Heavy nuclei

Am undergo fission with thermal neutrons of these isotopes and Pu are the most important as they are most readily obtainable. Other heavy nuclei require fast neutrons to induce fission such neutrons are much more difficult to control into a self-sustaining chain-reaction. 

The Franck-Condon principle says that the intensities of die various vibrational bands of an electronic transition are proportional to these Franck-Condon factors. (Of course, the frequency factor must be included for accurate treatments.) The idea was first derived qualitatively by Franck through the picture that the rearrangement of the light electrons in die electronic transition would occur quickly relative to the period of motion of the heavy nuclei, so die position and iiioiiientiim of the nuclei would not change much during the transition [9]. The quaiitum mechanical picture was given shortly afterwards by Condon, more or less as outlined above [10]. 

Nuclei have many times more mass than electrons. Diiringa very small period of tim e wh en th e mo vein en t of heavy nuclei is n egli-gible, electrons are moving so fast that their distribution is smooth. Th is leads to the approximation that the elec iron distri-biition IS dependent only on the fixed positions of nuclei and not on their velocities. This approximaiion allows two simplifications... 

As NRA is sensitive only to the nuclei present in the sample, it does not provide information on chemical bonding or microscopic structure. Hence, it is often used in conjunction with other techniques that do provide such information, such as ESCA, optical absorption. Auger, or electron microscopy. As NRA is used to detect mainly light nuclei, it complements another accelerator-based ion-beam technique, Rutherford backscattering (RBS), which is more sensitive to heavy nuclei than to light nuclei. 

Proton capture processes by heavy nuclei have already been briefly mentioned in several of the preceding sections. The (p,y) reaction can also be invoked to explain the presence of a number of proton-rich isotopes of lower abundance than those of nearby normal and neutron-rich isotopes (Fig. 1.5). Such isotopes would also result from expulsion of a neutron by a y-ray, i.e. (y,n). Such processes may again be associated with supernovae activity on a very short time scale. With the exceptions of " ln and " Sn, all of the 36 isotopes thought to be produced in this way have even atomic mass numbers the lightest is Se... 

Because the sequence of neutron captures inevitably leads to looFrn which has a fission half-life of only a few seconds, the remaining three actinides, loiMd, 102N0 and losLr, can only be prepared by bombardment of heavy nuclei with the light atoms jHe to foNe. This raises the mass number in multiple units and allows the f Fm barrier to be avoided even so, yields are minute and are measured in terms of the number of individual atoms produced. 

O. Hahn (Berlin-Dahlem) discovery of the fission of heavy nuclei. 

The energy of a Is-electron in a hydrogen-like system (one nucleus and one electron) is —Z /2, and classically this is equal to minus the kinetic energy, 1/2 mv, due to the virial theorem E — —T = 1/2 V). In atomic units the classical velocity of a Is-electron is thus Z m= 1). The speed of light in these units is 137.036, and it is clear that relativistic effects cannot be neglected for the core electrons in heavy nuclei. For nuclei with large Z, the Is-electrons are relativistic and thus heavier, which has the effect that the 1 s-orbital shrinks in size, by the same factor by which the mass increases (eq. (8.2)). 

Wlieii very heavy nuclei, such as those of uranium and plutonium, are split into lighter nuclei having less total mass than the very heavy nuclei, energy is released. The process is called nuclear fission. In either nuclear fission or nuclear fusion, much of the convened rest energy emerges as kinetic energy, heat, and light. 

Some heavy nuclei will fission spontaneously. Others can be induced to fission through interaction with a neutron. In both spontaneous nuclear fission and induced nuclear fission the pool of neutrons and protons is conseiwed. For example, the nucleus "" Cf (Californium) fissions spontaneously. The 98 protons and 154 neutrons in the nucleus of Cf are reconfigured into other nuclei. Usually a few neu-... 

Notice that the result of K-electron capture is the same as positron emission mass number remains unchanged, whereas atomic number decreases by one unit Electron capture is more common with heavy nuclei, presumably because the n = 1 level is closer to the nucleus. 

Asymmetric fission is observed in the spontaneous decomposition of sCf1Ji(15M and other very heavy nuclei. We may ask when the transition to symmetric fission would begin. The next elongated core, in the series represented in Figs. 11 and 12, would contain 31 spherons, and the transition to it should occur for 28 spherons in the core of the undistorted nucleus, that is, at N = 163 (calculated with use of Eq. 1). We conclude that lftf,Lw,(i,20 and adjacent nuclei should show both asymmetric and symmetric fission. 

NRA is a powerful method of obtaining concentration versus depth profiles of labelled polymer chains in films up to several microns thick with a spatial resolution of down to a few nanometres. This involves the detection of gamma rays produced by irradiation by energetic ions to induce a resonant nuclear reaction at various depths in the sample. In order to avoid permanent radioactivity in the specimen, the energy of the projectile is maintained at a relatively low value. Due to the large coulomb barrier around heavy nuclei, only light nuclei may be easily identified (atomic mass < 30). 

Alpha (a.) decay. As we shall see later, the alpha particle, which is a helium nucleus, is a stable particle. For some unstable heavy nuclei, the emission of this particle occurs. Because the a particle contains a magic number of both protons and neutrons (2), there is a tendency for this particular combination of particles to be the one emitted rather than some other combination such as s3Li. In alpha decay, the mass number decreases by 4 units, the number of protons decreases by 2, and the number of neutrons decreases by 2. An example of alpha decay is the following ... 

Helium has long been related to nuclear chemistry because of the formation of alpha particles (a = 4He2+) during the decay of heavy nuclei, an example of which is... 

Stars of mass greater than 1.4 solar masses have thermonuclear reactions that generate heavier elements (see Table 4.3) and ultimately stars of approximately 20 solar masses are capable of generating the most stable nucleus by fusion processes, Fe. The formation of Fe terminates all fusion processes within the star. Heavier elements must be formed in other processes, usually by neutron capture. The ejection of neutrons during a supernova allows neutron capture events to increase the number of neutrons in an atomic nucleus. Two variations on this process result in the production of all elements above Fe. A summary of nucleosynthesis processes is summarised in Table 4.4. Slow neutron capture - the s-process - occurs during the collapse of the Fe core of heavy stars and produces some higher mass elements, however fast or rapid neutron capture - the r-process - occurs during the supernova event and is responsible for the production of the majority of heavy nuclei. 

The spectrum of the Sun contains the absorption lines associated with the atomic spectrum of heavier elements such as Fe (Figure 4.2), which indicates that the Sun is a second-generation star formed from a stellar nebula containing many heavy nuclei. The atomic spectra of heavier atoms are more complex. The simple expression for the H atom spectrum needs to be modified to include a quantum defect but this is beyond the scope of this book. Atomic spectra are visible for all other elements in the same way as for H, including transitions in ionised species such as Ca2+ and Fe2+ (Figure 4.2). 

Alpha particles, fission fragments, heavy nuclei 20... 

The r-process path is terminated by (neutron-induced or yd-delayed) fission near A max = 270, feeding matter back into the process at around Amax/2, followed by recycling as long as the neutron supply lasts, assuming sufficient seed nuclei to start the process off. The number of heavy nuclei is thus doubled at each cycle, which could take place in a period of a few seconds, yd-delayed fission also occurs after freeze-out, when the yd-decay leaves nuclei with A > 256 or so with an excessive positive charge (see Eq. 2.90). 

Fig. 8.35. According to their calculations, the efficiency of the s-process increases sharply as the metallicity decreases to about 0.1 solar, but thereafter decreases rapidly at still lower metallicities because of shortage of iron seeds and a relatively high amount of neutron poisons such as C, N and O. Thus below [Fe/H] = — 1 or so, heavy nuclei like Ba are predominantly due to the r-process and are assumed to track europium.

E in GeV), giving a flat spectrum for E <similar spectra in energy per nucleon. 

Heavy nuclei discovered in primary cosmic rays. 

Subsequently Furnstahl [20] in a more extensive study pointed out that within the framework of mean field models (both non-relativistic Skyrme as well as relativistic models) there exists an almost linear empirical correlation between theoretical predictions for both 04 and its density dependence, po, and the neutron skin, All lln — Rp, in heavy nuclei. This is illustrated for 208Pb in Fig. 5 (from ref.[20] a similar correlation is found between All and po). Note that whereas the Skyrme results cover a wide range of All values the RMF predictions in general lead to AR > 0.20 fm. 

The interpretation of the nuclear matter results in part depends on the question whether there is a surface contribution to the SE in finite nuclei. In ref. [24] it was found that for heavy nuclei the latter is of minor importance, which has also been confirmed in ref. [20],... 

Hatton, J. V., Schneider, W. G., Siebrand, W. Nuclear Spin-Spin Coupling Involving Heavy Nuclei. The Coupling between Hg199 and H1 Nuclei in CH3HgX and CH3CH2HgX Compounds. J. Chem. Phys. 39, 1330 (1963). 

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