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

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


\begin{displaymath}
Z(K')=c_{K'-1} \langle j_{K'-1}(Q) \rangle+c_{K'+1} \langle j_{K'+1}(Q) \rangle
\end{displaymath} (160)

and it is the coefficients $c_{K'\pm 1}$ that are listed in the format required for a single ion property file. Note that $Gd^{3+}$ is not listed because for $L=0$ the terms with $l>0$ are zero, i.e. the dipole approximation is valid. $Eu^{3+}$ is not listed because it has $J=0$ 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