Emission of nucleons

The various decay modes are listed in Table 5.1. Unstable, radioactive nuclei may be transformed by emission of nucleons (a decay and, very rarely, emission of protons or neutrons) or by emission of electrons or positrons and decay, respectively). Alternatively to the emission of a positron, the unstable nucleus may capture an electron of the electron shell of the atom (symbol e). 

In most cases the emission of nucleons, electrons or positrons leads to an excited state of the new nucleus, which gives off its excitation energy in the form of one or several photons (y rays). This de-excitation occurs most frequently within about 10 s after the preceding or P decay, but in some cases the transition to the ground state is forbidden resulting in a metastable isomeric state that decays independently of the way it was formed. 

Tho critical baryon density corresponds to pmax = 0. This leads to the ( (juations Uv + Us = G or Uv — Us — 2Mg = 0 or both. The first condition Uv + Us = 0 is fulfilled earlier than the second one. When the first condition is reached the nucleus becomes unbound, i.e., unstable with respect to emission of nucleons. So it is impossible to compress the nucleus more than the critical density in a self-consistent manner such densities should occur only as shortlived intermediate stages in a heavy-ion collision. Wc performed a constraint calculation with the monopole moment [23, 24, 25], which produced self-consistent solutions up to w 3po for the case of Pb. A chart for the critical densities of nuclear matter with different parameter sets is given in ref. [26]. We found that the critical densities are much larger for nuclear matter c ompared to finite nuclei in all available parameter sets. The TMl parameter set was chosen for our calculations, because it gives a larger critical density of about 3po ... 

In most cases the emission of nucleons and electrons leads to an excited state of the resulting new nucleus. The excitation energy is given off in the form of one or several gamma-ray photons. In most cases this de-excitation takes place within an extremely short period of time (less than 10 s) but in some cases this transition is delayed. Such a type is called an isomeric state of a nuclide. 

While the forward and backward rates would be equal and thus cancel, giving no net rate in an imagined equilibrium, in the kinetic process the net-rate (unconfined to a box and thus with no backward rate) is equal to the outgoing one-way rate. Thus the rate of emission of nucleons or clusters in any specified state from an initial parent level of excitation energy and spin / is the result of a sum over the product intrinsic state-to-state rates and final-state level densities, where the sum is over (a) the possible f-values (iimer sum Eq. (3.76)) and (b) the so called channel spin S = j + s, where j and s are the intrinsic spin of the residual and ejectile spin (outer sum). With consideration of the possible spin combinations, the HF equation for the emission rate of a particle of type t energy and separation energy in terms of the inverse cross section (Tf i and the density of levels of the parent and the daughterf is. 

Cluster emission is an exotic decay that has some commonalities with a-decay. In a-decay, two protons and two neutrons that are moving in separate orbits within the nucleus come together and leak out of the nucleus as a single particle. Cluster emission occurs when other groups of nucleons form a single particle and leak out. Several of the observed decays are shown in Table 10. The emitted clusters include C, Ne, Mg, and Si. The... 

Nuclear electromagnetic decay occurs in two ways, y decay and internal conversion (IC). In y-ray decay a nucleus in an excited state decays by the emission of a photon. In internal conversion the same excited nucleus transfers its energy radia-tionlessly to an orbital electron that is ejected from the atom. In both types of decay, only the excitation energy of the nucleus is reduced with no change in the number of any of the nucleons. 

We can continue our survey of the lightest nuclei with A = 3. Only the combinations of two protons and one neutron, 3He, and one proton with two neutrons, 3H, are bound, while the combinations of three protons, 3Li, and three neutrons are unbound. Again we see a balance between the numbers of neutrons and protons with the extreme cases being unbound. The nuclear spins of both bound A = 3 nuclei are j indicative of a pair of nucleons plus one unpaired nucleon three unpaired nucleons would have had a total spin of. In the A = 3 system the more neutron-rich nucleus, tritium, 3H, is very slightly less stable than 3He and, it decays by (3 emission with a 12.3-y half-life. 

As we have seen in the overview of the nuclear mass surface in Chapter 2, the a particle, or 4He nucleus, is an especially strongly bound particle. This combined with the fact that the binding energy per nucleon has a maximum value near A fs 56 and systematically decreases for heavier nuclei creates the situation that nuclei with A > 150 have positive Qa values for the emission of a particles. This behavior can be seen in Figure 7.1. 

In the course of the fusion of the projectile and target nuclei, it is possible that one of the partners will emit a single nucleon or a nucleonic cluster prior to the formation of a completely fused system. Such processes are referred to as preequilibrium emission (in the case of nucleon emission) or incomplete fusion (in the case of cluster emission). As the projectile energy increases, these emission processes become more important and they generally dominate over fusion at projectile energies... 

The nucleons inside a radioactive nucleus contained in a molecule interact with the electron-neutrino field and undergo the / transition—a transformation of a neutron into a proton accompanied by the emission of a / electron and a neutrino.5 The weak interaction does not affect the electron shell and the other nuclei of the molecule. For them the / decay is an instantaneous change (a jump) in the charge of the radioactive nucleus by unity. Besides this, the nucleus obtains a recoil momentum due to the emission... 

Cold fusion by use of target nuclei with closed nucleon shells is most promising, because of the low excitation energies (emission of only 1 or 2 neutrons). However, the stabilizing effect of closed shells fades at excitation energies of the order ofSOMeV. 

Beta Decay. For some heavy nuclides and for almost all those with atomic numbers below 60, stability is achieved by a rearrangement of the nucleus in which the total number of nucleons is unchanged. In terms of the neutron-proton model of the nucleus, this rearrangement is the conversion of a neutron to a proton, or vice versa. During such conversions, the nucleus emits either a negative electron or its positive equivalent, a positron. The emission of the negative electron, named the beta ([3-) particle, is what is usually meant by the term [3-decay. 

We saw in section 1.1.1, how atoms with identical atom number but with different amount of neutrons are called isotopes. Likewise did we see that the combined number of protons and neutrons are called nucleons and that radioactive species decay under emission of different types of radiation. The rate of such decay is in principle similar to the rate of reaction for the transition of reactants to products in a chemical reaction. We imagine that for a specific time r = 0 we have an amount of specie with No radioactive nuclei. It has been found that all nuclei have a specific probability of decaying within the next second. If this probability is e.g. 1/100 pr. second this means that on an average 1% of all nuclei decay each second. The number of radioactive nuclei is thereby a decreasing function with time and may formally be written as N(t). The rate for the average number of decays pr. time is thereby defined analogously to equation (3-1) as ... 

The nucleus would thus seem to consist of independrat substructures of neutrons and protons, with each type of nucleon paired off as far as possible. Further, the nucleons obviously grouped together in the magic numbers. From the decay of radioactive nuclei we know that the total decay energy (Q-value) of any particular nuclide has a definite value. Moreover, y-emission from any particular nucleus involves discrete, definite values. These facts resemble the quantized emission of electromagnetic radiation (X-ray, UV, visible light. 

Radioactive cobalt-60 is used to study defects in vitamin B12 absorption because cobalt is the metallic atom at the center of the vitamin molecule. The nuclear synthesis of this cobalt isotope involves a three-step process. The overall reaction is iron-58 reacting with two neutrons to produce cobalt-60 along with the emission of another particle. What particle is emitted in this nuclear synthesis What is the binding energy in J per nucleon for the cobalt-60 nucleus (atomic masses Co = 59.9338 amu ... 

The concept of isotopes was introduced in Chap. 2, and it was used to describe a family of nuclei of the same element which have the same atomic number (number of protons), but different numbers of neutrons. The atomic masses used in chemical calculations are averages of the atomic masses of an element consisting of a number of isotopes with varying abundances in nature. In discussing nuclear processes, we refer to a particular isotope because we are interested in the precise number of nucleons (the name for either the protons or neutrons in the nucleus) and any changes in that number as a result of particulate emissions. We use the name nuclide for referring to particular isotopes of different elements. 

Other emissions of interest are P-rays, positrons, and y-rays. /3-particles have been shown to be electrons, and in nuclear reactions are given the symbol e. The superscript denotes the infinitesimal mass of an electron relative to a nucleon, and the subscript refers to the electron s charge. 

If one omits the yields of radionuclides which may arise from the emission of one or two nucleons, then the contour diagrams become independent of the type of bombarding particle. 

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