Neutral-current supernova neutrino-nucleus scattering off <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">I</mml:mi><mml:mprescripts /><mml:none /><mml:mn>127</mml:mn></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Cs</mml:mi><mml:mprescripts /><mml:none /><mml:mn>133</mml:mn></mml:mmultiscripts></mml:math>

A large number of the presently running neutrino and dark-matter experiments use thallium-doped cesium-iodide CsI[Tl] crystals, sodium-doped CsI[Na] or sodium-iodide NaI[Tl] crystals. In present paper we calculate elastic inelastic cross sections for neutral-current supernova-neutrino scattering off $^{127}\mathrm{I}$ $^{133}\mathrm{Cs}$, relevant using CsI[Tl], CsI[Na], We study also folded with two-parameter Fermi-Dirac distributions spectrum. The adopted nuclear-theory framework is microscopic quasiparticle-phonon model, able to operate in single-particle valence bases G-matrix based two-nucleon interactions a phenomenological renormalization.