Potential barrier, nuclear

E. Pollard, Nuclear Potential Barriers Experiment and Theory, Phys. Rev. 47 (1935) 611-620. 

In this case, the activation yield first increases with the atomic number of the irradiated element and then decreases rapidly beyond calcium. This is due to the existence of a nuclear potential barrier within the target nucleus, which opposes the ejection of charged particles. This effect, which becomes more important when the atomic number of the element concerned increases, is sometimes favourable as it may substantially reduce the influence of competing nuclear reactions, i.e. reactions that yield radioisotope B from elements other than A. 

Similar to the case without consideration of the GP effect, the nuclear probability densities of Ai and A2 symmetries have threefold symmetry, while each component of E symmetry has twofold symmetry with respect to the line defined by (3 = 0. However, the nuclear probability density for the lowest E state has a higher symmetry, being cylindrical with an empty core. This is easyly understand since there is no potential barrier for pseudorotation in the upper sheet. Thus, the nuclear wave function can move freely all the way around the conical intersection. Note that the nuclear probability density vanishes at the conical intersection in the single-surface calculations as first noted by Mead [76] and generally proved by Varandas and Xu [77]. The nuclear probability density of the lowest state of Aj (A2) locates at regions where the lower sheet of the potential energy surface has A2 (Ai) symmetry in 5s. Note also that the Ai levels are raised up, and the A2 levels lowered down, while the order of the E levels has been altered by consideration of the GP effect. Such behavior is similar to that encountered for the trough states [11]. 

The height of the potential barrier separating the initial and final states of the nuclear subsystem decreases and, hence, the Franck-Condon factor increases (Fig. 6). In the classical limit, this results in a decrease of the activation free energy. 

R. Atkinson and F. Houtermans apply Gamow s theory of potential barrier penetration by quantum tunnelling to suggest how stars can release nuclear energy by synthesis of hydrogen into helium by an (unspecified) cyclic process. 

Intersection region, but small enough so that It may be neglected In calculating the height of the potential barrier (Hab Eth) Under these conditions the rate constant for the conversion of the precursor to the successor complex Is Independent of the magnitude of the electronic coupling and depends only on the nuclear factor... 

Another important quantum mechanical problem of interest to nuclear chemists is the penetration of a one-dimensional potential barrier by a beam of particles. The results of solving this problem (and more complicated variations of the problem) will be used in our study of nuclear a decay and nuclear reactions. The situation is shown in Figure E.5. A beam of particles originating at — oo is incident on a barrier of thickness L and height V0 that extends from x = 0 to x = L. Each particle has a total energy E. (Classically, we would expect if E < V0, the particles would bounce off the barrier, whereas if E > V0, the particles would pass by the barrier... 

In Sect. 7, we raised the question of what were the chemical stimuli to which the reactivity indices defined in Sect. 6, the softness kernels, were presumed to be the responses, our seventh issue. Now there are various broad categories of reactions to be considered, unimolecular, bimolecular, and multimolecular. The former occur via thermal activation over a barrier, tunneling through the barrier, or some combination of both. There is no stimulus, and the softness kernels defined as responses of the electron density to changes in external or nuclear potential are irrelevant. For the study of unimolecular reactions, one needs only information about the total energy in the relevant configuration space of the molecule. 

Because typical metal-ligand stretching frequencies are ca. 2 kT at room temperature (T), the possibility that the inner-shell nuclei will tunnel through the potential barrier needs to be considered. This is allowed for through the nuclear-tunneling factor, T j, which is defined by ... 

Suppose En(6) comprises an infinite potential barrier over the angular range 0 G [i , -1 + A ], 0 < A < 2tt, creating an inaccessible part C (A ) of Cjv for the nuclear motion. Then, it is consistent with the boundary condition X( ) — A ( + — 0 to absorb the vector potential into the phase of... 

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