Decay probabilities nucleus

As an example we treat the decay process of IV.6 in terms of the master equation. The decay probability y per unit time is a property of the radioactive nucleus or the excited atom, and can, in principle, be computed by solving the Schrodinger equation for that system. To find the long-time evolution of a collection of emitters write P(n, t) for the probability that there are n surviving emitters at time t. The transition probability for a... 

The half-life is the time required for the number of nuclei present to decrease by a factor of 2. The number of decays that occur in a radioactive sample in a given amount of time is called the activity A of the sample. The activity is equal to the number of nuclei present, N, multiplied by the probability of decay per nucleus, A, that is, A = N. Therefore, the activity will also decrease exponentially with time,... 

The decay constant A. represents the average probability per nucleus of decay occurring per unit time. Therefore, we are taking the probability of decay per nucleus, and multiplying it by the number of nuclei present so as to get the rate of particle emission. The units of rate are (disintegration of nuclei/time) making the units of the decay constant (1/time), that is, probability/time of decay. 

In general case, the spontaneous decay probability at presence of material bodies always differs from the corresponding probability for the free space. Of much importance is the circumstance that decay parameters in this case greatly depend on the radiation shift of resonant level position determined by the processes of nucleus interaction with all the modes of electromagnetic field. It is shown that resonant screen effect in all cases occurs to be more essential than the effect of a nonresonant one. The most influence on the nucleus spontaneous decay process will be achieved in case when the modes of electromagnetic field in the ground (the lowest by energy) state, which interact with the nucleus, occur to be mutually synchronized. Such synchronization process may be due to the amplification of mutual mode interaction processes, for example, at the expense of the processes of controlled dissipation on the resonant screen surface at excitation of the intensive sound oscillations with the frequency >p To in it. 

The measures taken to improve the reliability of measurements in the frequency-response regime allow to connect with a high degree of certainty the experimental results with theoretically predicted controlled charge of nucleus gamma decay probability and lifetime and not with false factors. 

The Co nucleus decays with a half-life of 5.27 years by /5 emission to the levels in Ni. These levels then deexcite to the ground state of Ni by the emission of one or more y-rays. The spins and parities of these levels are known from a variety of measurements and require that the two strong y-rays of 1173 and 1332 keV both have E2 character, although the 1173 y could contain some admixture of M3. However, from the theoretical lifetime shown ia Table 7, the E2 contribution is expected to have a much shorter half-life and therefore also to dominate ia this decay. Although the emission probabilities of the strong 1173- and 1332-keV y-rays are so nearly equal that the difference cannot be determined by a direct measurement, from measurements of other parameters of the decay it can be determined that the 1332 is the stronger. Specifically, measurements of the continuous electron spectmm from the j3 -decay have shown that there is a branch of 0.12% to the 1332-keV level. When this, the weak y-rays, the internal conversion, and the internal-pair formation are all taken iato account, the relative emission probabilities of the two strong y-rays can be determined very accurately, as shown ia Table 8. 

The magic numbers which impart stability to a nucleus are 2, 8, 20, 28, 50, 82 or 122. The isotope, 39K, has a magic number equal to its number of neutrons, so it is probably stable. The others have a larger neutron-to-proton ratio, making them neutron-rich nuclei, so 40K and 41K might be expected to decay by beta emission. In fact, both 39K and 41K are stable, and 40K does decay by beta emission. 

The radioactive decay of a nucleus is a random process, but the decay of a particular element is characterized by a number known as the half-life (7 1/2), which is the time taken for half of the original material to change into another element by radioactive decay. Half-lives vary from fractions of a second to many billions of years, depending on the isotope. The half-life is only meaningful when considered in terms of the behavior of an assemblage of atoms of the radioactive element for any particular atom, the probability that it will undergo radioactive decay in any particular time period is essentially unpredictable it may happen in the next second, or it may not happen for millennia. It is possible that the atom we have selected to watch... 

Three channels should be taken into account [3] i) a radiative, purely nuclear /-pole transition (probability P/) ii) a non-radiative decay, when the proton transits to the ground state and the muon leaves the nucleus with the following... 

The process is simply a combination of the mutually independent decay processes of the individual nuclei. Let w be the probability for a single nucleus to survive at time tx. Even before computing w one may state that... 

Next we have to compute the survival chance w = w(t1), knowing that the probability per unit time for a still surviving nucleus to decay is a constant y. This task has already been performed in (III.6.3), which for constant y yields... 

Excited nuclei that have attained statistical equilibrium will decay into different products in proportion to the number of states available to the whole system after the decay. The different decays are often called channels, and we speak of the probability to decay into a given channel. A very schematic representation of the energy levels and the energies involved in the decay of an excited nucleus into various channels is shown in Figure 6.20. The total sum of the probabilities for decay into all channels is, of course, one. We can simply count the number of states available for a decay channel and obtain a general expression for the relative probability, P(e, n), for an excited nucleus to emit a portion with size n, requiring an energy e. The expression is... 

Figure 6.20 A representation of the branching decays from a highly excited compound nucleus. In the statistical model, the relative probability for the excited nucleus to decay into a specific channel is proportional to the number of possibilities or statistical weight of that channel divided by the sum of all of the statistical weights of all of the channels.

Example Problem In a certain nuclear reaction, a beam of lsO was combined with 233U nuclei to form a compound nucleus of 256Fm. The nuclei were produced with an excitation energy of 95 MeV. Calculate the nuclear temperature assuming that y = 1, and then the relative probability of neutron to fission decay of the excited system. 

The theoretical description of a emission relies on calculating the rate in terms of two factors. The overall rate of emission consists of the product of the rate at which an a particle appears at the inside wall of the nucleus times the (independent) probability that the a particle tunnels through the barrier. Thus, the rate of emission, or the partial decay constant ka, is written as the product of a frequency factor,/, and a transmission coefficient, T, through the barrier ... 

The cross section for a compound nuclear reaction can be written as the product of two factors, the probability of forming the compound nucleus and the probability that the compound nucleus decays in a given way. As described above, the probability of forming the compound nucleus can be written as ... 

The probability of decay of the compound nucleus (CN) into a given set of products (3 can be written as ... 

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