code: def pos_branch(incl, chi):
      
      if incl == 0:
          chi_eff = chi
      else:
          rISSO = PG_ISSO_solver(chi,incl)
          chi_eff = scipy.optimize.fsolve(ISCO_eq_chi_first, 1.0, args=(rISSO))
  
      return chi_eff
docs: Determines the effective [as defined in Stone, Loeb,
      Berger, PRD 87, 084053 (2013)] aligned dimensionless
      spin parameter of a NS-BH binary with tilted BH spin.
      This means finding the root chi_eff of
      ISCO_eq_chi_first(chi_eff, PG_ISSO_solver(chi,incl)).
      The result returned by this function belongs to the
      branch of the greater solutions, i.e. the greater of
      the two possible solutions is returned.
  
      Parameters
      -----------
      incl: float
          the inclination angle between the BH spin and the orbital
          angular momentum in radians
      chi: float
          the BH dimensionless spin parameter
  
      Returns
      ----------
      chi_eff: float
          the (greater) effective dimensionless spin parameter solution