1823:
493:. The photon must have higher energy than the sum of the rest mass energies of an electron and positron (2 ⋅ 511 keV = 1.022 MeV, resulting in a photon-wavelength of 1.2132 picometer) for the production to occur. (Thus, pair production does not occur in medical X-ray imaging because these X-rays only contain ~150 keV.) The photon must be near a nucleus in order to satisfy conservation of momentum, as an electron–positron pair produced in free space cannot satisfy conservation of both energy and momentum. Because of this, when pair production occurs, the atomic nucleus receives some
443:
142:
427:
36:
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303:) of the produced particles must sum to zero – thus the created particles shall have opposite values of each other. For instance, if one particle has electric charge of +1 the other must have electric charge of −1, or if one particle has
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of the two particles created. (As the electron is the lightest, hence, lowest mass/energy, elementary particle, it requires the least energetic photons of all possible pair-production processes.) Conservation of energy and
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is the combined rest mass of the electron–positron. In general the electron and positron can be emitted with different kinetic energies, but the average transferred to each (ignoring the recoil of the nucleus) is:
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creating an electron–positron pair near a nucleus. As energy must be conserved, for pair production to occur, the incoming energy of the photon must be above a threshold of at least the total
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223:
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Diagram showing the process of electron–positron pair production. In reality the produced pair are nearly collinear. The black dot labelled 'Z' represents an adjacent atom, with
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value for the process on the right becomes larger than the cross section for the process on the left. For calcium (Z=20), Compton scattering starts to dominate at
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1992:
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519:
216:
1356:{\displaystyle -2\,m_{\text{e}}^{2}c^{2}+2\left(-{\frac {E^{2}}{c^{2}}}+\mathbf {p} _{{\text{e}}^{-}}\cdot \mathbf {p} _{{\text{e}}^{+}}\right)\approx 0}
689:
2124:
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However, in most cases the recoil of the nucleus is small compared to the energy of the photon and can be neglected. Taking this approximation of
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is some complex-valued function that depends on the energy and atomic number. Cross sections are tabulated for different materials and energies.
209:
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Therefore, this approximation can only be satisfied if the electron and positron are emitted in very nearly the same direction, that is,
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833:
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scale and higher), pair production is the dominant mode of photon interaction with matter. These interactions were first observed in
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This derivation is a semi-classical approximation. An exact derivation of the kinematics can be done taking into account the full
53:
1209:{\displaystyle (p_{\gamma })^{2}\approx (p_{{\text{e}}^{-}})^{2}+2p_{{\text{e}}^{-}}p_{{\text{e}}^{+}}+(p_{{\text{e}}^{+}})^{2}}
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361:. If the photon is near an atomic nucleus, the energy of a photon can be converted into an electron–positron pair:
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of electron–positron pair production. One must calculate multiple diagrams to get the net cross section
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1462:{\displaystyle 2\,(\gamma ^{2}-1)\,m_{\text{e}}^{2}\,c^{2}\,(\cos \theta _{\text{e}}-1)\approx 0}
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The exact analytic form for the cross section of pair production must be calculated through
1801:{\displaystyle ({\bar {E}}_{k}^{pp})_{\text{tr}}={\frac {1}{2}}(h\nu -2\,m_{\text{e}}c^{2})}
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The energy transfer to electron and positron in pair production interactions is given by:
1016:{\displaystyle (p_{\gamma })^{2}=(p_{{\text{e}}^{-}}+p_{{\text{e}}^{+}}+p_{\text{Ę€}})^{2}}
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and results in a complicated function. To simplify, the cross section can be written as:
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type of stellar explosion, where pair production suddenly lowers the pressure inside a
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2087:, leading to a partial implosion, and then explosive thermonuclear burning. Supernova
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notation, the conservation of energy-momentum before and after the interaction gives:
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Plot of photon energies calculated for a given element (atomic number Z) at which the
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Interaction of a photon with matter resulting into creation of electron-positron pair
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are the principal constraints on the process. All other conserved quantum numbers (
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774:{\displaystyle A^{2}=A^{\mu }A_{\mu }=-(A^{0})^{2}+\mathbf {A} \cdot \mathbf {A} }
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These properties can be derived through the kinematics of the interaction. Using
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The probability of pair production in photon–matter interactions increases with
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593:{\displaystyle p_{\gamma }=p_{{\text{e}}^{-}}+p_{{\text{e}}^{+}}+p_{\text{Ę€}}}
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2306:. PHYS 5012. Sydney, Australia: The University of Sydney. Archived from
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Pair production is invoked in the heuristic explanation of hypothetical
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target, was used to generate positron–electron pairs in large numbers.
2258:"Electron positron pair production by photons: A historical overview"
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The photon's energy is converted to particle mass in accordance with
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1600:{\displaystyle (E_{k}^{pp})_{\text{tr}}=h\nu -2\,m_{\text{e}}c^{2}}
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is the recoil of the nucleus. Note the modulus of the four vector
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1909:{\displaystyle \sigma =\alpha \,r_{\text{e}}^{2}\,Z^{2}\,P(E,Z)}
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903:{\displaystyle (p_{{\text{e}}^{-}})^{2}=-m_{\text{e}}^{2}c^{2}}
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Pair production is also the mechanism behind the hypothesized
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29:
2205:"Exploring dark matter in the inaugural Blackett Colloquium"
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of +1 then another one must have strangeness of −1.
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is hypothesized to have been a pair production type
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quantum mechanical scattering of photon and nucleus
60:. Unsourced material may be challenged and removed.
2376:Theory of photon-impact bound-free pair production
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318:of (hence, number of protons in) the nearby atom.
314:and also increases approximately as the square of
278:. Pair production often refers specifically to a
2346:"Laser technique produces bevy of antimatter"
217:
8:
2330:: CS1 maint: multiple names: authors list (
2153:Introduction to Nuclear and Particle Physics
673:{\displaystyle A\equiv (A^{0},\mathbf {A} )}
2072:. When this happens in the region around a
1498:{\displaystyle \theta _{\text{e}}\approx 0}
910:. We can square the conservation equation:
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120:Learn how and when to remove this message
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1654:is the frequency of the photon and the
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2323:
2231:"XCOM: Photon Cross Sections Database"
2064:. In a region of strong gravitational
1059:and expanding the remaining relation:
2295:Kuncic, Zdenka, Dr. (12 March 2013).
2040:, aimed at a 1 millimeter-thick
7:
1688:{\displaystyle 2\,m_{\text{e}}c^{2}}
58:adding citations to reliable sources
2304:Index of Dr. Kuncic's Lectures
823:{\displaystyle (p_{\gamma })^{2}=0}
2297:"PRadiation Physics and Dosimetry"
2180:"How photons interact with matter"
2149:Das, A.; Ferbel, T. (2003-12-23).
446:Subatomic particle pair production
25:
2282:10.1016/j.radphyschem.2005.10.008
2203:Bywater, Jenn (29 October 2015).
497:. The reverse of this process is
2125:Landau–Pomeranchuk–Migdal effect
1323:
1299:
767:
759:
663:
140:
34:
2262:Radiation Physics and Chemistry
2229:Seltzer, Stephen (2009-09-17).
438:=0.08 MeV and ceases at 12 MeV.
322:Photon to electron and positron
254:. Examples include creating an
45:needs additional citations for
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1052:{\displaystyle p_{R}\approx 0}
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499:electron–positron annihilation
1:
1963:{\displaystyle r_{\text{e}}}
623:{\displaystyle p_{\text{Ę€}}}
2256:Hubbell, J.H. (June 2006).
2417:
2081:pair-instability supernova
1815:
1972:classical electron radius
135:Light–matter interaction
2209:Imperial College London
1941:fine-structure constant
1932:{\displaystyle \alpha }
1835:quantum electrodynamics
1818:Gamma ray cross section
2184:Meroli Stefano Webpage
2120:Meitner–Hupfeld effect
2027:
2026:{\displaystyle P(E,Z)}
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359:Nobel Prize in Physics
357:, leading to the 1948
353:'s counter-controlled
341:For photons with high
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180:High-energy phenomena:
2105:Breit–Wheeler process
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1998:of the material, and
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452:Einstein's equation,
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239:is the creation of a
161:Mid-energy phenomena:
149:Low-energy phenomena:
2157:. World Scientific.
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1647:{\displaystyle \nu }
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155:Photoelectric effect
54:improve this article
2274:2006RaPC...75..614H
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784:which implies that
193:Photodisintegration
2130:Two-photon physics
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830:for all cases and
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241:subatomic particle
174:Compton scattering
167:Thomson scattering
2178:Stefano, Meroli.
2058:quantum mechanics
2054:Hawking radiation
1987:{\displaystyle Z}
1957:
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1632:Planck's constant
1623:{\displaystyle h}
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69:"Pair production"
16:(Redirected from
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2313:on 11 March 2016
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2115:Matter creation
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2085:supergiant star
2056:. According to
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186:Pair production
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2370:External links
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2268:(6): 614–623.
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2110:Dirac equation
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1517:
1514:
1494:
1491:
1482:
1470:
1469:
1458:
1455:
1452:
1449:
1446:
1437:
1433:
1430:
1427:
1421:
1417:
1410:
1401:
1396:
1393:
1390:
1385:
1381:
1377:
1373:
1363:
1352:
1349:
1345:
1337:
1325:
1320:
1313:
1301:
1296:
1289:
1285:
1279:
1275:
1269:
1265:
1261:
1258:
1253:
1249:
1243:
1234:
1229:
1226:
1216:
1203:
1199:
1191:
1180:
1176:
1173:
1166:
1155:
1147:
1136:
1132:
1129:
1124:
1120:
1112:
1101:
1097:
1094:
1089:
1085:
1079:
1075:
1071:
1048:
1045:
1040:
1036:
1024:
1023:
1010:
1006:
996:
992:
985:
974:
970:
963:
952:
948:
945:
940:
936:
930:
926:
922:
897:
893:
887:
878:
874:
871:
866:
862:
854:
843:
839:
819:
816:
811:
807:
801:
797:
793:
782:
781:
769:
765:
761:
757:
752:
748:
742:
738:
734:
731:
728:
723:
719:
713:
709:
705:
700:
696:
681:
680:
669:
665:
661:
656:
652:
648:
645:
642:
613:
601:
600:
583:
579:
572:
561:
557:
550:
539:
535:
530:
526:
506:
503:
491:speed of light
418:
410:
398:
390:
378:
370:
323:
320:
232:
231:
229:
228:
221:
214:
206:
203:
202:
196:
195:
189:
188:
182:
181:
177:
176:
170:
169:
163:
162:
158:
157:
151:
150:
146:
145:
137:
136:
128:
127:
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2413:
2402:
2399:
2397:
2394:
2392:
2389:
2388:
2386:
2377:
2374:
2373:
2369:
2353:
2352:
2347:
2341:
2338:
2333:
2327:
2309:
2305:
2298:
2291:
2288:
2283:
2279:
2275:
2271:
2267:
2263:
2259:
2252:
2249:
2244:
2240:
2236:
2232:
2225:
2222:
2210:
2206:
2199:
2196:
2185:
2181:
2174:
2171:
2166:
2164:9789814483339
2160:
2155:
2154:
2145:
2142:
2135:
2131:
2128:
2126:
2123:
2121:
2118:
2116:
2113:
2111:
2108:
2106:
2103:
2102:
2098:
2096:
2094:
2090:
2086:
2082:
2077:
2075:
2071:
2067:
2063:
2059:
2055:
2047:
2045:
2043:
2039:
2034:
2017:
2014:
2011:
2005:
1997:
1996:atomic number
1981:
1973:
1951:
1942:
1926:
1900:
1897:
1894:
1888:
1882:
1878:
1871:
1862:
1857:
1854:
1851:
1844:
1843:
1842:
1840:
1836:
1828:
1824:
1819:
1812:Cross section
1811:
1790:
1786:
1776:
1771:
1768:
1765:
1762:
1754:
1751:
1746:
1731:
1728:
1723:
1713:
1699:
1698:
1697:
1680:
1676:
1666:
1661:
1641:
1633:
1617:
1592:
1588:
1578:
1573:
1570:
1567:
1564:
1561:
1546:
1543:
1538:
1534:
1523:
1522:
1521:
1515:
1513:
1511:
1506:
1492:
1489:
1480:
1456:
1453:
1447:
1444:
1435:
1431:
1428:
1419:
1415:
1408:
1399:
1391:
1388:
1383:
1379:
1371:
1364:
1350:
1347:
1343:
1335:
1318:
1311:
1294:
1287:
1283:
1277:
1273:
1267:
1263:
1259:
1256:
1251:
1247:
1241:
1232:
1227:
1224:
1217:
1201:
1189:
1178:
1171:
1164:
1153:
1145:
1134:
1130:
1127:
1122:
1110:
1099:
1092:
1087:
1077:
1073:
1062:
1061:
1060:
1046:
1043:
1038:
1034:
1008:
994:
990:
983:
972:
968:
961:
950:
943:
938:
928:
924:
913:
912:
911:
895:
891:
885:
876:
872:
869:
864:
852:
841:
817:
814:
809:
799:
795:
763:
755:
750:
740:
736:
729:
726:
721:
717:
711:
707:
703:
698:
694:
686:
685:
684:
659:
654:
650:
643:
640:
633:
632:
631:
611:
581:
577:
570:
559:
555:
548:
537:
533:
528:
524:
516:
515:
514:
512:
504:
502:
500:
496:
492:
487:
482:
477:
472:
467:
462:
460:
456:
444:
437:
433:
432:cross section
428:
424:
422:
404: +
402:
382:
362:
360:
356:
355:cloud chamber
352:
348:
344:
343:photon energy
333:
332:atomic number
328:
321:
319:
317:
316:atomic number
313:
312:photon energy
308:
306:
302:
301:lepton number
298:
294:
290:
285:
281:
277:
273:
269:
265:
261:
257:
253:
250:
246:
242:
238:
227:
222:
220:
215:
213:
208:
207:
205:
204:
201:
198:
197:
194:
191:
190:
187:
184:
183:
178:
175:
172:
171:
168:
165:
164:
159:
156:
153:
152:
147:
143:
139:
138:
133:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
18:Pair creation
2356:. Retrieved
2349:
2340:
2315:. Retrieved
2308:the original
2303:
2290:
2265:
2261:
2251:
2234:
2224:
2212:. Retrieved
2208:
2198:
2187:. Retrieved
2183:
2173:
2152:
2144:
2078:
2066:tidal forces
2062:quantum foam
2051:
2036:In 2008 the
2035:
1918:
1832:
1609:
1519:
1507:
1471:
1025:
783:
682:
602:
508:
485:
475:
465:
458:
454:
449:
435:
363:
340:
309:
245:antiparticle
236:
235:
200:Photofission
185:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
2038:Titan laser
511:four vector
305:strangeness
2401:Antimatter
2385:Categories
2358:2019-05-27
2317:2015-04-14
2189:2016-08-28
2136:References
2074:black hole
2070:annihilate
1816:See also:
276:antiproton
80:newspapers
2214:29 August
2093:supernova
2089:SN 2006gy
2048:Astronomy
1927:α
1858:α
1852:σ
1769:−
1766:ν
1717:¯
1642:ν
1571:−
1568:ν
1490:≈
1481:θ
1454:≈
1445:−
1436:θ
1432:
1389:−
1380:γ
1348:≈
1319:⋅
1312:−
1268:−
1225:−
1146:−
1111:−
1093:≈
1078:γ
1044:≈
962:−
929:γ
873:−
853:−
800:γ
764:⋅
730:−
722:μ
712:μ
644:≡
549:−
529:γ
2326:cite web
2099:See also
463:; where
289:momentum
268:antimuon
260:positron
256:electron
243:and its
110:May 2013
2270:Bibcode
1994:is the
1970:is the
1939:is the
999:ʀ
616:ʀ
586:ʀ
489:is the
384:→
274:and an
270:, or a
266:and an
249:neutral
247:from a
94:scholar
2354:. 2008
2161:
1919:where
1610:where
603:where
495:recoil
471:energy
374:γ
280:photon
272:proton
258:and a
96:
89:
82:
75:
67:
2351:MSNBC
2311:(PDF)
2300:(PDF)
459:m â‹… c
252:boson
101:JSTOR
87:books
2332:link
2235:NIST
2216:2016
2159:ISBN
2042:gold
683:is:
483:and
481:mass
364:(Z+)
264:muon
262:, a
73:news
2278:doi
2239:doi
1630:is
1429:cos
479:is
469:is
347:MeV
56:by
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2324:{{
2302:.
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2264:.
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2284:.
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2241::
2218:.
2192:.
2167:.
2021:)
2018:Z
2015:,
2012:E
2009:(
2006:P
1982:Z
1956:e
1952:r
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1901:Z
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1895:E
1892:(
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1426:(
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1190:+
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1175:(
1172:+
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925:p
921:(
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796:p
792:(
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760:A
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727:=
718:A
708:A
704:=
699:2
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668:)
664:A
660:,
655:0
651:A
647:(
641:A
612:p
582:p
578:+
571:+
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556:+
544:e
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534:=
525:p
486:c
476:m
466:E
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414:e
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345:(
337:.
335:Z
225:e
218:t
211:v
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117:(
112:)
108:(
98:·
91:·
84:·
77:·
50:.
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