  We investigate the correlation properties of the ground state of
Tonks-Gigrardeal gases in the momentum space. With Bose-Fermi mapping method
the exact ground state wavefunction in coordinate space can be obtained basing
on the wavefunction of spin-polarized Fermions. By Fourier transformation we
obtain the ground state wavefunction in momentum space, and therefore the
momentum distribution, pair correlation and the reduced one-body density matrix
(ROBDM) in momentum space. The ROBDM in momentum space is the Fourier
transformation of the ROBDM in coordinate space and the pair correlation in
momentun space is the Fourier transformation of the reduced two-body density
matrix in coordinate space. The correlations in momentum space display larger
values only in small momentum region and vanish in most other regions. The
lowest natural orbital and occupation distribution are also obtained.
