The key parameter to discuss the possibility of the pion condensation in nuclear matter, i.e., the so-called Landau-Migdal parameter

g^{'}

, was extracted by measuring the double-differential cross sections for the

(p, n)

reaction at

216 MeV / u

on a neutron-rich doubly magic unstable nucleus,

{}^{132}{Sn}

with the quality comparable to data taken with stable nuclei. The extracted strengths for Gamow-Teller (GT) transitions from

{}^{132}{Sn}

leading to

{}^{132}{Sb}

exhibit the GT giant resonance (GTR) at the excitation energy of

16.3 \pm 0.4 (stat) \pm 0.4 (syst) MeV

with the width of

Γ = 4.7 \pm 0.8 MeV

. The integrated GT strength up to

E_{x} = 25 MeV

S_{GT}^{-} = 53 \pm {5 (stat)}_{- 10}^{+ 11} (syst)

, corresponding to 56% of Ikeda’s sum rule of

3 (N - Z) = 96

. The present result accurately constrains the Landau-Migdal parameter as

g^{'} = 0.68 \pm 0.07

, thanks to the high sensitivity of the GTR energy to

g^{'}

. In combination with previous studies on the GTR for

{}^{90}{Zr}

and

{}^{208}{Pb}

, the result of this work shows the constancy of this parameter in the nuclear chart region with

(N - Z) / A = 0.11

to 0.24 and

A = 90

to 208.

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