The particular nucleus is relatively highly unstable and internal resonances are such that two mass distributions form such that the coulomb force/pressure overcomes the nuclear force binding them.
So the more unstable the nucleas, higher the chances that it will sustain fission?(I said fissile not fissionable) And what do you mean by internal resonances?
It's a particular type of instability. Some unstable nuclei decay by beta emission or alpha emission, while others decay by positron emission. Fissile nuclei include those of U-233, U-235, Pu-239, Pu-241, Am-242, Cm-243 and other heavier nuclei (these generally tend to be odd A isotopes, and Am-242 is an exception). These have the ability to fission with low energy neutrons, but there is also the probability that they will absorb a neutron and not fission. Example - http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/u235chn.html#c1 Whatever happens, when fissile nuclei absorb a low energy neutron, it sets ups oscillations within the nucleus that causes two charge distributions to form such that they repel one another. These become the fission product nuclei. Two or three neutrons are released.
I think Astronuc's answer involving resonances is about something more specialized, which is the question of why some substances are able to sustain a nuclear chain reaction. The OP's question was more general: why are some materials fissile? In answer to the more general question, this is mainly a classical physics thing. The liquid drop model of the nucleus says that the nucleus has a certain energy as a function of deformation. There are various ways of parametrizing nuclear deformation, but say we define some deformation parameter x. x=0 is a sphere, x=.4 or something might be an American football. For large values of x (say ~1 for most parametrizations) you get shapes that want to form a neck -- in the sense that of all shapes with a specific amount of elongation, the one that minimizes the energy is one with a neck. Once the neck forms, you're basically on your way to fission. The main terms in the liquid drop model that determine the shape of the curve of E versus x are the surface energy and the Coulomb energy. The latter scales with Z^2, so it's much more important for heavy nuclei. For nuclei with Z greater than about 120 or something, there is no stable minimum at all, and that's why we don't ever expect to be able to form such nuclei, even artificially. The main quantum-mechanical ingredient you need is that there is a barrier in the potential energy curve, and the nucleus has to tunnel through this barrier in order to fission. This is why you get spontaneous fission. If you look at heavy nuclei in general, some tend to decay by spontaneous fission, some by alpha decay, and some do both, with some branching ratio. This difference is mainly quantum-mechanical in origin. The N and Z of the parent nucleus influence the detailed shape of the E(x) curve. In addition, the N's and Z's of the daughter nuclei determine their binding energies, and therefore influence the amount of phase space available for the decay.
Actually, no. I was trying to explain why some isotopes are fissile (readily fission), while others are fissionable or fertile. In fact, in the case of U-235, roughly 5/6 (85%) absorptions of thermal neutrons cause fission, while ~1 in 6 (16%) result in the formation of U-236, which spontaneously emits a gamma-ray. Similary, Pu-239 can either fission, or form Pu-240, which spontaneously emits a gamma-ray. Fissionable and fertile nuclides can fission, but require higher energy neutrons. U-235, U-236 and U-238 all undergo alpha decay as well as spontaneous fission, but only U-235 is fissile. The SF rates are 7.0E-9 %, 9.4E-8 % and 5.5E-5 % of decays, respectively. Ref: http://www.nndc.bnl.gov/chart/reCenter.jsp?z=92&n=143 (hit zoom 1 to see detail) When I used the term resonance, I was meaning nuclear oscillations, which are not to be confused with neutron (absorption) resonances. The emission of extra neutrons ( 2 or 3) is what makes possible a fission chain reaction, provided that at least one of the two or three neutrons survives to cause a new fission.
I wrote: Are you talking about (1) spontaneous fission, or (2) neutron-induced fission? I read the initial post as being a question about #1, although it's possible that #2 was intended. In order to get #2, you have to have #1 first, although the branching ratio, as you point out, may be very small. When you refer to "nuclear oscillations," are you talking about shape oscillations? If so, then I'm pretty sure resonances are not at all relevant to spontaneous fission. If you're talking about resonances of shape oscillations, maybe you could clarify what you're referring to; are you talking about a potential with two different minima, as in the fission isomers? When 235U absorbs a neutron, the compound nucleus is above the fission barrier ( http://www.nature.com/nature/journal/v409/n6822/full/409785a0.html ), so I don't see how a resonance of shape oscillations could be relevant there. Figures 4 and 5 of the Nature paper give some examples of potential energy landscapes.
Yes neutron induced fission was intended. I'm sorry I didn't make myself clear. We haven't been taught about spontaneous fission yet.
The term fissile infers that an isotope is readily fissioned with low energy (thermal) neutrons - neutron induced fission. Fissile also means that a particular nucleus forms an excited nucleus that is closer to the threshold for fission as opposed to just decaying by gamma emission. I was referring to oscillations in shape, or some distortion that allows two fission products form as opposed to gamma emission. When U-235 absorbs a neutron, the resulting U-236* has an ~85% change of fissioning, and a ~15% of gamma emission. Pu 239, 240 and 241 have spontaneous fission rates of 3E-10%, 5.7E-6 %, and 2.5E-3%, respectively, but 240 is not fissile, whereas 239 and 241 are fissile. Evenso, there is a probability that Pu-239 will form Pu-240, which decays by gamma emission rather than fission following thermal neutron capture. http://www.nndc.bnl.gov/chart/reCenter.jsp?z=94&n=146 (use zoom 1) Fissile, fissionable and fertile isotopes do have potential for spontaneous fission, but the probability varies over orders of magnitude.
An explanation is here -MIT NE 22-05 But I'm not satsified with that discussion. I'd like to find the papers on nuclear structure, particularly U-235 and U-236. Once U-235 absorbs a thermal neutron and forms an excited nucleus, it may fission (asymmetrically) or it may decay by gamma emission. The fission or gamma emission is determined by the nuclear shape - going from an oblate spheroid (by the models in the Nature paper). The gamma emission allows the nucleus to fall into a more stable shape or energy state - whereas if the nucleus assumes a more elongated necked shape - it will fission. Fission of U-235 and Pu-239 are almost always asymmetric, but there is a small probability of symmetric fissioning - one the order of 0.01% of fissions. Ref: S. Katcoff, "Fission-Product Yields from Neutron Induced Fission," Nucleonics 18, 11, 201 (Nov 1960). Both U-235 and U-236 can also experience spontaneous fission, which are very low probability compared to alpha decay. See also a past discussion why is U235 used for chain reaction but not U238 https://www.physicsforums.com/showthread.php?t=115453
I wrote: The word "resonance" never occurs in that lecture. As far as I can tell at this point, you're just mistaken about resonances involving shape oscillations having anything to do with the general phenomena of spontaneous and neutron-induced fission. There may be such an effect in certain special cases, as in the isotopes that have a pronounced second minimum in the potential (isotopes that display fission isomers). As I pointed out in post # 8, the compound nucleus in 235U+n is always above the height of the barrier, so I don't see how you can get any resonance effect there. My field is low-energy nuclear structure, not nuclear reactions or nuclear engineering, so it's possible that I'm wrong about this. If so, then I would be interested to learn more. But so far it seems to me that you are incorrect on this point.
I'm using the term 'resonance' to refer to 'oscillations' with respect to "The nucleus, like a drop of liquid, oscillates, and forms an ellipsoid. If the oscillations grow, the ellipsoid splits in two. This splitting in two is the fission process." This is what I learned 30 years ago. I believe it was an effort to explain U-235 + n => U236* => fission or U236 + γ (no fission). Ostensibly the shape U236 after γ-emission is quite different than U236* which fissions. What does one consider a 'resonance' or 'resonance effect'?
I see. I think the standard way to refer to the phenomenon you're talking about would be "zero-point motion," not "resonance." You have a deformation parameter, call it x. To some approximation, you can treat x as a quantum-mechanical coordinate. (This is only an approximation, because the inner product <x|x'> is not exactly a delta function of x-x'.) Then x has a conjugate momentum, and you can apply the Heisenberg uncertainty principle. For these reasons, there have to be fluctuations of the nuclear shape about its equilibrium value. Spontaneous fission occurs because the extreme low-probability tails of these shape fluctuations reach past scission. I think resonance, in a reaction of this kind, would refer to a case where the incoming projectile (a neutron, say) has just the right energy to excite some specific, discrete state in the compound nucleus. I'm not clear on what you mean by this. The 236U* has an excitation energy that's higher than the barrier to fission. That means that it can't be modeled in terms of fluctuations about some equilibrium shape, and I don't think it makes any sense to talk about its shape. Re the shape of the 236U after gamma emission, are you thinking of a superdeformed fission isomer? I don't know whether 236U has a superdeformed second minimum or not. Some heavy nuclei do; they were the first known examples of superdeformation.