We propose a new model for hadrons with quantum mechanical attractive and repulsive interactions sensitive to some spatial
correlation length parameter inspired by the Beth-Uhlenbeck quantum mechanical nonideal gas model (Uhlenbeck and Beth,
1937). We confront the thermodynamics calculated using our model with a corresponding recent lattice data at four different
values of the baryon chemical potential, μb = 0, 170, 340, 425 MeV over temperatures ranging from 130 MeV to 200 MeV and for
five values for the correlation length ranging from 0 to 0.2 fm. For equilibrium temperatures up to the vicinity of the chiral
phase transition temperature ≃160 MeV, a decent fitting between the model and the lattice data is observed for different values
of r, especially at ðμb , rÞ = ð170, 0:05Þ, ð340, 0:1Þ, and ð340, 0:15Þ, where μb is in MeV and r is in fm. For the vanishing chemical
potential, the uncorrelated model ðr = 0Þ, which corresponds to the ideal hadron resonance gas model, seems to offer the best fit.
The quantum hadron correlations seem to be more probable at nonvanishing chemical potentials, especially within the range μb
∈ 1⁄2170, 340 MeV.
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