743:
other processes. The phenomena which determine the development of the hadronic showers are: hadron production, nuclear deexcitation and pion and muon decays. Neutral pions amount, on average to 1/3 of the produced pions and their energy is dissipated in the form of electromagnetic showers. Another important characteristic of the hadronic shower is that it takes longer to develop than the electromagnetic one. This can be seen by comparing the number of particles present versus depth for pion and electron initiated showers. The longitudinal development of hadronic showers scales with the
45:
1248:
828:
439:). The shower depth increases logarithmically with the energy, while the lateral spread of the shower is mainly due to the multiple scattering of the electrons. Up to the shower maximum the shower is contained in a cylinder with radius < 1 radiation length. Beyond that point electrons are increasingly affected by multiple scattering, and the lateral size scales with the
128:. These two processes (pair production and bremsstrahlung) continue, leading to a cascade of particles of decreasing energy until photons fall below the pair production threshold, and energy losses of electrons other than bremsstrahlung start to dominate. The characteristic amount of matter traversed for these related interactions is called the radiation length
822:
let γ(E,E')dE' be the probability per unit path length for a photon of energy E to produce an electron with energy between E' and E'+dE'. Finally let π(E,E')dE' be the probability per unit path length for an electron of energy E to emit a photon with energy between E' and E'+dE'. The set of integro-differential equations which govern Π and Γ are given by
1243:{\displaystyle {\begin{aligned}{\frac {d\Pi (E,x)}{dx}}&=2\int _{E}^{\infty }\Gamma (u,x)\gamma (u,E)du+\int _{E}^{\infty }\Pi (u,x)\pi (u,u-E)du-\int _{0}^{E}\Pi (E,x)\pi (E,E-u)du\\{\frac {d\Gamma (E,x)}{dx}}&=\int _{E}^{\infty }\Pi (u,x)\pi (u,E)du-\int _{0}^{E}\Gamma (E,x)\gamma (E,u)du.\end{aligned}}}
35:
particle interacting with dense matter. The incoming particle interacts, producing multiple new particles with lesser energy; each of these then interacts, in the same way, a process that continues until many thousands, millions, or even billions of low-energy particles are produced. These are then
821:
A simple model for the cascade theory of electronic showers can be formulated as a set of integro-partial differential equations. Let Π (E,x) dE and Γ(E,x) dE be the number of particles and photons with energy between E and E+dE respectively (here x is the distance along the material). Similarly
742:
The physical processes that cause the propagation of a hadron shower are considerably different from the processes in electromagnetic showers. About half of the incident hadron energy is passed on to additional secondaries. The remainder is consumed in multiparticle production of slow pions and in
182:
is both the mean distance over which a high-energy electron loses all but 1/e of its energy by bremsstrahlung and 7/9 of the mean free path for pair production by a high energy photon. The length of the cascade scales with
621:
303:
808:
437:
833:
471:. The propagation of the photons in the shower causes deviations from Molière radius scaling. However, roughly 95% of the shower are contained laterally in a cylinder with radius
501:
469:
366:
665:
692:
333:
208:
180:
153:
1307:
records the energy of particles by causing them to produce a shower and then measuring the energy deposited as a result. Many large modern detectors have both an
732:
712:
1405:, The structure of ionization showers in air generated by electrons with 1 MeV energy or less, Plasma Sources Sci. Technol. (2014), vol. 23, no. 045001
1355:
512:
1587:
216:
753:
506:
The mean longitudinal profile of the energy deposition in electromagnetic cascades is reasonably well described by a gamma distribution:
1315:, with each designed specially to produce that particular kind of shower and measure the energy of the associated type of particle.
375:
372:(the critical energy can be defined as the energy in which the bremsstrahlung and ionization rates are equal. A rough estimate is
96:
An electromagnetic shower begins when a high-energy electron, positron or photon enters a material. At high energies (above a few
1264:
hit Earth's atmosphere on a regular basis, and they produce showers as they proceed through the atmosphere. It was from these
1304:
1277:
744:
1328:
1360:
1345:
1289:
1292:, have detected the remains of a shower by sampling the energy deposited over a large area on the ground.
1276:
were detected experimentally, and they are used today by a number of experiments as a means of observing
1375:
1371:
57:
1332:
474:
445:
342:
1558:
1506:
1469:
1428:
1324:
1300:
1265:
369:
101:
85:
44:
1548:
105:
28:
1497:
Migdal, A. B (1956). "Bremsstrahlung and Pair
Production in Condensed Media at High Energies".
629:
1381:
1350:
1296:
440:
1566:
1514:
1477:
1436:
1365:
336:
20:
670:
311:
186:
158:
131:
109:
1562:
1510:
1473:
1432:
717:
697:
125:
117:
1581:
97:
1570:
1462:
Proceedings of the Royal
Society A: Mathematical, Physical and Engineering Sciences
1421:
Proceedings of the Royal
Society A: Mathematical, Physical and Engineering Sciences
1285:
1281:
1530:
124:. High-energy electrons and positrons primarily emit photons, a process called
1339:
1261:
616:{\displaystyle {\frac {dE}{dt}}=E_{0}b{\frac {(bt)^{a-1}e^{-bt}}{\Gamma (a)}}}
1518:
1458:"On the Stopping of Fast Particles and on the Creation of Positive Electrons"
1402:
1482:
1457:
1441:
1416:
56:
are produced by a particle that interacts primarily or exclusively via the
1553:
121:
113:
65:
1327:, an extensive (many kilometres wide) cascade of ionized particles and
77:
73:
61:
32:
298:{\displaystyle X=X_{0}{\frac {\ln(E_{0}/E_{\mathrm {c} })}{\ln 2}},}
803:{\displaystyle \lambda ={\frac {A}{N_{A}\sigma _{\mathrm {abs} }}}}
734:
are parameters to be fitted with Monte Carlo or experimental data.
1253:γ and π are found in for low energies and in for higher energies.
81:
43:
210:; the "shower depth" is approximately determined by the relation
1273:
1269:
108:
are insignificant, photons interact with matter primarily via
1342:(i.e. one of extraterrestrial origin) enters our atmosphere.
432:{\displaystyle E_{\mathrm {c} }=800\,\mathrm {MeV} /(Z+1.2)}
1288:
produced at the peak intensity of the shower; others, like
813:
The lateral shower development does not scale with λ.
1536:
831:
756:
720:
700:
673:
632:
515:
477:
448:
378:
345:
314:
219:
189:
161:
134:
1242:
802:
726:
706:
686:
659:
615:
495:
463:
431:
360:
327:
297:
202:
174:
147:
112:— that is, they convert into an electron-
1384:, a set of collisions between atoms in a solid
8:
1417:"The Cascade Theory of Electronic Showers"
1552:
1481:
1440:
1185:
1180:
1125:
1120:
1074:
1016:
1011:
950:
945:
890:
885:
836:
832:
830:
784:
783:
773:
763:
755:
719:
699:
678:
672:
651:
642:
631:
584:
568:
552:
543:
516:
514:
486:
485:
476:
454:
453:
447:
409:
398:
397:
384:
383:
377:
351:
350:
344:
319:
313:
268:
267:
258:
252:
236:
230:
218:
194:
188:
166:
160:
139:
133:
1356:High Altitude Water Cherenkov Experiment
1284:, have observed the visible atmospheric
1394:
52:There are two basic types of showers.
48:The start of an electromagnetic shower.
16:Extra particles from a particle impact
1531:"Passage of particles through matter"
7:
36:stopped in the matter and absorbed.
1191:
1131:
1126:
1080:
1022:
956:
951:
896:
891:
842:
791:
788:
785:
598:
487:
455:
405:
402:
399:
385:
352:
269:
14:
1535:S. Eidelman; et al. (2004).
496:{\displaystyle 2R_{\mathrm {M} }}
120:or electron in order to conserve
31:produced as the result of a high-
464:{\displaystyle R_{\mathrm {M} }}
361:{\displaystyle E_{\mathrm {c} }}
1571:10.1016/j.physletb.2004.06.001
1224:
1212:
1206:
1194:
1164:
1152:
1146:
1134:
1095:
1083:
1061:
1043:
1037:
1025:
995:
977:
971:
959:
929:
917:
911:
899:
857:
845:
607:
601:
565:
555:
426:
414:
275:
245:
84:), and proceed mostly via the
1:
1588:Experimental particle physics
1456:Bethe, H; Heitler, W (1934).
1366:ATLAS experiment calorimeters
1278:ultra-high-energy cosmic rays
1537:"Review of Particle Physics"
1415:Landau, L; Rumer, G (1938).
80:and other particles made of
1309:electromagnetic calorimeter
1604:
1280:. Some experiments, like
745:nuclear interaction length
694:is the initial energy and
116:pair, interacting with an
27:is a cascade of secondary
1351:MAGIC Cherenkov Telescope
1329:electromagnetic radiation
660:{\displaystyle t=X/X_{0}}
1519:10.1103/PhysRev.103.1811
1361:Pierre Auger Observatory
1346:Telescope Array Project
1290:Haverah Park experiment
92:Electromagnetic showers
54:Electromagnetic showers
1483:10.1098/rspa.1934.0140
1442:10.1098/rspa.1938.0088
1244:
804:
728:
708:
688:
661:
617:
497:
465:
433:
362:
329:
299:
204:
176:
149:
49:
1301:particle accelerators
1299:built at high-energy
1245:
805:
729:
709:
689:
687:{\displaystyle E_{0}}
662:
618:
498:
466:
434:
363:
330:
328:{\displaystyle X_{0}}
300:
205:
203:{\displaystyle X_{0}}
177:
175:{\displaystyle X_{0}}
150:
148:{\displaystyle X_{0}}
58:electromagnetic force
47:
1325:Air shower (physics)
1313:hadronic calorimeter
1303:, a device called a
829:
817:Theoretical analysis
754:
718:
698:
671:
630:
513:
475:
446:
376:
343:
312:
217:
187:
159:
132:
102:photoelectric effect
86:strong nuclear force
1563:2004PhLB..592....1P
1511:1956PhRv..103.1811M
1474:1934RSPSA.146...83B
1433:1938RSPSA.166..213L
1190:
1130:
1021:
955:
895:
339:of the matter, and
1297:particle detectors
1240:
1238:
1176:
1116:
1007:
941:
881:
800:
724:
704:
684:
657:
613:
493:
461:
429:
358:
325:
295:
200:
172:
145:
106:Compton scattering
50:
1541:Physics Letters B
1382:Collision cascade
1107:
869:
798:
727:{\displaystyle b}
707:{\displaystyle a}
611:
534:
290:
1595:
1574:
1556:
1554:astro-ph/0406663
1523:
1522:
1505:(6): 1811–1820.
1494:
1488:
1487:
1485:
1453:
1447:
1446:
1444:
1427:(925): 213–228.
1412:
1406:
1399:
1370:CMS experiment,
1331:produced in the
1249:
1247:
1246:
1241:
1239:
1189:
1184:
1129:
1124:
1108:
1106:
1098:
1075:
1020:
1015:
954:
949:
894:
889:
870:
868:
860:
837:
809:
807:
806:
801:
799:
797:
796:
795:
794:
778:
777:
764:
738:Hadronic showers
733:
731:
730:
725:
713:
711:
710:
705:
693:
691:
690:
685:
683:
682:
666:
664:
663:
658:
656:
655:
646:
622:
620:
619:
614:
612:
610:
596:
595:
594:
579:
578:
553:
548:
547:
535:
533:
525:
517:
502:
500:
499:
494:
492:
491:
490:
470:
468:
467:
462:
460:
459:
458:
438:
436:
435:
430:
413:
408:
390:
389:
388:
367:
365:
364:
359:
357:
356:
355:
337:radiation length
334:
332:
331:
326:
324:
323:
304:
302:
301:
296:
291:
289:
278:
274:
273:
272:
262:
257:
256:
237:
235:
234:
209:
207:
206:
201:
199:
198:
181:
179:
178:
173:
171:
170:
154:
152:
151:
146:
144:
143:
100:), in which the
72:are produced by
70:Hadronic showers
21:particle physics
1603:
1602:
1598:
1597:
1596:
1594:
1593:
1592:
1578:
1577:
1534:
1527:
1526:
1499:Physical Review
1496:
1495:
1491:
1468:(856): 83–112.
1455:
1454:
1450:
1414:
1413:
1409:
1400:
1396:
1391:
1372:electromagnetic
1321:
1268:that the first
1259:
1237:
1236:
1109:
1099:
1076:
1071:
1070:
871:
861:
838:
827:
826:
819:
779:
769:
768:
752:
751:
740:
716:
715:
696:
695:
674:
669:
668:
647:
628:
627:
597:
580:
564:
554:
539:
526:
518:
511:
510:
481:
473:
472:
449:
444:
443:
379:
374:
373:
370:critical energy
346:
341:
340:
315:
310:
309:
279:
263:
248:
238:
226:
215:
214:
190:
185:
184:
162:
157:
156:
135:
130:
129:
110:pair production
94:
42:
17:
12:
11:
5:
1601:
1599:
1591:
1590:
1580:
1579:
1576:
1575:
1525:
1524:
1489:
1448:
1407:
1393:
1392:
1390:
1387:
1386:
1385:
1379:
1368:
1363:
1358:
1353:
1348:
1343:
1320:
1317:
1258:
1255:
1251:
1250:
1235:
1232:
1229:
1226:
1223:
1220:
1217:
1214:
1211:
1208:
1205:
1202:
1199:
1196:
1193:
1188:
1183:
1179:
1175:
1172:
1169:
1166:
1163:
1160:
1157:
1154:
1151:
1148:
1145:
1142:
1139:
1136:
1133:
1128:
1123:
1119:
1115:
1112:
1110:
1105:
1102:
1097:
1094:
1091:
1088:
1085:
1082:
1079:
1073:
1072:
1069:
1066:
1063:
1060:
1057:
1054:
1051:
1048:
1045:
1042:
1039:
1036:
1033:
1030:
1027:
1024:
1019:
1014:
1010:
1006:
1003:
1000:
997:
994:
991:
988:
985:
982:
979:
976:
973:
970:
967:
964:
961:
958:
953:
948:
944:
940:
937:
934:
931:
928:
925:
922:
919:
916:
913:
910:
907:
904:
901:
898:
893:
888:
884:
880:
877:
874:
872:
867:
864:
859:
856:
853:
850:
847:
844:
841:
835:
834:
818:
815:
811:
810:
793:
790:
787:
782:
776:
772:
767:
762:
759:
739:
736:
723:
703:
681:
677:
654:
650:
645:
641:
638:
635:
624:
623:
609:
606:
603:
600:
593:
590:
587:
583:
577:
574:
571:
567:
563:
560:
557:
551:
546:
542:
538:
532:
529:
524:
521:
489:
484:
480:
457:
452:
441:Molière radius
428:
425:
422:
419:
416:
412:
407:
404:
401:
396:
393:
387:
382:
354:
349:
322:
318:
306:
305:
294:
288:
285:
282:
277:
271:
266:
261:
255:
251:
247:
244:
241:
233:
229:
225:
222:
197:
193:
169:
165:
142:
138:
126:bremsstrahlung
118:atomic nucleus
93:
90:
41:
38:
15:
13:
10:
9:
6:
4:
3:
2:
1600:
1589:
1586:
1585:
1583:
1572:
1568:
1564:
1560:
1555:
1550:
1546:
1542:
1538:
1532:
1529:
1528:
1520:
1516:
1512:
1508:
1504:
1500:
1493:
1490:
1484:
1479:
1475:
1471:
1467:
1463:
1459:
1452:
1449:
1443:
1438:
1434:
1430:
1426:
1422:
1418:
1411:
1408:
1404:
1398:
1395:
1388:
1383:
1380:
1377:
1373:
1369:
1367:
1364:
1362:
1359:
1357:
1354:
1352:
1349:
1347:
1344:
1341:
1338:
1334:
1330:
1326:
1323:
1322:
1318:
1316:
1314:
1310:
1306:
1302:
1298:
1293:
1291:
1287:
1283:
1279:
1275:
1271:
1267:
1263:
1256:
1254:
1233:
1230:
1227:
1221:
1218:
1215:
1209:
1203:
1200:
1197:
1186:
1181:
1177:
1173:
1170:
1167:
1161:
1158:
1155:
1149:
1143:
1140:
1137:
1121:
1117:
1113:
1111:
1103:
1100:
1092:
1089:
1086:
1077:
1067:
1064:
1058:
1055:
1052:
1049:
1046:
1040:
1034:
1031:
1028:
1017:
1012:
1008:
1004:
1001:
998:
992:
989:
986:
983:
980:
974:
968:
965:
962:
946:
942:
938:
935:
932:
926:
923:
920:
914:
908:
905:
902:
886:
882:
878:
875:
873:
865:
862:
854:
851:
848:
839:
825:
824:
823:
816:
814:
780:
774:
770:
765:
760:
757:
750:
749:
748:
746:
737:
735:
721:
701:
679:
675:
652:
648:
643:
639:
636:
633:
604:
591:
588:
585:
581:
575:
572:
569:
561:
558:
549:
544:
540:
536:
530:
527:
522:
519:
509:
508:
507:
504:
482:
478:
450:
442:
423:
420:
417:
410:
394:
391:
380:
371:
347:
338:
320:
316:
292:
286:
283:
280:
264:
259:
253:
249:
242:
239:
231:
227:
223:
220:
213:
212:
211:
195:
191:
167:
163:
140:
136:
127:
123:
119:
115:
111:
107:
103:
99:
91:
89:
87:
83:
79:
75:
71:
67:
63:
59:
55:
46:
39:
37:
34:
30:
26:
22:
1547:(1–4): 1–5.
1544:
1540:
1502:
1498:
1492:
1465:
1461:
1451:
1424:
1420:
1410:
1397:
1378:calorimeters
1336:
1312:
1308:
1294:
1286:fluorescence
1260:
1252:
820:
812:
741:
625:
505:
307:
95:
69:
60:, usually a
53:
51:
24:
18:
1305:calorimeter
1266:air showers
1262:Cosmic rays
1401:Köhn, C.,
1389:References
1340:cosmic ray
1333:atmosphere
1403:Ebert, U.
1282:Fly's Eye
1210:γ
1192:Γ
1178:∫
1174:−
1150:π
1132:Π
1127:∞
1118:∫
1081:Γ
1056:−
1041:π
1023:Π
1009:∫
1005:−
990:−
975:π
957:Π
952:∞
943:∫
915:γ
897:Γ
892:∞
883:∫
843:Π
781:σ
758:λ
599:Γ
586:−
573:−
284:
243:
29:particles
1582:Category
1376:hadronic
1319:See also
1257:Examples
122:momentum
114:positron
78:nucleons
66:electron
1559:Bibcode
1533:, from
1507:Bibcode
1470:Bibcode
1429:Bibcode
1337:primary
1335:when a
368:is the
335:is the
74:hadrons
1311:and a
626:where
308:where
82:quarks
76:(i.e.
62:photon
33:energy
25:shower
1549:arXiv
1274:pions
1270:muons
40:Types
1374:and
1272:and
714:and
104:and
23:, a
1567:doi
1545:592
1515:doi
1503:103
1478:doi
1466:146
1437:doi
1425:166
1295:In
424:1.2
395:800
98:MeV
68:.
64:or
19:In
1584::
1565:.
1557:.
1543:.
1539:.
1513:.
1501:.
1476:.
1464:.
1460:.
1435:.
1423:.
1419:.
747::
667:,
503:.
281:ln
240:ln
155:.
88:.
1573:.
1569::
1561::
1551::
1521:.
1517::
1509::
1486:.
1480::
1472::
1445:.
1439::
1431::
1234:.
1231:u
1228:d
1225:)
1222:u
1219:,
1216:E
1213:(
1207:)
1204:x
1201:,
1198:E
1195:(
1187:E
1182:0
1171:u
1168:d
1165:)
1162:E
1159:,
1156:u
1153:(
1147:)
1144:x
1141:,
1138:u
1135:(
1122:E
1114:=
1104:x
1101:d
1096:)
1093:x
1090:,
1087:E
1084:(
1078:d
1068:u
1065:d
1062:)
1059:u
1053:E
1050:,
1047:E
1044:(
1038:)
1035:x
1032:,
1029:E
1026:(
1018:E
1013:0
1002:u
999:d
996:)
993:E
987:u
984:,
981:u
978:(
972:)
969:x
966:,
963:u
960:(
947:E
939:+
936:u
933:d
930:)
927:E
924:,
921:u
918:(
912:)
909:x
906:,
903:u
900:(
887:E
879:2
876:=
866:x
863:d
858:)
855:x
852:,
849:E
846:(
840:d
792:s
789:b
786:a
775:A
771:N
766:A
761:=
722:b
702:a
680:0
676:E
653:0
649:X
644:/
640:X
637:=
634:t
608:)
605:a
602:(
592:t
589:b
582:e
576:1
570:a
566:)
562:t
559:b
556:(
550:b
545:0
541:E
537:=
531:t
528:d
523:E
520:d
488:M
483:R
479:2
456:M
451:R
427:)
421:+
418:Z
415:(
411:/
406:V
403:e
400:M
392:=
386:c
381:E
353:c
348:E
321:0
317:X
293:,
287:2
276:)
270:c
265:E
260:/
254:0
250:E
246:(
232:0
228:X
224:=
221:X
196:0
192:X
168:0
164:X
141:0
137:X
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
