Angular centrifugal potential

Finally, taking the limit N- oo gives the angular centrifugal potential for the infinite lattice... 

The probability of fusion is a sensitive function of the product of the atomic numbers of the colliding ions. The abrupt decline of the fusion cross section as the Coulomb force between the ions increases is due to the emergence of the deep inelastic reaction mechanism. This decline and other features of the fusion cross section can be explained in terms of the potential between the colliding ions. This potential consists of three contributions, the Coulomb potential, the nuclear potential, and the centrifugal potential. The variation of this potential as a function of the angular momentum l and radial separation is shown as Figure 10.26. 

Figure 10.26 Sum of the nuclear, Coulomb, and centrifugal potential for lsO + 120Sn as a function of radial distance for various values of the orbital angular momentum l.

Fig. 2.4 Coulomb and centrifugal potentials (—) which are summed to give the effective radial potential (—) in which an electron of angular momentum i moves.

Here, Vc is the sum of all the two-body interactions and A( 2C) is the angular momentum operator suitable for the five-dimensional angular space. The latter is referred to as the grand angular momentum operator. It introduces the centrifugal potential for the motion in p. It takes an explicit form... 

There are a number of differences between the BOSLN and the present adiabtic bending model. First, the total angular momentum J is used in Equation S. whereas the orbital angular momentum il appears in the B( RLN equations. Second, the centrifugal potentials containing these angular momenta are different, the one given in BCRLM does not vanish asymptotically, whereas the one in Equation... 

Here, r and 6 are plane polar coordinates of the projectile referred to the target at the origin, and p is the reduced mass. L is the angular momentum about the centre of mass and the second term in eqn. (50) is, of course, the centrifugal potential. 

Figure Bl.6.7 An angular momentum barrier created by the addition of the centrifugal potential to the electron-atom potential. 

Orbital angular momentum is assumed to be conserved from the centrifugal barrier to products so that the centrifugal potential is converted to product relative translational energy. 

Before considering other atoms, we note a problem with the above subhamiltonian, and malce a correction for it. The problem is that we are seeking to incorporate into the centrifugal potential the effects of both the radial and angular second derivatives, but have paid attention to only the radial part of the problem in writing down Eq. (11). To make this clear, we note that the simple subhamiltonian could also be written... 

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