We show that an atom of atomic number Z described by the time-dependent Thomas-Fermi equation or the Vlasov equation cannot bind more than 4Z electrons.

1.
Benguria
,
R.
,
Hoops
,
S.
, and
Siedentop
,
H.
, “
Bounds on the excess charge and the ionization energy for the Hellmann-Weizsäcker model
,”
Ann. Inst. Henri Poincare
57
(
1
),
47
65
(
1992
).
2.
Benguria
,
R.
and
Lieb
,
E. H.
, “
The most negative ion in the Thomas-Fermi-von Weizsäcker theory of atoms and molecules
,”
J. Phys. B: At. Mol. Phys.
18
,
1045
1059
(
1985
).
3.
Bloch
,
F.
, “
Bremsvermögen von Atomen mit mehreren Elektronen
,”
Z. Phys.
81
(
5-6
),
363
376
(
1933
).
4.
Chen
,
L.
and
Siedentop
,
H.
, “
Blow-up of solutions to the Patlak-Keller-Segel equation in dimension ν ≥ 2
,”
Appl. Math. Lett.
74
,
102
107
(
2017
).
5.
Frank
,
R. L.
,
Nam
,
P. T.
, and
van den Bosch
,
H.
, “
The maximal excess charge in Müller density-matrix-functional theory
,” preprint arXiv:1608.05625 (
2016
).
6.
Frank
,
R. L.
,
Nam
,
P. T.
, and
Bosch
,
H. V. D.
, “
The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory
,”
Commun. Pure Appl. Math.
71
(
3
),
577
614
(
2018
).
7.
Gombás
,
P.
,
Die Statistische Theorie des Atoms und ihre Anwendungen
, 1st ed. (
Springer-Verlag
,
Wien
,
1949
).
8.
Hill
,
R. N.
, “
Proof that the H ion has only one bound state. Details and extension to finite nuclear mass
,”
J. Math. Phys.
18
(
12
),
2316
2330
(
1977
).
9.
Hill
,
R. N.
, “
Proof that the H ion has only one bound state
,”
Phys. Rev. Lett.
38
,
643
646
(
1977
).
10.
Hill
,
R. N.
, “
Proof that the H-ion has only one bound state: A review, a new result, and some related unsolved problems
,” in
Mathematical Problems in Theoretical Physics
(
Springer
,
1980
), pp.
52
56
.
11.
Kehle
,
C.
, “
The maximal excess charge for a family of density-matrix-functional theories including Hartree-Fock and Müller theories
,”
J. Math. Phys.
58
(
1
),
011901
(
2017
).
12.
Lenzmann
,
E.
and
Lewin
,
M.
, “
Dynamical ionization bounds for atoms
,”
Anal. PDE
6
(
5
),
1183
1211
(
2013
).
13.
Lieb
,
E. H.
, “
Bound on the maximum negative ionization of atoms and molecules
,”
Phys. Rev. A
29
(
6
),
3018
3028
(
1984
).
14.
Lieb
,
E. H.
,
Sigal
,
I. M.
,
Simon
,
B.
, and
Thirring
,
W.
, “
Asymptotic neutrality of large Z atoms
,”
Phys. Rev. Lett.
52
,
994
(
1984
).
15.
Lieb
,
E. H.
,
Sigal
,
I. M.
,
Simon
,
B.
, and
Thirring
,
W.
, “
Asymptotic neutrality of large Z ions
,”
Commun. Math. Phys.
116
,
635
644
(
1988
).
16.
Lieb
,
E. H.
and
Simon
,
B.
, “
The Thomas-Fermi theory of atoms, molecules and solids
,”
Adv. Math.
23
(
1
),
22
116
(
1977
).
17.
Massey
,
H. S. W.
,
Negative Ions
, 3rd ed. (
Cambridge University Press
,
London
,
1976
).
18.
Massey
,
H. S. W.
, “
Negative ions
,”
Adv. At. Mol. Phys.
15
,
1
36
(
1979
).
19.
Nam
,
P. T.
, “
New bounds on the maximum ionization of atoms
,”
Commun. Math. Phys.
312
(
2
),
427
445
(
2012
).
20.
Narnhofer
,
H.
and
Sewell
,
G. L.
, “
Vlasov hydrodynamics of a quantum mechanical model
,”
Commun. Math. Phys.
79
(
1
),
9
24
(
1981
).
21.
Perry
,
P. A.
, in
Scattering Theory by the Enss Method
, edited by
Simon
,
B.
(
Harwood Academic Publishers
,
Chur
,
1983
).
22.
Porta
,
M.
,
Rademacher
,
S.
,
Saffirio
,
C.
, and
Schlein
,
B.
, “
Mean field evolution of fermions with Coulomb interaction
,”
J. Stat. Phys.
166
(
6
),
1345
1364
(
2017
).
23.
Ruskai
,
M. B.
, “
Absence of discrete spectrum in highly negative ions
,”
Commun. Math. Phys.
82
,
457
469
(
1981
).
24.
Ruskai
,
M. B.
, “
Absence of discrete spectrum in highly negative ions II. Extension to fermions
,”
Commun. Math. Phys.
85
,
325
327
(
1982
).
25.
Sigal
,
I. M.
, “
Geometric methods in the quantum many-body problem. Nonexistence of very negative ions
,”
Commun. Math. Phys.
85
,
309
324
(
1982
).
26.
Solovej
,
J. P.
, “
Proof of the ionization conjecture in a reduced Hartree-Fock model
,”
Invent. Math.
104
(
2
),
291
311
(
1991
).
27.
Solovej
,
J. P.
, “
The ionization conjecture in Hartree-Fock theory
,”
Ann. Math.
158
(
2
),
509
576
(
2003
).
28.
Sucher
,
J.
, “
Foundations of the relativistic theory of many-electron atoms
,”
Phys. Rev. A
22
(
2
),
348
362
(
1980
).
29.
Teller
,
E.
, “
On the stability of molecules in the Thomas-Fermi theory
,”
Rev. Mod. Phys.
34
(
4
),
627
631
(
1962
).
30.
Vlasov
,
A.
, “
The vibrational properties of an electron gas [in Russian]
,”
Zh. Eksper. Teoret. Fis.
8
,
291
318
(
1938
).
31.
Vlasov
,
A. A.
, “
The vibrational properties of an electron gas
,”
Sov. Phys. Usp.
10
(
6
),
721
733
(
1968
).
You do not currently have access to this content.