122:
288:
22:
63:
1286:
significant as sharp peaks, or inconspicuous buried in the background. More importantly, it shows a simple quantity proposed by Zhu and
Nakamura to classify the coupling strength of nonadiabatic interactions, can be well applied to quantitatively estimate the importance of resonances in the AC region.
1285:
studied this problem in the New J. Phys. 22 (2020). Exemplified in particle scattering, resonances in the AC region are comprehensively investigated. The effects of resonances in the AC region on the scattering cross sections strongly depend on the nonadiabatic couplings of the system, it can be very
1042:
can give rise to significant mixing between the two channels; this manifests itself as a drastic dependence of the outcome of the scattering event on the parameter or parameters that control the energy of the entrance channel. These couplings can arise from spin-exchange interactions or relativistic
1280:
In molecules, the nonadiabatic couplings between two adiabatic potentials build the avoided crossing (AC) region. The rovibronic resonances in the AC region of two-coupled potentials are very special, since they are not in the bound state region of the adiabatic potentials, and they usually do not
1267:
As the magnetic field is swept through the resonance, the states in the open and closed channel can also mix and a large number of atoms, sometimes near 100% efficiency, convert to
Feshbach molecules. These molecules have high vibrational states, so they then need to be transitioned to lower, more
1294:
A virtual state, or unstable state is a bound or transient state which can decay into a free state or relax at some finite rate. This state may be the metastable state of a certain class of
Feshbach resonance, "A special case of a Feshbach-type resonance occurs when the energy level lies near the
291:
The interatomic potential of the open (red) and closed (blue) channel are shown. When the incoming energy of the free atoms, given by the dotted line, is approximately equivalent to that of the bound state in the closed channel, a temporary molecular state can
1535:
Donald C. Lorents, Walter Ernst
Meyerhof, James R. Peterson Electronic and atomic collisions: invited papers of the XIV International Conference on the Physics of Electronic and Atomic Collisions, Palo Alto, California, 24-30 July, 1985 North-Holland,
271:, of elastic collisions. For atomic species that possess these resonances (like K and K), it is possible to vary the interaction strength by applying a uniform magnetic field. Among many uses, this tool has served to explore the transition from a
1534:
1492:
On the
Dynamics of Single-Electron Tunneling in Semiconductor Quantum Dots under Microwave Radiation Dissertation Physics Department of Ludwig-Maximilians-Universitat Munchen by Hua Qin from Wujin, China 30 July 2001,
1182:
987:
621:
427:
The combination of the species and quantum states of the two reactant particles before or after the scattering event is referred to as a reaction channel. Specifically, the species and states of
743:
1032:
373:
267:
of a colliding pair of atoms. In experimental settings, the
Feshbach resonances provide a way to vary interaction strength between atoms in the cloud by changing scattering length, a
279:
in Fermi clouds. For the BECs, Feshbach resonances have been used to study a spectrum of systems from the non-interacting ideal Bose gases to the unitary regime of interactions.
421:
547:
511:
1098:
816:
1705:
APS Meeting
Abstracts: First Joint Meeting of the Nuclear Physicists of the American and Japanese Physical Societies October 17–20, 2001 Maui, Hawaii Meeting ID: HAW01
1648:
Nishimura, Tamio; Gianturco, Franco A. (2003-05-08). "Virtual-State
Formation in Positron Scattering from Vibrating Molecules: A Gateway to Annihilation Enhancement".
868:
661:
1262:
787:
1215:
1242:
895:
1562:
Field, D.; Jones, N. C.; Lunt, S. L.; Ziesel, J.-P. (2001-07-09). "Experimental evidence for a virtual state in a cold collision: Electrons and carbon dioxide".
1069:
767:
1071:
is approximately 0. Since the channels differ in internal degrees of freedom such as spin and angular momentum, their difference in energy is dependent on
1303:
depending on the angular momentum. Because of their transient existence, they can require special techniques for analysis and measurement, for example.
1505:"Schulz George Resonances in Electron Impact on Atoms and Diatomic Molecules Reviews of Modern Physics vol 45 no 3 pp378-486 July 1973"
1110:
217:
906:
208:, when they temporarily stick together forming an unstable compound with short lifetime (so-called resonance). It is a feature of
1926:
Per-Olov Löwdin (1962). "Studies in
Perturbation Theory. IV. Solution of Eigenvalue Problem by Projection Operator Formalism".
1549:
1272:. Other methods include inducing stimulated emission through an oscillating magnetic field and atom-molecule thermalization.
552:
1504:
769:
denotes the total kinetic energy of the relative motion (center-of-mass motion plays no role in the two-body interaction),
1051:
In ultracold atomic experiments, the resonance is controlled via the magnetic field and we assume that the kinetic energy
1268:
stable states to prevent dissociation. This can be done through stimulated emissions or other optical techniques such as
35:
549:, respectively. The interaction energy of the two particles will usually depend only on the magnitude of the separation
676:
1799:
1542:
1359:
183:
165:
143:
103:
49:
995:
136:
1390:
Chin, Cheng; Grimm, Rudolf; Julienne, Paul; Tiesinga, Eite (2010-04-29). "Feshbach resonances in ultracold gases".
1322:
1264:
is the resonance width. This allows for manipulation of the scattering length to 0 or arbitrarily high values.
1312:
272:
252:
330:
1731:
R.J. Fletcher; A.L. Gaunt; N. Navon; R. Smith; Z. Hadzibabic (2013). "Stability of a
Unitary Bose Gas".
259:
processes in many-body systems, the Feshbach resonance occurs when the energy of a bound state of an
516:
480:
624:
225:
130:
81:
1443:
Yang, Yu Kun; Cheng, Yongjun; Wu, Yong; Qu, Yi Zhi; Wang, Jian Guo; Zhang, Song Bin (2020-12-01).
1993:
1700:
85:
41:
1074:
792:
378:
147:
1841:(1935). "Sullo spettro di assorbimento dei gas nobili presso il limite dello spettro d'arco".
837:
630:
1247:
772:
260:
1190:
1964:
1935:
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8:
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1460:
1413:
1874:
1788:
1774:
1740:
1425:
1399:
1365:
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752:
1889:(1961-12-15). "Effects of Configuration Interaction on Intensities and Phase Shifts".
1605:
Girard, B. A.; Fuda, M. G. (1979-03-01). "Virtual state of the three nucleon system".
1976:
1914:
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1987:
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play important roles on the scatterings and are less discussed. Yu Kun Yang
1770:
1685:
664:
1351:
789:
is the contribution to the energy from couplings to external fields, and
228:, vanish. The opposite situation, when a bound state is not formed, is a
213:
1955:
Claude Bloch (1958). "Sur la théorie des perturbations des états liés".
300:
scattering event between two particles. In this reaction, there are two
1862:
1730:
276:
256:
1947:
663:. Often, this potential will have a pronounced minimum and thus admit
1699:
Kurokawa, Chie; Masui, Hiroshi; Myo, Takayuki; Kato, Kiyoshi (2001).
287:
248:
209:
1701:"Study of the virtual state in νc10Li with the Jost function method"
451:. An energetically accessible reaction channel is referred to as an
1886:
1838:
301:
1745:
1404:
1177:{\displaystyle a=a_{bg}\left(1-{\frac {\Delta }{B-B_{0}}}\right)}
670:
The total energy of the two particles in the entrance channel is
297:
197:
1034:. When this condition is met, then any coupling between channel
275:
of fermionic molecules to weakly interacting fermion-pairs the
1809:
Herman Feshbach (1958). "Unified theory of nuclear reactions".
1445:"Particle scattering and resonances involving avoided crossing"
1295:
very top of the potential well. Such a state is called 'virtual
1269:
982:{\displaystyle E_{D}\approx T+V_{c}(R)+\Delta ({\vec {P}}_{0})}
216:
is achieved if the coupling(s) between at least one internal
1275:
1244:
is the magnetic field strength where resonance occurs, and
205:
243:
Feshbach resonances have become important in the study of
1389:
237:
826:. We consider now a second reaction channel, denoted by
1849:(3). Springer Science and Business Media LLC: 154–161.
616:{\displaystyle R\equiv |{\vec {r}}_{A}-{\vec {r}}_{B}|}
1344:
Dictionary of Material Science and High Energy Physics
818:
represents a vector of one or more parameters such as
1250:
1223:
1193:
1113:
1077:
1057:
998:
909:
876:
840:
795:
775:
755:
679:
633:
555:
519:
483:
381:
333:
1698:
1561:
477:. The positions of these two particles are given by
1787:
1647:
1256:
1236:
1209:
1176:
1092:
1063:
1026:
981:
889:
862:
810:
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761:
737:
655:
615:
541:
505:
415:
367:
1897:(6). American Physical Society (APS): 1866–1878.
1985:
1790:Bose–Einstein Condensation in Dilute Gases
738:{\displaystyle E=T+V_{c}(R)+\Delta ({\vec {P}})}
623:, and this function, sometimes referred to as a
1925:
1808:
1656:(18). American Physical Society (APS): 183201.
1613:(3). American Physical Society (APS): 579–582.
1385:
1383:
1381:
1379:
1570:(2). American Physical Society (APS): 022708.
1046:
1027:{\displaystyle \lbrace {\vec {P}}_{0}\rbrace }
1442:
1954:
1785:
1376:
1021:
999:
84:. There might be a discussion about this on
50:Learn how and when to remove these messages
1604:
465:Consider the interaction of two particles
455:, whereas a reaction channel forbidden by
324:), we may denote this scattering event by
1744:
1468:
1403:
184:Learn how and when to remove this message
166:Learn how and when to remove this message
104:Learn how and when to remove this message
1276:Feshbach resonances in avoided crossings
1104:. The scattering length is modified as
320:. For the case of a reaction (such as a
286:
129:This article includes a list of general
312:, and two product particles denoted by
1986:
1707:. American Physical Society: #DE.004.
830:, which is closed for large values of
1299:" and may be further contrasted to a
1217:is the background scattering length,
204:can occur upon collision of two slow
1885:
1837:
1341:
992:for some range of parameter vectors
368:{\displaystyle A+B\rightarrow A'+B'}
115:
56:
15:
13:
1342:Basu, Dipak K., ed. (2018-10-08).
1251:
1146:
951:
776:
714:
135:it lacks sufficient corresponding
14:
2005:
1289:
900:A Feshbach resonance occurs when
31:This article has multiple issues.
870:admit a bound state with energy
439:, while the types and states of
120:
61:
20:
1692:
282:
253:Bose–Einstein condensates
39:or discuss these issues on the
1763:10.1103/PhysRevLett.111.125303
1641:
1598:
1555:
1528:
1497:
1485:
1455:(12). IOP Publishing: 123022.
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542:{\displaystyle {\vec {r}}_{B}}
527:
506:{\displaystyle {\vec {r}}_{A}}
491:
402:
385:
343:
1:
1670:10.1103/physrevlett.90.183201
1328:
1043:spin-dependent interactions.
1977:10.1016/0029-5582(58)90116-0
1831:10.1016/0003-4916(58)90007-1
1313:Resonance (particle physics)
7:
1306:
1047:Magnetic Feshbach resonance
834:. Let this potential curve
10:
2010:
1584:10.1103/physreva.64.022708
1422:10.1103/RevModPhys.82.1225
1323:Feshbach–Fano partitioning
1093:{\displaystyle {\vec {B}}}
811:{\displaystyle {\vec {P}}}
255:(BECs). In the context of
1392:Reviews of Modern Physics
416:{\displaystyle A(B,B')A'}
1911:10.1103/physrev.124.1866
1470:10.1088/1367-2630/abcfed
863:{\displaystyle V_{D}(R)}
656:{\displaystyle V_{c}(R)}
1786:Pethick; Smith (2002).
1650:Physical Review Letters
1627:10.1103/physrevc.19.579
1257:{\displaystyle \Delta }
782:{\displaystyle \Delta }
473:in an entrance channel
150:more precise citations.
1449:New Journal of Physics
1258:
1238:
1211:
1210:{\displaystyle a_{bg}}
1178:
1094:
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1028:
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891:
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625:potential energy curve
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543:
507:
417:
369:
293:
1352:10.1201/9781420049855
1259:
1239:
1237:{\displaystyle B_{0}}
1212:
1179:
1095:
1066:
1029:
984:
892:
890:{\displaystyle E_{D}}
865:
813:
784:
764:
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658:
618:
544:
508:
418:
370:
304:particles denoted by
290:
261:interatomic potential
1248:
1221:
1191:
1111:
1075:
1055:
996:
907:
874:
838:
793:
773:
753:
677:
631:
553:
517:
481:
459:is referred to as a
379:
331:
247:systems, including
232:. It is named after
222:reaction coordinates
74:confusing or unclear
1969:1958NucPh...6..329B
1940:1962JMP.....3..969L
1903:1961PhRv..124.1866F
1855:1935NCim...12..154F
1823:1958AnPhy...5..357F
1755:2013PhRvL.111l5303F
1713:2001APS..HAW.DE004K
1662:2003PhRvL..90r3201N
1619:1979PhRvC..19..579G
1576:2001PhRvA..64b2708F
1461:2020NJPh...22l3022Y
1414:2010RvMP...82.1225C
457:energy conservation
296:Consider a general
212:systems in which a
82:clarify the article
1863:10.1007/bf02958288
1254:
1234:
1207:
1174:
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1024:
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735:
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613:
539:
503:
413:
365:
294:
202:Feshbach resonance
1948:10.1063/1.1724312
1811:Annals of Physics
1607:Physical Review C
1564:Physical Review A
1550:978-0-444-86998-2
1167:
1087:
1064:{\displaystyle T}
1012:
967:
805:
762:{\displaystyle T}
729:
599:
577:
530:
494:
236:, a physicist at
218:degree of freedom
194:
193:
186:
176:
175:
168:
114:
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106:
54:
2001:
1980:
1951:
1922:
1882:
1843:Il Nuovo Cimento
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1602:
1596:
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1559:
1553:
1532:
1526:
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1523:
1522:
1516:
1510:. Archived from
1509:
1501:
1495:
1489:
1483:
1482:
1472:
1440:
1434:
1433:
1407:
1398:(2): 1225–1286.
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627:, is denoted by
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437:entrance channel
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353:
322:nuclear reaction
263:is equal to the
224:, which lead to
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146:this article by
137:inline citations
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1733:Phys. Rev. Lett
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1301:shape resonance
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234:Herman Feshbach
230:shape resonance
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1994:Atomic physics
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1934:(5): 969–982.
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1883:
1845:(in Italian).
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1739:(12): 125303.
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