HYPERNETTED-CHAIN TREATMENT AND THE EXTENDED SHADOW WAVE-FUNCTIONS FOR FRACTIONAL QUANTUM HALL HIERARCHICAL STATES

The hypernetted-chain theory is applied to study hierarchical states i n the fractional quantum Hall effect. It is noted that a class of wave functions introduced by Girvin [Phys. Rev. B 29, 6012 (1984)] and Mac Donald, Aers, and Dharma-wardana [Phys. Rev. B 31, 5529 (1985)], based on charge-conjugation procedures, is of the extended shadow wave-func tion type. The correlation energy, pair distribution function, and sta tic structure function have been calculated in the thermodynamic limit at various filling factors. The results obtained agree with those of previous calculations performed with a finite number of electrons.