Kohn variational method

Although the Kohn variational method is not a bounded method (except at zero energy when, subject to certain conditions, it can yield an upper bound on the scattering length), it is found in practice that the phase shift usually becomes more positive as the flexibility of the trial function is enhanced by increasing w it converges towards what is assumed to be the exact value according to a pattern which is quite accurately represented by... 

Various techniques have been devised for coping with Schwartz singularities. They may either be ignored, or they can be avoided by using a modified form of the Kohn variational method in which the asymptotic form of the trial function has an amplitude different from that of equation (3.42) ... 

The scattering length can be calculated using the Kohn variational method in a similar manner to that employed for the phase shift, but the Kohn functional then becomes... 

This form of trial function was used in the Kohn variational method by Armstead (1968) and Humberston and Campeanu (1980) to obtain well-converged p-wave phase shifts. 

Among the most detailed and accurate investigations of positronium formation in the Ore gap are those of Humberston (1982, 1984) and Brown and Humberston (1984, 1985), who used an extension of the Kohn variational method described previously, see section 3.2, to two open channels. The single-channel Kohn functional, equation (3.37), is now replaced by the following stationary functional for the K-matrix ... 

Theoretical aspects of annihilation and scattering in gases 333 using the Kohn variational method with trial functions of the form... 

Armour, E.A.G. (1984). Application of a generalisation of the Kohn variational method to the calculation of cross sections for low-energy positron-hydrogen molecule scattering. J. Phys. B At. Mol. Opt. Phys. 17 L375-L382. 

J. Chang, N. J. Brown, M. D Mello, R. E. Wyatt, and H. Rabitz, Quantum functional sensitivity analysis within the log-derivative Kohn variational method for reactive scattering, J. Chem. Phys. 97 6240 (1992). 

I. Shimamura, Resonances and pseudoresonances in the Kohn variational method and the Feshbach method, J. Physcal. Soc. Japan 31 (1971) 852. 

Previous studies [37, 38] of the doubly excited autoionizing states of H2 show that the lowest resonance is dominated by the s and d partial waves. Therefore, we use three Is-cSTO-fVGs and three 3d-cSTO-A/Gs. As discussed in Introduction, the selection of complex orbital exponents is not an easy task at all, and in this work, we attempt to propose a systematic way to select the orbital exponents for cSTOs. A hint for the selection can be obtained by relating the CBF method to the complex Kohn variation method [22, 39]. In the latter method, the outgoing continuum wave function is represented as a linear combination of basis functions and a few non functions satisfying the outgoing asymptotic behavior. In the CBF method, only functions are used thus, additional basis functions need to... 

Kohn variational method that has been described in detail in previous publications [5, 25, 26]. We briefly review this approach for quantum reactive scattering below [27]. In addition, we demonstrate how to apply functional sensitivity analysis within the 5—matrix Kohn framework. We report the cross section calculations resulting from the two PESs for total angular momenta J = 0 and 10. We find that the theoretical cross sections do not change significantly when the LSTH PES is replaced by the DMBE [28]. This suggests that the theoretical prediction — that there is no sharp resonance in the H+H2 integraJ cross section — may be correct. 

The Kohn variational method described above for potential scattering extends in a straightforward way to the collinear reactive scattering problem described in Section 2 without the need to introduce any special coordinates (i.e., one can continue to work with the optimum mass-scaled Jacobi coordinates of the reactant and product arrangements). Moreover, the extensions that are required are comparatively minor, and the overall structure of the method remains the same. 

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