Positronium formation in xenon gas near the critical point

Volume 72A, number 4,5

PHYSICS LETTERS

23 July 1979

POSITRONIUM FORMATION IN XENON GAS NEAR THE CRITICAL POINT~ P.K. TSENG and S.Y. CHUANG Physics Department, National Taiwan University, Taipei, Republic of China

S.-H.CHEN Massachusetts Institute of Technology, Cambridge, MA 02139, USA

and S.J. TAO The New England Institute, Ridgefield, CT 06877, USA

Received 9 May 1979

The amount of positronium formation in xenon gas has been determined from the intensity of the long lived component, 13, in the positron decay spectrum. 13 remains essentially constant for temperatures T> Tc + 1 along the critical isochore. It decreases from the constant value for T < Tc + L~Twhere ~T -~- 1 K, while for T < T~,13 of the vapor phase is found to be proportional to the vapor density of xenon. 13 also decreases from strict proportionality at T> Tc — ~T. These variations of the positron formation are interpreted as due to scattering of the slowing down positrons by the increasing critical fluctuations which occur when T is near T~.

Critical phenomena in gases have been an active field of study for many years. It has been investigated by various experimental methods but the use of positrons as a probe in a fluctuating medium has not been attempted until recently. In a previous letter [1] we were the first to point out that orthopositronium might become one of the useful probes for the investigation of the critical slowing down of the density fluctuations near the gas—liquid critical point. We have shown that there is a similarity in the slowing down of the orthopositronium (o-Ps) quenching rate and the slowing down of the density fluctuation of certain wave vectors as probed by Rayleigh scattering, as the temperature of the gas approaches T~ (where T~is the gas—liquid critical temperature) [1]. Our new investigations reveal that the intensity*l, 13, of the longest decay component in the life-time

spectrum of positrons in xenon gas at the critical density, p~,also shows a deviation from the regular ternperature dependence in the non-critical region, T— T~I~ 1 K.

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Research supported by NSF CHE 75-00329, USA, and NSC, Republic of China.

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TEMPERATU~(K)

The spectra were analyzed by a standard iterative least-

Fig. 1. Plot of X

squares technique of Tao [2].

13 versus temperature T (upper curve).

3 versus temperature T (lower curve) and of

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Volume 72A, number 4,5

PHYSICS LETTERS

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23 July 1979

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8 290 I

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TEMPERATURE

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(K)

Fig. 2. Expanded view ofI

3 versus temperature Tnear the

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critical temperature (T~= 289.7 K). The uncertainty in the temperature measurement is

±0.2

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K.

In fig. 1, the temperature dependence of!3 and the decay constant, X3, of o-Ps in xenon gas at the critical density, p~,are plotted. Since the behavior of X3 for T> T~has been described in our previous paper [1] we here concentrate only on 13. The ternperature dependence of 13 can be divided into two parts, T> T~and T< T~. except at ternFornamely T> T~, 13 remains constant peratures close to T~.In order to investigate the behavior near the critical point, precise measurements with fine temperature controls have been performed. The temperature dependence of 13 near T~is plotted in the expanded temperature scale in fig. 2. It is found that 13 deviates from constancy and decreases when T T~is less than 1 K. For the temperature region T< T~,xenon separates into two phases, namely the liquid and the saturated vapor. Because the saturated vapor density decreases drastically on decreasing the temperature, 13 is expected to decrease rapidly if 13 is proportionalto the density of the vapor, p. In this case, one obtains a more meaningful physical picture, if one plots the 13 curves as a function of the vapor density as shown in fig. 3. In this curve, one can also find that 13 deviates from the linear dependence on p near p~. The interval of p where 13 deviates from the normal dependence on p is 15 to 20 amagats from p~ and is equivalent to about 0.5 to 1 K in the xenon vapor temperature. Since 13 is the percent intensity of quenched o-Ps, 4/3 times ~ represents the total amount of positroni,

—

urn formed (in %) in the xenon gas. Therefore we can say that the positronium formation in xenon gas

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I I I I I I I I I 200 VAPOUR DENSITY (AMAGAT I

Fig. 3. Plot of!3 versus vapor pressure in amagat for Tbelow T~.The horizontal error bars shown are due to the uncertainty in the estimation of the vapor pressures of the xenon gas.

with p = p~and in the region I T T~I< 1 K deviates from that in the region I T I ~ 1 K which is thought to be normal. This fact may be interpreted 1/2fl~)of as follows. with The wave number K (= (2mE) a positron a kinetic energy equal to the positroniurn formation threshold energy is about 1.2 X 108 cm~.On the other hand, the correlation length, of xenon gas near the critical point is given by [31 = 2 0’T /(T T v~0.63 A —

—

~,

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where for T T~= 1 K ~is 7.1 X 1 0~ cm and thus k~> 1. This means that for T T~~ 1 K the test particle positron is well inside the critical regime and that scattering of the positron by the density fluctuation can take place. Within this narrow ternperature range it has therefore had an opportunity to be scattered into less dense areas with a consequent limitation on the formation of positronium. —

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The authors P.K. Tseng and S.Y. Chuang are pleased to thank Professor B.G. Hogg for stimulating disciissions and reading of the manuscript. References [1] P.K. Tseng, S.H. Chuang and S.J. Tao, Phys. Lett. 60A (1979) 14. [2] S.J. Tao IEEE Trans. NucI. Sci. NS-15 (1968) 175. [3] H.L. Swinney and D.L. Henny, Phys. Rev. A8 (1973) 2586.