117:
the potential scattering for the particle of energy E is controlled by the shape of the nucleus. In fact the shape resonance occurs where the integral number of wavelengths of the particle sit within the potential of the nucleus of radius R. Therefore, the measure of the energies of the shape resonances in the neutron-nucleus scattering have been used in the years from 1947 to 1954 to measure the radii R of the nuclei with the precision of ±1×10 cm as it can be seen in the chapter "Elastic Cross
Sections" of
20:
is a metastable state in which an electron is trapped due to the shape of a potential barrier. Altunata describes a state as being a shape resonance if, "the internal state of the system remains unchanged upon disintegration of the quasi-bound level." A more general discussion of resonances and their
151:
The shape resonances are related with the existence of nearly stable bound states (that is, resonances) of two objects that dramatically influences how those two objects interact when their total energy is near that of the bound state. When the total energy of the objects is close to the energy of
116:
The shape resonances were observed around the years 1949–54 in nuclear scattering experiments. They indicate broad asymmetric peaks in the scattering cross section of neutrons or protons scattered by nuclei. The name "shape resonance" has been introduced to describe the fact that the resonance in
71:
Of course in one-dimensional systems, resonances are shape resonances. In a system with more than one degree of freedom, this definition makes sense only if the separable model, which supposes the two groups of degrees of freedom uncoupled, is a meaningful approximation. When the coupling becomes
159:
due to quantum interference of a first pairing channel in a first wide band and a second pairing channel in a second band where the chemical potential is tuned near a
Lifshitz transition at the band edge or at the topological electronic transitions of the Fermi surface type "neck-collapsing" or
113:"It is well known that the scattering from a potential shows characteristics peaks, as a function of energy, for such values of E that make the integral number of wave lengths sit within the potential. The resulting shape resonances are rather broad, their width being of the order of ...."
98:
Today, there is some debate about the definition and even existence of the shape resonance in some systems observed with molecular spectroscopy. It has been experimentally observed in the anionic yields from photofragmentation of small molecules to provide details of internal structure.
127:
The shape resonances arise from the quantum interference between closed and an open scattering channels. At the resonance energy a quasi bound state is degenerate with a continuum. This quantum interference in many body system has been described using quantum mechanics by
785:
Innocenti, Davide; Poccia, Nicola; Ricci, Alessandro; Valletta, Antonio; Caprara, Sergio; et al. (2010-11-19). "Resonant and crossover phenomena in a multiband superconductor: Tuning the chemical potential near a band edge".
61:) are set to zero. More simply, the shape resonance total energy is more than the separated fragment energy. Practical implications of this difference for lifetimes and spectral widths are mentioned in works such as Zobel.
714:
394:
Vittorini-Orgeas, Alessandra; Bianconi, Antonio (2009-01-07). "From
Majorana Theory of Atomic Autoionization to Feshbach Resonances in High Temperature Superconductors".
219:
576:
Stock, René; Deutsch, Ivan H.; Bolda, Eric L. (2003-10-31). "Quantum State
Control via Trap-Induced Shape Resonance in Ultracold Atomic Collisions".
124:
The "shape resonances" are discussed in general introductory academic courses of quantum mechanics in the frame of potential scattering phenomena.
54:
661:
155:
A particular type of "shape resonance" occurs in multiband or two-band superconducting heterostructures at atomic limit called
201:
293:
236:
520:"Absolute differential cross sections for electron-impact excitation of CO near threshold: II. The Rydberg states of CO"
758:
174:
216:
196:
Physics Survey
Committee, Board on Physics and Astronomy, National Research Council, National Academic Press
169:
65:
644:
657:
141:
21:
taxonomies in molecular system can be found in the review article by Schulz,; for the discovery of the
29:
pioneering work in this field by
Antonio Bianconi; and for a mathematical review by Combes et al.
749:
506:
Resonances in
Electron-Molecule Scattering Van Der Waals Complexes, and Reactive Chemical Dynamics
858:
152:
the resonance they interact strongly, and their scattering cross-section becomes very large.
75:
In the case of atomic and molecular electronic structure problems, it is well known that the
518:
Zobel, J; Mayer, U; Jung, K; Ehrhardt, H; Pritchard, H; Winstead, C; McKoy, V (1996-02-28).
193:
79:(SCF) approximation is relevant at least as a starting point of more elaborate methods. The
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for the atomic auto-ionization states in the continuum of helium atomic spectrum and by
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Atomic, Molecular, and
Optical Physics Panel on Atomic, Molecular, and Optical Physics
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Donald G. Truhlar, Ed, American
Chemical Society Symposium Series, ACS No. 263 (1984)
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91:) are shape resonances if only one electronic transition is required to emit one
26:
685:
353:. X-ray and Inner Shell Processes (19th Int. Conference Roma June 24–28, 2002).
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22:
662:"Anionic Photofragmentation of CO: A Selective Probe of Core-Level Resonances"
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In nuclear physics the concept of "Shape
Resonance" is described by
137:
92:
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408:
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Related terms include a special kind of shape resonance, the
784:
660:; Dominguez Lopez, I.; Rizvi, A.; et al. (2001-05-14).
57:
and the degrees of freedom associated to the fragmentation (
527:
Journal of Physics B: Atomic, Molecular and Optical Physics
136:
for the dissociation processes and quasi bound states, by
447:
Combes, J. M.; Duclos, P.; Klein, M.; Seiler, R. (1987).
393:
459:(2). Springer Science and Business Media LLC: 215–236.
446:
517:
213:
cite A Generalized Quantum Defect Methods in Chemistry
294:"Resonances in Electron Impact on Diatomic Molecules"
738:
McGraw-Hill Books, p. 448-450 and p. 455-456 (1955)
724:
John Wiley & Sons Inc, New York, page 87 (1974)
672:(20). American Physical Society (APS): 4504–4507.
575:
132:, for the interpretation of the Auger effect, by
845:
502:"Roles Played by Metastable States in Chemistry"
396:Journal of Superconductivity and Novel Magnetism
794:(18). American Physical Society (APS): 184528.
307:(3). American Physical Society (APS): 423–486.
250:(3). American Physical Society (APS): 378–422.
775:John Wiley & Sons, Inc., New York (1952)
753:Addison-Wesley Longman (2005) pag. 418-421
355:Unsolved Problems of Noise and Fluctuations
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589:
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72:large, the situation is much less clear.
348:
237:"Resonances in Electron Impact on Atoms"
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453:Communications in Mathematical Physics
291:
234:
41:, a shape resonance, in contrast to a
148:for nuclear scattering experiments.
68:, and trap-induced shape resonance.
32:
13:
715:Nuclear Physics: Nuclear structure
357:. Vol. 652. AIP. p. 13.
14:
870:
771:J. M. Blatt and V. F. Weisskopf
292:Schulz, George J. (1973-07-01).
235:Schulz, George J. (1973-07-01).
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215:Altunata, PhD Thesis, MIT 2006
656:Stolte, W. C.; Hansen, D. L.;
533:(4). IOP Publishing: 839–856.
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1:
608:10.1103/physrevlett.91.183201
351:Ugo Fano and shape resonances
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119:A Textbook in Nuclear Physics
53:if the coupling between some
170:Resonance (particle physics)
66:core-excited shape resonance
7:
773:Theoretical Nuclear Physics
686:10.1103/physrevlett.86.4504
163:
49:which is not turned into a
10:
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818:10.1103/physrevb.82.184528
547:10.1088/0953-4075/29/4/022
349:Bianconi, Antonio (2003).
175:Feshbach–Fano partitioning
142:Victor Frederick Weisskopf
418:10.1007/s10948-008-0433-x
321:10.1103/revmodphys.45.423
301:Reviews of Modern Physics
264:10.1103/revmodphys.45.378
244:Reviews of Modern Physics
83:built from SCF orbitals (
750:Modern Quantum Mechanics
666:Physical Review Letters
645:LBL Mol Spec Discussion
578:Physical Review Letters
25:line-shape and for the
449:"The shape resonance"
77:self-consistent field
59:reaction coordinates
810:2010PhRvB..82r4528I
720:Amos de Shalit and
678:2001PhRvL..86.4504S
658:Piancastelli, M. N.
600:2003PhRvL..91r3201S
539:1996JPhB...29..839Z
465:1987CMaPh.110..215C
313:1973RvMP...45..423S
256:1973RvMP...45..378S
81:Slater determinants
736:The Atomic Nucleus
473:10.1007/bf01207364
222:2011-06-05 at the
160:"neck-disrupting"
144:. J. M. Blatt and
89:molecular orbitals
55:degrees of freedom
43:Feshbach resonance
788:Physical Review B
373:10.1063/1.1536357
202:978-0-309-07371-4
39:quantum mechanics
33:Quantum mechanics
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134:Ettore Majorana
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108:Herman Feshbach
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104:Amos de-Shalit
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51:bound state
854:Scattering
848:Categories
181:References
834:119232655
826:1098-0121
801:1007.0510
694:0031-9007
616:0031-9007
563:250751335
555:0953-4075
489:119536657
481:0010-3616
434:118439516
426:1557-1939
409:0812.1551
381:0094-243X
329:0034-6861
272:0034-6861
217:full text
47:resonance
702:11384269
632:33876413
624:14611281
220:Archived
164:See also
138:Ugo Fano
93:electron
27:Majorana
806:Bibcode
674:Bibcode
596:Bibcode
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309:Bibcode
252:Bibcode
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359:arXiv
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