-
3
-
-
0346332115
-
-
S. Tarucha, D.G. Austing, T. Honda, R.J. van der Hage, and L.P. Kouwenhoven, Phys. Rev. Lett. 77, 3613 (1996).
-
(1996)
Phys. Rev. Lett.
, vol.77
, pp. 3613
-
-
Tarucha, S.1
Austing, D.2
Honda, T.3
van der Hage, R.4
Kouwenhoven, L.5
-
6
-
-
33744580965
-
-
The failure of Bohr-type models, based on the orbiting of spatially correlated electrons in conjunction with the Bohr-Sommerfeld quantization rule, to yield a reasonable estimate of the ground state of the He atom signaled a looming crisis in physics in the 1920s, which Bohr himself, as well as others, had been keenly aware of, as summarized succintly by Sommerfeld: “All attempts made hitherto to solve the problem of the neutral helium atom have proved to be unsuccessful” [A. Sommerfeld, Rev. Sci. Instrum. 7, 509 (1923)]. Also see A. Pais, Niels-Bohr’s Times (Clarendon, Oxford, 1991), Chap 10;
-
(1923)
Rev. Sci. Instrum.
, vol.7
, pp. 509
-
-
Sommerfeld, A.1
-
8
-
-
0004039765
-
-
Ungar, New York
-
M. Born, The Mechanics of the Atom (Ungar, New York, 1927). Subsequently, numerical solutions of the two-electron Schrödinger equation provided a quantitative resolution to the problem, but the first successful semiclassical treatment of the three-body Coulomb system did not occur untill 1980;
-
(1927)
The Mechanics of the Atom
-
-
Born, M.1
-
10
-
-
0002125327
-
-
D. Wintgen, K. Richter, and G. Tanner, Chaos 2, 19 (1992). Furthermore, based on rather general group-theoretical arguments arising from the observation of hierarchies with lower symmetry in the excited spectra, and motivated by ideas originating in nuclear-physics spectroscopy, it was discovered in the late 1970s and early 1980s that electron correlations in doubly excited He lead to a quantization of the spectrum much like in a linear triatomic molecule, (Formula presented). This molecular picture, with near rigidity and separability, results in “infinite sequences of vibrational levels, on each of which is built an infinite sequence of rotational levels”;
-
(1992)
Chaos
, vol.2
, pp. 19
-
-
Wintgen, D.1
Richter, K.2
Tanner, G.3
-
13
-
-
0000782751
-
-
Phys. Rev. AS. Watanabe and C.D. Lin, 34, 823 (1986). Interestingly, as in the aforementioned semiclassical treatments, the collinear configuration plays a special role in the moleculelike model, serving perhaps as a “partial vindication” of the geometry considered originally by Bohr.
-
(1986)
Phys. Rev. A
, vol.34
, pp. 823
-
-
Watanabe, S.1
Lin, C.2
-
16
-
-
0003754955
-
-
Wiley, New York
-
W. Ekardt, Metal Clusters (Wiley, New York, 1999), Chaps. 1 and 4.
-
(1999)
Metal Clusters
-
-
Ekardt, W.1
-
17
-
-
0032679023
-
-
see I. Amlani, A.O. Orlov, G. Toth, G.H. Bernstein, C.S. Lent, and G.L. Snider, Science 284, 289 (1999).
-
(1999)
Science
, vol.284
, pp. 289
-
-
Amlani, I.1
Orlov, A.2
Toth, G.3
Bernstein, G.4
Lent, C.5
Snider, G.6
-
20
-
-
0038137959
-
-
H.-M. Müller and S.E. Koonin, Phys. Rev. B 54, 14 532 (1996).
-
(1996)
Phys. Rev. B
, vol.54
, pp. 14532
-
-
Koonin, S.1
-
21
-
-
0344717984
-
-
R. Egger, W. Häusler, C.H. Mak, and H. Grabert, Phys. Rev. Lett. 82, 3320 (1999).
-
(1999)
Phys. Rev. Lett.
, vol.82
, pp. 3320
-
-
Egger, R.1
Häusler, W.2
Mak, C.3
Grabert, H.4
-
26
-
-
0041514804
-
-
For studies pertaining to the arrangement of classical point charges in a harmonic confinement, see Yu.E. Lozovik, Usp. Fiz. Nauk 153, 356 (1987) [Sov. Phys. Usp. 30, 912 (1987)];
-
(1987)
Sov. Phys. Usp.
, vol.30
, pp. 912
-
-
-
31
-
-
21344475852
-
-
M. Taut, J. Phys. A 27, 1045 (1994).
-
(1994)
J. Phys. A
, vol.27
, pp. 1045
-
-
Taut, M.1
-
33
-
-
0000848450
-
-
M. Rontani, F. Rossi, F. Manghi, and E. Molinari, Phys. Rev. B 59, 10 165 (1999).
-
(1999)
Phys. Rev. B
, vol.59
, pp. 10165
-
-
Rontani, M.1
Rossi, F.2
Manghi, F.3
Molinari, E.4
-
34
-
-
4143093060
-
-
Here we differentiate between the exact solution of the Hamiltonian specified by Eqs. (1) and (2) from “exact diagonalization methods” of Hubbard-type Hamiltonians used as models of QD’s [see, e.g., R. Berkovits, Phys. Rev. Lett. 81, 2128 (1998)].
-
(1998)
Phys. Rev. Lett.
, vol.81
, pp. 2128
-
-
Berkovits, R.1
-
35
-
-
3342906428
-
-
see Modern Quantum Chemistry (Ref. 14) of WM’s but only for fully polarized QD’s (i.e., under high magnetic fields where the spin unrestriction is not at play).
-
(1954)
J. Chem. Phys.
, vol.22
, pp. 571
-
-
Pople, J.1
Nesbet, R.2
-
37
-
-
0004283451
-
-
Hilger, Bristol
-
E.K.U. Gross, E. Runge, and O. Heinonen, Many-Particle theory (Hilger, Bristol, 1991), Chap. 8.
-
(1991)
Many-Particle theory
-
-
Gross, E.1
Runge, E.2
Heinonen, O.3
-
38
-
-
85037904463
-
-
The orientational degeneracy of the sS-UHF solutions describing an electron molecule in a cirularly symmetric QD is a residue of the rotational invariance of the exact Hamiltonian, and naturally it suggests the possible emergence of a rovibrational spectrum associated with the excitations of the electron molecule. Depending on the value of the parameter (Formula presented) the electron molecule may exhibit different degrees of “rigidity,” with electron molecules of high rigidity (forming for large (Formula presented) exhibiting well-developed rovibrational bands; for the value of (Formula presented) used by us here, the electron molecule is rather “floppy” [C. Yannouleas and U. Landman, cond-mat/0003245]. Such rovibrational spectra can be described by several theoretical approaches, for example (i) at a more phenomenological level, by a quantization of the collective classical motions associated with the molecule, such as rotations, and bending and stretching vibrations [see Kellman and Herrick in Ref. 17).
-
Such rovibrational spectra can be described by several theoretical approaches, for example (i) at a more phenomenological level, by a quantization of the collective classical motions associated with the molecule, such as rotations, and bending and stretching vibrations
-
-
Yannouleas, C.1
Landman, U.2
-
43
-
-
0000524884
-
-
For an early review of the application of Hartree-Fock methods to the description of open-shell, deformed nuclei, see G. Ripka, Adv. Nucl. Phys. 1, 183 (1968).
-
(1968)
Adv. Nucl. Phys.
, vol.1
, pp. 183
-
-
Ripka, G.1
-
44
-
-
0348058299
-
-
R.E. Peierls and J. Yoccoz, Proc. Phys. Soc., London, Sect. A 70, 381 (1957).
-
(1957)
Proc. Phys. Soc., London, Sect. A
, vol.70
, pp. 381
-
-
Peierls, R.1
Yoccoz, J.2
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