Jae Gil Kim^a and Eok Kyun Lee^a and Soonchil Lee^b

^a Department of Chemistry, Korea Advanced Institute of Science and Technology, Taejon, Republic of Korea
^b Department of Physics, Korea Advanced Institute of Science and Technology, Taejon, Republic of Korea

The analytical expression of the free-electron spin susceptibilities chi (q) and chi (r) in one dimension are derived at finite temperature, where the Sommerfeld expansion is not applicable near q=2k_F, by a series expansion method which does not require the restriction of the Sommerfeld method. The main results are (i) the oscillation of the range function decays exponentially as exp(- pi k_Frk_BT / epsilon _F) in the long-range limit and (ii) the logarithmic divergence of chi (q) at q=2k_F near T=0 is in the form of [N(0)µ²_B / 2]ln(4 epsilon _F / pi k_BT).