On the Fission of Elementary Particles and the Evidence for Fractional Electrons in Liquid Helium

Journal of Low Temperature Physics

Volumn 120, Issue 3-4, 2000, Pages 173-204

  Maris, H J ^a,b  

^a BROWN UNIVERSITY   (United States)

^b ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMS; ELECTRON ENERGY LEVELS; ELECTRON MOBILITY; ELEMENTARY PARTICLES; PHOTOCONDUCTIVITY; SUPERFLUID HELIUM;

FRACTIONAL ELECTRON; IONIC MOBILITY MEASUREMENT; LIQUID HELIUM;

QUANTUM THEORY;

EID: 0034240710     PISSN: 00222291     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004605626054     Document Type: Article

References (49)

1. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
2. N. Bohr, Phys. Rev. 48, 696 (1935). See also, N. Bohr, in Albert Einstein: Philosopher-Scientist, P. A. Schilpp (ed.), Library of Living Philosophers, Evanston (1949), p. 200. For a discussion of the arguments put forward by Einstein, Podolsky and Rosen, and by Bohr, see D. Bohm, Quantum Theory, Prentice-Hall, New York (1951).
3. N. Bohr, Phys. Rev. 48, 696 (1935). See also, N. Bohr, in Albert Einstein: Philosopher-Scientist, P. A. Schilpp (ed.), Library of Living Philosophers, Evanston (1949), p. 200. For a discussion of the arguments put forward by Einstein, Podolsky and Rosen, and by Bohr, see D. Bohm, Quantum Theory, Prentice-Hall, New York (1951).
4. N. Bohr, Phys. Rev. 48, 696 (1935). See also, N. Bohr, in Albert Einstein: Philosopher-Scientist, P. A. Schilpp (ed.), Library of Living Philosophers, Evanston (1949), p. 200. For a discussion of the arguments put forward by Einstein, Podolsky and Rosen, and by Bohr, see D. Bohm, Quantum Theory, Prentice-Hall, New York (1951).
5. For a discussion, see A. J. Leggett, The Problems of Physics, Oxford, Oxford (1987).
6. The properties of ions in helium have been reviewed by A. L. Fetter, in The Physics of Liquid and Solid Helium, K. H. Benneman and J. B. Ketterson (eds.), Wiley, New York (1976), Chap. 3.
7. W. T. Sommer, Phys. Rev. Lett. 12, 271 (1964).
8. L. B. Lurio, T. A. Rabedeau, P. S. Pershan, I. F. Silvera, M. Deutsch, S. D. Kosowsky, and B. M. Ocko, Phys. Rev. B 48, 9644 (1993). This width is the distance over which the density changes from 10 to 90% of its bulk value.
9. J. Classen, C.-K. Su, M. Mohazzab, and H. J. Maris, Phys. Rev. 57, 3000 (1998).
10. In recent unpublished work with D. Konstantinov, we have shown that the standard expression for the helium polarization contribution to the energy (as given, for example, in Ref. 4) is wrong. A corrected result will be published shortly. To calculate the polarization energy it is essential to make allowance for the quantum fluctuations in position of the electron inside the bubble.
11. For example, the theory of D. Amit and E. P. Gross (Phys. Rev. 145, 130 (1966)) predicts that the surface tension increases by almost a factor of 2 when the pressure is varied from zero to 25 bars.
12. 0 at zero pressure to be 1.02 eV.
13. C. C. Grimes and G. Adams, Phys. Rev. B 45, 2305 (1992).
14. C. L. Zipfel, Ph.D. thesis, University of Michigan (1969), unpublished.
15. C. L. Zipfel and T. M. Sanders, in Proceedings of the 11th International Conference on Low Temperature Physics, J. F. Allen, D. M. Finlayson, and D. M. McCall (eds.), St. Andrews University, St. Andrews, Scotland (1969), p. 296.
16. B. DuVall and V. Celli, Phys. Lett. A 26, 524 (1968), and Phys. Rev. 180, 276 (1969).
17. B. DuVall and V. Celli, Phys. Lett. A 26, 524 (1968), and Phys. Rev. 180, 276 (1969).
18. W. B. Fowler and D. L. Dexter, Phys. Rev. 176, 337 (1968).
19. See, for example, R. Schinke, Photodissociation Dynamics, Cambridge (1993).
20. Note that the bubble radius is now 19.4 Å instead of 17.9 Å because the wave function is required to go to zero at the bubble surface.
21. 2 that is important for the fission process.
22. T. Ellis, P. V. E. McClintock, and R. M. Bowley, J. Phys. C 16, L485 (1983).
23. E. P. Gross and H. Tung-Li, Phys. Rev. 170, 190 (1968).
24. J. A. Northby, Ph.D. thesis, University of Minnesota (1966), unpublished.
25. J. A. Northby and T. M. Sanders, Phys. Rev. Lett. 18, 1184 (1967).
26. T. Miyakawa and D. L. Dexter, Phys. Rev. A 1, 513 (1970).
27. A. Y. Parshin and S. V. Pereverzev, JETP Lett. 52, 282 (1990) and JETP 74, 68 (1992).
28. A. Y. Parshin and S. V. Pereverzev, JETP Lett. 52, 282 (1990) and JETP 74, 68 (1992).
29. See, for example, P. V. E. McClintock, Z. Phys. B 98, 429 (1995).
30. C. S. M. Doake and P. W. F. Gribbon, Phys. Lett. A 30, 251 (1969).
31. G. G. Ihas and T. M. Sanders, Phys. Rev. Lett. 27, 383 (1971).
32. G. G. Ihas and T. M. Sanders, in Proceedings of the 13th International Conference on Low Temperature Physics, K. D. Timmerhaus, W. J. O'Sullivan, and E. F. Hammel (eds.), Plenum, New York (1972), Vol. 1, p. 477.
33. Our Fig. 11 uses the data and numbering scheme of Fig. 18 of Ref. 30. In Ref. 28 the ions that we have numbered as 2, 4, 8 are numbered 2, 6, and 11.
34. G. G. Ihas, Ph.D. thesis, University of Michigan (1971).
35. V. L. Eden and P. V. E. McClintock, Phys. Lett. A 102, 197 (1984).
36. V. L. Eden, M. Phil. thesis, University of Lancaster (1986).
37. R. J. Donnelly and P. H. Roberts, Phil. Trans. Roy. Soc. A 271, 41 (1971). See, in particular, Table 10 of this paper. The fact that the critical velocity could be used to estimate the size of the exotic ions has been pointed out by C. D. H. Williams, P. C. Hendry, and P. V. E. McClintock, Phys. Rev. Lett. 60, 865 (1988). For more recent theory, see C. M. Muirhead, W. F. Vinen, and R. J. Donnelly, Phil. Trans. Roy. Soc. A 311, 433 (1984).
38. R. J. Donnelly and P. H. Roberts, Phil. Trans. Roy. Soc. A 271, 41 (1971). See, in particular, Table 10 of this paper. The fact that the critical velocity could be used to estimate the size of the exotic ions has been pointed out by C. D. H. Williams, P. C. Hendry, and P. V. E. McClintock, Phys. Rev. Lett. 60, 865 (1988). For more recent theory, see C. M. Muirhead, W. F. Vinen, and R. J. Donnelly, Phil. Trans. Roy. Soc. A 311, 433 (1984).
39. R. J. Donnelly and P. H. Roberts, Phil. Trans. Roy. Soc. A 271, 41 (1971). See, in particular, Table 10 of this paper. The fact that the critical velocity could be used to estimate the size of the exotic ions has been pointed out by C. D. H. Williams, P. C. Hendry, and P. V. E. McClintock, Phys. Rev. Lett. 60, 865 (1988). For more recent theory, see C. M. Muirhead, W. F. Vinen, and R. J. Donnelly, Phil. Trans. Roy. Soc. A 311, 433 (1984).
40. D. L. Dexter and W. B. Fowler, Phys. Rev. 183, 307 (1969). For an attempt to understand the exotic ions in terms of multielectron bubbles, see T. M. Sanders and G. G. Ihas, Phys. Rev. Lett. 59, 1722 (1987).
41. D. L. Dexter and W. B. Fowler, Phys. Rev. 183, 307 (1969). For an attempt to understand the exotic ions in terms of multielectron bubbles, see T. M. Sanders and G. G. Ihas, Phys. Rev. Lett. 59, 1722 (1987).
42. In fact, if the binding is too large, the ion will form a snowball rather than a bubble.
43. Unpublished work. We thank Milton Cole for helpful discussions on this topic.
44. K. W. Schwarz and R. W. Stark, Phys. Rev. Lett. 22, 1278 (1969).
45. R. Barrera and G. Baym, Phys. Rev. A 6, 1558 (1972).
46. R. M. Bowley, J. Phys. C 4, 1645 (1971).
47. The results of IS show that there is one exotic ion (#9) that has a mobility that lies between the mobility of the exotic ion #8 and the normal ion. If exotic ion #8 corresponds to f = 1/2, ion #9 would have to have f greater than 1/2. In order for f to be greater than 1/2, it would be necessary for a normal electron bubble to split into two unequal parts. This seems unlikely, and so perhaps our assignment of f = 1/2 to ion #8 is incorrect.
48. Here we have used what we believe to be the correct formula for the polarization energy. See Ref. 8.
49. This data trace is part of Fig. 15 of the thesis, and also appears in Ref. 28 with different numbering.