Quantum mechanical treatment of molecules. Part 1.—Calculation of the potential energy curve and molecular constants of the ground state of CO

Abstract

The self-consistent field molecular orbital method in L.C.A.O. (linear combination of atomic orbitals) approximation is applied to the ground state of CO at a number of internuclear distances for the computation of the potential energy curve. In this calculation both the L.C.A.O. coefficients and the screening constants of the atomic orbitals have been optimized. The molecular constants a , , oexe, Be, ae, Re and De have been calculated from the computed potential energy curve of CO and compared with the experimental data. The computed spectral results are more encouraging than hitherto reported in the literature from ab initio calculations.

Experimental study of the bifurcation nature of the electrostatic potential of a toroidal helical plasma

“…The previous theoretical work shows that the ion loss cone current does not make any significant difference in the radial electric field in the CHS case. 40 On the other hand, it was experimentally observed that a transition was forced to occur when ECR-heating of 140 kW was applied at the plasma periphery. 24 The result was explained by electron loss cone current enhanced by the ECR-heating.…”

“…Then the particles escape from the plasma owing to a larger loss cone. [38][39][40] The radial electric field is determined by maintenance of ambipolarity, or local balance of ion and electron fluxes. The flux balance equation can be written as ⌫ i ͑ E r ,r,X ͒ϭ⌫ e ͑ E r ,r,X ͒, ͑3͒…”

“…Figure 41͑c͒ indicates two examples of the neoclassical radial current during the transitions as a function of the radial electric field. 21,22,40 In this calculation, plausible parameters of the CHS plasma are chosen to satisfy bifurcation conditions. The profiles of ion temperature and electron density in calculation are assumed to be all parabolic, with the central values being 0.35 keV and 0.5ϫ10 13 cm Ϫ3 .…”

Direct observation of potential profiles with a 200 keV heavy ion beam probe on the Compact Helical System

“…Hence, the experimentally obtained electric field can be compared with the electric-field predicted by the ambipolarity condition ⌫ i NC (E r )ϭ⌫ e NC (E r ), where ⌫ i NC (E r ) and ⌫ e NC (E r ) represent the electron and ion fluxes in neoclassical theory. [13][14][15] The dash-dotted line in Fig. 2͑b͒ shows this neoclassical radial electric field.…”

“…13, 16 The loss cone boundaries for deeply trapped particles are expressed as W m ϽWϽW p , where W is the particle energy, W m ϭϪq(0) f (x)/͓⑀ ha (1Ϫx 2 )ϩ⑀ ta (1Ϫx)͔, and W p ϭ Ϫ q(0) f (x)/͓⑀ ha (1Ϫx 2 )Ϫ⑀ ta (1ϩx)͔. Here, ⑀ ta and ⑀ ha represent the toroidal and helical ripple coefficients, x indicates the horizontal coordinate whose origin is on the magnetic axis, and f (x) is a normalized function fitted to the experimental profiles with f (0)ϭ1 and f (Ϯ1)ϭ0.…”