Reduced nuclear probability

Here B[E/(M)X is the reduced nuclear probability, atomic radial matrix elements of electric (magnetic) [E/M] multipolarity A ji f and 7i,f are the angular momenta of the electronic and nuclear states correspondingly. The atomic radial matrix elements P (ft)jv) of electric (magnetic) [E/M] multipolarity A are expressed by means of the integral ... 

Present nuclear power plants must be designed and operated to current safety objectives and principles in order to achieve a high level of safety. Nuclear power has a small environmental impact when operating as designed, but faces serious public concerns about the risk of oif-design accidental releases. This has stimulated the current engineering concentration on reducing the probability of such accidents. 

Table 13.1 gives the most common accelerator-induced nuclear reactions leading to the production of neutrons. In general, the neutron yield increases with increasing beam energy up to some maximum value of the latter after which competition of other nuclear reactions reduces the probability of the initial neutron producing reaction (Fig. 13.11). The least expensive way to get a neutron flux of suffici t intensity for producing radioactive nuclides... 

Nuclear wastes are generated from spent nuclear fuel from electric power plants, dismantled weapons, and products such as radio pharmaceuticals. The most important design item for the safe storage of nuclear waste is the effective shielding of radiation. To reduce the probability of nuclear radiation exposure, special packaging is designed to meet the protection standards for temporary dry or wet storage or for... 

Now the occurrence of well defined resonances implies that the width / is i.e. that the lifetime t of a virtual state is long compared with the time hJD in which the nuclear motion repeats. This is because the barrier effects at the nuclear boundary in the resonance region reduce the probability of emission of a particle. It then follows that if T is the barrier penetration [given by Eq. (7.6)]... 

E2 transition probabilities from Coulomb excitation. Some reduced transition probabilities obtained by Coulomb excitation are listed in Table 6. These quantities are expressed in units of i0 cm. The reduced transition probability corresponding to Weisskopf s estimate of the transition probability of 2 radiation, in the same units, is given by 3 x where is the nuclear... 

The quantities gQ and g in (77-5) are the gyromagnetic ratios corresponding to the intrinsic angular momentum of the odd particle and to the rotational motion respectively. The former is a characteristic of the state of the odd particle and the latter is theoretically equal to Z/A. Thus the reduced transition probabilities for magnetic transitions are of the order of the square of the nuclear magneton number, while those oi E 2 transitions are of the order of or cm. ... 

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In general, the equations for the density operator should be solved to describe the kinetics of the process. However, if the nondiagonal matrix elements of the density operator (with respect to electron states) do not play an essential role (or if they may be expressed through the diagonal matrix elements), the problem is reduced to the solution of the master equations for the diagonal matrix elements. Equations of two types may be considered. One of them is the equation for the reduced density matrix which is obtained after the calculation of the trace over the states of the nuclear subsystem. We will consider the other type of equation, which describes the change with time of the densities of the probability to find the system in a given electron state as a function of the coordinates of heavy particles Pt(R, q, Q, s,...) and Pf(R, q, ( , s,... ).74,77 80... 

For entirely nonadiabatic transitions, the transition probabilities are so small that the reaction does not disturb the equilibrium distribution in the nuclear subsystems (q9 Q, s), and the calculation of the mean transition probability is reduced to averaging the corresponding local transition probability over the equilibrium distribution of the coordinates q, Q, s ... 

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