Barriers, coulombic

For quantitative evaluation of ERDA energy spectra considerable deviations of recoil cross-sections from the Rutherford cross-section (Eq. 3.51) must be taken into account. Light projectiles with high energy can penetrate the Coulomb barrier of the recoil atom the nuclear interaction generally leads to a cross-section that is larger than ctr, see Eq. (3.51). For example, the H recoil cross-section for MeV He projec-... 

The evolution of a. star after it leaves the red-giant phase depends to some extent on its mass. If it is not more than about 1.4 M it may contract appreciably again and then enter an oscillatory phase of its life before becoming a white dwarf (p. 7). When core contraction following helium and carbon depletion raises the temperature above I0 K the y-ray.s in the stellar assembly become sufficiently energetic to promote the (endothermic) reaction Ne(y,a) 0. The a-paiticle released can penetrate the coulomb barrier of other neon nuclei to form " Mg in a strongly exothermic reaction ... 

The small and weakly time-dependent CPG that persisLs at longer delays can be explained by the slower diffusion of excitons approaching the localization edge [15]. An alternative and intriguing explanation is, however, field-induced on-chain dissociation, a process that does not depend on the local environment but on the nature of the intrachain state. The one-dimensional Wannier exciton model describes the excited state [44]. Dissociation occurs because the electric field reduces the Coulomb barrier, thus enhancing the escape probability. This picture is interesting, but so far we do not have any clear proof of its validity. 

The energy of the y-rays is indicative of the isotope present, and the intensity of the y-rays is a measure of the concentration of the isotope in the sample. The limitation of this method is that, in order to have a nuclear reaction, the repulsive Coulomb barrier has to be overcome. For incident particles of energy up to 3 MeV, the only accessible elements are the light elements with Z< 15 the cross-sections of the remaining elements become rapidly negligible. 

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). 

Such cross sections must be measured at energies typical of the different astrophysical scenarios, i.e. at much lower energies with respect to the Coulomb barrier of the interacting particles. This leads to big difficulties in the experimental measurements since the considered cross sections are very low (of the order of picobarn). In order to determine reaction rates within the astrophysical energy range extrapolations from higher energies are usually performed [2]. 

There is no Coulomb barrier for neutrons, but free neutrons are unstable so that they have to be generated in situ, which again demands high temperatures. 

Fig. 2.7. Coulomb barrier penetration by a charged particle, a is the range of the nuclear force and b the classical turning point.

The matrix elements in angle brackets contain nuclear factors and (in the case of charged particles) the Coulomb barrier penetration probabilities or Gamow factors, originally calculated in the theory of a-decay, which can be roughly estimated as follows (Fig. 2.7). 

The hrst term in E is the K.E. of the centre of mass, which conserves its momentum and hence its velocity (almost, as the change in mass from Q is relatively very small), and the second term is the K.E. in the CM system which is available for penetrating the Coulomb barrier. 

The hydrogen Is orbital encloses a positively charged nucleus that repels other nuclei by a Coulombic R 1 potential. However, such a Coulombic barrier between nuclei is much weaker than the steric repulsion between electronic cores, which varies exponentially with distance. 

I. Any bound state, in which (he sum of the kinetic energy and the potential energy, the latter reckoned relative to zero at infinity, is less than zero. The existence of such states is essential for the stability of any system that is not surrounded by a region nf positive potential energy, such as tile Coulomb barrier. 

Fig. 9. Schematic representation of barriers for electron tunneling, (a) A Coulomb barrier (b) a rectangular barrier.

Figure 7.5 A (reasonably accurate) one-dimensional potential energy diagram for 238U indicating the energy and calculated distances for a decay into 234Th. Fermi energy Rs30 MeV, Coulomb barrier -28 MeV at 9.3 fm, Qa 4.2 MeV, distance of closest approach 62 fm. (Figure also appears in color figure section.)...

One can evaluate the effect of this centrifugal potential upon a-decay half-lives by simply adding this energy to the Coulomb barrier height. If we define... 

We should also note that the double-shell closures at Z = 82 and N = 126 lead to especially large positive Q values, as already shown in Figure 7.2. Thus, the emission of other heavy nuclei, particularly 12C, has been predicted or at least anticipated for a long time. Notice also that 12C is an even-even nucleus and. v-wave emission without a centrifugal barrier is possible. However, the Coulomb barrier will be significantly larger for higher Z nuclei than that for a particles. 

Calculate the heights of the centrifugal barrier for the emission of a particles carrying away two units of angular momentum in the decay of 244Cm. Assume R0 = 1 x 10 13 cm. What fraction of the Coulomb barrier height does this represent ... 

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