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<img src='content_image/370703.jpg'>

because the integrand is smooth as a function of β . The doubly extrapolated values are listed in Table I. 

Clearly, the plasmon form has superior convergence properties when compared to the integral form, and, additionally, does not require any particular extrapolation or discretiza- tion procedures. Helium presents a rather simple case: more complex atoms (or molecules) will require progressively larger basis sets to converge the integrals and the plasmon form should prove even more useful in practice. A hint of this is provided by comparing He to B in Table I. For B, the integral form of the correlation energy converges more slowly, and the calculations at N$_{max}$ = 300 were already quite demanding in terms of time (and patience). The plasmon form, again, shows rapid convergence versus N$_{max}$ . 

We now examine the accuracy of the approximate forms derived in Sections 9 and 10 above. In Tables II and III we present these correlation energies for the helium and boron atoms using LSDA or HF wave functions and eigenenergies. These are to be compared to 

