Extraction of the Landau-Migdal Parameter from the Gamow-Teller Giant Resonance in Sn132

The key parameter to discuss the possibility of the pion condensation in nuclear matter, i.e., the so-called Landau-Migdal parameter $g^{\prime }$, was extracted by measuring the double-differential cross sections for the $(p,n)$ reaction at $216\mathrm{MeV}/\mathrm{u}$ on a neutron-rich doubly magic unstable nucleus, ${}^{132}\mathrm{Sn}$ with the quality comparable to data taken with stable nuclei. The extracted strengths for Gamow-Teller (GT) transitions from ${}^{132}\mathrm{Sn}$ leading to ${}^{132}\mathrm{Sb}$ exhibit the GT giant resonance (GTR) at the excitation energy of $16.3\pm 0.4(\mathrm{stat})\pm 0.4(\mathrm{syst})\mathrm{MeV}$ with the width of $\mathrm{\Gamma }=4.7\pm 0.8\mathrm{MeV}$. The integrated GT strength up to $E_x=25\mathrm{MeV}$ is $S_{\mathrm{GT}}^{-}=53\pm {5(\mathrm{stat})}_{-10}^{+11}(\mathrm{syst})$, corresponding to 56% of Ikeda’s sum rule of $3(N-Z)=96$. The present result accurately constrains the Landau-Migdal parameter as $g^{\prime }=0.68\pm 0.07$, thanks to the high sensitivity of the GTR energy to $g^{\prime }$. In combination with previous studies on the GTR for ${}^{90}\mathrm{Zr}$ and ${}^{208}\mathrm{Pb}$, 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.