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Spontaneous fission

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1213:" term is introduced which promotes the spherical shape of the nucleus. Acting in opposition is coulombic repulsion term, which acts to increase the distance between repelling proton pairs and thus promotes elongation of the nucleus into an oval shape. As the deformation of the nucleus increases, and particularly for large nuclei due to their stronger coulombic repulsion, the nucleus may find itself in a state where a thin 'neck' develops, forming a bridge between two clusters of nuclear matter which may exceed the ability of the surface tension to restore the undeformed shape, eventually breaking into two fragments at the "scission point". Introducing the effects of quantum tunnelling, the nucleus always has a chance to scission which increases with increasing deformation, and may do so even if the deformation is insufficient to trigger rupture of the neck. After separation, both fragments are highly positively charged and therefore gain significant kinetic energy via their mutual repulsion as they accelerate away from each other. 1223:) are excited nuclear states existing before scission which may deviate from the spherical geometry, increasing nuclear deformation compared to the ground state without undergoing full fission. These states are 'metastable' – a nucleus is this state may, on timescales between nanoseconds and microseconds, either decay back to the ground state via gamma-emission, or tunnel through the scission barrier and break apart. Should the nucleus find itself in this state, either through quantum tunnelling or via random statistical fluctuation, the barrier for fission is much reduced, as shape isomers are always at a higher energy level than the ground sate and therefore are no longer required to tunnel through the entire barrier. The resulting increased probability for fission reduces the effective half-life of the nuclide. Triple-humped barriers have been suggested for some nuclear species such as 805: 1343: 818: 33: 1286:, mostly observed as kinetic energy of the fission fragments, with the lighter fragment receiving the larger proportion of energy. For a given decay path, the number of emitted neutrons is not consistent, and instead follows a gaussian distribution. The distribution about the average, however, is consistent across all decay paths. Prompt neutrons are emitted with energies approximated by (but not precisely fitting) a 1279: ≈ 140. Spontaneous fission does not favour equal-mass fragments, and no convincing explanation has been found to explain this. In rare instances (0.3%), three or more fission fragments may be created. Ternary products are usually alpha-particles, though can be as massive as oxygen nuclei. 1250:
Fission fragments are usually neutron-rich and always generated in excited states. Thus, daughter decays occur rapidly after scission. Decays occurring within 10s of scission are termed "prompt" and are initially dominated by a series of neutron emissions which remain the dominant decay mode until
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provides a primarily qualitative description of the phenomenology by treating the nucleus as a classical drop of liquid to which quantum corrections can be applied, which provides a useful conceptual picture that matches in part with experimental data, but ignores much of the quantum nature of the
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began conducting experiments to explore the effects of incident neutron energy on uranium nuclei. Their equipment recorded fission fragments even when no neutrons were present to induce the decay, and the effect persisted even after the equipment was moved 60 meters underground into the tunnels of
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Bender, Michael; Bernard, Rémi; Bertsch, George; Chiba, Satoshi; Dobaczewski, Jacek; Dubray, Noël; Giuliani, Samuel A; Hagino, Kouichi; Lacroix, Denis; Li, Zhipan; Magierski, Piotr; Maruhn, Joachim; Nazarewicz, Witold; Pei, Junchen; Péru, Sophie; Pillet, Nathalie; Randrup, Jørgen; Regnier, David;
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and x-ray emission complete the prompt emissions. Daughter products created by prompt decays are often unstable against beta-decay, and further photon and neutron emissions are also expected. Such emissions are termed 'delayed emissions' and take place with half-lives ranging from picoseconds to
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Capote, R.; Chen, Y.-J.; Hambsch, F.-J.; Kornilov, N.V.; Lestone, J.P.; Litaize, O.; Morillon, B.; Neudecker, D.; Oberstedt, S.; Ohsawa, T.; Otuka, N.; Pronyaev, V.G.; Saxena, A.; Serot, O.; Shcherbakov, O.A.; Shu, N.-C.; Smith, D.L.; Talou, P.; Trkov, A.; Tudora, A.C.; Vogt, R.; Vorobyev, A.S.
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Reinhard, Paul-Gerhard; Robledo, Luis M; Ryssens, Wouter; Sadhukhan, Jhilam; Scamps, Guillaume; Schunck, Nicolas; Simenel, Cédric; Skalski, Janusz; Stetcu, Ionel; Stevenson, Paul; Umar, Sait; Verriere, Marc; Vretenar, Dario; Warda, Michał; Åberg, Sven (1 November 2020).
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In crystals containing high proportions of uranium, fission products generated via spontaneous fission produce damage trails as the fragments recoil through the crystal structure. The number of trails, or fission tracks, may be used to estimate the age of a sample via
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As a result of the large number of decay pathways presented to a fissioning nucleus, there is a large variation in the final products. Fragment masses are normally distributed about two peaks centred at
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may further affect observed half-lives. Decays of odd-A nuclides are hindered by 3–5 orders of magnitude compared to even–even nuclides. The barrier to fission is expected to be zero around
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is small and a sizeable fission barrier exists. As nuclear mass increases, so too does the fissility parameter, eventually approaching and exceeding
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The most common application for spontaneous fission is as neutron source for further use. These neutrons may be used for applications such as
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through a potential barrier, with a probability determined by the height of the barrier. Such a barrier is energetically possible for all
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approaches have been developed, however computational complexity makes it difficult to reproduce the full behaviour. The semi-classical
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Spontaneous fission is usually a slow process, as the nucleus cannot simply jump to the lower energy (divided) state. Instead it must
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ratio. Nuclides of the same element are linked with a red line. The green line shows the upper limit of half-life. Data taken from
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The stability of a nuclide against fission is expressed as the ratio of the Coulomb energy to the surface energy, which can be
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To date, true ab initio models describing the complete fission process are not possible. Computational theories based on
112: 2235: 2152: 1006: ≥ 93, though its height generally decreases with increasing Z, and fission is only practically observed for 1857: 416: 2080: 804: 2256: 1717: 608: 1342: 313: 1318:, or may drive additional nuclear reactions, including initiating induced fission of a target as is common in 1298:. Prompt gamma emission constitutes a further 8 MeV, while beta decay and delayed-gammas contribute a further 1251:
the fragment energy is reduced to the same order of magnitude as the neutron separation energy (approximately
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Ivanov, M. P; Buklanov, G. V; David, I.; Kushniruk, V. F; Sobolev, Yu. G.; Fomichev, A. S. (1 July 2000).
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Schunck, N; Robledo, L M (1 November 2016). "Microscopic theory of nuclear fission: a review".
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Spontaneous fission arises as a result of competition between the attractive properties of the
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Simultaneous Emission of Two Light Charged Particles in the Spontaneous Fission of Cm and Cf
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respectively. Less than 1% of emitted neutrons are emitted as delayed neutrons.
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of the constituent protons. Nuclear binding energy increases in proportion to
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Spontaneous fission half-life of various nuclides depending on their
947: 885: 698: 648: 475: 463: 458: 337: 2241: 1910: 1780: 2046: 32: 160: 133: 125: 57: 47: 1817: 2225: 2100:(January 2016). "Prompt Fission Neutron Spectra of Actinides". 2028:
McDonnell, J. D.; Nazarewicz, W.; Sheikh, J. A. (22 May 2013).
52: 1080:{\displaystyle x\approx {\frac {Z^{2}}{50.88A(1-\eta I^{2})}}} 1259: 2078: 1290:, peaking between 0.5 and 1 MeV, with an average energy of 1282:
Total energy release across all products is approximately
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Shultis, J. Kenneth; Faw, Richard E. (7 September 2007).
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Observed fission half-lives range from 4.1 microseconds (
2088:. XIV International Workshop on Nuclear Fission Physics. 873:
splits into two or more lighter nuclei. In contrast to
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In this model, as with a classical liquid drop, a "
913:) to greater than the current age of the universe ( 1991:Journal of Physics G: Nuclear and Particle Physics 1148: 1122: 1079: 880:Spontaneous fission is a dominant decay mode for 2518: 1762:Schunck, Nicolas; Regnier, David (1 July 2022). 991:(A), however coulombic repulsion increases with 967:in an effort to insulate it from the effects of 2171:Fundamentals of Nuclear Science and Engineering 2145:Fundamentals of Nuclear Science and Engineering 1206:system and fails at more rigorous predictions. 1895: 1761: 946:Following the discovery of induced fission by 2257: 2168:Shultis, J. Kenneth; Faw, Richard E. (2008). 1891: 1889: 1887: 1757: 1755: 1753: 1751: 1749: 1747: 1745: 1743: 843: 1818:"How the spontaneous fission was discovered" 1337: 1955: 1242:, further reducing its observed half-life. 2264: 2250: 2238:, with filter on spontaneous fission decay 2167: 2142: 1884: 1874:"What is Spontaneous Fission - Definition" 1740: 1017:estimated as the fissility parameter, x: 850: 836: 2063: 2045: 2012: 2002: 1951: 1949: 1947: 1945: 1909: 1797: 1779: 1979: 1977: 1956:Randrup, J.; Vogt, R. (3 October 2012). 1768:Progress in Particle and Nuclear Physics 1341: 1843: 1841: 1839: 1837: 1835: 1833: 1831: 1829: 1827: 2519: 1942: 2271: 2245: 1974: 1847: 1635: 1824: 1812: 1294:and maximum energy of approximately 1123:{\displaystyle I={\tfrac {N-Z}{A}}} 13: 1987:"Future of nuclear fission theory" 14: 2553: 2218: 1149:{\displaystyle \eta \approx 1.78} 2224: 817: 816: 803: 31: 2203: 2192: 2161: 2136: 2092: 1718:Natural nuclear fission reactor 1309: 2072: 2021: 1928:10.1088/0034-4885/79/11/116301 1898:Reports on Progress in Physics 1866: 1806: 1071: 1049: 1: 2178:. pp. 141 (table 6.2). 1850:Introductory nuclear physics 1178: = 300, though an 974: 942:Discovery of nuclear fission 7: 1764:"Theory of nuclear fission" 1706: 1245: 954:in 1938, Soviet physicists 597:High-energy nuclear physics 10: 2558: 2210:Entry at periodictable.com 2199:Entry at periodictable.com 2147:. CRC Press. p. 148. 2065:10.1103/PhysRevC.87.054327 1848:Krane, Kenneth S. (1988). 1799:10.1016/j.ppnp.2022.103963 1363:Spontaneous fission rates 939: 935: 2494: 2473: 2450: 2359: 2279: 2231:The LIVEChart of Nuclides 2122:10.1016/j.nds.2015.12.002 1391: 1386: 1383: 1375: 1370: 1367: 1338:Spontaneous fission rates 1199:density-functional theory 1182:may exist centred around 16:Form of radioactive decay 2004:10.1088/1361-6471/abab4f 1733: 2316:Double electron capture 1172:nucleon pairing effects 108:Interacting boson model 1852:. Hoboken, NJ: Wiley. 1359: 1150: 1124: 1081: 1345: 1151: 1125: 1082: 495:High-energy processes 193:– equal all the above 91:Models of the nucleus 1814:Petrzhak, Konstantin 1332:fission track dating 1288:Maxwell distribution 1275: ≈ 95 and 1156:. 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processes 2185:978-1-4200-5135-3 2034:Physical Review C 1704: 1703: 1203:liquid-drop model 1117: 1075: 869:in which a heavy 867:radioactive decay 860: 859: 546: 292:Radioactive decay 248:Nuclear stability 75:Nuclear structure 2549: 2471: 2470: 2371:Deuterium fusion 2336:Neutron emission 2321:Electron capture 2266: 2259: 2252: 2243: 2242: 2228: 2212: 2207: 2201: 2196: 2190: 2189: 2165: 2159: 2158: 2140: 2134: 2133: 2096: 2090: 2089: 2087: 2076: 2070: 2069: 2067: 2049: 2025: 2019: 2018: 2016: 2006: 1981: 1972: 1971: 1953: 1940: 1939: 1913: 1893: 1882: 1881: 1870: 1864: 1863: 1845: 1822: 1821: 1810: 1804: 1803: 1801: 1783: 1759: 1693: 1681: 1676: 1674: 1673: 1666: 1665: 1646: 1637: 1631: 1626: 1624: 1623: 1616: 1615: 1587: 1582: 1580: 1579: 1572: 1571: 1552: 1549: 1535: 1533: 1532: 1525: 1524: 1505: 1502: 1488: 1486: 1485: 1478: 1477: 1458: 1455: 1441: 1439: 1438: 1431: 1430: 1410: 1408: 1407: 1402: 1399: 1389:half-life (yrs) 1365: 1361: 1356:French Knowledge 1320:nuclear reactors 1305: 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2384: 2382: 2379: 2377: 2374: 2372: 2369: 2368: 2366: 2364: 2358: 2352: 2349: 2347: 2344: 2342: 2339: 2337: 2334: 2332: 2329: 2327: 2324: 2322: 2319: 2317: 2314: 2312: 2309: 2307: 2306:Cluster decay 2304: 2302: 2299: 2297: 2294: 2292: 2289: 2288: 2286: 2284: 2278: 2274: 2267: 2262: 2260: 2255: 2253: 2248: 2247: 2244: 2237: 2233: 2232: 2227: 2223: 2222: 2211: 2206: 2200: 2195: 2187: 2181: 2177: 2173: 2172: 2164: 2156: 2150: 2146: 2139: 2131: 2127: 2123: 2119: 2115: 2111: 2107: 2103: 2095: 2084: 2083: 2075: 2066: 2061: 2057: 2053: 2048: 2043: 2040:(5): 054327. 2039: 2035: 2031: 2024: 2015: 2010: 2005: 2000: 1996: 1992: 1988: 1980: 1978: 1969: 1965: 1961: 1960: 1952: 1950: 1948: 1946: 1937: 1933: 1929: 1925: 1921: 1917: 1912: 1907: 1903: 1899: 1892: 1890: 1888: 1879: 1875: 1869: 1861: 1859:9780471805533 1855: 1851: 1844: 1842: 1840: 1838: 1836: 1834: 1832: 1830: 1828: 1820:(in Russian). 1819: 1815: 1809: 1800: 1795: 1791: 1787: 1782: 1777: 1773: 1769: 1765: 1758: 1756: 1754: 1752: 1750: 1748: 1746: 1744: 1739: 1729: 1728:Cluster decay 1726: 1724: 1721: 1719: 1716: 1714: 1711: 1710: 1699: 1696: 1690: 1687: 1684: 1678: 1675: 1657: 1656: 1652: 1649: 1643: 1640: 1634: 1628: 1625: 1607: 1606: 1602: 1599: 1596: 1593: 1590: 1584: 1581: 1563: 1562: 1558: 1555: 1546: 1543: 1540: 1537: 1534: 1516: 1515: 1511: 1508: 1499: 1496: 1493: 1490: 1487: 1469: 1468: 1464: 1461: 1452: 1449: 1446: 1443: 1440: 1422: 1421: 1417: 1414: 1413: 1406: 1398: 1384:Neutrons per 1379: 1366: 1357: 1353: 1349: 1344: 1335: 1333: 1327: 1325: 1321: 1317: 1307: 1289: 1280: 1278: 1274: 1268: 1265: 1261: 1256: 1243: 1222: 1219:(also called 1218: 1217:Shape isomers 1214: 1212: 1207: 1204: 1200: 1196: 1191: 1189: 1185: 1181: 1177: 1173: 1169: 1168:Shell effects 1165: 1163: 1159: 1143: 1140: 1137: 1114: 1110: 1107: 1104: 1097: 1094: 1066: 1062: 1058: 1055: 1052: 1046: 1043: 1037: 1033: 1027: 1024: 1016: 1011: 1009: 1005: 1001: 996: 994: 993:proton number 990: 986: 982: 972: 970: 966: 961: 957: 953: 949: 943: 933: 892: 890: 888: 883: 878: 876: 872: 868: 864: 853: 848: 846: 841: 839: 834: 833: 831: 830: 824: 814: 811: 806: 800: 799: 798: 797: 790: 787: 785: 782: 780: 777: 775: 772: 770: 767: 765: 762: 760: 757: 755: 752: 750: 747: 745: 742: 740: 737: 735: 732: 730: 727: 725: 722: 720: 717: 715: 712: 710: 707: 705: 702: 700: 697: 695: 692: 690: 687: 685: 682: 680: 677: 675: 672: 670: 667: 665: 662: 660: 657: 655: 652: 650: 647: 645: 642: 640: 637: 635: 632: 631: 628: 623: 622: 615: 612: 610: 607: 605: 602: 601: 598: 593: 592: 583: 580: 578: 575: 573: 570: 569: 567: 566: 561: 558: 556: 553: 551: 548: 547: 543: 542: 539: 536: 535: 532: 527: 522: 521: 514: 511: 507: 506:by cosmic ray 504: 503: 502: 499: 498: 492: 491: 482: 479: 477: 474: 473: 472: 469: 465: 462: 460: 457: 456: 455: 452: 448: 445: 444: 443: 440: 439: 433: 432: 425: 422: 418: 417:pair breaking 415: 414: 413: 410: 408: 405: 404: 401: 396: 395: 388: 385: 383: 382:Decay product 380: 378: 375: 373: 370: 369: 366: 363: 361: 358: 356: 355:Cluster decay 353: 351: 348: 344: 341: 339: 336: 335: 334: 331: 329: 326: 322: 319: 315: 312: 311: 310: 307: 306: 305: 302: 300: 297: 296: 293: 288: 287: 280: 277: 275: 272: 270: 267: 265: 262: 260: 257: 255: 252: 251: 245: 244: 235: 232: 231: 230: 227: 225: 222: 220: 217: 215: 212: 211: 208: 204: 200: 199:Mirror nuclei 197: 196: 192: 189: 188: 185: 184: 181: −  180: 175: 172: 171: 168: 167: 162: 159: 158: 155: 154: 149: 146: 145: 141: 140: 135: 132: 131: 127: 122: 121: 114: 111: 109: 106: 104: 101: 99: 96: 95: 92: 87: 86: 81: 78: 76: 73: 71: 70:Nuclear force 68: 66: 63: 59: 56: 54: 51: 50: 49: 46: 44: 41: 40: 39: 38: 34: 30: 29: 26: 23: 22: 19: 2465:Photofission 2429: 2421: 2350: 2229: 2205: 2194: 2170: 2163: 2144: 2138: 2105: 2101: 2094: 2081: 2074: 2037: 2033: 2023: 1994: 1990: 1958: 1901: 1897: 1877: 1868: 1849: 1808: 1771: 1767: 1404: 1396: 1351: 1347: 1328: 1313: 1310:Applications 1284:200 MeV 1281: 1276: 1272: 1269: 1249: 1220: 1215: 1208: 1195:Hartree–Fock 1192: 1187: 1183: 1175: 1166: 1157: 1012: 1007: 1003: 997: 978: 945: 893: 886: 879: 862: 861: 424:Photofission 406: 372:Decay energy 349: 299:Alpha α 206: 202: 182: 178: 165: 152: 138: 18: 2291:Alpha decay 2281:Radioactive 2014:1885/224561 1723:Alpha decay 1387:Spontaneous 1300:19 MeV 1296:10 MeV 1015:empirically 969:cosmic rays 729:Oppenheimer 407:Spontaneous 377:Decay chain 328:K/L capture 304:Beta β 174:Isodiaphers 98:Liquid drop 2521:Categories 2442:rp-process 2416:Si burning 2406:Ne burning 2376:Li burning 2296:Beta decay 1911:1511.07517 1781:2201.02719 1304:7 MeV 1292:2 MeV 1260:yrast line 940:See also: 759:Strassmann 749:Rutherford 627:Scientists 582:Artificial 577:Cosmogenic 572:Primordial 568:Nuclides: 545:Processes: 501:Spallation 2453:processes 2437:p-process 2411:O burning 2401:C burning 2391:α process 2386:CNO cycle 2176:CRC Press 2108:: 1–106. 2047:1302.1165 1418:Gram-sec 1371:Half-life 1141:≈ 1138:η 1108:− 1059:η 1056:− 1028:≈ 975:Mechanism 948:Otto Hahn 764:Świątecki 679:Pi. Curie 674:Fr. Curie 669:Ir. Curie 664:Cockcroft 639:Becquerel 560:Supernova 264:Drip line 259:p–n ratio 234:Borromean 113:Ab initio 2495:Exchange 2432:-process 2424:-process 2396:Triple-α 1936:27727148 1707:See also 1650:1.12·10 1600:1.16·10 1491:4.47·10 1444:7.04·10 1415:Fission 1376:Fission 1368:Nuclide 1246:Products 889:-process 823:Category 724:Oliphant 709:Lawrence 689:Davisson 659:Chadwick 555:Big Bang 442:electron 412:Products 333:Isomeric 224:Even/odd 201: – 176:– equal 163:– equal 161:Isotones 150:– equal 136:– equal 134:Isotopes 126:Nuclides 48:Nucleons 2474:Capture 2361:Stellar 2130:1239564 2110:Bibcode 2052:Bibcode 1968:1124864 1916:Bibcode 1786:Bibcode 1694:2.3·10 1682:2.6468 1647:1.6·10 1591:5.0·10 1556:5.5·10 1541:4.4·10 1509:8.4·10 1506:0.0136 1494:5.4·10 1462:3.5·10 1459:0.0003 1447:2.0·10 1409:⁠ 1393:⁠ 1267:years. 1253:7  936:History 779:Thomson 769:Szilárd 739:Purcell 719:Meitner 654:N. Bohr 649:A. Bohr 634:Alvarez 550:Stellar 454:neutron 338:Gamma γ 191:Isomers 148:Isobars 43:Nucleus 2182:  2151:  2128:  1966:  1934:  1904:(11). 1856:  1553:0.022 1538:24100 1373:(yrs) 1000:tunnel 821:  789:Wigner 784:Walton 774:Teller 704:Jensen 471:proton 214:Stable 2451:Other 2283:decay 2086:(PDF) 2042:arXiv 1906:arXiv 1776:arXiv 1734:Notes 1700:38.1 1697:85.7 1688:3.73 1685:3.09 1653:36.9 1641:3.31 1632:8300 1603:36.8 1594:2.21 1588:6569 1559:37.0 1544:2.16 1512:35.6 1497:2.07 1465:36.0 1450:1.86 1162:unity 1087:with 1044:50.88 754:Soddy 734:Proca 714:Mayer 694:Fermi 644:Bethe 219:Magic 2236:IAEA 2180:ISBN 2149:ISBN 2126:OSTI 1964:OSTI 1932:PMID 1854:ISBN 1597:920 1322:and 1302:and 1170:and 1144:1.78 1130:and 958:and 950:and 744:Rabi 699:Hahn 609:RHIC 229:Halo 2234:at 2118:doi 2106:131 2060:doi 2009:hdl 1999:doi 1924:doi 1794:doi 1772:125 1638:74 1255:MeV 1197:or 932:). 900:102 614:LHC 528:and 2523:: 2174:. 2124:. 2116:. 2104:. 2058:. 2050:. 2038:87 2036:. 2032:. 2007:. 1995:47 1993:. 1989:. 1976:^ 1944:^ 1930:. 1922:. 1914:. 1902:79 1900:. 1886:^ 1876:. 1826:^ 1816:. 1792:. 1784:. 1774:. 1770:. 1766:. 1742:^ 1667:Cf 1617:Cm 1573:Pu 1526:Pu 1334:. 1326:. 1233:Th 1229:90 923:Th 919:90 904:No 481:rp 447:2× 314:0v 309:2β 205:↔ 2430:s 2422:r 2265:e 2258:t 2251:v 2188:. 2157:. 2132:. 2120:: 2112:: 2068:. 2062:: 2054:: 2044:: 2017:. 2011:: 2001:: 1970:. 1938:. 1926:: 1918:: 1908:: 1862:. 1802:. 1796:: 1788:: 1778:: 1692:0 1680:0 1645:0 1636:~ 1630:0 1586:0 1551:0 1548:0 1504:0 1501:0 1479:U 1457:0 1454:0 1432:U 1405:A 1401:/ 1397:Z 1358:. 1352:A 1350:/ 1348:Z 1277:A 1273:A 1188:N 1184:Z 1176:A 1158:x 1115:A 1111:Z 1105:N 1098:= 1095:I 1072:) 1067:2 1063:I 1053:1 1050:( 1047:A 1038:2 1034:Z 1025:x 1008:A 1004:A 887:r 851:e 844:t 837:v 476:p 464:r 459:s 321:β 207:N 203:Z 183:Z 179:N 166:N 153:A 139:Z 58:n 53:p

Index

Nuclear physics

Nucleus
Nucleons
p
n
Nuclear matter
Nuclear force
Nuclear structure
Nuclear reaction
Models of the nucleus
Liquid drop
Nuclear shell model
Interacting boson model
Ab initio
Nuclides
Isotopes
Z
Isobars
A
Isotones
N
Isodiaphers
N − Z
Isomers
Mirror nuclei
Stable
Magic
Even/odd
Halo

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