418:. A tamper also tends to act as a neutron reflector. Because a bomb relies on fast neutrons (not ones moderated by reflection with light elements, as in a reactor), the neutrons reflected by a tamper are slowed by their collisions with the tamper nuclei, and because it takes time for the reflected neutrons to return to the fissile core, they take rather longer to be absorbed by a fissile nucleus. But they do contribute to the reaction, and can decrease the critical mass by a factor of four. Also, if the tamper is (e.g. depleted) uranium, it can fission due to the high energy neutrons generated by the primary explosion. This can greatly increase yield, especially if even more neutrons are generated by fusing hydrogen isotopes, in a so-called
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fraction of them come later, when the fission products decay, which may be on the average from microseconds to minutes later. This is fortunate for atomic power generation, for without this delay "going critical" would be an immediately catastrophic event, as it is in a nuclear bomb where upwards of 80 generations of chain reaction occur in less than a microsecond, far too fast for a human, or even a machine, to react. Physicists recognize two points in the gradual increase of neutron flux which are significant: critical, where the chain reaction becomes self-sustaining thanks to the contributions of both kinds of neutron generation, and
140:
385:). An ideal mass will become subcritical if allowed to expand or conversely the same mass will become supercritical if compressed. Changing the temperature may also change the density; however, the effect on critical mass is then complicated by temperature effects (see "Changing the temperature") and by whether the material expands or contracts with increased temperature. Assuming the material expands with temperature (enriched
1367:
1354:. In fact, even for a homogeneous solid sphere, the exact calculation is by no means trivial. Finally, note that the calculation can also be performed by assuming a continuum approximation for the neutron transport. This reduces it to a diffusion problem. However, as the typical linear dimensions are not significantly larger than the mean free path, such an approximation is only marginally applicable.
43:
440:
946:
density means that the distance travelled before leaving the system is 1% less. This is something that must be taken into consideration when attempting more precise estimates of critical masses of plutonium isotopes than the approximate values given above, because plutonium metal has a large number of different crystal phases which can have widely varying densities.
942:
use of a neutron reflector like beryllium can substantially drop this amount, however: with a 5 centimetres (2.0 in) reflector, the critical mass of 19.75%-enriched uranium drops to 403 kilograms (888 lb), and with a 15 centimetres (5.9 in) reflector it drops to 144 kilograms (317 lb), for example.
1319:
This is applied in implosion-type nuclear weapons where a spherical mass of fissile material that is substantially less than a critical mass is made supercritical by very rapidly increasing ρ (and thus Σ as well) (see below). Indeed, sophisticated nuclear weapons programs can make a functional device
1315:
to account for the fact that the two values may differ depending upon geometrical effects and how one defines Σ. For example, for a bare solid sphere of Pu criticality is at 320 kg/m, regardless of density, and for U at 550 kg/m. In any case, criticality then depends upon a typical neutron
941:
The critical mass for lower-grade uranium depends strongly on the grade: with 45% U, the bare-sphere critical mass is around 185 kilograms (408 lb); with 19.75% U it is over 780 kilograms (1,720 lb); and with 15% U, it is well over 1,350 kilograms (2,980 lb). In all of these cases, the
367:
of the U resonances but is common to all fuels/absorbers/configurations. Neglecting the very important resonances, the total neutron cross-section of every material exhibits an inverse relationship with relative neutron velocity. Hot fuel is always less reactive than cold fuel (over/under moderation
1357:
Finally, note that for some idealized geometries, the critical mass might formally be infinite, and other parameters are used to describe criticality. For example, consider an infinite sheet of fissionable material. For any finite thickness, this corresponds to an infinite mass. However, criticality
430:
The critical size is the minimum size of a nuclear reactor core or nuclear weapon that can be made for a specific geometrical arrangement and material composition. The critical size must at least include enough fissionable material to reach critical mass. If the size of the reactor core is less than
333:
It is possible for a fuel assembly to be critical at near zero power. If the perfect quantity of fuel were added to a slightly subcritical mass to create an "exactly critical mass", fission would be self-sustaining for only one neutron generation (fuel consumption then makes the assembly subcritical
1323:
Aside from the math, there is a simple physical analog that helps explain this result. Consider diesel fumes belched from an exhaust pipe. Initially the fumes appear black, then gradually you are able to see through them without any trouble. This is not because the total scattering cross section of
389:
at room temperature for example), at an exactly critical state, it will become subcritical if warmed to lower density or become supercritical if cooled to higher density. Such a material is said to have a negative temperature coefficient of reactivity to indicate that its reactivity decreases when
372:
is a different topic). Thermal expansion associated with temperature increase also contributes a negative coefficient of reactivity since fuel atoms are moving farther apart. A mass that is exactly critical at room temperature would be sub-critical in an environment anywhere above room temperature
324:
The mass where criticality occurs may be changed by modifying certain attributes such as fuel, shape, temperature, density and the installation of a neutron-reflective substance. These attributes have complex interactions and interdependencies. These examples only outline the simplest ideal cases:
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The critical mass is inversely proportional to the square of the density. If the density is 1% more and the mass 2% less, then the volume is 3% less and the diameter 1% less. The probability for a neutron per cm travelled to hit a nucleus is proportional to the density. It follows that 1% greater
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The event of fission must release, on the average, more than one free neutron of the desired energy level in order to sustain a chain reaction, and each must find other nuclei and cause them to fission. Most of the neutrons released from a fission event come immediately from that event, but a
350:
A mass may be exactly critical without being a perfect homogeneous sphere. More closely refining the shape toward a perfect sphere will make the mass supercritical. Conversely changing the shape to a less perfect sphere will decrease its reactivity and make it subcritical.
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Several uncertainties contribute to the determination of a precise value for critical masses, including (1) detailed knowledge of fission cross sections, (2) calculation of geometric effects. This latter problem provided significant motivation for the development of the
1407:
design. In reality, this is impractical because even "weapons grade" Pu is contaminated with a small amount of Pu, which has a strong propensity toward spontaneous fission. Because of this, a reasonably sized gun-type weapon would suffer nuclear reaction
308:(U) with a mass of about 52 kilograms (115 lb) would experience around 15 spontaneous fission events per second. The probability that one such event will cause a chain reaction depends on how much the mass exceeds the critical mass. If there is
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until it either escapes from the medium or causes a fission reaction. So long as other loss mechanisms are not significant, then, the radius of a spherical critical mass is rather roughly given by the product of the mean free path
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1238:
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Similarly, if the perfect quantity of fuel were added to a slightly subcritical mass, to create a barely supercritical mass, the temperature of the assembly would increase to an initial maximum (for example:
1302:
342:
above the ambient temperature) and then decrease back to the ambient temperature after a period of time, because fuel consumed during fission brings the assembly back to subcriticality once again.
236:
mass is a mass that does not have the ability to sustain a fission chain reaction. A population of neutrons introduced to a subcritical assembly will exponentially decrease. In this case, known as
363:
increase as the relative neutron velocity decreases. As fuel temperature increases, neutrons of a given energy appear faster and thus fission/absorption is less likely. This is not unrelated to
381:
The higher the density, the lower the critical mass. The density of a material at a constant temperature can be changed by varying the pressure or tension or by changing crystal structure (see
486:
are listed in the following table. Most information on bare sphere masses is considered classified, since it is critical to nuclear weapons design, but some documents have been declassified.
162:. The original experiment was designed to measure the radiation produced when an extra block was added. The mass went supercritical when the block was placed improperly by being dropped.
1630:
1725:. Proceedings of the Seventh International Conference on Nuclear Criticality Safety. Vol. II. Tokai, Ibaraki, Japan: Japan Atomic Energy Research Institute. pp. 618–623.
414:
In a bomb, a dense shell of material surrounding the fissile core will contain, via inertia, the expanding fissioning material, which increases the efficiency. This is known as a
1038:
1446:, where the immediate "prompt" neutrons alone will sustain the reaction without need for the decay neutrons. Nuclear power plants operate between these two points of
1067:
1895:
In the description of the Soviet equivalent of the CP1 startup at the
University of Chicago in 1942, the long waits for those tardy neutrons is described in detail
1336:, and therefore proportional to the areal density of soot particles: we can make it easier to see through the imaginary cube just by making the cube larger.
229:, the average number of neutrons released per fission event that go on to cause another fission event rather than being absorbed or leaving the material.
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must be kept subcritical. In the case of a uranium gun-type bomb, this can be achieved by keeping the fuel in a number of separate pieces, each below the
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1599:
1415:
Instead, the plutonium is present as a subcritical sphere (or other shape), which may or may not be hollow. Detonation is produced by exploding a
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1852:
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The shape with minimal critical mass and the smallest physical dimensions is a sphere. Bare-sphere critical masses at normal density of some
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1386:
either because they are too small or unfavorably shaped. To produce detonation, the pieces of uranium are brought together rapidly. In
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126:
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1809:
Glaser, Alexander (2006). "On the
Proliferation Potential of Uranium Fuel for Research Reactors at Various Enrichment Levels".
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1602:, Republic of France, Institut de Radioprotection et de Sûreté Nucléaire, Département de Prévention et d'étude des Accidents.
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A theoretical 100% pure Pu weapon could also be constructed as a gun-type weapon, like the
Manhattan Project's proposed
312:(U) present, the rate of spontaneous fission will be much higher. Fission can also be initiated by neutrons produced by
1450:, while above the prompt critical point is the domain of nuclear weapons and some nuclear power accidents, such as the
1915:
86:
1324:
all the soot particles has changed, but because the soot has dispersed. If we consider a transparent cube of length
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which clearly recovers the aforementioned result that critical mass depends inversely on the square of the density.
390:
its temperature increases. Using such a material as fuel means fission decreases as the fuel temperature increases.
1747:"Critical and Subcritical Mass Calculations of Curium-243 to -247 Based on JENDL-3.2 for Revision of ANSI/ANS-8.15"
1473:
53:
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a certain minimum, too many fission neutrons escape through its surface and the chain reaction is not sustained.
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metal. This reduces the number of neutrons which escape the fissile material, resulting in increased reactivity.
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1930:
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93:
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1404:
1396:
382:
209:
When a nuclear chain reaction in a mass of fissile material is self-sustaining, the mass is said to be in a
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mass is a mass which, once fission has started, will proceed at an increasing rate. In this case, known as
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1920:
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1316:"seeing" an amount of nuclei around it such that the areal density of nuclei exceeds a certain threshold.
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is the nuclear number density. Most interactions are scattering events, so that a given neutron obeys a
990:
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198:
190:
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mass is a mass of fissile material that self-sustains a fission chain reaction. In this case, known as
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144:
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surrounding the sphere, increasing the density (and collapsing the cavity, if present) to produce a
1844:
1370:
If two pieces of subcritical material are not brought together fast enough, nuclear predetonation (
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a supercritical mass will undergo a chain reaction. For example, a spherical critical mass of pure
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266:
167:
1600:
Final Report, Evaluation of nuclear criticality safety data and limits for actinides in transport
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1436:
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increases the efficiency of the reactions and also allows the reaction to become self-sustaining.
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By increasing the mass of the sphere to a critical mass, the reaction can become self-sustaining.
364:
194:
1412:) before the masses of plutonium would be in a position for a full-fledged explosion to occur.
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1858:
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1506:
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Alternatively, one may restate this more succinctly in terms of the areal density of mass, Σ:
475:
402:
further reduces the mass needed for criticality. A common material for a neutron reflector is
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156:
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and the square root of one plus the number of scattering events per fission event (call this
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1818:
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Note that not all neutrons contribute to the chain reaction. Some escape and others undergo
159:
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100:
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Original 1943 "LA-1", declassified in 1965, plus commentary and historical introduction
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denote the probability that a given neutron induces fission in a nucleus. Consider only
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1784:"Evaluation of nuclear criticality safety. data and limits for actinides in transport"
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1374:) can occur, whereby a very small explosion will blow the bulk of the material apart.
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982:. The dependence of this upon geometry, mass, and density appears through the factor
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which takes into account geometrical and other effects, criticality corresponds to
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denote the number of prompt neutrons generated in a nuclear fission. For example,
297:
become critical again) at an elevated temperature/power level or destroy itself.
1502:
1129:{\displaystyle R_{c}\simeq \ell {\sqrt {s}}\simeq {\frac {\sqrt {s}}{n\sigma }}}
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1679:, U.S. Department of Energy: Office of Scientific & Technical Information
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Reevaluated
Critical Specifications of Some Los Alamos Fast-Neutron Systems
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is only achieved once the thickness of this slab exceeds a critical value.
439:
17:
213:
state in which there is no increase or decrease in power, temperature, or
1797:
Nuclear
Weapons Frequently Asked Questions: Section 6.0 Nuclear Materials
483:
1541:
The Los Alamos Primer: The First
Lectures on How to Build an Atomic Bomb
27:
Smallest amount of fissile material needed to sustain a nuclear reaction
1390:, this was achieved by firing a piece of uranium (a 'doughnut') down a
455:
214:
175:
807:
788:
769:
750:
731:
447:
339:
197:, purity, temperature, and surroundings. The concept is important in
30:
This article is about nuclear fission reactions. For other uses, see
1648:
1233:{\displaystyle 1={\frac {f\sigma }{m{\sqrt {s}}}}\rho ^{2/3}M^{1/3}}
1365:
438:
138:
1320:
from less material than more primitive weapons programs require.
1862:
1394:
onto another piece (a 'spike'). This design is referred to as a
182:. The critical mass of a fissionable material depends upon its
1723:
Challenges in the
Pursuit of Global Nuclear Criticality Safety
36:
359:
A mass may be exactly critical at a particular temperature.
1501:(12th ed.). 300 Beach Drive NE, 1103, St. Petersburg:
1332:
of this medium is inversely proportional to the square of
1297:{\displaystyle 1={\frac {f'\sigma }{m{\sqrt {s}}}}\Sigma }
269:
causes a proportionally steady level of neutron activity.
1139:
Note again, however, that this is only a rough estimate.
1613:
Troubles tomorrow? Separated
Neptunium 237 and Americium
1714:
Dias, Hemanth; Tancock, Nigel; Clayton, Angela (2003).
1582:
220:
A numerical measure of a critical mass depends on the
1631:"Neptunium Nukes? Little-studied metal goes critical"
1255:
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1082:
1055:
1007:
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increases. The material may settle into equilibrium (
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1699:, Vol. 283, No. 5750, pp. 817–823, February 28, 1980
67:. Unsourced material may be challenged and removed.
1296:
1232:
1128:
1061:
1032:
1677:Updated Critical Mass Estimates for Plutonium-238
975:for uranium-235. Then, criticality occurs when
287:. The constant of proportionality increases as
1716:"Critical Mass Calculations for Am, Am and Am"
450:of fissile material is too small to allow the
398:Surrounding a spherical critical mass with a
8:
1745:Okuno, Hiroshi; Kawasaki, Hiromitsu (2002).
1693:Nuclear weapons and power-reactor plutonium
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1841:Dark Sun: The Making of the Hydrogen Bomb
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1751:Journal of Nuclear Science and Technology
1543:, (University of California Press, 1992)
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1617:Challenges of Fissile Material Control
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1583:The Nuclear Threat Initiative website
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361:Fission and absorption cross-sections
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1362:Criticality in nuclear weapon design
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65:adding citations to reliable sources
1423:configuration. This is known as an
1033:{\displaystyle \ell ^{-1}=n\sigma }
1291:
25:
320:Changing the point of criticality
373:due to thermal expansion alone.
178:material needed for a sustained
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1479:Geometric and material buckling
1378:Until detonation is desired, a
377:Varying the density of the mass
52:needs additional citations for
435:Critical mass of a bare sphere
186:properties (specifically, its
32:Critical mass (disambiguation)
1:
1764:10.1080/18811248.2002.9715296
454:to become self-sustaining as
1629:P. Weiss (26 October 2002).
1346:in computational physics by
1811:Science and Global Security
1142:In terms of the total mass
155:is surrounded by blocks of
1947:
1474:Nuclear criticality safety
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989:Given a total interaction
394:Use of a neutron reflector
329:Varying the amount of fuel
174:is the smallest amount of
143:A re-creation of the 1945
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1823:10.1080/08929880600620542
993:σ (typically measured in
1525:: CS1 maint: location (
1497:Hewitt, Paul G. (2015).
355:Changing the temperature
1619:(1999), isis-online.org
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145:criticality accident
61:improve this article
1655:on 15 December 2012
1348:Nicholas Metropolis
1146:, the nuclear mass
302:spontaneous fission
267:spontaneous fission
265:. A steady rate of
193:), density, shape,
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157:neutron-reflective
1854:978-0-68-480400-2
1839:(1 August 1995).
1799:February 20, 1999
1757:(10): 1072–1085.
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785:
784:
782:
779:
776:
773:
766:
765:
763:
760:
757:
754:
747:
746:
744:
741:
738:
735:
728:
727:
725:
722:
719:
716:
710:
709:
707:
704:
701:
698:
696:americium-242m
692:
691:
689:
686:
683:
680:
674:
673:
671:
668:
665:
662:
656:
655:
653:
650:
647:
644:
638:
637:
635:
632:
629:
626:
620:
619:
617:
614:
611:
608:
602:
601:
599:
596:
593:
590:
584:
583:
581:
578:
575:
572:
566:
565:
563:
560:
557:
554:
548:
547:
545:
542:
539:
536:
530:
529:
527:
524:
521:
518:
512:
511:
508:
503:
498:
493:
452:chain reaction
436:
433:
427:
424:
411:
408:
395:
392:
378:
375:
356:
353:
347:
344:
330:
327:
321:
318:
289:
284:
279:
262:
257:
244:
239:
238:subcriticality
225:
206:
203:
135:
134:
49:
47:
40:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1943:
1932:
1929:
1927:
1924:
1922:
1921:Radioactivity
1919:
1917:
1914:
1912:
1909:
1908:
1906:
1892:
1888:
1884:
1880:
1876:
1872:
1868:
1864:
1860:
1856:
1850:
1846:
1842:
1838:
1832:
1829:
1824:
1820:
1816:
1812:
1805:
1802:
1798:
1792:
1789:
1785:
1779:
1777:
1775:
1771:
1765:
1760:
1756:
1752:
1748:
1741:
1739:
1737:
1735:
1733:
1729:
1724:
1717:
1710:
1708:
1706:
1702:
1698:
1694:
1688:
1686:
1682:
1678:
1673:
1671:
1667:
1654:
1650:
1646:
1642:
1638:
1637:
1632:
1625:
1622:
1618:
1614:
1608:
1605:
1601:
1596:
1594:
1592:
1588:
1584:
1580:
1575:
1573:
1571:
1569:
1565:
1562:
1557:
1554:
1550:
1549:0-520-07576-5
1546:
1542:
1536:
1533:
1528:
1522:
1514:
1508:
1504:
1500:
1493:
1490:
1484:
1480:
1477:
1475:
1472:
1470:
1467:
1465:
1462:
1461:
1457:
1455:
1453:
1449:
1445:
1438:
1430:
1428:
1426:
1422:
1418:
1417:shaped charge
1413:
1411:
1410:predetonation
1406:
1401:
1399:
1398:
1393:
1389:
1385:
1384:critical size
1381:
1373:
1368:
1361:
1359:
1355:
1353:
1349:
1345:
1344:
1337:
1335:
1331:
1330:optical depth
1327:
1321:
1317:
1314:
1310:
1283:
1278:
1273:
1269:
1266:
1259:
1256:
1249:
1248:
1247:
1244:
1225:
1221:
1217:
1213:
1207:
1203:
1199:
1195:
1186:
1181:
1176:
1173:
1167:
1164:
1157:
1156:
1155:
1153:
1149:
1145:
1140:
1120:
1117:
1112:
1106:
1101:
1096:
1093:
1088:
1084:
1076:
1075:
1074:
1072:
1056:
1047:
1043:
1027:
1024:
1021:
1016:
1013:
1009:
1000:
996:
992:
991:cross section
987:
985:
979:
972:
967:
963:
959:
954:
952:
947:
943:
935:
932:
929:
926:
923:
920:
919:
916:
913:
910:
907:
904:
901:
900:
897:
894:
891:
888:
885:
882:
881:
878:
875:
872:
869:
866:
863:
862:
859:
856:
853:
850:
847:
844:
843:
840:
837:
834:
831:
828:
825:
824:
821:
818:
815:
812:
809:
806:
805:
802:
799:
796:
793:
790:
787:
786:
783:
780:
777:
774:
771:
768:
767:
764:
761:
758:
755:
752:
749:
748:
745:
742:
739:
736:
733:
730:
729:
726:
723:
720:
717:
715:
714:americium-243
712:
711:
708:
705:
702:
699:
697:
694:
693:
690:
687:
684:
681:
679:
678:americium-241
676:
675:
672:
669:
666:
663:
661:
660:plutonium-242
658:
657:
654:
651:
648:
645:
643:
642:plutonium-241
640:
639:
636:
633:
630:
627:
625:
624:plutonium-240
622:
621:
618:
615:
612:
609:
607:
606:plutonium-239
604:
603:
600:
597:
594:
591:
589:
588:plutonium-238
586:
585:
582:
579:
576:
573:
571:
570:neptunium-237
568:
567:
564:
561:
558:
555:
553:
552:neptunium-236
550:
549:
546:
543:
540:
537:
535:
532:
531:
528:
525:
522:
519:
517:
514:
513:
509:
504:
500:Critical mass
499:
494:
491:
490:
487:
485:
477:
473:
467:
461:
458:generated by
457:
453:
449:
445:
441:
434:
432:
426:Critical size
425:
423:
421:
417:
409:
407:
405:
401:
393:
391:
388:
384:
376:
374:
371:
366:
362:
354:
352:
345:
343:
341:
335:
328:
326:
319:
317:
315:
311:
307:
303:
298:
296:
282:
277:
275:
274:supercritical
270:
268:
260:
255:
253:
248:
242:
237:
235:
230:
223:
218:
216:
212:
204:
202:
200:
196:
192:
191:cross-section
189:
185:
181:
177:
173:
172:critical mass
169:
161:
158:
154:
153:plutonium pit
150:
146:
141:
131:
128:
120:
109:
106:
102:
99:
95:
92:
88:
85:
81:
78: –
77:
73:
72:Find sources:
66:
62:
56:
55:
50:This article
48:
44:
39:
38:
33:
19:
1889:– via
1840:
1831:
1814:
1810:
1804:
1791:
1754:
1750:
1722:
1696:
1657:. Retrieved
1653:the original
1640:
1636:Science News
1634:
1624:
1607:
1556:
1540:
1535:
1498:
1492:
1440:
1414:
1402:
1395:
1377:
1356:
1341:
1338:
1333:
1325:
1322:
1318:
1312:
1308:
1306:
1245:
1242:
1151:
1147:
1143:
1141:
1138:
1070:
1041:
988:
983:
977:
970:
965:
957:
955:
948:
944:
940:
481:
471:
465:
443:
429:
413:
397:
380:
358:
349:
336:
332:
323:
299:
294:
273:
271:
251:
249:
233:
231:
219:
217:population.
210:
208:
171:
165:
123:
114:
104:
97:
90:
83:
71:
59:Please help
54:verification
51:
1643:(17): 259.
1611:Chapter 5,
1046:random walk
922:einsteinium
903:californium
884:californium
865:californium
538:703,800,000
534:uranium-235
516:uranium-233
387:uranium-235
314:cosmic rays
310:uranium-238
306:uranium-235
256:criticality
234:subcritical
18:Subcritical
1905:Categories
1887:Q105755363
1659:7 November
1485:References
1448:reactivity
1392:gun barrel
1388:Little Boy
964:, and let
813:15,600,000
595:9.04–10.07
195:enrichment
149:Demon core
147:using the
87:newspapers
1871:456652278
1521:cite book
1292:Σ
1274:σ
1196:ρ
1177:σ
1121:σ
1107:≃
1097:ℓ
1094:≃
1057:ℓ
1028:σ
1014:−
1010:ℓ
857:16.1-16.6
846:berkelium
838:11.8-12.2
827:berkelium
816:6.94–7.06
778:9.41–12.3
574:2,144,000
495:Half-life
484:actinides
404:beryllium
1883:Wikidata
1879:7720934M
1863:95011070
1817:: 1–24.
1458:See also
1405:Thin Man
1270:′
505:Diameter
460:fissions
456:neutrons
334:again).
252:critical
211:critical
117:May 2012
1786:, p. 16
1503:Pearson
997:), the
797:39–70.1
762:12.4–16
759:13.5–30
740:7.34–10
721:180–280
664:375,000
598:9.5–9.9
556:154,000
520:159,200
492:Nuclide
472:Bottom:
466:Middle:
338:1
300:Due to
215:neutron
184:nuclear
176:fissile
101:scholar
1885:
1877:
1869:
1861:
1851:
1697:Nature
1547:
1509:
1372:fizzle
1040:where
808:curium
789:curium
770:curium
751:curium
732:curium
667:75–100
610:24,110
448:sphere
416:tamper
285:> 1
245:< 1
103:
96:
89:
82:
74:
1719:(PDF)
995:barns
973:≈ 2.5
927:0.755
800:18–21
781:11–12
743:10–11
724:30–35
706:11–13
688:20–23
685:55–77
682:432.2
670:19–21
108:JSTOR
94:books
1911:Mass
1867:OCLC
1859:LCCN
1849:ISBN
1661:2013
1545:ISBN
1527:link
1507:ISBN
1350:and
956:Let
930:9.89
924:-254
911:2.73
905:-252
892:5.46
886:-251
867:-249
848:-249
835:75.7
832:1380
829:-247
810:-247
794:4760
791:-246
775:8500
772:-245
756:18.1
753:-244
737:29.1
734:-243
718:7370
703:9–14
652:10.5
646:14.3
628:6561
592:87.7
510:Ref
507:(cm)
502:(kg)
444:Top:
295:i.e.
170:, a
151:: a
80:news
1819:doi
1759:doi
1645:doi
1641:162
980:= 1
978:ν·q
933:7.1
914:6.9
908:2.6
895:8.5
889:900
870:351
854:192
851:0.9
819:9.9
700:141
616:9.9
562:8.7
497:(y)
370:LWR
368:in
263:= 1
166:In
63:by
1907::
1881:.
1875:OL
1873:.
1865:.
1857:.
1847:.
1843:.
1815:14
1813:.
1773:^
1755:39
1753:.
1749:.
1731:^
1721:.
1704:^
1695:,
1684:^
1669:^
1639:.
1633:.
1615:,
1590:^
1581:,
1567:^
1523:}}
1519:{{
1454:.
1427:.
1400:.
1313:f'
986:.
953:.
649:12
634:15
631:40
613:10
580:18
577:60
544:17
541:52
526:11
523:15
446:A
422:.
316:.
280:,
272:A
258:,
250:A
247:.
240:,
232:A
201:.
1893:.
1825:.
1821::
1767:.
1761::
1663:.
1647::
1585:.
1529:)
1515:.
1408:(
1334:L
1326:L
1309:f
1284:s
1279:m
1267:f
1260:=
1257:1
1226:3
1222:/
1218:1
1214:M
1208:3
1204:/
1200:2
1187:s
1182:m
1174:f
1168:=
1165:1
1152:f
1148:m
1144:M
1118:n
1113:s
1102:s
1089:c
1085:R
1071:s
1042:n
1025:n
1022:=
1017:1
984:q
971:ν
966:ν
958:q
876:9
873:6
559:7
340:K
290:k
283:k
261:k
243:k
226:k
130:)
124:(
119:)
115:(
105:·
98:·
91:·
84:·
57:.
34:.
20:)
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