1819:
432:
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25:
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489:) 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
1357:
1210:
292:) 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
1463:
1802:
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775:
275:
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
1216:
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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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1499:
482:. The photon must have higher energy than the sum of the rest mass energies of an electron and positron (2 Ă— 511 keV = 1.022 MeV, resulting in a photon wavelength of
1689:
824:
319:
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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1363:
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2027:
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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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1988:
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212:
515:
1505:
1352:{\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}
685:
2327:
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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.
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1522:
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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,
205:
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338:
scale and higher), pair production is the dominant mode of photon interaction with matter. These interactions were first observed in
2120:
1504:
This derivation is a semi-classical approximation. An exact derivation of the kinematics can be done taking into account the full
1205:{\displaystyle (p_{\gamma })^{2}\approx (p_{{\text{e}}^{-}})^{2}+2p_{{\text{e}}^{-}}p_{{\text{e}}^{+}}+(p_{{\text{e}}^{+}})^{2}}
89:
198:
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68:
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350:. 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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1458:{\displaystyle 2\,(\gamma ^{2}-1)\,m_{\text{e}}^{2}\,c^{2}\,(\cos \theta _{\text{e}}-1)\approx 0}
420:
35:
347:
1918:
82:
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1997:
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The exact analytic form for the cross section of pair production must be calculated through
1797:{\displaystyle ({\bar {E}}_{k}^{pp})_{\text{tr}}={\frac {1}{2}}(h\nu -2\,m_{\text{e}}c^{2})}
2265:
143:
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1012:{\displaystyle (p_{\gamma })^{2}=(p_{{\text{e}}^{-}}+p_{{\text{e}}^{+}}+p_{\text{Ę€}})^{2}}
8:
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1837:
and results in a complicated function. To simplify, the cross section can be written as:
1516:
The energy transfer to electron and positron in pair production interactions is given by
181:
2269:
2072:, one particle may escape while its antiparticle partner is captured by the black hole.
2125:
2079:
type of stellar explosion, where pair production suddenly lowers the pressure inside a
1973:
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229:
162:
155:
130:
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2083:, leading to a partial implosion, and then explosive thermonuclear burning. Supernova
509:
notation, the conservation of energy–momentum before and after the interaction gives:
419:
Plot of photon energies calculated for a given element (atomic number Z) at which the
2321:
2154:
2053:
2049:
431:
415:
16:
Interaction of a photon with matter resulting into creation of electron-positron pair
280:
are the principal constraints on the process. All other conserved quantum numbers (
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770:{\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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589:{\displaystyle p_{\gamma }=p_{{\text{e}}^{-}}+p_{{\text{e}}^{+}}+p_{\text{Ę€}}}
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2302:. PHYS 5012. Sydney, Australia: The University of Sydney. Archived from
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Pair production is invoked in the heuristic explanation of hypothetical
2069:
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target, was used to generate positron–electron pairs in large numbers.
264:
2254:"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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24:
1596:{\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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277:
256:
248:
244:
2056:, particle pairs are constantly appearing and disappearing as a
1905:{\displaystyle \sigma =\alpha \,r_{\text{e}}^{2}\,Z^{2}\,P(E,Z)}
899:{\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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2201:"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
49:. Unsourced material may be challenged and removed.
2372:Theory of photon-impact bound-free pair production
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307:of (hence, number of protons in) the nearby atom.
303:and also increases approximately as the square of
267:. Pair production often refers specifically to a
2378:
2342:"Laser technique produces bevy of antimatter"
206:
2326:: CS1 maint: multiple names: authors list (
2149:Introduction to Nuclear and Particle Physics
669:{\displaystyle A\equiv (A^{0},\mathbf {A} )}
2068:. When this happens in the region around a
1494:{\displaystyle \theta _{\text{e}}\approx 0}
906:. We can square the conservation equation
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109:Learn how and when to remove this message
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1650:is the frequency of the photon and the
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2290:
2227:"XCOM: Photon Cross Sections Database"
2060:. In a region of strong gravitational
2291:Kuncic, Zdenka, Dr. (12 March 2013).
2036:, aimed at a 1 millimeter-thick
1055:and expanding the remaining relation
1684:{\displaystyle 2\,m_{\text{e}}c^{2}}
47:adding citations to reliable sources
18:
2300:Index of Dr. Kuncic's Lectures
2173:
819:{\displaystyle (p_{\gamma })^{2}=0}
500:
13:
2293:"PRadiation Physics and Dosimetry"
2176:"How photons interact with matter"
2145:Das, A.; Ferbel, T. (2003-12-23).
1511:
435:Subatomic particle pair production
14:
2408:
2365:
2278:10.1016/j.radphyschem.2005.10.008
2199:Bywater, Jenn (29 October 2015).
493:. The reverse of this process is
2121:Landau–Pomeranchuk–Migdal effect
1807:
1319:
1295:
763:
755:
659:
129:
23:
2258:Radiation Physics and Chemistry
2225:Seltzer, Stephen (2009-09-17).
427:=0.08 MeV and ceases at 12 MeV.
311:Photon to electron and positron
243:. Examples include creating an
34:needs additional citations for
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1048:{\displaystyle p_{R}\approx 0}
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742:
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663:
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495:electron–positron annihilation
1:
2131:
2043:
1959:{\displaystyle r_{\text{e}}}
619:{\displaystyle p_{\text{Ę€}}}
7:
2252:Hubbell, J.H. (June 2006).
2094:
10:
2413:
2077:pair-instability supernova
1811:
1968:classical electron radius
124:Light–matter interaction
2205:Imperial College London
1937:fine-structure constant
1928:{\displaystyle \alpha }
1831:quantum electrodynamics
1814:Gamma ray cross section
2180:Meroli Stefano Webpage
2116:Meitner–Hupfeld effect
2023:
2022:{\displaystyle P(E,Z)}
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348:Nobel Prize in Physics
346:, leading to the 1948
342:'s counter-controlled
330:For photons with high
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169:High-energy phenomena:
2101:Breit–Wheeler process
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1994:of the material, and
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441:Einstein's equation,
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228:is the creation of a
150:Mid-energy phenomena:
138:Low-energy phenomena:
2153:. World Scientific.
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1643:{\displaystyle \nu }
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144:Photoelectric effect
43:improve this article
2270:2006RaPC...75..614H
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885:
780:which implies that
182:Photodisintegration
2126:Two-photon physics
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826:for all cases and
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230:subatomic particle
163:Compton scattering
156:Thomson scattering
2174:Stefano, Meroli.
2054:quantum mechanics
2050:Hawking radiation
1983:{\displaystyle Z}
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1619:{\displaystyle h}
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58:"Pair production"
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2309:on 11 March 2016
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1835:Feynman diagrams
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501:Basic kinematics
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340:Patrick Blackett
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282:angular momentum
273:rest mass energy
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2392:Nuclear physics
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2111:Matter creation
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2081:supergiant star
2052:. According to
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1628:Planck constant
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1512:Energy transfer
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286:electric charge
226:Pair production
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175:Pair production
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2366:External links
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2264:(6): 614–623.
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2106:Dirac equation
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1544:
1541:
1536:
1532:
1528:
1513:
1510:
1490:
1487:
1478:
1466:
1465:
1454:
1451:
1448:
1445:
1442:
1433:
1429:
1426:
1423:
1417:
1413:
1406:
1397:
1392:
1389:
1386:
1381:
1377:
1373:
1369:
1359:
1348:
1345:
1341:
1333:
1321:
1316:
1309:
1297:
1292:
1285:
1281:
1275:
1271:
1265:
1261:
1257:
1254:
1249:
1245:
1239:
1230:
1225:
1222:
1212:
1199:
1195:
1187:
1176:
1172:
1169:
1162:
1151:
1143:
1132:
1128:
1125:
1120:
1116:
1108:
1097:
1093:
1090:
1085:
1081:
1075:
1071:
1067:
1044:
1041:
1036:
1032:
1020:
1019:
1006:
1002:
992:
988:
981:
970:
966:
959:
948:
944:
941:
936:
932:
926:
922:
918:
893:
889:
883:
874:
870:
867:
862:
858:
850:
839:
835:
815:
812:
807:
803:
797:
793:
789:
778:
777:
765:
761:
757:
753:
748:
744:
738:
734:
730:
727:
724:
719:
715:
709:
705:
701:
696:
692:
677:
676:
665:
661:
657:
652:
648:
644:
641:
638:
609:
597:
596:
579:
575:
568:
557:
553:
546:
535:
531:
526:
522:
502:
499:
480:speed of light
407:
399:
387:
379:
367:
359:
312:
309:
221:
220:
218:
217:
210:
203:
195:
192:
191:
185:
184:
178:
177:
171:
170:
166:
165:
159:
158:
152:
151:
147:
146:
140:
139:
135:
134:
126:
125:
117:
116:
31:
29:
22:
15:
9:
6:
4:
3:
2:
2409:
2398:
2395:
2393:
2390:
2388:
2385:
2384:
2382:
2373:
2370:
2369:
2349:
2348:
2343:
2337:
2329:
2323:
2305:
2301:
2294:
2287:
2279:
2275:
2271:
2267:
2263:
2259:
2255:
2248:
2240:
2236:
2232:
2228:
2221:
2206:
2202:
2195:
2181:
2177:
2170:
2162:
2160:9789814483339
2156:
2151:
2150:
2141:
2137:
2127:
2124:
2122:
2119:
2117:
2114:
2112:
2109:
2107:
2104:
2102:
2099:
2098:
2092:
2090:
2086:
2082:
2078:
2073:
2071:
2067:
2063:
2059:
2055:
2051:
2041:
2039:
2035:
2030:
2013:
2010:
2007:
2001:
1993:
1992:atomic number
1977:
1969:
1947:
1938:
1922:
1896:
1893:
1890:
1884:
1878:
1874:
1867:
1858:
1853:
1850:
1847:
1840:
1839:
1838:
1836:
1832:
1824:
1820:
1815:
1808:Cross section
1786:
1782:
1772:
1767:
1764:
1761:
1758:
1750:
1747:
1742:
1727:
1724:
1719:
1709:
1695:
1694:
1693:
1676:
1672:
1662:
1657:
1637:
1629:
1613:
1588:
1584:
1574:
1569:
1566:
1563:
1560:
1557:
1542:
1539:
1534:
1530:
1519:
1518:
1517:
1509:
1507:
1502:
1488:
1485:
1476:
1452:
1449:
1443:
1440:
1431:
1427:
1424:
1415:
1411:
1404:
1395:
1387:
1384:
1379:
1375:
1367:
1360:
1346:
1343:
1339:
1331:
1314:
1307:
1290:
1283:
1279:
1273:
1269:
1263:
1259:
1255:
1252:
1247:
1243:
1237:
1228:
1223:
1220:
1213:
1197:
1185:
1174:
1167:
1160:
1149:
1141:
1130:
1126:
1123:
1118:
1106:
1095:
1088:
1083:
1073:
1069:
1058:
1057:
1056:
1042:
1039:
1034:
1030:
1004:
990:
986:
979:
968:
964:
957:
946:
939:
934:
924:
920:
909:
908:
907:
891:
887:
881:
872:
868:
865:
860:
848:
837:
813:
810:
805:
795:
791:
759:
751:
746:
736:
732:
725:
722:
717:
713:
707:
703:
699:
694:
690:
682:
681:
680:
655:
650:
646:
639:
636:
629:
628:
627:
607:
577:
573:
566:
555:
551:
544:
533:
529:
524:
520:
512:
511:
510:
508:
498:
496:
492:
487:
481:
476:
471:
466:
461:
456:
451:
449:
445:
433:
426:
422:
421:cross section
417:
413:
411:
393: +
391:
371:
351:
349:
345:
344:cloud chamber
341:
337:
333:
332:photon energy
322:
321:atomic number
317:
308:
306:
305:atomic number
302:
301:photon energy
297:
295:
291:
290:lepton number
287:
283:
279:
274:
270:
266:
262:
258:
254:
250:
246:
242:
239:
235:
231:
227:
216:
211:
209:
204:
202:
197:
196:
194:
193:
190:
187:
186:
183:
180:
179:
176:
173:
172:
168:
167:
164:
161:
160:
157:
154:
153:
149:
148:
145:
142:
141:
137:
136:
132:
128:
127:
123:
122:
113:
110:
102:
91:
88:
84:
81:
77:
74:
70:
67:
63:
60: –
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
2352:. Retrieved
2345:
2336:
2311:. Retrieved
2304:the original
2299:
2286:
2261:
2257:
2247:
2230:
2220:
2208:. Retrieved
2204:
2194:
2183:. Retrieved
2179:
2169:
2148:
2140:
2074:
2062:tidal forces
2058:quantum foam
2047:
2032:In 2008 the
2031:
1914:
1828:
1605:
1515:
1503:
1467:
1021:
779:
678:
598:
504:
484:1.2132
474:
464:
454:
447:
443:
438:
424:
352:
329:
298:
234:antiparticle
225:
224:
189:Photofission
174:
105:
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
2034:Titan laser
507:four vector
294:strangeness
2397:Antimatter
2381:Categories
2354:2019-05-27
2313:2015-04-14
2185:2016-08-28
2132:References
2070:black hole
2066:annihilate
1812:See also:
265:antiproton
69:newspapers
2210:29 August
2089:supernova
2085:SN 2006gy
2044:Astronomy
1923:α
1854:α
1848:σ
1765:−
1762:ν
1713:¯
1638:ν
1567:−
1564:ν
1486:≈
1477:θ
1450:≈
1441:−
1432:θ
1428:
1385:−
1376:γ
1344:≈
1315:⋅
1308:−
1264:−
1221:−
1142:−
1107:−
1089:≈
1074:γ
1040:≈
958:−
925:γ
869:−
849:−
796:γ
760:⋅
726:−
718:μ
708:μ
640:≡
545:−
525:γ
2322:cite web
2095:See also
452:; where
278:momentum
257:antimuon
249:positron
245:electron
232:and its
99:May 2013
2266:Bibcode
1990:is the
1966:is the
1935:is the
1626:is the
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612:ʀ
582:ʀ
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263:and an
259:, or a
255:and an
238:neutral
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1606:where
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460:energy
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269:photon
261:proton
247:and a
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2307:(PDF)
2296:(PDF)
241:boson
90:JSTOR
76:books
2328:link
2231:NIST
2212:2016
2155:ISBN
2038:gold
472:and
470:mass
353:(Z+)
253:muon
251:, a
62:news
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2235:doi
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679:is
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336:MeV
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