Abstract
We use the semiclassical periodic orbit theory to describe large metal clusters with axial quadrupole, octupole, or hexadecapole deformations. The clusters are regarded as cavities with ideally reflecting walls. We start from the case of spherical symmetry and then apply a perturbative approach for calculating the oscillating part of the level density in the deformed case. The advantage of this approach is that one only has to know the periodic orbits of the spherical cavity, which makes the calculation very simple. This perturbative method is a priori restricted to small deformations. However, the results agree quite well with those of quantum-mechanical calculations for deformations that are not too large, such as typically occur for the ground states of metal clusters. We also calculate shell-correction energies. With this, it becomes possible to predict at least qualitatively the deformation energy of metal clusters.
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References
W. D. Knight et al.: Phys. Rev. Lett. 52, 2141 (1984)
W. A. de Heer: Rev. Mod. Phys. 65, 661 (1993)
W. Ekardt: Phys. Rev. B 29, 1558 (1984)
M. Brack: Rev. Mod. Phys. 65, 677 (1993)
K. Clemenger: Phys. Rev. B 32, 1359 (1985)
J. Pedersen et al.: Nature 353, 733 (1991)
R. Balian, C. Bloch: Ann. Phys. (N.Y.) 69, 76 (1972)
H. Nishioka, K. Hansen, B. R. Mottelson: Phys. Rev. B 42, 9377 (1990)
O. Genzken, M. Brack: Phys. Rev. Lett. 67, 3286 (1991); O. Genzken: Mod. Phys. Lett. B 4, 197 (1993)
J. Lermé et al.: Phys. Rev. B 52, 2868 (1995)
E. Koch, O. Gunnarsson: Phys. Rev. B 54, 5168 (1996)
S. G. Nilsson: Mat.-Fys. Medd. Dan. Vidensk. Selsk. 29, 16 (1955)
S. M. Reimann, M. Brack, K. Hansen: Z. Phys. D 28, 235 (1993)
V. M. Strutinsky: Nucl. Phys. A 122, 1 (1968)
V. M. Strutinsky: Nukleonika (Poland) 20, 679 (2975) V. M. Strutinsky, A. G. Magner: Sov. J. Part. Nucl. 7, 138 (1976); V. M. Strutinsky, A. G. Magner, S. R. Ofengenden, T. Døssing: Z. Phys. A 283, 269 (1977)
M. Gutzwiller: J. Math. Phys. 12, 343 (1971)
S. M. Reimann, M. Brack: J. Comp. Math. Sci. 2, 433 (1994)
M. Brack, R. K. Bhaduri: Semiclassical Physics. Reading, Mass.: Addison-Wesley 1997
M. Brack et al.; in: Large Clusters of Atoms and Molecules, p. 1, T. P. Martin (ed.). Dordrecht: Kluwer Academic Publishers 1996
S. C. Creagh, R. G. Littlejohn; Phys. Rev. A 44, 836 (1991); J. Phys. A 25, 1643 (1992)
M. V. Berry, M. Tabor: Proc. Roy. Soc. Lond. A 349, 101 (1976); ibid. 356, 375 (1977)
A. Einstein: Verh. Dtsch. Phys. Ges. 19, 82 (1917); C. R. Brillouin: Acad. Sci. (Paris) 183, 24 (1926); J. B. Keller: Ann. Phys. (NY) 4, 180 (1958); J. B. Keller, S. I. Rubinow: Ann. Phys. (NY) 9, 24 (1960)
Ozorio de Almeida, in: Quantum Chaos and Statistical Nuclear Physics, T. H. Seligmann, H. Nishioka (eds.) Lecture Notes in Physics, Vol. 263. Berlin, Heidelberg, New York: Springer 1986
S. C. Creagh: Ann. Phys. (N.Y.) 248, 60 (1996)
S. Tomsovic, M. Grinberg, D. Ullmo: Phys. Rev. Lett. 75, 4346 (1995); D. Ullmo, M. Grinberg, S. Tomsovic: Phys. Rev. E 54, 136 (1996)
J. M. Gel’Fand, R. A. Minlos, Z. Ya. Shapiro: Representations of the rotation and Lorentz groups and their applications. Oxford: Oxford University Press 1963
A. G. Magner et al.: submitted to Ann. Phys. (Leipzig)
S. Frauendorf, V. V. Pashkevich: Ann. Phys. (Leipzig) 5, 34 (1996)
B. Montag, T. Hirschmann, J. Meyer, M. Brack: Phys. Rev. B 52, 4775 (1995)
M. Brack: Rev. Mod. Phys. 44, 320 (1972)
H. A. Bethe: Annu. Rev. Nucl. Sci. 21, 93 (1971)
M. Brack, P. Quentin: Nucl. Phys. A 361, 35 (1981)
R. Balian, C. Bloch: Ann. Phys. 60, 401 (1970)
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Meier, P., Brack, M. & Creagh, S. Semiclassical description of large multipole-deformed metal clusters. Z Phys D - Atoms, Molecules and Clusters 41, 281–290 (1997). https://doi.org/10.1007/s004600050324
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DOI: https://doi.org/10.1007/s004600050324