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4He solutions
PHYSICA
Physica B 194-196 (1994) 843-844 North-Holland
Anomalous temperature dependence of the vortex nucleation rate due to negative ions in ultradilute superfluid 3He/4He solutions P.C. Hendry, N.S. Lawson, P.V.E. McClintock and M.Y.A. Wahab a School of Physics and Materials, Lancaster University, Lancaster, LA1 4YB, UK. The rate v at which negative ions create quantized vortex rings in superfluid aHe/4He solutions has been measured for temperatures T within 90 < T < 500 mK, for SHe/4He isotopic ratios zs < 10 -7, i~ressures P within 17 < P < 25 bar, and electric fields E within 102 < E < 106 Vm -1. For fixed P, zs and E, it has been found that u(T) exhibits unexpected sharp local maxima, together with associated small velocity anomalies.
1. I N T R O D U C T I O N Ions moving in He II are able to create quantized vortex rings [1] when their velocity exceeds a critical value which, for negative ions in isotopically pure 4He under a pressure P .~ 20 bar, is ~ 60 ms -1 [2]. The creation mechanism at low temperatures is believed [2], [3] to involve macroscopic quantum tunnelling through an energy barrier; thermal activation over the barrier dominates at higher temperatures. In common with vortex creation at orifices [4], [5] the mechanism is known [6] to be markedly influenced by tiny traces of SHe. A probable explanation [7], [8] involves the SHe atom binding to the ion surface [9] in a Shikin angular momentum state [10]. If its binding energy on the ion is weaker than that on the nascent vortex loop [2], [3] the energy conservation requirements for vortex creation are relaxed, leading to a reduced critical velocity and a much enhanced vortex nucleation rate v for any given velocity. Earlier investigations [7] of vortex nucleation in ultradilute 3He-4He solutions referred to temperatures T > 0.3K. We now report some preliminary data from experiments measuring a/ down to lower temperatures; part of the motivation has been to probe the regime where the discrete nature of the Shikin states [10] might start to be important. 2. E X P E R I M E N T A L
DETAILS
Values of u, and of the ionic drift velocity U, were obtained using the electric induction technique and 1.5£ cell already described in detail elsewhere [2], with z3 being controlled and ad-
justed by the methods described in [7]. The investigation is inherently more difficult than the earlier work [2] over the same temperature range in pure 4He because the signals were considerably weaker, presumably on account of the 3Heenhanced vortex nucleation in the high electric field region near the field emission ion sources. Nonetheless, it has proved possible to obtain data down to 90 m K for several isotopic ratios zs <
I0 -~.
3. R E S U L T S The measurements of v agree within experimental error with the earlier work at higher temperatures [7] in the region where the parameter ranges overlap. A quite unexpected feature of the results, however, was the occurrence of a sharp local maximum in u(T) measured for fixed P, z3 and electric field E. An example of this phenomenon is shown in Fig l(a). The temperature T,~ at which the peak occurred was found to be almost independent of E but to vary quite rapidly with P: e.g. for E -- 7.0 ×10 s Vm -1, z3 --- 2.12 xlO -s, T m = 295 -t- 5 m K at P -----19 bar and 190 -4- 10 m K at 24 bar. It has also been noted that there is always a small (,-, 2-4%) velocity anomaly associated with the local maximum in u, as shown for example in Fig 1 (b). Apart from the anomalous behaviour of v(T), U(T) shown in Fig 1, the general form of the results was qualitatively rather similar to that observed earlier at higher temperatures [7].
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E1002-4
844
d~ 0
0
o
10 v
(a)
O
(lo3s -1) % 0
0 0
x 3 : 2-12x10 P = 20 b a r E
=
o o
3.0× 10/, vm_l oO 0
J
0
O
%
!
0
#% (ms"1) 0 0
53
oo d;~
52
q~a~:b 250
%%o% j 300
T (mK)
350
Figure 1. Anomalies in the temperature dependence of (a) the vortex nucleation rate z/and (b) the ionic drift velocity U.
4. D I S C U S S I O N The general behaviour of ~(E, T, P, x3) appears to be consistent with the model [7] proposed previously, involving a competition between the processes of absorption of 3He into, and emission from, surface states on the ion. Thus, for very small T, l/(T) is independent of T because thermally activated emission is of negligible importance compared to emission of the 3He with rotons [7], which depends on E but not on T. At higher temperatures, thermally activated emission becomes important, and drives v(T) down towards zero as the average residence time of a 3He on the ion becomes too short for it to influence the nucleation process. This picture provides a satisfactory explanation of the general behaviour of z/(E, T, P, x3), but is of no obvious help in accounting for the phenomena of Fig 1. The narrowness of the local maximum could be regarded as indicative of a
phase transition, but there is no reason to anticipate any such phenomenon for the negative ion under these conditions. The rapid pressure dependence of T,~ suggests that the highest bound Shikin level may be of primary importance: its separation A E from the ~vacuum state = of a free 3 He also changes quite rapidly with pressure, varying from A E / k B ~- 0.4K at 13 bar to A E / k B ~0 at 25 bar. We may note also that this is the level which, when occupied, is likely to have the largest effect on v because movement of the 3He atom to a bound state on the nascent vortex loop will result in the largest energy change. Finally, a caveat must be entered. We cannot at present eliminate the possibility of more than one species of ion being present, although there is no reason a priori to expect that this might be the case. We conclude that the phenomena shown in Fig 1 still await an explanation and that some interesting new physics may be involved. We acknowledge valuable discussions with R M Bowley. The work was supported by the Science and Engineering Research Council (UK). REFERENCES 1. G.W. Rayfield and R. Reif, Phys. Rev. 136 (1964) Al194. 2. P.C. Hendry, N.S. Lawson, P.V.E. McClintock, C.D.H. Williams and R.M. Bowley, Phil. Trans. R. Soc. (Lond.) A 332 (1990) 387. 3. C.M. Muirhead, W.F. Vinen and R.J. Donnelly, Phil. Trans. R. Soc. (Lond.) A 311 (1984) 433. 4. J.C. Davis, J. Steinhauer, K. Schwab, Yu. M. Mukharsky, A. Amar, Y. Sasaki and R.E. Packard, Phys. Rev. Lett. 69 (1992) 323. 5. G.G. lhas, O. Avene], R. Aarts and R. Salmelin, Phys. Rev. Lett. 69 (1992) 327. 6. R.M. Bowley, P.V.E. McClintock, F.E. Moss and P.C.E. Stamp, Phys. Rev. Lett. 44 (1980) 161. 7. G.G. Nancolas, R.M. Bowley and P.V.E. McClintock, Phil. Trans. R. Soc. (Lond.) A 313
(1985) 537. 8.
C.M. Muirhead, W.F. Vinen and R.J. Donnelly, Proc. Roy. Soc. (Lond.) A 402 (1985) 225. 9. A.J. Dahm, Phys. Rev. 180 (1969) 259. 10. V.B. Shikin, Soy. Phys. J E T P 37 (1973) 718.
Physica B 194-196 (1994) 843-844 North-Holland
Anomalous temperature dependence of the vortex nucleation rate due to negative ions in ultradilute superfluid 3He/4He solutions P.C. Hendry, N.S. Lawson, P.V.E. McClintock and M.Y.A. Wahab a School of Physics and Materials, Lancaster University, Lancaster, LA1 4YB, UK. The rate v at which negative ions create quantized vortex rings in superfluid aHe/4He solutions has been measured for temperatures T within 90 < T < 500 mK, for SHe/4He isotopic ratios zs < 10 -7, i~ressures P within 17 < P < 25 bar, and electric fields E within 102 < E < 106 Vm -1. For fixed P, zs and E, it has been found that u(T) exhibits unexpected sharp local maxima, together with associated small velocity anomalies.
1. I N T R O D U C T I O N Ions moving in He II are able to create quantized vortex rings [1] when their velocity exceeds a critical value which, for negative ions in isotopically pure 4He under a pressure P .~ 20 bar, is ~ 60 ms -1 [2]. The creation mechanism at low temperatures is believed [2], [3] to involve macroscopic quantum tunnelling through an energy barrier; thermal activation over the barrier dominates at higher temperatures. In common with vortex creation at orifices [4], [5] the mechanism is known [6] to be markedly influenced by tiny traces of SHe. A probable explanation [7], [8] involves the SHe atom binding to the ion surface [9] in a Shikin angular momentum state [10]. If its binding energy on the ion is weaker than that on the nascent vortex loop [2], [3] the energy conservation requirements for vortex creation are relaxed, leading to a reduced critical velocity and a much enhanced vortex nucleation rate v for any given velocity. Earlier investigations [7] of vortex nucleation in ultradilute 3He-4He solutions referred to temperatures T > 0.3K. We now report some preliminary data from experiments measuring a/ down to lower temperatures; part of the motivation has been to probe the regime where the discrete nature of the Shikin states [10] might start to be important. 2. E X P E R I M E N T A L
DETAILS
Values of u, and of the ionic drift velocity U, were obtained using the electric induction technique and 1.5£ cell already described in detail elsewhere [2], with z3 being controlled and ad-
justed by the methods described in [7]. The investigation is inherently more difficult than the earlier work [2] over the same temperature range in pure 4He because the signals were considerably weaker, presumably on account of the 3Heenhanced vortex nucleation in the high electric field region near the field emission ion sources. Nonetheless, it has proved possible to obtain data down to 90 m K for several isotopic ratios zs <
I0 -~.
3. R E S U L T S The measurements of v agree within experimental error with the earlier work at higher temperatures [7] in the region where the parameter ranges overlap. A quite unexpected feature of the results, however, was the occurrence of a sharp local maximum in u(T) measured for fixed P, z3 and electric field E. An example of this phenomenon is shown in Fig l(a). The temperature T,~ at which the peak occurred was found to be almost independent of E but to vary quite rapidly with P: e.g. for E -- 7.0 ×10 s Vm -1, z3 --- 2.12 xlO -s, T m = 295 -t- 5 m K at P -----19 bar and 190 -4- 10 m K at 24 bar. It has also been noted that there is always a small (,-, 2-4%) velocity anomaly associated with the local maximum in u, as shown for example in Fig 1 (b). Apart from the anomalous behaviour of v(T), U(T) shown in Fig 1, the general form of the results was qualitatively rather similar to that observed earlier at higher temperatures [7].
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E1002-4
844
d~ 0
0
o
10 v
(a)
O
(lo3s -1) % 0
0 0
x 3 : 2-12x10 P = 20 b a r E
=
o o
3.0× 10/, vm_l oO 0
J
0
O
%
!
0
#% (ms"1) 0 0
53
oo d;~
52
q~a~:b 250
%%o% j 300
T (mK)
350
Figure 1. Anomalies in the temperature dependence of (a) the vortex nucleation rate z/and (b) the ionic drift velocity U.
4. D I S C U S S I O N The general behaviour of ~(E, T, P, x3) appears to be consistent with the model [7] proposed previously, involving a competition between the processes of absorption of 3He into, and emission from, surface states on the ion. Thus, for very small T, l/(T) is independent of T because thermally activated emission is of negligible importance compared to emission of the 3He with rotons [7], which depends on E but not on T. At higher temperatures, thermally activated emission becomes important, and drives v(T) down towards zero as the average residence time of a 3He on the ion becomes too short for it to influence the nucleation process. This picture provides a satisfactory explanation of the general behaviour of z/(E, T, P, x3), but is of no obvious help in accounting for the phenomena of Fig 1. The narrowness of the local maximum could be regarded as indicative of a
phase transition, but there is no reason to anticipate any such phenomenon for the negative ion under these conditions. The rapid pressure dependence of T,~ suggests that the highest bound Shikin level may be of primary importance: its separation A E from the ~vacuum state = of a free 3 He also changes quite rapidly with pressure, varying from A E / k B ~- 0.4K at 13 bar to A E / k B ~0 at 25 bar. We may note also that this is the level which, when occupied, is likely to have the largest effect on v because movement of the 3He atom to a bound state on the nascent vortex loop will result in the largest energy change. Finally, a caveat must be entered. We cannot at present eliminate the possibility of more than one species of ion being present, although there is no reason a priori to expect that this might be the case. We conclude that the phenomena shown in Fig 1 still await an explanation and that some interesting new physics may be involved. We acknowledge valuable discussions with R M Bowley. The work was supported by the Science and Engineering Research Council (UK). REFERENCES 1. G.W. Rayfield and R. Reif, Phys. Rev. 136 (1964) Al194. 2. P.C. Hendry, N.S. Lawson, P.V.E. McClintock, C.D.H. Williams and R.M. Bowley, Phil. Trans. R. Soc. (Lond.) A 332 (1990) 387. 3. C.M. Muirhead, W.F. Vinen and R.J. Donnelly, Phil. Trans. R. Soc. (Lond.) A 311 (1984) 433. 4. J.C. Davis, J. Steinhauer, K. Schwab, Yu. M. Mukharsky, A. Amar, Y. Sasaki and R.E. Packard, Phys. Rev. Lett. 69 (1992) 323. 5. G.G. lhas, O. Avene], R. Aarts and R. Salmelin, Phys. Rev. Lett. 69 (1992) 327. 6. R.M. Bowley, P.V.E. McClintock, F.E. Moss and P.C.E. Stamp, Phys. Rev. Lett. 44 (1980) 161. 7. G.G. Nancolas, R.M. Bowley and P.V.E. McClintock, Phil. Trans. R. Soc. (Lond.) A 313
(1985) 537. 8.
C.M. Muirhead, W.F. Vinen and R.J. Donnelly, Proc. Roy. Soc. (Lond.) A 402 (1985) 225. 9. A.J. Dahm, Phys. Rev. 180 (1969) 259. 10. V.B. Shikin, Soy. Phys. J E T P 37 (1973) 718.