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We construct polarized spin reversal operator (PSRO) which yields a class ofrepresentations for the $BC_N$ type of Weyl algebra, and subsequently use thisPSRO to find out novel exactly solvable variants of the $BC_N$ type of spinCalogero model. The strong coupling limit of such spin Calogero modelsgenerates the $BC_N$ type of Polychronakos spin chains with PSRO. We derive theexact spectra of the $BC_N$ type of spin Calogero models with PSRO and computethe partition functions of the related spin chains by using the freezing trick.We also find out an interesting relation between the partition functions of the$BC_N$ type and $A_{N-1}$ type of Polychronakos spin chains. Finally, we studyspectral properties like level density and distribution of spacing betweenconsecutive energy levels for $BC_N$ type of Polychronakos spin chains withPSRO.

Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators