# Magnetic Form factors for Neutrons- ZK coefficients for Rare Earth Ions

The coefficients defined by equation (52) are given for the tri-positive rare earth ions. From (52) it follows that

 (160)

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


Martin Rotter 2017-01-10