The coefficients defined by equation (52) are given for the tri-positive rare earth ions. From (52) it follows that
and it is the coefficients that are listed in the format required for a single ion property file. Note that is not listed because for the terms with are zero, i.e. the dipole approximation is valid. is not listed because it has and therefore this approach restricted to the ground state multiplet is not applicable (higher multiplets have to be considered).
# Ce3+ Z1c0=1.07142857 Z1c2=1.71428571 Z3c2=0.09583148 Z3c4=0.31943828 Z5c4=0.00360750 Z5c6=0.04329004 Z7c6=0 # Pr3+ Z1c0=1.6 Z1c2=2.63111111 Z3c2=-0.09865803 Z3c4=-0.13453368 Z5c4=-0.01836547 Z5c6=-0.11678557 Z7c6=0.002233133 # Nd3+ Z1c0=1.63636364 Z1c2=2.95041322 Z3c2=-0.20896503 Z3c4=-0.25329095 Z5c4=0.03820789 Z5c6=0.14258681 Z7c6=-0.00614959 # Pm3+ Z1c0=1.2 Z1c2=2.71515152 Z3c2=-0.10866182 Z3c4=-0.07024602 Z5c4=0.00509439 Z5c6=-0.06449156 Z7c6=0.00232318 # Sm3+ Z1c0=0.35714286 Z1c2=1.93650794 Z3c2=0.04614109 Z3c4=0.06291966 Z5c4=-0.00426341 Z5c6=0.00335243 Z7c6=0 # Tb3+ Z1c0=4.5 Z1c2=1.666666666 Z3c2=0 Z3c4=0.28459047 Z5c4=-0.05050505 Z5c6=0.03496503 Z7c6=-0.01131382 # Dy3+ Z1c0=5.0 Z1c2=2.666666667 Z3c2=-0.22360680 Z3c4=-0.08131156 Z5c4=0.02525253 Z5c6=-0.12432012 Z7c6=0.05656908 # Ho3+ Z1c0=5.0 Z1c2=3.066666667 Z3c2=-0.31304952 Z3c4=-0.28459047 Z5c4=0.12626263 Z5c6=0.14763015 Z7c6=-0.11313815 # Er3+ Z1c0= 4.5 Z1c2=2.9333333333 Z3c2=-0.13416408 Z3c4=-0.16262313 Z5c4=-0.02525253 Z5c6=-0.04662005 Z7c6= 0.11313815 # Tm3+ Z1c0=3.5 Z1c2=2.333333333 Z3c2=0.22360680 Z3c4=0.08131156 Z5c4=-0.17676768 Z5c6=-0.02719503 Z7c6=-0.05656908 # Yb3+ Z1c0=2.0 Z1c2=1.333333333 Z3c2=0.44721360 Z3c4=0.16262313 Z5c4=0.10101010 Z5c6=0.01554002 Z7c6=0.01131382