope

K. A. Tumanov

Progress in the physics of liquid helium and in isotope-separation techniques has made the task of separating the isotope He³ a promising one. The study of the properties of He³ is of interest both for nuclear physics and for the theory of superfluidity. He³ could be used as a working particle in a cyclotron. An exact determination of the mass of the He³ atom is of theoretical interest. As is known, no substance dissolves in liquid helium in appreciable quantities; a solution of He³ in He⁴ may be regarded as the sole exception. Finally, an investigation of the relation of He³ to the phenomenon of superfluidity would be highly important.

The content of He³ in helium is very small: mass-spectrographic measurements by Alvarez and Cornog¹ and by Aldrich and Nier² showed that the ratio of the number of He³ atoms to the number of He⁴ atoms in helium obtained from air is \(12 \cdot 10^{-7}\), while in helium contained in natural gases it is \(1.6 \cdot 10^{-7}\). In their subsequent work²² Aldrich and Nier carried out a systematic investigation of the isotopic composition of helium contained in various minerals and in various natural gases. It turned out that the ratio He³/He⁴ varies over wide limits, from \(120 \cdot 10^{-7}\) to \(0.5 \cdot 10^{-7}\), and differently even for samples of one and the same mineral from different deposits. In helium samples obtained from radioactive ores, the amount of He³ proved not to be measurable \((\mathrm{He}^3/\mathrm{He}^4 < 0.2 \cdot 10^{-7})\). The diversity of the concentration of He³ in helium obtained from different minerals, natural gases, and air indicates that the sources of origin of the two isotopes are different. The supposition that continuously operating sources of He³ exist is quite plausible. For example, the following nuclear reactions leading to the formation of He³ are possible. Neutrons associated with cosmic radiation act on Li⁶ in the earth’s crust and on N¹⁴ in the atmosphere:

\[ \mathrm{Li}^6(n,\alpha)\mathrm{H}^3,\quad \mathrm{N}^{14}(n,\mathrm{C}^{12})\mathrm{H}^3 \quad \text{or} \quad \mathrm{N}^{14}(n,3\alpha)\mathrm{H}^3; \]

the tritium \(\mathrm{H}^3\) thus produced is converted into He³ as a result of β-decay. The authors point out that additional experimental data are necessary to prove the hypothesis of the continuous formation of He³.

The separation of the isotope He³, which occurs in such small concentrations, is naturally associated with considerable difficulties. Therefore attempts were made to use, for separation, the anomalous properties of liquid helium, above all the property of superfluidity.

SEPARATION OF HELIUM BY MEANS OF CRYOGENIC TECHNIQUE

The first attempts to explain the phenomenon of superfluidity belong to F. London and Tisza. In the opinion of these authors, helium atoms (He⁴) in the state with zero energy form an ideal gas obeying Bose–Einstein statistics. F. London and Tisza connect the phenomenon of superfluidity with the degeneracy of this Bose–Einstein gas. On this basis, Frank³*) concluded that, since atoms of the isotope He³ do not obey Bose–Einstein statistics, they cannot take part in superfluid motion. Frank suggested that it might be possible to separate helium by a filtration method.

The theoretical attempts of F. London and Tisza are based on unfounded assumptions and lead to results not confirmed by experiment. A consistent theory of superfluidity was developed by L. D. Landau**). On the basis of the principles of Landau’s theory, the author of the theory and Pomeranchuk⁵ criticized Frank’s argumentation. Landau and Pomeranchuk pointed out that, since the property of superfluidity is connected not with individual atoms but with a collective of identical He⁴ atoms, any other atoms forming small impurities, such as He³ and the still rarer isotope He⁶, will not participate in the superfluid motion regardless of whether they themselves, in pure form, possess the property of superfluidity.

According to Landau’s theory, helium II consists of a normal and a superfluid component. Evidently, impurities enter into the composition of the normal component. In pure helium the amount of the normal component rapidly decreases with decreasing temperature. In the case of impurities, however, the amount of the normal component at the lowest temperatures will differ from zero. This leads to the fact that at low temperatures, even in the case of very small impurities, the thermodynamic functions of helium with impurities will differ noticeably from the thermodynamic functions of pure helium. Pomeranchuk²³ calculated the change in the normal density, entropy, heat capacity, and also the velocity of second sound in helium caused by the presence of impurities. It turned out, for example, that owing to impurities the temperature dependence of the velocity of second sound undergoes a qualitative change: as the temperature is lowered, the velocity of second sound does not increase, approaching a finite value, but decreases.

*) A similar idea was also expressed by L. Onsager (see ⁹).

**) Landau’s theory is presented in the review by E. M. Lifshitz⁴.

The Isotope He³

Dount, Probst, Johnston, Aldrich, and Nier⁶ experimentally investigated the possibility of separating isotopes on the basis of superfluidity. In their experiment they used the apparatus shown in Fig. 1. In a vessel with liquid atmospheric helium \(A\) there was a small Dewar \(D\), partly immersed in liquid helium. The opening of the Dewar was plugged with a ground-glass stopper, preventing the penetration of helium vapor from vessel \(A\) into Dewar \(D\). In the Dewar there was an electric heater \(T_1\). The apparatus was placed in a helium bath \(B\) at a temperature of \(1.3^\circ\mathrm{K}\). When current was passed through the heater, a superfluid flow of helium into the small Dewar was produced in the form of a surface film*), which flowed freely through the gap in the ground joint. Mass-spectrometric investigation of the contents of the small Dewar established that the ratio \(\mathrm{He}^3/\mathrm{He}^4\) in it was less than \(5\cdot 10^{-8}\), whereas the initial \(\mathrm{He}^3/\mathrm{He}^4\) was \(1.2\cdot 10^{-6}\). This proved that \(\mathrm{He}^3\) atoms do not take part in superfluid motion. The authors hoped to detect during the experiment an increase in the concentration of \(\mathrm{He}^3\) in the helium vapor in vessel \(A\). It turned out, however, that in vapor samples withdrawn through tube \(a\), the ratio \(\mathrm{He}^3/\mathrm{He}^4\) was smaller than in the original helium by approximately a factor of 3; in other words, most of the \(\mathrm{He}^3\) was in the liquid helium. This decrease in the content of \(\mathrm{He}^3\) in the vapor above liquid helium below the \(\lambda\)-point, as the authors indicated, might be a new property of helium. Another possible explanation, proposed by the authors, consists in a disturbance of the equilibrium distribution of the isotopes, associated with the fact that the evaporation conditions of the two isotopes are not the same—\(\mathrm{He}^4\) evaporates much more intensely, because in the form of a film it flows over into warmer places and evaporates from the entire surface of the film.

Fig. 1. Apparatus for separating helium isotopes by means of a superfluid film. With this apparatus it was first experimentally proved that \(\mathrm{He}^3\) does not participate in superfluid motion.

In the next work, Dount, Probst, and Johnston⁸, condensing helium in vessel \(A\) (Fig. 1) above the level of the ground joint, filtered liquid helium through a narrow slit (width of the order of \(1\,\mu\)) and again obtained enrichment of the helium in vessel \(A\) with the isotope \(\mathrm{He}^3\). The increase in the concentration of \(\mathrm{He}^3\) outside Dewar \(D\) in both works by Dount and co-workers was by a factor of 4–5.

Lane, Fairbank, Aldrich, and Nier⁹ succeeded in considerably intensifying the separation of isotopes by creating a heat flow in the mass

*) For a description of the phenomenon of superfluidity, see, for example, ⁷ (Ch. 1).

of liquid helium. As is known, the heat flux in liquid helium is carried by a flow of the normal component (see\(^7\), Ch. I, § 6). Opposite to it, from colder to warmer places, moves the superfluid component with entropy equal to zero. Since He\(^3\) atoms can take part only in the motion of the normal component, they are concentrated in the places with the lowest temperature.

Fig. 2. Apparatus for separating helium isotopes by means of a heat flux in the mass of liquid helium.

Figure 2 shows the apparatus used by Lane and others. A thick-walled glass vessel \(B\) with an electric heater \(H\) is connected by means of a glass capillary \(C\) with a metal capillary \(K\) (made of the alloy “Kovar”) and, further, with a tube \(T\) extending beyond the cryostat. The vessel and the capillary were filled with liquid helium. When current was passed through the heater, heat was transferred by convection in the liquid helium into capillary \(K\), and then, through the metal walls, entered the helium bath. To determine the concentration of He\(^3\) in capillary \(K\), the authors took samples of gaseous helium above the surface of the liquid in \(K\). With time, at a temperature of \(2.01^\circ\) K, the content of He\(^3\) in the vapor gradually increased, rising in 45 minutes by a factor of 130 compared with the initial value. This result allowed the authors to express the hope that, on the basis of the heat-flux method, it would be possible to construct equipment for the practical separation of helium isotopes.

At a temperature of \(1.83^\circ\) K, on the contrary, a considerable decrease in the content of He\(^3\) in the vapor was observed, despite an increase in the heat flux.

DISTRIBUTION OF ISOTOPES BETWEEN THE LIQUID AND VAPOR PHASES

A successful solution of the problem of separating He\(^3\) and He\(^4\) proved to depend on clarifying the question of the distribution of the isotopes between the liquid and vapor phases at different temperatures. Two works by Fairbank, Lane, Aldrich, and Nier were devoted to this. In the first work\(^10\) the temperature dependence of the ratio of the concentrations of He\(^3\) in vapor and liquid was obtained in the temperature interval from 4.2 to \(2.2^\circ\) K. In the second work\(^11\) the temperature interval was extended from 5.2 to \(1.7^\circ\) K. The authors used an apparatus consisting of a small glass vessel immersed in a helium bath; the helium under investigation was condensed in the vessel. Through a tube from the vessel, samples of helium vapor were taken by admitting the vapor into an attached-

attached to the tube, small vessels that had previously been evacuated. With the aid of a mass spectrometer the ratio \(\mathrm{He}^3/\mathrm{He}^4\) in the vapor—\(C_V\)—was determined. From the known \(C_V\) it was possible to calculate the concentration of \(\mathrm{He}^3\) in the liquid \(C_L\) by means of the isotope mass-balance equations.

Before samples were taken, the cryostat was kept at a constant temperature above the \(\lambda\)-point for 30 minutes, and below the \(\lambda\)-point for 15 minutes.

The authors paid special attention to evaporation of the surface film, which is the most probable and significant source of errors. Since the amount of helium carried by the film is proportional to the perimeter of the connecting surface, a capillary with a cross section of 1.5 mm was used as the supply tube. In order to prevent partial evaporation of the film on the walls of the vessel before entry into the capillary, the vessel was protected by a screen. Assuming that the film in the vessel does not evaporate, the authors calculated the amount of helium evaporated from the film during the time between samplings, and found that even under the most unfavorable assumption—that all this helium enters the sample—the true value of \(C_V/C_L\) would differ from the measured one by no more than 10%.

Fig. 3. Dependence of the ratio of the concentration of \(\mathrm{He}^3\) in the vapor and liquid phases on temperature.

In Fig. 3 are shown the results of the measurements of Färbenk et al. The authors regarded the quantity \(C_V/C_L\) as the most convenient and universal description of the phenomenon, since according to Henry’s law for dilute solutions this quantity at a given temperature does not depend on the total concentration. The results of the work, in the opinion of its authors, suggest a simple method of enriching helium with the isotope \(\mathrm{He}^3\), namely, evaporation of helium at a temperature considerably below the \(\lambda\)-point.

The results of the next experimental work, belonging to Daunt, Probst, and Smith\(^{12}\), are shown in Fig. 4. Along the abscissa is plotted the reciprocal temperature \(1/T\), and along the ordinate \(\lg C_V/C_L\). In the He I region the experimental points lie approximately on one curve; in the He II region, on the contrary, each total concentration corresponds to its own curve. Circles are values taken from the work of Färbenk et al. (Fig. 3, total concentration \(\mathrm{He}^3/\mathrm{He}^4 = 1.2 \cdot 10^{-6}\)); squares and crosses are the results of the experiments of Daunt et al.; the squares correspond to a total concentration of \(10 \cdot 10^{-6}\), the crosses to \((30 \div 40)\cdot 10^{-6}\). From Fig. 4 it is evident that the results of the experiments of Färbenk et al. and Daunt et al. agree with one another and indicate ...

increase in \(C_v, C_L\) with increasing total concentration of \(\mathrm{He}^3/\mathrm{He}^4\), which is in contradiction with Henry’s law.

In the communication by Daunt and co-workers no description is given of the apparatus and the experimental procedure; the authors note, however, that they took measures to prevent the harmful influence of the surface film*).

Fig. 4. Dependence of the logarithm of the ratio of the concentrations of \(\mathrm{He}^3\) in the vapor-like and liquid phases on reciprocal temperature. The triangles correspond to a total concentration \(\mathrm{He}^3/\mathrm{He}^4 = 10^{-6}\), the squares to \(10 \cdot 10^{-6}\), the crosses to \((30 \div 40)\cdot 10^{-6}\). Circles denote the results of the experiments of Fairbank et al.\(^{11}\), \(\mathrm{He}^3/\mathrm{He}^4 = 1.2 \cdot 10^{-6}\).

Rollin and Hatton\(^{13}\), measuring \(C_V/C_L\) for helium whose initial concentration was \(\mathrm{He}^3/\mathrm{He}^4 = 1.5 \cdot 10^{-3}\), found that at \(1.3^\circ\mathrm{K}\) the relative content of \(\mathrm{He}^3\) in the vapor was 10 times greater than in the liquid.

DISCUSSION OF RESULTS

From the results of the work of Fairbank et al.\(^{11}\), Daunt et al.\(^{12}\), and Rollin and Hatton\(^{13}\), it follows that the ratio of the contents of \(\mathrm{He}^3\) in the vapor and liquid below the \(\lambda\)-point does not remain constant, but increases with increasing total concentration of \(\mathrm{He}^3\). This means that the results are in contradiction with Henry’s law already at concentrations of the order of \(\mathrm{He}^3/\mathrm{He}^4 \sim 10^{-6}\). It should be recalled that Henry’s law

*) In their communication Daunt and co-workers state that they have built an apparatus for isotope separation in which the film transfers \(0.5\) liters of liquid helium per hour.

are derived from the equations of thermodynamics under the sole assumption that the solution is dilute (see, e.g., \(^{14}\)). Deviations from Henry’s law occur when the interaction between molecules of the dissolved substance begins to make itself felt. It is impossible to suppose that the interaction of He\(^3\) atoms, separated from one another by hundreds of He\(^4\) atoms, has any noticeable influence on the thermodynamic functions of liquid helium. Consequently, Henry’s law must hold for weak solutions of He\(^3\) in He\(^4\). On the other hand, the establishment of equilibrium in He II is a very difficult matter; equilibrium is disturbed both by the motion and evaporation of the film and by convection in the liquid, arising at the slightest temperature differences. According to Pomeranchuk’s calculations \(^{23}\), in helium II with the usual content of He\(^3\) (\(\mathrm{He}^3/\mathrm{He}^4 \sim 10^6\)) a supercooling of \(10^{-5}\) degrees at some point is sufficient for all the He\(^3\) atoms to collect there. Therefore one must agree with the opinion of Rollin and Hatton that in the work of Fairbank et al., despite all precautions and estimates, the influence of the film was nevertheless not fully taken into account. The smaller the total concentration of He\(^3\), the more strongly the excess of He\(^4\) produced by the film affects the result, and the smaller is the measured relative content of He\(^3\) in the vapor.

Of course, the theoretical works of F. London and Rice \(^{15}\) and of Stout \(^{16}\), based on the results of Fairbank and others, are likewise erroneous.

OTHER PROPERTIES OF A SOLUTION OF He\(^3\) IN He\(^4\)

In addition to the question of the distribution of the isotope He\(^3\) between the two phases of the solvent, other properties of a solution of He\(^3\) in He\(^4\) were also studied, namely the osmotic pressure produced by the isotope He\(^3\) in the solution, and the change in the vapor pressure of helium in the presence of the isotope He\(^3\) in the helium. It should be noted, however, that these two phenomena were not studied quantitatively as functions of various factors; only their existence was demonstrated.

Fig. 5. Apparatus for measuring the osmotic pressure of He\(^3\).

The first phenomenon was discovered by Daunt, Probst, and Johnston \(^{17}\). Their apparatus (Fig. 5) consisted of a U-shaped tube. In the upper part the tube was blocked by a ground-glass joint, which prevented helium vapor from flowing from one arm of the tube into the other. The ends of the arms were connected to tubes leading out of the cryostat; through them helium could be introduced into the apparatus. The apparatus was immersed in a helium bath at a temperature of \(1.57^\circ\) K. In one of the arms helium condensed, its initial concentration being \(\mathrm{He}^3/\mathrm{He}^4 = 2.4 \cdot 10^{-5}\), and flowed in the form of a film

into the other arm. However, the levels in the arms did not become equal; the difference of the levels under these conditions proved to be equal to 2.1 mm. The authors pointed out the difficulty of interpreting this result, since He\(^3\) is contained both in the liquid and in the vapor and in different concentrations.

Fig. 6. Change in vapor pressure produced by the isotope He\(^3\).

The change in vapor pressure produced by the isotope He\(^3\) was discovered by Fairbank, Reynolds, Lane, McInteer, Aldrich, and Nier\(^ {18}\). They used an apparatus consisting of two identical thin-walled glass vessels connected by tubes to the two ends of an oil differential manometer. The vessels were immersed in a helium bath. One of the vessels contained ordinary helium from sources (He\(^3\)/He\(^4\) = \(1.6 \cdot 10^{-7}\)), and the other enriched helium (He\(^3\)/He\(^4\) = \(1.6 \cdot 10^{-3}\)). The results of this work are given in Fig. 6. The authors note that the discontinuity at the \(\lambda\)-point was reproduced in all measurements.

SEPARATION OF HELIUM BY THE METHOD OF THERMODIFFUSION

In the book by K. Jones and W. Furry\(^ {19}\) a calculation is given of a thermodiffusion installation for the separation of helium. As the authors note, this calculation is based on tables and formulas not applicable to helium, and is therefore very approximate. According to the calculation, the installation should yield 3.8 cm\(^3\) per day of helium with He\(^3\)/He\(^4\) = \(10^{-2}\)—\(10^{-3}\) and have a characteristic time of approach to operating conditions of 14 days.

McInteer, Aldrich, and Nier\(^ {20}\) built an installation similar to that proposed by Jones and Furry. It consists of two columns with concentric tubes and one column with a hot wire. This installation, according to the authors’ measurements, with a time of approach to operating conditions of 29 days, gives 7 cm\(^3\) of helium per day (under normal conditions), whose concentration is He\(^3\)/He\(^4\) = \(4.2 \cdot 10^{-3}\), if the initial concentration is \(1.15 \cdot 10^7\) (enrichment 36,600). The enrichment can be increased by reducing the daily yield of enriched gas; in this case the time of approach to operating conditions increases.

Andrew and Smith\(^ {21}\) built an installation in which, in series with a Clusius and Dickel column (a column with a hot wire), a Hertz pump was installed, whose action is based on the different rates of diffusion of isotopes through a jet of mercury vapor.

The sample obtained by them after two weeks of processing, with a mass of approximately 0.07 mg, contained 0.5% He$^3$.

It should be noted that in the majority of the works considered above in which enriched helium was used, this helium was obtained by the thermodiffusion method.

References

1. L. W. Alvarez and R. Cornog, Phys. Rev. 56, 613, 379 (1939).
2. L. T. Aldrich and A. O. Nier, Phys. Rev. 70, 983 (1946).
3. J. Franck, Phys. Rev. 70, 561 (1946).
4. E. M. Lifshitz, UFN 34, 512 (1948).
5. L. Landau and I. Pomeranchuk, DAN SSSR, 59, 669 (1948).
6. J. G. Daunt, R. E. Probst, H. L. Johnston, L. T. Aldrich and A. O. Nier, Phys. Rev. 72, 502 (1947).
7. E. L. Andronikashvili and K. A. Tumanov, UFN 33, 469 (1947).
8. J. G. Daunt, R. E. Probst and H. L. Johnston, J. Chem. Phys. 15, 759 (1947).
9. C. T. Lane, H. A. Fairbank, L. T. Aldrich and A. O. Nier, Phys. Rev. 73, 256 (1948).
10. H. A. Fairbank, C. T. Lane, L. T. Aldrich and A. O. Nier, Phys. Rev. 71, 911 (1947).
11. H. A. Fairbank, C. T. Lane, L. T. Aldrich and A. O. Nier, Phys. Rev. 73, 729 (1948).
12. J. G. Daunt, R. E. Probst and S. R. Smith, Phys. Rev. 74, 495 (1948).
13. B. V. Rollin and J. Hatton, Phys. Rev. 74, 508 (1948).
14. L. Landau and E. Lifshitz, Statistical Physics, ONTI, Moscow, 1938, § 49.
15. F. London and O. K. Rice, Phys. Rev. 73, 1188 (1948).
16. J. W. Stout, Phys. Rev. 74, 605 (1948).
17. J. G. Daunt, R. E. Probst and H. L. Johnston, Phys. Rev. 73, 638 (1948).
18. H. A. Fairbank, C. A. Reynolds, C. T. Lane, B. B. McInteer, L. T. Aldrich and A. O. Nier, Phys. Rev. 74, 345 (1948).
19. K. Jones and V. Furry, Separation of Isotopes by the Thermodiffusion Method, IL, Moscow, 1947, p. 134.
20. B. B. McInteer, L. T. Aldrich and A. O. Nier, Phys. Rev. 72, 510 (1947); 74, 946 (1948).
21. A. Andrew and W. R. Smythe, Phys. Rev. 74, 496 (1948).
22. L. T. Aldrich and A. O. Nier, Phys. Rev. 74, 1590 (1948).
23. I. Pomeranchuk, ZhETF 19, 42 (1949).