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The energy-dependence of the slow positron elastic scattering cross-section in helium
Volume 35A, number 4
PHYSICS LETTERS
THE ENERGY-DEPENDENCE SCATTERING
14 June 1971
OF THE SLOW POSITRON
CROSS-SECTION
ELASTIC
IN HELIUM
S. N. RODIONOV, B. P. SANNIKOV and E. P. SOLODOY institute of Nuclear Physics, Siberian Division of the USSR Academy of Sciences
Received 13 April 1971 The momentum—transfer cross—section of slow positrons in helium was found to be constant in the energy 2. region of 1—5 eV and equal to (O.O23~O.OO6)ira~
We have reported [1] about anomalous behaviour of positron electric drift in helium which might be connected with the effect analogous to the Ramsauer-Townsend effect for electrons. The experiments described below were performed in order to make situation more clear. The experimental layout was similar to that described previously [1]. The positrons from a 22Na source of about 1 mCi entered a cylindrical glass chamber of 50 mm diameter placed into a homogeneous longitudinal magnetic field of 500 Oe and filled with helium up to a pressure of several hundred torr. It was possible to create a longitudinal electric field inside the chamber. At a distance of 36 cm from the source a thin target - metallized 0.5mg/cm2 thick plastic foil - was located. The annihilation quanta from the target were registred with two narrow scmtillation detectors conneceted into coincidence. The difference in counting rate M for two opposite directions of electric field was measured. It was confirmed that fast-positron background counting rate is independent of the applied voltage. Thus, the value of M is determined only by change of the character of slowpositron electric drift. For this case the solution of a simplest one-dimensional diffusion equation gives the following result (radial motion of positrons was neglected due to the magnetic field effect): M
NuT
2
where U is the drift velocity, T = (~~oc?~effY’ the Dirac annihilation life time, N the linear density of slowing-down positrons which is nearly constant along the chamber axis under our conditions. Fig. 1 shows the measured dependence of i~I
Al 15
10
+ 4 0
+ 0.5
10
20
50
-t
-,
100
E/p voIts~cm atm
Fig. 1. The dependence of ~ion the absolute value of - helium pressure 1 atm, 4~-helium pressure O.4atm. ~I is in relative units.
El/i. $
on the absolute value of E/p. Since T is partically independent of the positron energy in the region of 0 - 17.8 eV [2, 3], these results represent “u” as a function of Elp. “u” is proportional to (E/p)1/2 in the interval E/p = 1 - 4 V/cm -atm what is typical for the Druyvesteyn distribution with constant transport cross-section 00. In order to determine we have measured the dependences of 1,J on the length of the region with electric field as well as on the pressure of helium at constant geometry of electric field (the value of E/p was constant in each experiment). Using the Druyvesteyn distribution one may calculate these dependences with only one free parameter ~ In both cases the best fit to experimental results was obtained with = (2±0.5)x 10-18 cm2 =(0.023±0.006)ira~. For value of Zeff we used results of Lee et al. [2]. Solid line on fig. 1 represented calculations based on the following simple model:
297
Volume35A, number4 a a
0 . O23~2 a~ 0.046
—
=
PHYSICS LETTERS
0
l4June 1971
last theoretical proceeds to increase worksslowly give aup very to 17.8 similar eV. picture The (see [3] for their review). The experiments were performed with impurity volume level of the order of 10-5. The purity of helium itself was of the same order. It should be noted that at higher impurity level (0.1 - 1% of air) interpretation of experimental data was similar to that of Hughes et al. [4]. The preliminary experiments with neon showed that the momentum transfer cross-section is close to 0.3 7ra~in a wide energy range.
It is supposed also that positrons are fully absorbed at 17.8 eV, i.e., the positronium formation cross-section is infinetely large. This suggestion is unreal, of course, but for any finite value of positronium formation cross-section one may choose a proper linear rise of scattering cross-section above 5 eV (beginning from 0.0467Ta~)in order to fit experimental data. Unfortunately, the present experimental data do not allow to distinguish between all possible models. From the other hand the experimental data at low values of E/p disagree with above calculations. It may be explained by the increase of scattering cross-section below 1 eV (approximately, a Thus, the energy-dependence of the positron momentum-transfer cross-section in helium j~ imagined as follows: at low energies the crosssection drops with ener 9 up to 1 eV where it becomes constant (0.023na0) to 5 eV. At the energy of 5 eV the cross-section is doubled by jump and
The authors are grateful to Dr. L. M. Barkov for valuable advices and useful discussions.
References [1] S. N. Rodionov, B. P. Sannikov and E. P. Solodov,
JETP Letters 10 (1969) 325. [2] G.F. P.H. Orth and G. Jones. Phys. Letters [3] S.J.Tao and T:H.Kelly, Phys.Rev. 185 (1969) 135. [4] S.Marder, V.H.Hughes, C.G.Wu and W.Benneth, Phys. Rev. 103 (1956) 1258.
DEPRESSION IN ORDER PARAMETER OF A SUPERCONDUCTOR CONTAINING A MAGNETIC IMPURITY
*
A. N. CHABA and A. D. SINGH NAGI Physics Department, University of Waterloo, Waterloo, Ontario, Canada Received 19 April 1971
We show that the depression in order parameter, -b~(r), for the case when the scattering of conduction electrons by a magnetic impurity is strong, is about 5 times more that the value one gets by using the Born approximation. We assume T near Tc and r >> coherence length ~o For r>> ~o (= VF/21r Tc), we can use momentum representation. The variation in order parameter is [1,2], ~(q)
+
T ~ f~{~0(p+,
~
~)
oA(q) öO(p, wn)}14 =
(2ir)
f~~{ôo(p+,wn)Lo(p+,p;wn)ôo(p, w~ (air)
-T~
*
(1) ‘°n~}l4
Supported in part by the National Research Council of Canada. 298
PHYSICS LETTERS
THE ENERGY-DEPENDENCE SCATTERING
14 June 1971
OF THE SLOW POSITRON
CROSS-SECTION
ELASTIC
IN HELIUM
S. N. RODIONOV, B. P. SANNIKOV and E. P. SOLODOY institute of Nuclear Physics, Siberian Division of the USSR Academy of Sciences
Received 13 April 1971 The momentum—transfer cross—section of slow positrons in helium was found to be constant in the energy 2. region of 1—5 eV and equal to (O.O23~O.OO6)ira~
We have reported [1] about anomalous behaviour of positron electric drift in helium which might be connected with the effect analogous to the Ramsauer-Townsend effect for electrons. The experiments described below were performed in order to make situation more clear. The experimental layout was similar to that described previously [1]. The positrons from a 22Na source of about 1 mCi entered a cylindrical glass chamber of 50 mm diameter placed into a homogeneous longitudinal magnetic field of 500 Oe and filled with helium up to a pressure of several hundred torr. It was possible to create a longitudinal electric field inside the chamber. At a distance of 36 cm from the source a thin target - metallized 0.5mg/cm2 thick plastic foil - was located. The annihilation quanta from the target were registred with two narrow scmtillation detectors conneceted into coincidence. The difference in counting rate M for two opposite directions of electric field was measured. It was confirmed that fast-positron background counting rate is independent of the applied voltage. Thus, the value of M is determined only by change of the character of slowpositron electric drift. For this case the solution of a simplest one-dimensional diffusion equation gives the following result (radial motion of positrons was neglected due to the magnetic field effect): M
NuT
2
where U is the drift velocity, T = (~~oc?~effY’ the Dirac annihilation life time, N the linear density of slowing-down positrons which is nearly constant along the chamber axis under our conditions. Fig. 1 shows the measured dependence of i~I
Al 15
10
+ 4 0
+ 0.5
10
20
50
-t
-,
100
E/p voIts~cm atm
Fig. 1. The dependence of ~ion the absolute value of - helium pressure 1 atm, 4~-helium pressure O.4atm. ~I is in relative units.
El/i. $
on the absolute value of E/p. Since T is partically independent of the positron energy in the region of 0 - 17.8 eV [2, 3], these results represent “u” as a function of Elp. “u” is proportional to (E/p)1/2 in the interval E/p = 1 - 4 V/cm -atm what is typical for the Druyvesteyn distribution with constant transport cross-section 00. In order to determine we have measured the dependences of 1,J on the length of the region with electric field as well as on the pressure of helium at constant geometry of electric field (the value of E/p was constant in each experiment). Using the Druyvesteyn distribution one may calculate these dependences with only one free parameter ~ In both cases the best fit to experimental results was obtained with = (2±0.5)x 10-18 cm2 =(0.023±0.006)ira~. For value of Zeff we used results of Lee et al. [2]. Solid line on fig. 1 represented calculations based on the following simple model:
297
Volume35A, number4 a a
0 . O23~2 a~ 0.046
—
=
PHYSICS LETTERS
0
l4June 1971
last theoretical proceeds to increase worksslowly give aup very to 17.8 similar eV. picture The (see [3] for their review). The experiments were performed with impurity volume level of the order of 10-5. The purity of helium itself was of the same order. It should be noted that at higher impurity level (0.1 - 1% of air) interpretation of experimental data was similar to that of Hughes et al. [4]. The preliminary experiments with neon showed that the momentum transfer cross-section is close to 0.3 7ra~in a wide energy range.
It is supposed also that positrons are fully absorbed at 17.8 eV, i.e., the positronium formation cross-section is infinetely large. This suggestion is unreal, of course, but for any finite value of positronium formation cross-section one may choose a proper linear rise of scattering cross-section above 5 eV (beginning from 0.0467Ta~)in order to fit experimental data. Unfortunately, the present experimental data do not allow to distinguish between all possible models. From the other hand the experimental data at low values of E/p disagree with above calculations. It may be explained by the increase of scattering cross-section below 1 eV (approximately, a Thus, the energy-dependence of the positron momentum-transfer cross-section in helium j~ imagined as follows: at low energies the crosssection drops with ener 9 up to 1 eV where it becomes constant (0.023na0) to 5 eV. At the energy of 5 eV the cross-section is doubled by jump and
The authors are grateful to Dr. L. M. Barkov for valuable advices and useful discussions.
References [1] S. N. Rodionov, B. P. Sannikov and E. P. Solodov,
JETP Letters 10 (1969) 325. [2] G.F. P.H. Orth and G. Jones. Phys. Letters [3] S.J.Tao and T:H.Kelly, Phys.Rev. 185 (1969) 135. [4] S.Marder, V.H.Hughes, C.G.Wu and W.Benneth, Phys. Rev. 103 (1956) 1258.
DEPRESSION IN ORDER PARAMETER OF A SUPERCONDUCTOR CONTAINING A MAGNETIC IMPURITY
*
A. N. CHABA and A. D. SINGH NAGI Physics Department, University of Waterloo, Waterloo, Ontario, Canada Received 19 April 1971
We show that the depression in order parameter, -b~(r), for the case when the scattering of conduction electrons by a magnetic impurity is strong, is about 5 times more that the value one gets by using the Born approximation. We assume T near Tc and r >> coherence length ~o For r>> ~o (= VF/21r Tc), we can use momentum representation. The variation in order parameter is [1,2], ~(q)
+
T ~ f~{~0(p+,
~
~)
oA(q) öO(p, wn)}14 =
(2ir)
f~~{ôo(p+,wn)Lo(p+,p;wn)ôo(p, w~ (air)
-T~
*
(1) ‘°n~}l4
Supported in part by the National Research Council of Canada. 298