Atomic scattering factors

Cowley, J. M.

doi:10.1107/97809553602060000593

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 4.3, pp. 259-260

Section 4.3.1.2. Atomic scattering factors

J. M. Cowley^b ^‡

4.3.1.2. Atomic scattering factors

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All such calculations require a knowledge of the potential distribution, $[\varphi({\bf r})]$ , or its Fourier coefficients, $[V({\bf h})]$ . It is usually convenient to express the potential distribution in terms of the sum of contributions of individual atoms centred at the positions $[{\bf r}={\bf r}_i]$ . Thus: $[\varphi({\bf r})=\textstyle\sum\limits_i \varphi_i({\bf r}-{\bf r}_i) \eqno (4.3.1.10)]$ or, in terms of the Fourier transforms, [V_i] , of the $[\varphi_i({\bf r})]$ $[V({\bf h})=\textstyle\sum\limits_i V_i({\bf h})\exp\{+2\pi i{\bf h}\cdot{\bf r}_i\}. \eqno (4.3.1.11)]$

As a first approximation, the functions $[\varphi_i({\bf r})]$ may be identified with the potential distributions for individual, isolated atoms or ions, with the usual spreading due to thermal motion. The interatomic binding and the interactions of ions that are thereby neglected may have important effects on diffraction intensities in some cases.

In this approximation, the Fourier transforms for individual atoms may be written $[V_i(s)=f^B_i(s)/K, \eqno (4.3.1.12)]$ where $[s=4\pi\lambda^{-1}\sin\theta=|{\bf k}-{\bf k}_0|]$ and the [f^B] are the Born electron scattering amplitudes, as conventionally defined, in units of Å. Here $[\theta]$ is half the scattering angle and, again, K = σ/λ. Some values of [f^B(s)] listed in the accompanying Tables 4.3.1.1 and 4.3.1.2 are obtained from the atomic potentials $[\varphi_0({\bf r})]$ for isolated, spherically symmetrical atoms or ions by the relation $[f^{B}(s)=4\pi K \int\limits^\infty_0 r^2\varphi(r){\sin sr\over sr}{\rm d} r.\eqno (4.3.1.13)]$

Table 4.3.1.1| top | pdf |
Atomic scattering amplitudes (Å) for electrons for neutral atoms

Self-consistent field calculations: HF: non-relativistic Hartree–Fock; RHF, *RHF: relativistic Hartree–Fock.

Element	H	He	Li	Be	B	C	N	O	F	Ne	Na
Z	1	2	3	4	5	6	7	8	9	10	11
Method	HF	RHF	RHF	RHF	RHF	RHF	RHF	RHF	RHF	RHF	RHF
(sin $[\theta]$ )/λ (Å⁻¹)
0.00	0.529	0.418	3.286	3.052	2.794	2.509	2.211	1.983	1.801	1.652	4.778
0.01		0.418	3.265	3.042	2.788	2.505	2.209	1.982	1.800	1.651	4.749
0.02		0.417	3.200	3.011	2.768	2.492	2.201	1.976	1.796	1.648	4.663
0.03		0.415	3.097	2.961	2.736	2.471	2.187	1.966	1.789	1.642	4.527
0.04	0.51	0.413	2.961	2.892	2.693	2.442	2.168	1.953	1.779	1.635	4.348
0.05	0.51	0.410	2.800	2.807	2.638	2.406	2.144	1.937	1.767	1.626	4.138

0.06	0.50	0.407	2.622	2.710	2.574	2.363	2.116	1.917	1.752	1.615	3.908
0.07	0.49	0.404	2.435	2.601	2.502	2.313	2.083	1.893	1.735	1.602	3.667
0.08	0.48	0.399	2.245	2.484	2.423	2.259	2.047	1.867	1.716	1.587	3.425
0.09	0.47	0.395	2.058	2.362	2.339	2.200	2.007	1.839	1.694	1.570	3.190
0.10	0.45	0.390	1.879	2.237	2.250	2.138	1.963	1.808	1.671	1.552	2.967

0.11	0.44	0.384	1.710	2.111	2.159	2.072	1.918	1.774	1.646	1.533	2.759
0.12	0.425	0.378	1.554	1.987	2.067	2.005	1.870	1.739	1.619	1.512	2.569
0.13	0.411	0.372	1.411	1.865	1.974	1.936	1.821	1.702	1.591	1.490	2.395
0.14	0.396	0.366	1.282	1.748	1.882	1.866	1.770	1.664	1.562	1.467	2.239
0.15	0.382	0.359	1.166	1.635	1.791	1.796	1.718	1.625	1.532	1.443	2.099

0.16	0.366	0.352	1.063	1.528	1.702	1.727	1.666	1.585	1.501	1.418	1.974
0.17	0.353	0.345	0.971	1.427	1.616	1.658	1.614	1.545	1.469	1.393	1.863
0.18	0.338	0.338	0.889	1.332	1.533	1.591	1.561	1.504	1.436	1.367	1.763
0.19	0.324	0.330	0.817	1.243	1.453	1.524	1.510	1.463	1.404	1.340	1.674
0.20	0.311	0.323	0.753	1.161	1.377	1.460	1.458	1.422	1.371	1.313	1.594

0.22	0.285	0.308	0.646	1.013	1.235	1.337	1.358	1.341	1.304	1.259	1.458
0.24	0.261	0.293	0.562	0.887	1.107	1.222	1.262	1.261	1.238	1.204	1.344
0.25	0.249	0.286	0.526	0.832	1.048	1.168	1.216	1.222	1.206	1.176	1.295
0.26	0.238	0.278	0.494	0.781	0.993	1.117	1.171	1.184	1.173	1.149	1.249
0.28	0.218	0.264	0.440	0.690	0.892	1.020	1.085	1.110	1.110	1.095	1.167
0.30	0.199	0.250	0.396	0.614	0.803	0.932	1.006	1.040	1.049	1.043	1.095

0.32	0.182	0.236	0.359	0.549	0.725	0.853	0.932	0.974	0.991	0.991	1.031
0.34	0.167	0.224	0.328	0.494	0.657	0.781	0.863	0.911	0.935	0.942	0.973
0.35	0.160	0.217	0.314	0.469	0.625	0.748	0.831	0.881	0.908	0.918	0.946
0.36	0.153	0.211	0.301	0.446	0.596	0.717	0.800	0.853	0.882	0.894	0.921
0.38	0.141	0.200	0.279	0.406	0.543	0.658	0.742	0.798	0.831	0.849	0.872
0.40	0.130	0.189	0.259	0.371	0.497	0.606	0.689	0.747	0.784	0.805	0.827

0.42	0.120	0.178	0.241	0.341	0.455	0.559	0.641	0.700	0.739	0.764	0.785
0.44	0.111	0.169	0.226	0.314	0.419	0.517	0.596	0.656	0.697	0.725	0.746
0.45	0.107	0.164	0.219	0.302	0.402	0.497	0.575	0.635	0.677	0.706	0.727
0.46	0.103	0.159	0.212	0.291	0.387	0.479	0.555	0.615	0.658	0.687	0.709
0.48	0.096	0.151	0.200	0.271	0.358	0.444	0.518	0.577	0.621	0.652	0.675
0.50	0.089	0.143	0.188	0.253	0.333	0.413	0.484	0.542	0.586	0.619	0.642

0.55	0.075	0.125	0.164	0.215	0.280	0.348	0.411	0.466	0.510	0.544	0.569
0.60	0.064	0.110	0.145	0.186	0.239	0.297	0.353	0.403	0.445	0.479	0.505
0.65	0.055	0.097	0.128	0.164	0.207	0.256	0.305	0.350	0.390	0.424	0.450
0.70	0.048	0.086	0.115	0.145	0.182	0.223	0.266	0.307	0.344	0.376	0.403
0.80	0.037	0.068	0.093	0.117	0.144	0.175	0.208	0.241	0.272	0.300	0.325
0.90	0.029	0.055	0.077	0.096	0.118	0.141	0.167	0.193	0.219	0.244	0.266
1.00	0.024	0.046	0.064	0.081	0.098	0.117	0.137	0.159	0.180	0.201	0.221

1.10	0.020	0.038	0.054	0.069	0.083	0.099	0.115	0.133	0.150	0.168	0.185
1.20	0.017	0.032	0.046	0.059	0.072	0.085	0.098	0.113	0.128	0.143	0.158
1.30	0.014	0.028	0.040	0.051	0.062	0.073	0.085	0.097	0.110	0.123	0.135
1.40	0.012	0.024	0.035	0.045	0.055	0.064	0.074	0.085	0.095	0.106	0.117
1.50	0.011	0.021	0.031	0.040	0.048	0.057	0.065	0.074	0.084	0.093	0.103

1.60		0.019	0.028	0.035	0.043	0.051	0.058	0.066	0.074	0.083	0.092
1.70		0.016	0.024	0.031	0.038	0.045	0.052	0.059	0.066	0.074	0.081
1.80		0.015	0.022	0.028	0.035	0.041	0.047	0.053	0.060	0.066	0.073
1.90		0.013	0.019	0.026	0.031	0.037	0.043	0.048	0.054	0.060	0.065
2.00		0.012	0.017	0.023	0.028	0.034	0.039	0.044	0.049	0.054	0.059

Element	Mg	Al	Si	P	S	Cl	Ar	K	Ca	Sc	Ti
Z	12	13	14	15	16	17	18	19	20	21	22
Method	RHF	RHF	RHF	RHF	RHF	RHF	RHF	RHF	RHF	RHF	RHF
(sin $[\theta]$ )/λ (Å⁻¹)
0.00	5.207	5.889	5.828	5.488	5.161	4.857	4.580	8.984	9.913	9.307	8.776
0.01	5.187	5.867	5.810	5.476	5.152	4.851	4.576	8.921	9.860	9.264	8.740
0.02	5.124	5.800	5.759	5.439	5.124	4.830	4.559	8.731	9.699	9.134	8.631
0.03	5.022	5.692	5.675	5.378	5.079	4.795	4.531	8.434	9.442	8.926	8.455
0.04	4.884	5.547	5.561	5.296	5.016	4.746	4.493	8.054	9.104	8.649	8.220
0.05	4.717	5.371	5.421	5.192	4.938	4.685	4.444	7.619	8.703	8.318	7.937

0.06	4.527	5.170	5.258	5.071	4.845	4.613	4.386	7.157	8.258	7.946	7.618
0.07	4.320	4.949	5.077	4.935	4.740	4.529	4.320	6.691	7.789	7.548	7.274
0.08	4.102	4.717	4.882	4.785	4.623	4.436	4.245	6.239	7.312	7.139	6.917
0.09	3.879	4.478	4.677	4.625	4.496	4.335	4.163	5.815	6.841	6.729	6.556
0.10	3.656	4.237	4.467	4.457	4.362	4.227	4.074	5.426	6.388	6.328	6.199

0.11	3.437	3.999	4.255	4.285	4.222	4.113	3.980	5.073	5.959	5.944	5.853
0.12	3.226	3.767	4.043	4.109	4.078	3.994	3.881	4.756	5.560	5.580	5.522
0.13	3.025	3.544	3.835	3.933	3.931	3.871	3.779	4.474	5.192	5.239	5.209
0.14	2.835	3.330	3.632	3.758	3.783	3.746	3.674	4.222	4.855	4.924	4.916
0.15	2.657	3.128	3.437	3.586	3.635	3.620	3.566	3.997	4.550	4.633	4.643

0.16	2.492	2.938	3.249	3.417	3.487	3.493	3.458	3.795	4.273	4.366	4.390
0.17	2.340	2.760	3.070	3.253	3.342	3.367	3.348	3.612	4.023	4.122	4.157
0.18	2.199	2.595	2.900	3.094	3.200	3.242	3.239	3.446	3.797	3.899	3.943
0.19	2.071	2.441	2.740	2.942	3.061	3.118	3.130	3.295	3.593	3.695	3.745
0.20	1.953	2.299	2.589	2.796	2.927	2.997	3.022	3.154	3.408	3.509	3.564

0.22	1.748	2.046	2.315	2.525	2.671	2.763	2.811	2.902	3.086	3.183	3.242
0.24	1.577	1.832	2.076	2.281	2.436	2.543	2.609	2.680	2.815	2.906	2.967
0.25	1.502	1.737	1.969	2.169	2.326	2.438	2.512	2.578	2.695	2.783	2.844
0.26	1.434	1.650	1.869	2.064	2.221	2.337	2.417	2.481	2.584	2.669	2.730
0.28	1.313	1.495	1.689	1.872	2.026	2.148	2.238	2.299	2.383	2.462	2.523
0.30	1.211	1.363	1.534	1.702	1.851	1.974	2.070	2.134	2.206	2.281	2.341

0.32	1.123	1.251	1.400	1.553	1.694	1.816	1.915	1.982	2.048	2.119	2.178
0.34	1.047	1.154	1.284	1.422	1.554	1.672	1.772	1.842	1.905	1.974	2.032
0.35	1.013	1.111	1.231	1.362	1.490	1.606	1.705	1.776	1.838	1.906	1.964
0.36	0.980	1.070	1.182	1.306	1.429	1.542	1.641	1.714	1.775	1.842	1.899
0.38	0.921	0.997	1.094	1.205	1.318	1.425	1.522	1.595	1.657	1.722	1.778
0.40	0.868	0.932	1.017	1.115	1.218	1.319	1.412	1.487	1.548	1.612	1.668

0.42	0.821	0.875	0.949	1.036	1.130	1.224	1.313	1.387	1.449	1.511	1.566
0.44	0.777	0.825	0.888	0.965	1.051	1.138	1.223	1.295	1.357	1.418	1.472
0.45	0.757	0.801	0.861	0.933	1.014	1.098	1.181	1.252	1.314	1.374	1.428
0.46	0.738	0.779	0.834	0.903	0.980	1.061	1.141	1.211	1.272	1.332	1.385
0.48	0.701	0.737	0.786	0.847	0.917	0.991	1.066	1.134	1.194	1.252	1.305
0.50	0.667	0.700	0.743	0.797	0.860	0.928	0.998	1.064	1.123	1.179	1.230

0.55	0.592	0.618	0.651	0.692	0.741	0.796	0.854	0.912	0.966	1.018	1.067
0.60	0.528	0.551	0.578	0.610	0.648	0.692	0.740	0.790	0.838	0.885	0.930
0.65	0.473	0.494	0.517	0.543	0.573	0.609	0.648	0.690	0.733	0.775	0.816
0.70	0.425	0.445	0.465	0.487	0.513	0.541	0.574	0.609	0.647	0.684	0.721
0.80	0.347	0.366	0.383	0.401	0.419	0.440	0.462	0.488	0.515	0.544	0.573
0.90	0.286	0.304	0.320	0.335	0.350	0.366	0.383	0.402	0.422	0.444	0.467

1.00	0.239	0.255	0.270	0.284	0.298	0.311	0.324	0.339	0.354	0.371	0.389
1.10	0.202	0.217	0.231	0.243	0.255	0.267	0.278	0.290	0.303	0.316	0.330
1.20	0.172	0.185	0.198	0.210	0.221	0.232	0.242	0.252	0.262	0.273	0.285
1.30	0.148	0.160	0.172	0.183	0.193	0.202	0.212	0.220	0.230	0.239	0.249
1.40	0.129	0.139	0.150	0.160	0.169	0.178	0.187	0.194	0.202	0.211	0.219
1.50	0.113	0.123	0.132	0.141	0.150	0.158	0.166	0.174	0.181	0.188	0.195

1.60	0.100	0.109	0.117	0.125	0.133	0.141	0.148	0.156	0.162	0.169	0.175
1.70	0.089	0.096	0.104	0.111	0.119	0.126	0.132	0.138	0.144	0.151	0.157
1.80	0.080	0.087	0.093	0.100	0.107	0.113	0.119	0.127	0.132	0.137	0.143
1.90	0.072	0.078	0.084	0.090	0.096	0.102	0.108	0.112	0.118	0.124	0.129
2.00	0.065	0.070	0.076	0.082	0.087	0.093	0.098	0.101	0.107	0.112	0.117

Element	V	Cr	Mn	Fe	Co	Ni	Cu	Zn	Ga	Ge	As
Z	23	24	25	26	27	28	29	30	31	32	33
Method	RHF	RHF	RHF	RHF	RHF	RHF	RHF	RHF	RHF	RHF	RHF
(sin $[\theta]$ )/λ (Å⁻¹)
0.00	8.305	6.969	7.506	7.165	6.854	6.569	5.600	6.065	7.108	7.378	7.320
0.01	8.274	6.945	7.484	7.145	6.836	6.552	5.587	6.051	7.088	7.359	7.306
0.02	8.180	6.875	7.412	7.081	6.779	6.501	5.547	6.009	7.027	7.303	7.260
0.03	8.029	6.762	7.296	6.978	6.687	6.418	5.482	5.941	6.927	7.211	7.184
0.04	7.826	6.610	7.140	6.839	6.562	6.306	5.395	5.849	6.792	7.088	7.081
0.05	7.581	6.427	6.949	6.669	6.410	6.169	5.287	5.735	6.629	6.935	6.953

0.06	7.303	6.221	6.732	6.474	6.234	6.010	5.165	5.603	6.441	6.759	6.803
0.07	7.002	5.997	6.493	6.260	6.040	5.834	5.029	5.457	6.236	6.562	6.634
0.08	6.686	5.764	6.241	6.032	5.834	5.646	4.886	5.299	6.017	6.351	6.449
0.09	6.365	5.527	5.981	5.796	5.619	5.449	4.737	5.133	5.792	6.129	6.253
0.10	6.045	5.291	5.719	5.558	5.401	5.249	4.585	4.962	5.564	5.902	6.048

0.11	5.732	5.061	5.459	5.320	5.182	5.048	4.434	4.790	5.337	5.672	5.838
0.12	5.430	4.838	5.206	5.087	4.967	4.848	4.285	4.618	5.113	5.442	5.625
0.13	5.142	4.625	4.962	4.861	4.758	4.654	4.139	4.449	4.896	5.217	5.411
0.14	4.871	4.423	4.728	4.644	4.555	4.465	3.998	4.283	4.686	4.996	5.200
0.15	4.616	4.231	4.506	4.436	4.361	4.283	3.862	4.123	4.486	4.783	4.992

0.16	4.378	4.051	4.297	4.240	4.177	4.110	3.731	3.969	4.295	4.578	4.789
0.17	4.158	3.882	4.100	4.054	4.002	3.944	3.607	3.822	4.114	4.382	4.593
0.18	3.953	3.723	3.916	3.880	3.836	3.788	3.488	3.681	3.942	4.195	4.404
0.19	3.763	3.574	3.743	3.716	3.681	3.640	3.375	3.547	3.781	4.017	4.222
0.20	3.588	3.434	3.583	3.562	3.534	3.500	3.267	3.421	3.629	3.849	4.048

0.22	3.276	3.179	3.292	3.284	3.267	3.245	3.067	3.186	3.352	3.541	3.724
0.24	3.006	2.953	3.039	3.039	3.032	3.018	2.885	2.977	3.108	3.268	3.433
0.25	2.885	2.849	2.924	2.928	2.924	2.914	2.800	2.880	2.997	3.143	3.299
0.26	2.772	2.750	2.817	2.824	2.823	2.816	2.719	2.789	2.892	3.026	3.172
0.28	2.568	2.568	2.620	2.632	2.637	2.636	2.568	2.620	2.701	2.813	2.940
0.30	2.386	2.403	2.445	2.461	1.471	2.474	2.428	2.468	2.531	2.623	2.733

0.32	2.225	2.252	2.288	2.308	2.321	2.328	2.299	2.329	2.379	2.455	2.548
0.34	2.079	2.114	2.146	2.168	2.184	2.195	2.180	2.203	2.242	2.304	2.384
0.35	2.011	2.049	2.080	2.104	2.121	2.133	2.123	2.144	2.179	2.235	2.308
0.36	1.947	1.987	2.017	2.042	2.060	2.073	2.069	2.087	2.119	2.169	2.237
0.38	1.826	1.870	1.899	1.925	1.946	1.962	1.965	1.980	2.006	2.048	2.105
0.40	1.716	1.761	1.790	1.818	1.841	1.858	1.868	1.882	1.903	1.938	1.986

0.42	1.614	1.660	1.690	1.719	1.743	1.763	1.777	1.790	1.808	1.837	1.878
0.44	1.520	1.567	1.597	1.628	1.653	1.674	1.691	1.704	1.720	1.745	1.780
0.45	1.476	1.523	1.553	1.584	1.610	1.631	1.651	1.663	1.679	1.702	1.734
0.46	1.433	1.480	1.511	1.542	1.569	1.591	1.611	1.624	1.639	1.661	1.691
0.48	1.352	1.399	1.431	1.462	1.490	1.513	1.535	1.549	1.563	1.583	1.608
0.50	1.277	1.323	1.356	1.388	1.416	1.440	1.464	1.478	1.492	1.510	1.533

0.55	1.111	1.155	1.189	1.222	1.251	1.277	1.303	1.319	1.334	1.349	1.367
0.60	0.973	1.014	1.047	1.080	1.110	1.136	1.163	1.181	1.197	1.212	1.228
0.65	0.856	0.894	0.927	0.959	0.988	1.015	1.041	1.061	1.078	1.093	1.108
0.70	0.757	0.792	0.824	0.854	0.883	0.909	0.935	0.955	0.973	0.989	1.004
0.80	0.602	0.631	0.659	0.686	0.712	0.737	0.761	0.781	0.800	0.817	0.832
0.90	0.490	0.514	0.538	0.561	0.583	0.605	0.626	0.646	0.665	0.681	0.697
1.00	0.408	0.427	0.446	0.466	0.485	0.504	0.523	0.541	0.558	0.574	0.589

1.10	0.345	0.361	0.377	0.393	0.409	0.425	0.442	0.457	0.473	0.488	0.502
1.20	0.297	0.310	0.323	0.336	0.350	0.364	0.378	0.391	0.405	0.418	0.431
1.30	0.259	0.269	0.280	0.291	0.303	0.315	0.327	0.339	0.350	0.362	0.374
1.40	0.228	0.237	0.246	0.255	0.265	0.275	0.285	0.296	0.306	0.317	0.327
1.50	0.203	0.210	0.218	0.226	0.235	0.243	0.252	0.261	0.270	0.279	0.288

1.60	0.182	0.188	0.195	0.202	0.209	0.217	0.224	0.232	0.240	0.248	0.256
1.70	0.163	0.169	0.175	0.181	0.188	0.194	0.201	0.208	0.215	0.222	0.229
1.80	0.148	0.154	0.159	0.165	0.170	1.176	0.182	0.188	0.194	0.200	0.206
1.90	0.134	0.139	0.144	0.149	0.154	0.160	0.165	0.170	0.175	0.181	0.187
2.00	0.122	0.127	0.132	0.136	0.141	0.146	0.150	0.155	0.160	0.165	0.170

Element	Se	Br	Kr	Rb	Sr	Y	Zr	Nb	Mo	Tc	Ru
Z	34	35	36	37	38	39	40	41	42	43	44
Method	RHF	RHF	RHF	RHF	RHF	*RHF	*RHF	*RHF	*RHF	*RHF	*RHF
(sin $[\theta]$ )/λ (Å⁻¹)
0.00	7.205	7.060	6.897	11.778	13.109	12.674	12.166	10.679	10.260	10.856	9.558
0.01	7.192	7.049	6.889	11.699	13.035				10.230
0.02	7.154	7.016	6.861	11.460	12.816				10.138
0.03	7.090	6.962	6.814	11.088	12.468				9.989
0.04	7.004	6.888	6.750	10.613	12.013	11.79	11.41	10.13	9.790	10.35	9.18
0.05	6.895	6.795	6.670	10.073	11.476	11.34	11.04	9.86	9.548	10.10	8.99

0.06	6.767	6.684	6.574	9.504	10.888	10.84	10.62	9.54	9.272	9.80	8.77
0.07	6.621	6.558	6.464	8.934	10.273	10.31	10.15	9.20	8.972	9.48	8.53
0.08	6.460	6.418	6.341	8.385	9.655	9.77	9.68	8.85	8.655	9.14	8.27
0.09	6.288	6.266	6.207	7.872	9.052	9.23	9.20	8.49	8.330	8.78	8.00
0.10	6.105	6.104	6.064	7.402	8.478	8.70	8.72	8.12	8.004	8.42	7.73

0.11	5.916	5.935	5.913	6.976	7.940	8.20	8.26	7.77	7.680	8.07	7.46
0.12	5.722	5.760	5.755	6.593	7.443	7.722	7.818	7.421	7.364	7.720	7.190
0.13	5.525	5.580	5.593	6.248	6.988	7.278	7.400	7.090	7.058	7.383	6.928
0.14	5.328	5.399	5.428	5.938	6.575	6.865	7.007	6.772	6.763	7.057	6.672
0.15	5.132	5.217	5.260	5.658	6.200	6.485	6.640	6.472	6.481	6.746	6.426

0.16	4.938	5.036	5.092	5.403	5.862	6.136	6.299	6.187	6.213	6.451	6.188
0.17	4.749	4.857	4.925	5.170	5.555	5.816	5.983	5.918	5.957	6.171	5.960
0.18	4.564	4.680	4.759	4.954	5.278	5.523	5.689	5.665	5.715	5.907	5.741
0.19	4.384	4.507	4.595	4.754	5.025	5.254	5.419	5.427	5.486	5.658	5.533
0.20	4.211	4.339	4.434	4.566	4.794	5.008	5.168	5.203	5.269	5.423	5.332

0.22	3.884	4.017	4.123	4.224	4.387	4.570	4.721	4.792	4.868	4.994	4.959
0.24	3.585	3.718	3.829	3.916	4.039	4.195	4.333	4.426	4.507	4.614	4.618
0.25	3.446	3.578	3.690	3.773	3.882	4.027	4.158	4.258	4.341	4.439	4.459
0.26	3.314	3.443	3.556	3.636	3.735	3.869	3.995	4.099	4.182	4.273	4.306
0.28	3.069	3.192	3.303	3.382	3.465	3.583	3.697	3.804	3.888	3.969	4.021
0.30	2.849	2.963	3.071	3.149	3.224	3.329	3.433	3.539	3.622	3.695	3.759

0.32	2.651	2.757	2.858	2.936	3.007	3.101	3.196	3.298	3.379	3.448	3.518
0.34	2.475	2.570	2.665	2.742	2.810	2.895	2.982	3.080	3.158	3.223	3.296
0.35	2.393	2.484	2.575	2.651	2.718	2.799	2.883	2.978	3.054	3.118	3.192
0.36	2.316	2.402	2.490	2.564	2.630	2.708	2.789	2.880	2.955	3.018	3.092
0.38	2.173	2.250	2.330	2.402	2.466	2.538	2.613	2.698	2.770	2.830	2.904
0.40	2.045	2.113	2.186	2.254	2.315	2.383	2.452	2.531	2.600	2.658	2.730

0.42	1.929	1.989	2.055	2.119	2.178	2.241	2.305	2.379	2.444	2.500	2.570
0.44	1.824	1.877	1.936	1.995	2.052	2.111	2.171	2.239	2.300	2.355	2.421
0.45	1.776	1.825	1.881	1.938	1.993	2.049	2.108	2.173	2.233	2.287	2.351
0.46	1.729	1.775	1.828	1.883	1.936	1.991	2.047	2.110	2.168	2.221	2.284
0.48	1.642	1.683	1.730	1.780	1.830	1.881	1.934	1.991	2.046	2.098	2.157
0.50	1.562	1.598	1.640	1.686	1.733	1.780	1.829	1.883	1.934	1.984	2.040

0.55	1.389	1.416	1.447	1.483	1.522	1.562	1.603	1.646	1.690	1.734	1.782
0.60	1.245	1.266	1.290	1.319	1.350	1.383	1.417	1.452	1.490	1.528	1.569
0.65	1.124	1.141	1.160	1.182	1.208	1.235	1.263	1.292	1.324	1.357	1.391
0.70	1.019	1.034	1.050	1.068	1.089	1.111	1.135	1.159	1.185	1.214	1.243
0.80	0.847	0.860	0.873	0.887	0.902	0.918	0.935	0.952	0.971	0.992	1.013
0.90	0.711	0.725	0.737	0.749	0.762	0.774	0.787	0.800	0.814	0.830	0.845
1.00	0.603	0.616	0.628	0.640	0.651	0.662	0.673	0.684	0.695	0.707	0.719

1.10	0.515	0.528	0.540	0.551	0.562	0.572	0.582	0.591	0.601	0.611	0.621
1.20	0.444	0.456	0.467	0.478	0.488	0.498	0.507	0.516	0.525	0.534	0.542
1.30	0.385	0.396	0.407	0.417	0.427	0.436	0.445	0.454	0.462	0.470	0.478
1.40	0.337	0.347	0.357	0.365	0.375	0.384	0.393	0.401	0.408	0.416	0.423
1.50	0.297	0.306	0.315	0.325	0.333	0.341	0.349	0.356	0.364	0.371	0.378

1.60	0.264	0.272	0.280	0.290	0.297	0.303	0.311	0.318	0.325	0.332	0.338
1.70	0.236	0.243	0.250	0.257	0.264	0.272	0.278	0.285	0.291	0.298	0.304
1.80	0.212	0.219	0.225	0.233	0.239	0.244	0.251	0.257	0.263	0.269	0.275
1.90	0.192	0.198	0.204	0.208	0.214	0.221	0.227	0.233	0.238	0.244	0.249
2.00	0.175	0.180	0.185	0.188	0.194	0.201	0.206	0.211	0.216	0.222	0.227

Element	Rh	Pd	Ag	Cd	In	Sn	Sb	Te	I	Xe	Cs
Z	45	46	47	48	49	50	51	52	53	54	55
Method	*RHF	*RHF	RHF	RHF	RHF	RHF	RHF	*RHF	RHF	RHF	RHF
(sin $[\theta]$ )/λ (Å⁻¹)
0.00	9.242	7.583	8.671	9.232	10.434	10.859	10.974	11.003	10.905	10.794	16.508
0.01			8.654	9.213	10.406	10.833	10.950		10.887	10.777	16.391
0.02			8.599	9.153	10.320	10.750	10.876		10.828	10.725	16.050
0.03			8.510	9.057	10.181	10.615	10.755		10.731	10.638	15.521
0.04	8.90	7.43	8.391	8.926	9.995	10.433	10.591	10.65	10.599	10.520	14.855
0.05	8.73	7.35	8.244	8.764	9.768	10.209	10.387	10.47	10.434	10.371	14.106

0.06	8.53	7.26	8.075	8.577	9.509	9.950	10.150	10.25	10.238	10.194	13.326
0.07	8.31	7.16	7.888	8.369	9.224	9.664	9.884	10.01	10.017	9.993	12.556
0.08	8.01	7.03	7.689	8.144	8.923	9.357	9.596	9.74	9.773	9.771	11.823
0.09	7.83	6.91	7.480	7.909	8.612	9.037	9.291	9.46	9.511	9.530	11.145
0.10	7.58	6.77	7.267	7.666	8.297	8.709	8.976	9.16	9.235	9.274	10.525

0.11	7.33	6.62	7.052	7.421	7.983	8.380	8.654	8.85	8.948	9.007	9.965
0.12	7.079	6.474	6.837	7.176	7.674	8.053	8.331	8.538	8.654	8.732	9.458
0.13	6.836	6.319	6.625	6.933	7.374	7.732	8.010	8.224	8.357	8.451	9.000
0.14	6.598	6.162	6.418	6.695	7.084	7.419	7.694	7.914	8.059	8.167	8.583
0.15	6.366	6.003	6.215	6.464	6.805	7.118	7.386	7.608	7.764	7.884	8.201

0.16	6.143	5.843	6.018	6.240	6.539	6.829	7.088	7.309	7.472	7.603	7.848
0.17	5.929	5.684	5.827	6.024	6.286	6.552	6.800	7.018	7.186	7.325	7.519
0.18	5.722	5.526	5.643	5.817	6.045	6.289	6.524	6.738	6.908	7.053	7.212
0.19	5.524	5.369	5.464	5.618	5.817	6.039	6.261	6.467	6.639	6.787	6.922
0.20	5.334	5.214	5.293	5.427	5.601	5.803	6.010	6.209	6.379	6.529	6.649

0.22	4.976	4.913	4.967	5.070	5.203	5.368	5.547	5.727	5.889	6.039	6.143
0.24	4.648	4.626	4.665	4.745	4.846	4.979	5.131	3.291	5.442	5.586	5.684
0.25	4.493	4.487	4.522	4.592	4.682	4.801	4.940	5.090	5.234	5.374	5.471
0.26	4.345	4.352	4.384	4.447	4.525	4.633	4.760	4.899	5.036	5.172	5.268
0.28	4.066	4.093	4.122	4.173	4.236	4.323	4.428	4.548	4.670	4.795	4.890
0.30	3.809	3.850	3.878	3.922	3.973	4.044	4.131	4.234	4.341	4.454	4.547

0.32	3.572	3.622	3.651	3.690	3.734	3.792	3.865	3.952	4.046	4.147	4.235
0.34	3.353	3.408	3.440	3.476	3.515	3.564	3.625	3.700	3.780	3.870	3.953
0.35	3.249	3.306	3.339	3.375	3.412	3.458	3.514	3.583	3.658	3.742	3.822
0.36	3.150	3.208	3.242	3.278	3.313	3.356	3.408	3.472	3.541	3.620	3.697
0.38	2.962	3.022	3.058	3.093	3.127	3.165	3.210	3.265	3.325	3.394	3.465
0.40	2.788	2.848	2.886	2.922	2.955	2.990	3.030	3.078	3.130	3.191	3.255

0.42	2.626	2.686	2.726	2.762	2.795	2.828	2.864	2.907	2.953	3.006	3.064
0.44	2.477	2.535	2.576	2.613	2.646	2.678	2.712	2.750	2.791	2.838	2.890
0.45	2.406	2.464	2.505	2.542	2.576	2.608	2.640	2.677	2.715	2.759	2.809
0.46	2.338	2.395	2.436	2.474	2.507	2.539	2.571	2.606	2.642	2.684	2.731
0.48	2.210	2.264	2.306	2.344	2.378	2.409	2.440	2.473	2.506	2.543	2.586
0.50	2.090	2.143	2.185	2.223	2.257	2.288	2.318	2.350	2.380	2.414	2.453

0.55	1.828	1.875	1.915	1.953	1.987	2.019	2.048	2.077	2.104	2.132	2.163
0.60	1.609	1.650	1.688	1.724	1.758	1.790	1.819	1.847	1.871	1.897	1.923
0.65	1.426	1.462	1.497	1.531	1.563	1.594	1.622	1.649	1.673	1.697	1.721
0.70	1.273	1.304	1.335	1.366	1.397	1.426	1.453	1.479	1.503	1.526	1.548
0.80	1.035	1.058	1.082	1.107	1.132	1.157	1.181	1.205	1.227	1.248	1.269
0.90	0.861	0.879	0.897	0.916	0.936	0.956	0.976	0.997	1.016	1.036	1.055
1.00	0.731	0.745	0.758	0.773	0.789	0.805	0.821	0.838	0.855	0.871	0.888

1.10	0.631	0.641	0.652	0.664	0.676	0.688	0.701	0.715	0.729	0.743	0.758
1.20	0.551	0.559	0.568	0.578	0.587	0.597	0.608	0.619	0.630	0.642	0.654
1.30	0.485	0.493	0.500	0.508	0.516	0.525	0.533	0.542	0.551	0.561	0.570
1.40	0.431	0.437	0.444	0.451	0.458	0.465	0.472	0.480	0.487	0.495	0.502
1.50	0.384	0.391	0.397	0.403	0.409	0.416	0.422	0.428	0.435	0.442	0.450

1.60	0.345	0.351	0.357	0.362	0.368	0.374	0.379	0.385	0.391	0.397	0.405
1.70	0.310	0.316	0.321	0.327	0.332	0.337	0.343	0.348	0.353	0.358	0.363
1.80	0.281	0.286	0.291	0.297	0.302	0.307	0.311	0.316	0.321	0.325	0.332
1.90	0.255	0.260	0.265	0.270	0.274	0.279	0.284	0.288	0.293	0.297	0.299
2.00	0.232	0.237	0.241	0.246	0.250	0.255	0.259	0.264	0.268	0.272	0.272

Element	Ba	La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy
Z	56	57	58	59	60	61	62	63	64	65	66
Method	RHF	*RHF	*RHF	*RMF	*RHF	*RHF	*RHF	RHF	*RHF	*RHF	*RHF
(sin $[\theta]$ )/λ (Å⁻¹)
0.00	18.267	17.805	17.378	16.987	16.606	16.243	15.897	15.563	15.266	14.974	14.641
0.01	18.157							15.486
0.02	17.828							15.260
0.03	17.309							14.898
0.04	16.636	16.45	16.10	15.62	15.30	14.99	14.70	14.425	14.30	13.90	13.64
0.05	15.854	15.79	15.46	14.94	14.67	14.39	14.12	13.867	13.81	13.37	13.14

0.06	15.008	15.05	14.77	14.22	13.97	13.72	13.48	13.253	13.27	12.81	12.60
0.07	14.138	14.28	14.03	13.47	13.25	13.03	12.81	12.611	12.70	12.22	12.03
0.08	13.278	13.51	13.29	12.72	12.52	12.33	12.14	11.963	12.11	11.62	11.44
0.09	12.431	12.74	12.56	11.99	11.82	11.65	11.49	11.329	11.52	11.02	10.87
0.10	11.675	12.01	11.85	11.29	11.15	11.00	10.86	10.722	10.95	10.45	10.32

0.11	10.958	11.32	11.19	10.65	10.52	10.40	10.27	10.150	10.39	9.91	9.79
0.12	10.302	10.671	10.561	10.052	9.944	9.833	9.722	9.618	9.871	9.407	9.303
0.13	9.707	10.072	9.981	9.506	9.412	9.316	9.218	9.128	9.382	8.942	8.848
0.14	9.168	9.522	9.448	9.008	8.928	8.843	8.758	8.678	8.926	8.512	8.429
0.15	8.682	9.017	8.958	8.556	8.486	8.413	8.336	8.267	8.505	8.121	8.045

0.16	8.241	8.555	8.507	8.144	8.084	8.020	7.953	7.891	8.114	7.761	7.693
0.17	7.840	8.131	8.094	7.768	7.717	7.661	7.602	7.548	7.754	7.430	7.370
0.18	7.474	7.742	7.714	7.424	7.380	7.332	7.280	7.232	7.422	7.128	7.073
0.19	7.139	7.384	7.365	7.107	7.071	7.029	6.983	6.942	7.114	6.849	6.800
0.20	6.829	7.053	7.041	6.815	6.785	6.749	6.710	6.673	6.828	6.591	6.547

0.22	6.275	6.462	6.462	6.291	6.272	6.247	6.218	6.191	6.316	6.127	6.092
0.24	5.791	5.948	5.957	5.831	5.822	5.806	5.787	5.768	5.868	5.720	5.693
0.25	5.570	5.714	5.728	5.620	5.615	5.605	5.589	5.574	5.664	5.534	5.510
0.26	5.361	5.495	5.312	5.421	5.421	5.413	5.402	5.390	5.472	5.358	5.337
0.28	4.975	5.092	5.115	5.053	5.059	5.059	5.055	5.030	5.117	5.030	5.016
0.30	4.628	4.730	4.759	4.719	4.731	4.737	4.739	4.740	4.796	4.731	4.723

0.32	4.313	4.405	4.438	4.414	4.432	4.443	4.450	4.456	4.504	4.457	4.454
0.34	4.028	4.111	4.146	4.136	4.157	4.173	4.185	4.195	4.238	4.205	4.206
0.35	3.893	3.974	4.010	4.006	4.029	4.047	4.060	4.072	4.113	4.086	4.089
0.36	3.769	3.844	3.881	3.882	3.906	3.925	3.940	3.954	3.993	3.971	3.976
0.38	3.533	3.602	3.640	3.648	3.675	3.697	3.715	3.731	3.767	3.755	3.763
0.40	3.318	3.381	3.420	3.434	3.462	3.486	3.306	3.525	3.559	3.554	3.565

0.42	3.123	3.180	3.219	3.238	3.267	3.292	3.314	3.335	3.367	3.368	3.380
0.44	2.944	2.997	3.035	3.057	3.087	3.114	3.137	3.159	3.189	3.194	3.209
0.43	2.861	2.911	2.949	2.973	3.003	3.029	3.053	3.075	3.105	3.113	3.128
0.46	2.781	2.829	2.866	2.891	2.922	2.948	2.973	2.995	3.025	3.034	3.050
0.48	2.631	2.676	2.712	2.739	2.769	2.796	2.821	2.844	2.872	2.884	2.901
0.50	2.494	2.535	2.570	2.598	2.628	2.655	2.680	2.703	2.730	2.745	2.763

0.55	2.197	2.230	2.262	2.291	2.320	2.346	2.371	2.394	2.419	2.457	2.456
0.60	1.951	1.979	2.008	2.037	2.064	2.089	2.113	2.156	2.138	2.178	2.197
0.65	1.745	1.770	1.796	1.824	1.849	1.872	1.895	1.917	1.937	1.958	1.977
0.70	1.570	1.592	1.617	1.643	1.666	1.688	1.709	1.730	1.749	1.770	1.788
0.80	1.288	1.308	1.329	1.351	1.372	1.391	1.411	1.429	1.446	1.465	1.482
0.90	1.073	1.090	1.109	1.128	1.146	1.164	1.181	1.198	1.213	1.231	1.246
1.00	0.904	0.920	0.936	0.953	0.969	0.985	1.000	1.016	1.030	1.045	1.060

1.10	0.772	0.785	0.799	0.814	0.828	0.842	0.856	0.870	0.883	0.897	0.910
1.20	0.666	0.678	0.690	0.702	0.715	0.727	0.739	0.752	0.763	0.776	0.787
1.30	0.580	0.391	0.602	0.612	0.623	0.634	0.644	0.655	0.666	0.676	0.687
1.40	0.511	0.521	0.530	0.539	0.548	0.557	0.566	0.575	0.383	0.595	0.604
1.50	0.436	0.463	0.470	0.478	0.486	0.494	0.502	0.511	0.519	0.527	0.535

1.60	0.411	0.415	0.421	0.428	0.435	0.442	0.449	0.457	0.463	0.470	0.478
1.70	0.367	0.374	0.380	0.386	0.392	0.398	0.404	0.409	0.416	0.423	0.429
1.80	0.337	0.340	0.345	0.350	0.355	0.360	0.366	0.372	0.377	0.382	0.388
1.90	0.304	0.310	0.314	0.319	0.324	0.328	0.333	0.337	0.343	0.348	0.353
2.00	0.277	0.284	0.288	0.292	0.296	0.301	0.305	0.307	0.313	0.318	0.322

Element	Ho	Er	Tm	Yb	Lu	Hf	Ta	W	Re	Os	Ir
Z	67	68	69	70	71	72	73	74	75	76	77
Method	*RHF	*RHF	*RHF	*RHF	*RHF	*RHF	*RHF	*RHF	*RHF	*RHF	*RHF
(sin $[\theta]$ )/λ (Å⁻¹)
0.00	14.355	14.080	13.814	13.557	13.486	13.177	12.856	12.543	12.263	11.987	11.718
0.01
0.02
0.03
0.04	13.57	13.16	12.92	12.70	12.74	12.55	12.31	12.06	11.83	11.59	11.37
0.05	13.14	12.70	12.48	12.28	12.38	12.23	12.01	11.80	11.60	11.39	11.18

0.06	12.66	12.19	12.00	11.81	11.95	11.85	11.69	11.51	11.34	11.15	10.96
0.07	12.15	11.66	11.48	11.31	11.50	11.45	11.33	11.18	11.04	10.88	10.72
0.08	11.61	11.11	10.96	10.80	11.03	11.02	10.95	10.83	10.73	10.59	10.45
0.09	11.08	10.58	10.44	10.29	10.55	10.59	10.55	10.47	10.40	10.29	10.17
0.10	10.55	10.06	9.93	9.80	10.08	10.16	10.15	10.10	10.05	9.98	9.88

0.11	10.05	9.56	9.45	9.33	9.62	9.73	9.75	9.74	9.71	9.65	9.58
0.12	9.562	9.095	8.994	8.892	9.180	9.308	9.363	9.369	9.366	9.334	9.281
0.13	9.108	8.662	8.571	8.480	8.762	8.907	8.982	9.011	9.028	9.016	8.982
0.14	8.681	8.262	8.180	8.098	8.370	8.525	8.616	8.663	8.697	8.702	8.686
0.15	8.284	7.895	7.821	7.746	8.001	8.163	8.266	8.327	8.376	8.396	8.395

0.16	7.917	7.557	7.490	7.421	7.660	7.822	7.933	8.006	8.067	8.099	8.111
0.17	7.577	7.247	7.185	7.123	7.343	7.502	7.617	7.699	7.769	7.813	7.836
0.18	7.262	6.962	6.905	6.849	7.047	7.202	7.321	7.408	7.485	7.537	7.570
0.19	6.971	6.698	6.646	6.595	6.774	6.922	7.040	7.132	7.213	7.272	7.313
0.20	6.700	6.454	6.407	6.360	6.520	6.660	6.776	6.870	6.954	7.019	7.067

0.22	6.213	6.017	5.978	5.938	6.063	6.185	6.295	6.388	6.475	6.547	6.604
0.24	5.788	5.632	5.601	5.568	5.664	5.768	5.867	5.957	6.043	6.117	6.180
0.25	5.595	5.457	5.428	5.398	5.483	5.578	5.672	5.759	5.843	5.917	5.982
0.26	5.412	5.290	5.265	5.238	5.312	5.399	5.487	5.571	5.653	5.727	5.792
0.28	5.075	4.981	4.961	4.940	4.996	5.069	5.147	5.224	5.301	5.372	5.437
0.30	4.771	4.699	4.685	4.669	4.712	4.772	4.840	4.910	4.981	5.049	5.113

0.32	4.494	4.440	4.430	4.419	4.453	4.503	4.563	4.626	4.691	4.755	4.816
0.34	4.240	4.200	4.195	4.188	4.215	4.258	4.310	4.366	4.425	4.485	4.543
0.35	4.121	4.087	4.084	4.078	4.103	4.143	4.191	4.245	4.301	4.359	4.415
0.36	4.007	3.978	3.976	3.973	3.996	4.033	4.078	4.129	4.182	4.237	4.293
0.38	3.790	3.771	3.773	3.773	3.793	3.825	3.865	3.910	3.959	4.010	4.061
0.40	3.591	3.579	3.583	3.586	3.604	3.632	3.668	3.709	3.753	3.800	3.848

0.42	3.405	3.399	3.406	3.411	3.429	3.454	3.486	3.523	3.563	3.606	3.651
0.44	3.233	3.232	3.241	3.248	3.265	3.288	3.317	3.350	3.387	3.427	3.468
0.45	3.151	3.153	3.162	3.170	3.187	3.209	3.237	3.269	3.304	3.342	3.382
0.46	3.073	3.076	3.086	3.095	3.111	3.133	3.159	3.190	3.224	3.260	3.299
0.48	2.924	2.930	2.942	2.952	2.968	2.988	3.013	3.041	3.072	3.105	3.141
0.50	2.785	2.793	2.806	2.818	2.834	2.853	2.876	2.902	2.930	2.961	2.994

0.55	2.477	2.490	2.505	2.518	2.534	2.551	2.571	2.592	2.616	2.641	2.669
0.60	2.216	2.232	2.248	2.263	2.278	2.294	2.311	2.330	2.349	2.371	2.394
0.65	1.995	2.012	2.028	2.043	2.058	2.073	2.089	2.105	2.122	2.140	2.160
0.70	1.085	1.823	1.839	1.854	1.868	1.882	1.896	1.911	1.926	1.942	1.959
0.80	1.497	1.515	1.530	1.545	1.558	1.571	1.583	1.596	1.608	1.621	1.634
0.90	1.260	1.276	1.291	1.305	1.317	1.329	1.341	1.352	1.363	1.374	1.385
1.00	1.073	1.088	1.101	1.114	1.126	1.138	1.148	1.159	1.169	1.179	1.189

1.10	0.922	0.935	0.948	0.960	0.971	0.982	0.993	1.003	1.012	1.022	1.031
1.20	0.799	0.811	0.822	0.833	0.844	0.854	0.864	0.874	0.883	0.892	0.901
1.30	0.698	0.708	0.719	0.729	0.739	0.748	0.758	0.767	0.776	0.784	0.793
1.40	0.614	0.623	0.632	0.642	0.651	0.660	0.668	0.677	0.685	0.694	0.702
1.50	0.544	0.552	0.560	0.569	0.577	0.585	0.593	0.601	0.609	0.617	0.624

1.60	0.485	0.492	0.500	0.507	0.515	0.522	0.530	0.537	0.544	0.551	0.558
1.70	0.436	0.442	0.449	0.455	0.462	0.469	0.475	0.482	0.489	0.495	0.502
1.80	0.394	0.399	0.405	0.411	0.417	0.423	0.429	0.435	0.441	0.447	0.453
1.90	0.358	0.363	0.368	0.373	0.379	0.384	0.389	0.395	0.400	0.406	0.411
2.00	0.327	0.331	0.336	0.341	0.345	0.350	0.355	0.360	0.365	0.370	0.374

Element	Pt	Au	Hg	Tl	Pb	Bi	Po	At	Rn	Fr	Ra
Z	78	79	80	81	82	83	84	85	86	87	88
Method	*RHF	RHF	RHF	*RHF	RHF	RHF	*RHF	*RHF	RHF	*RHF	*RHF
(sin $[\theta]$ )/λ (Å⁻¹)
0.00	10.813	10.573	10.964	12.109	12.597	13.096	13.368	13.473	13.492	18.715	20.561
0.01		10.559	10.948		12.573	13.070			13.470
0.02		10.511	10.897		12.494	12.989			13.403
0.03		10.434	10.813		12.366	12.857			13.292
0.04	10.55	10.328	10.698	11.71	12.193	12.678	12.95	13.09	13.139	17.14	18.94
0.05	10.40	10.195	10.555	11.51	11.979	12.456	12.74	12.89	12.949	16.41	18.15

0.06	10.23	10.040	10.387	11.27	11.730	12.197	12.49	12.65	12.724	15.64	17.31
0.07	10.03	9.865	10.197	11.00	11.454	11.908	12.21	12.38	12.469	14.87	16.42
0.08	9.82	9.673	9.989	10.72	11.155	11.595	11.90	12.08	12.187	14.13	15.54
0.09	9.60	9.467	9.766	10.42	10.840	11.264	11.57	11.76	11.884	13.42	14.69
0.10	9.37	9.251	9.533	10.12	10.516	10.921	11.22	11.43	11.565	12.77	13.88

0.11	9.13	9.028	9.291	9.81	10.186	10.571	10.87	11.08	11.232	12.16	13.12
0.12	8.882	8.799	9.045	9.500	9.855	10.219	10.509	10.729	10.892	11.605	12.419
0.13	8.636	8.568	8.796	9.195	9.527	9.869	10.153	10.375	10.546	11.093	11.776
0.14	8.389	8.337	8.547	8.896	9.203	9.523	9.798	10.021	10.199	10.620	11.187
0.15	8.145	8.106	8.299	8.603	8.888	9.186	9.449	9.671	9.854	10.180	10.648

0.16	7.904	7.877	8.055	8.320	8.581	8.857	9.109	9.328	9.512	9.770	10.155
0.17	7.667	7.652	7.815	8.046	8.285	8.539	8.779	8.991	9.177	9.386	9.702
0.18	7.436	7.431	7.579	7.781	7.999	8.233	8.459	8.666	8.849	9.023	9.285
0.19	7.210	7.214	7.350	7.526	7.724	7.939	8.151	8.350	8.531	8.681	8.899
0.20	6.991	7.003	7.128	7.282	7.461	7.658	7.856	8.046	8.223	8.356	8.540

0.22	6.572	6.598	6.702	6.822	6.969	7.132	7.303	3.474	7.639	7.754	7.891
0.24	6.181	6.216	6.305	6.399	6.520	6.654	6.800	6.952	7.102	7.208	7.318
0.25	5.995	6.035	6.116	6.201	6.310	6.432	6.567	6.709	6.852	6.954	7.055
0.26	5.817	5.859	5.934	6.011	6.110	6.221	6.345	6.477	6.612	6.712	6.807
0.28	5.478	5.525	5.591	5.654	5.736	5.828	5.933	6.047	6.166	6.261	6.347
0.30	5.164	5.214	5.272	5.327	5.395	5.472	5.560	5.658	5.762	5.852	5.931

0.32	4.873	4.924	4.976	5.025	5.083	5.148	5.222	5.305	5.397	5.480	5.555
0.34	4.603	4.654	4.702	4.746	4.797	4.852	4.915	4.987	5.065	5.141	5.212
0.35	4.475	4.526	4.572	4.614	4.662	4.714	4.772	4.838	4.912	4.984	5.053
0.36	4.352	4.403	4.447	4.488	4.533	4.581	4.636	4.697	4.765	4.834	4.900
0.38	4.120	4.169	4.211	4.249	4.290	4.333	4.380	4.433	4.492	4.555	4.616
0.40	3.905	3.952	3.991	4.028	4.066	4.104	4.146	4.192	4.244	4.300	4.356

0.42	3.704	3.750	3.787	3.823	3.858	3.893	3.931	3.972	4.017	4.067	4.118
0.44	3.518	3.562	3.597	3.632	3.665	3.698	3.732	3.769	3.808	3.854	3.901
0.45	3.430	3.472	3.507	3.541	3.573	3.606	3.639	3.673	3.711	3.754	3.798
0.46	3.345	3.386	3.420	3.454	3.485	3.517	3.548	3.582	3.617	3.658	3.700
0.48	3.184	3.223	3.256	3.288	3.318	3.348	3.378	3.408	3.441	3.477	3.516
0.50	3.034	3.070	3.102	3.133	3.162	3.191	3.219	3.248	3.277	3.311	3.346

0.55	2.701	2.732	2.760	2.789	2.816	2.842	2.868	2.893	2.918	2.945	2.974
0.60	2.420	2.446	2.471	2.497	2.522	2.546	2.570	2.593	2.616	2.639	2.663
0.65	2.181	2.203	2.225	2.248	2.271	2.293	2.315	2.337	2.358	2.378	2.399
0.70	1.976	1.995	2.015	2.035	2.055	2.076	2.096	2.116	2.135	2.154	2.173
0.80	1.647	1.661	1.676	1.692	1.708	1.725	1.742	1.758	1.775	1.791	1.808
0.90	1.396	1.407	1.419	1.431	1.444	1.457	1.471	1.485	1.499	1.513	1.527
1.00	1.198	1.208	1.218	1.228	1.239	1.249	1.260	1.272	1.283	1.295	1.307

1.10	1.040	1.048	1.057	1.066	1.075	1.084	1.093	1.102	1.112	1.122	1.132
1.20	0.909	0.918	0.926	0.934	0.942	0.949	0.957	0.965	0.974	0.982	0.990
1.30	0.801	0.809	0.816	0.824	0.831	0.838	0.846	0.853	0.860	0.867	0.874
1.40	0.709	0.717	0.724	0.731	0.738	0.745	0.752	0.758	0.765	0.771	0.778
1.50	0.632	0.639	0.646	0.653	0.659	0.666	0.672	0.678	0.684	0.690	0.696

1.60	0.565	0.572	0.579	0.585	0.591	0.598	0.603	0.609	0.615	0.621	0.626
1.70	0.508	0.514	0.521	0.527	0.533	0.538	0.544	0.550	0.555	0.561	0.566
1.80	0.459	0.465	0.471	0.476	0.482	0.488	0.493	0.498	0.503	0.508	0.513
1.90	0.416	0.422	0.427	0.432	0.438	0.443	0.448	0.453	0.458	0.463	0.468
2.00	0.379	0.384	0.389	0.394	0.399	0.404	0.409	0.413	0.418	0.423	0.427

Element	Ac	Th	Pa	U	Np	Pu	Am	Cm	Bk	Cf
Z	89	90	91	92	93	94	95	96	97	98
Method	*RHF	*RHF	*RHF	RHF	*RHF	*RHF	*RHF	*RHF	*RHF	*RHF
(sin $[\theta]$ )/λ (Å⁻¹)
0.00	20.484	20.115	19.568	19.119	18.759	18.191	17.840	17.710	17.406	16.841
0.01				19.047
0.02				18.825
0.03				18.470
0.04	19.10	18.92	18.37	17.999	17.70	17.10	16.80	16.80	16.53	16.28
0.05	18.41	18.33	17.77	17.436	17.16	16.55	16.28	16.33	16.08	15.85

0.06	17.64	17.66	17.11	16.805	16.55	15.95	15.70	15.80	15.58	15.37
0.07	16.84	16.93	16.39	16.131	15.91	15.31	15.09	15.24	15.04	14.84
0.08	16.01	16.19	15.66	15.436	15.25	14.65	14.47	14.66	14.48	14.30
0.09	15.19	15.43	14.92	14.738	14.58	14.00	13.84	14.06	13.91	13.75
0.10	14.40	14.68	14.20	14.052	13.92	13.37	13.24	13.47	13.33	13.20

0.11	13.64	13.95	13.51	13.389	13.28	12.76	12.65	12.90	12.78	12.66
0.12	12.923	13.255	12.850	12.756	12.665	12.191	12.095	12.344	12.241	12.135
0.13	12.253	12.594	12.228	12.157	12.085	11.653	11.572	11.817	11.729	11.637
0.14	11.632	11.972	11.646	11.595	11.540	11.149	11.083	11.319	11.243	11.164
0.15	11.058	11.388	11.102	11.069	11.029	10.679	10.626	10.848	10.784	10.716

0.16	10.528	10.845	10.597	10.579	10.551	10.243	10.200	10.407	10.353	10.294
0.17	10.038	10.339	10.128	10.122	10.104	9.836	9.803	9.993	9.948	9.898
0.18	9.586	9.868	9.691	9.696	9.688	9.457	9.433	9.605	9.568	9.527
0.19	9.168	9.430	9.285	9.299	9.300	9.102	9.086	9.241	9.212	9.178
0.20	8.780	9.022	8.906	8.928	8.936	8.770	8.760	8.900	8.878	8.850

0.22	8.083	8.287	8.221	8.254	8.275	8.163	8.164	8.277	8.266	8.249
0.24	7.474	7.645	7.617	7.659	7.689	7.619	7.631	7.721	7.720	7.713
0.25	7.196	7.353	7.341	7.387	7.420	7.368	7.384	7.465	7.468	7.466
0.26	6.935	7.079	7.081	7.129	7.165	7.129	7.148	7.222	7.229	7.231
0.28	6.455	6.578	6.600	6.652	6.694	6.683	6.708	6.770	6.784	6.793
0.30	6.025	6.129	6.167	6.221	6.266	6.274	6.304	6.358	6.378	6.393

0.32	5.637	5.727	5.775	5.830	5.878	5.899	5.933	5.981	6.006	6.026
0.34	5.285	5.364	5.418	5.473	5.523	5.553	5.591	5.635	5.664	5.687
0.35	5.122	5.196	5.252	5.307	5.357	5.391	5.429	5.472	5.502	5.528
0.36	4.966	5.036	5.093	5.148	5.197	5.235	5.274	5.316	5.347	5.374
0.38	4.675	4.738	4.796	4.850	4.899	4.940	4.981	5.021	5.055	5.084
0.40	4.410	4.466	4.524	4.576	4.625	4.669	4.710	4.749	4.784	4.815

0.42	4.168	4.218	4.275	4.325	4.372	4.417	4.459	4.497	4.532	4.565
0.44	3.946	3.992	4.046	4.094	4.140	4.185	4.226	4.263	4.299	4.333
0.45	3.842	3.885	3.938	3.985	4.030	4.076	4.116	4.152	4.189	4.222
0.46	3.742	3.784	3.835	3.881	3.925	3.970	4.010	4.046	4.082	4.116
0.48	3.554	3.592	3.641	3.685	3.727	3.771	3.810	3.844	3.880	3.914
0.50	3.381	3.416	3.462	3.503	3.543	3.586	3.624	3.657	3.693	3.726

0.55	3.003	3.032	3.071	3.106	3.141	3.179	3.213	3.244	3.277	3.309
0.60	2.687	2.712	2.744	2.775	2.805	2.839	2.869	2.897	2.927	2.957
0.65	2.421	2.442	2.470	2.495	2.522	2.551	2.578	2.603	2.630	2.657
0.70	2.193	2.212	2.235	2.257	2.280	2.306	2.330	2.352	2.376	2.400
0.80	1.824	1.840	1.857	1.875	1.893	1.912	1.930	1.949	1.968	1.987
0.90	1.541	1.554	1.568	1.582	1.597	1.611	1.626	1.641	1.657	1.673
1.00	1.318	1.330	1.342	1.353	1.365	1.377	1.389	1.402	1.415	1.427

1.10	1.142	1.152	1.161	1.171	1.181	1.191	1.201	1.212	1.222	1.233
1.20	0.999	1.007	1.016	1.024	1.033	1.041	1.049	1.058	1.067	1.076
1.30	0.882	0.889	0.896	0.904	0.911	0.918	0.926	0.933	0.941	0.948
1.40	0.784	0.791	0.797	0.803	0.810	0.816	0.823	0.830	0.836	0.843
1.50	0.702	0.708	0.714	0.720	0.725	0.731	0.737	0.743	0.748	0.754

1.60	0.632	0.637	0.643	0.649	0.653	0.659	0.664	0.669	0.674	0.679
1.70	0.571	0.576	0.581	0.585	0.591	0.596	0.601	0.606	0.611	0.165
1.80	0.518	0.523	0.528	0.534	0.537	0.542	0.547	0.551	0.555	0.560
1.90	0.472	0.477	0.481	0.485	0.490	0.495	0.499	0.503	0.507	0.511
2.00	0.432	0.436	0.440	0.443	0.449	0.453	0.457	0.461	0.465	0.469

Table 4.3.1.2| top | pdf |
Atomic scattering amplitudes (Å) for electrons for ionized atoms

A discussion of the values quoted here for s = 0 is given in Subsection 4.3.1.6. Self-consistent field calculations: HF: non-relativistic Hartree–Fock; DS: modified Dirac–Slater; RHF, *RHF: relativistic Hartree–Fock.

Element	H¹⁻	Li¹⁺	Be²⁺	O¹⁻	F¹⁻	Na¹⁺	Mg²⁺	Al³⁺	Si⁴⁺	Cl¹⁻	K¹⁺
Z	1	3	4	8	9	11	12	13	14	17	19
Method	HF	RHF	RHF	HF	HF	RHF	RHF	HF	HF	RHF	RHF
(sin $[\theta]$ )/λ (Å⁻¹)
0.00		0.157	0.082			1.130	0.831			6.770	3.436
0.01		239.497	478.762			240.469	479.511			−232.585	242.773
0.02		59.992	119.752			60.963	120.500			−53.125	63.260
0.03		26.750	53.268			27.719	54.015			−19.957	30.004
0.04	−12.00	15.115	29.999	−11.74	−12.21	16.081	30.745	45.52	60.34	−8.423	18.349
0.05	−6.78	9.730	19.229	−6.41	−6.85	10.692	19.972	29.36	38.80	−3.162	12.939

0.06	−4.03	6.804	13.378	−3.55	−3.97	7.762	14.119	20.58	27.10	−0.381	9.983
0.07	−2.45	5.040	9.850	−1.86	−2.25	5.993	10.589	15.29	20.05	1.219	8.184
0.08	−1.48	3.894	7.560	−0.79	−1.16	4.841	8.296	11.85	15.46	2.187	6.999
0.09	−0.87	3.109	5.990	−0.09	−0.43	4.049	6.722	9.49	12.32	2.783	6.169
0.10	−0.47	2.546	4.867	0.39	0.08	3.480	5.595	7.81	10.08	3.147	5.559

0.11	−0.20	2.130	4.036	0.72	0.43	3.056	4.760	6.56	8.41	3.361	5.092
0.12	−0.023	1.813	3.404	0.949	0.688	2.731	4.123	5.610	7.147	3.472	4.720
0.13	0.095	1.567	2.912	1.107	0.870	2.475	3.626	4.868	6.162	3.513	4.416
0.14	0.173	1.370	2.522	1.215	1.000	2.269	3.230	4.280	5.379	3.504	4.160
0.15	0.224	1.212	2.207	1.285	1.092	2.100	2.909	3.804	4.747	3.461	3.939

0.16	0.257	1.082	1.949	1.329	1.157	1.960	2.645	3.413	4.230	3.393	3.745
0.17	0.276	0.974	1.735	1.352	1.200	1.841	2.425	3.089	3.800	3.308	3.571
0.18	0.286	0.883	1.556	1.359	1.226	1.738	2.239	2.817	3.440	3.211	3.414
0.19	0.288	0.806	1.404	1.355	1.239	1.650	2.081	2.585	3.135	3.108	3.269
0.20	0.287	0.740	1.274	1.343	1.242	1.571	1.944	2.387	2.873	3.000	3.135

0.22	0.276	0.634	1.066	1.300	1.228	1.440	1.720	2.066	2.451	2.779	2.893
0.24	0.259	0.552	0.907	1.243	1.194	1.332	1.546	1.819	2.129	2.563	2.676
0.25	0.250	0.518	0.841	1.212	1.173	1.284	1.472	1.716	1.995	2.458	2.575
0.26	0.240	0.487	0.783	1.179	1.150	1.240	1.406	1.624	1.876	2.357	2.479
0.28	0.221	0.435	0.685	1.112	1.099	1.161	1.290	1.466	1.674	2.165	2.300
0.30	0.203	0.393	0.605	1.046	1.046	1.092	1.193	1.336	1.509	1.988	2.135

0.32	0.186	0.357	0.539	0.981	0.992	1.029	1.110	1.228	1.372	1.827	1.983
0.34	0.170	0.327	0.485	0.918	0.939	0.972	1.038	1.136	1.257	1.680	1.843
0.35	0.163	0.314	0.461	0.889	0.912	0.946	1.005	1.094	1.206	1.613	1.778
0.36	0.156	0.301	0.439	0.860	0.887	0.920	0.974	1.056	1.159	1.548	1.715
0.38	0.143	0.279	0.400	0.804	0.837	0.872	0.917	0.987	1.075	1.429	1.596
0.40	0.132	0.259	0.366	0.753	0.789	0.827	0.866	0.925	1.001	1.322	1.488

0.42	0.122	0.242	0.337	0.704	0.744	0.785	0.820	0.871	0.937	1.226	1.388
0.44	0.112	0.227	0.312	0.660	0.702	0.746	0.777	0.822	0.880	1.139	1.296
0.45	0.108	0.220	0.300	0.639	0.682	0.727	0.757	0.799	0.853	1.099	1.253
0.46	0.104	0.213	0.290	0.618	0.662	0.709	0.738	0.778	0.829	1.061	1.212
0.48	0.096	0.200	0.270	0.580	0.625	0.675	0.701	0.737	0.783	0.991	1.135
0.50	0.090	0.189	0.252	0.544	0.590	0.642	0.668	0.701	0.741	0.928	1.064

0.55	0.075	0.165	0.216	0.467	0.512	0.569	0.593	0.620	0.652	0.796	0.912
0.60	0.064	0.145	0.188	0.403	0.446	0.506	0.529	0.553	0.580	0.691	0.789
0.65	0.055	0.129	0.165	0.351	0.391	0.451	0.474	0.496	0.519	0.608	0.690
0.70	0.048	0.115	0.146	0.307	0.345	0.403	0.426	0.447	0.468	0.541	0.609
0.80	0.037	0.093	0.118	0.241	0.272	0.325	0.347	0.367	0.385	0.439	0.488
0.90	0.029	0.077	0.097	0.193	0.219	0.266	0.286	0.305	0.321	0.366	0.402
1.00	0.024	0.064	0.081	0.159	0.180	0.221	0.239	0.256	0.271	0.311	0.338

1.10	0.020	0.054	0.069	0.133	0.150	0.185	0.201	0.217	0.231	0.267	0.290
1.20	0.017	0.046	0.059	0.113	0.128	0.157	0.172	0.186	0.198	0.232	0.252
1.30	0.014	0.040	0.052	0.097	0.110	0.135	0.148	0.160	0.172	0.202	0.221
1.40	0.012	0.035	0.045	0.085	0.095	0.118	0.129	0.140	0.150	0.178	0.195
1.50	0.011	0.031	0.040	0.075	0.084	0.103	0.113	0.123	0.132	0.158	0.173

1.60		0.027	0.035			0.091	0.100			0.141	0.155
1.70		0.024	0.032			0.081	0.089			0.126	0.139
1.80		0.022	0.028			0.073	0.080			0.113	0.125
1.90		0.020	0.026			0.066	0.072			0.102	0.114
2.00		0.018	0.023			0.060	0.065			0.093	0.103

Element	Ca²⁺	Sc³⁺	Ti²⁺	Ti³⁺	Ti⁴⁺	V²⁺	V³⁺	V⁵⁺	Cr²⁺	Cr³⁺	Mn²⁺
Z	20	21	22	22	22	23	23	23	24	24	25
Method	RHF	HF	HF	HF	HF	RHF	HF	HF	HF	HF	RHF
(sin $[\theta]$ )/λ (Å⁻¹)
0.00	2.711					2.904					2.846
0.01	481.390					481.582					481.525
0.02	122.375					122.566					122.510
0.03	55.883					56.074					56.018
0.04	32.602	47.08	32.80	47.15	61.67	32.791	47.18	76.36	32.79	47.19	32.738
0.05	21.817	30.91	22.01	30.98	40.13	22.005	31.02	49.43	22.00	31.03	21.953

0.06	15.948	22.13	16.14	22.19	28.42	16.134	22.23	34.80	16.13	22.24	16.085
0.07	12.399	16.82	12.59	16.89	21.35	12.583	16.92	25.98	12.58	16.93	12.537
0.08	10.085	13.37	10.27	13.44	16.77	10.267	13.47	20.24	10.26	13.48	10.225
0.09	8.489	11.00	8.67	11.07	13.62	8.668	11.10	16.31	8.67	11.11	8.630
0.10	7.336	9.30	7.52	9.36	11.36	7.514	9.39	13.49	7.51	9.41	7.479

0.11	6.473	8.03	6.65	8.09	9.68	6.648	8.13	11.41	6.65	8.14	6.618
0.12	5.807	7.057	5.977	7.120	8.400	5.980	7.155	9.815	5.983	7.172	5.954
0.13	5.279	6.295	5.444	6.359	7.400	5.449	6.394	8.574	5.455	6.410	5.428
0.14	4.850	5.684	5.011	5.747	6.603	5.018	5.782	7.584	5.026	5.800	5.002
0.15	4.495	5.185	4.653	5.247	5.954	4.661	5.284	6.784	4.671	5.302	4.650

0.16	4.196	4.770	4.349	4.832	5.418	4.360	4.868	6.126	4.372	4.888	4.353
0.17	3.939	4.421	4.089	4.481	4.971	4.102	4.518	5.577	4.116	4.539	4.100
0.18	3.716	4.121	3.863	4.182	4.591	3.877	4.220	5.113	3.894	4.242	3.880
0.19	3.519	3.863	3.663	3.923	4.266	3.679	3.961	4.719	3.698	3.984	3.686
0.20	3.343	3.637	3.485	3.697	3.984	3.503	3.735	4.378	3.523	3.759	3.514

0.22	3.041	3.259	3.178	3.318	3.520	3.200	3.358	3.824	3.224	3.384	3.220
0.24	2.787	2.953	2.920	3.012	3.155	2.946	3.053	3.391	2.973	3.081	2.975
0.25	2.674	2.821	2.806	2.879	2.998	2.833	2.921	3.209	2.862	2.950	2.865
0.26	2.568	2.699	2.699	2.757	2.857	2.727	2.799	3.045	2.758	2.830	2.764
0.28	2.376	2.482	2.504	2.540	2.610	2.536	2.584	2.761	2.569	2.616	2.579
0.30	2.204	2.294	2.331	2.352	2.399	2.365	2.396	2.524	2.401	2.430	2.415

0.32	2.049	2.128	2.174	2.185	2.217	2.211	2.231	2.322	2.249	2.266	2.266
0.34	1.907	1.980	2.032	2.037	2.057	2.071	2.073	2.147	2.111	2.120	2.131
0.35	1.842	1.911	1.966	1.968	1.984	2.005	2.015	2.068	2.046	2.053	2.068
0.36	1.778	1.846	1.903	1.903	1.915	1.943	1.950	1.994	1.984	1.988	2.007
0.38	1.660	1.725	1.783	1.781	1.788	1.825	1.829	1.858	1.867	1.868	1.893
0.40	1.551	1.614	1.673	1.670	1.673	1.716	1.718	1.736	1.759	1.758	1.787

0.42	1.451	1.512	1.572	1.568	1.569	1.615	1.616	1.627	1.659	1.657	1.688
0.44	1.359	1.419	1.478	1.474	1.473	1.522	1.522	1.528	1.566	1.563	1.597
0.45	1.316	1.375	1.433	1.429	1.428	1.477	1.477	1.481	1.522	1.519	1.553
0.46	1.274	1.333	1.391	1.387	1.385	1.435	1.434	1.437	1.480	1.476	1.511
0.48	1.196	1.253	1.310	1.306	1.304	1.354	1.354	1.354	1.399	1.395	1.432
0.50	1.124	1.180	1.235	1.232	1.229	1.279	1.279	1.277	1.324	1.320	1.357

0.55	0.967	1.019	1.070	1.068	1.066	1.113	1.113	1.110	1.156	1.154	1.190
0.60	0.838	0.886	0.933	0.931	0.930	0.973	0.974	0.971	1.015	1.013	1.049
0.65	0.733	0.776	0.818	0.817	0.816	0.856	0.857	0.855	0.895	0.894	0.928
0.70	0.647	0.685	0.722	0.722	0.721	0.757	0.758	0.756	0.793	0.792	0.824
0.80	0.515	0.544	0.574	0.574	0.574	0.602	0.603	0.603	0.632	0.632	0.659
0.90	0.422	0.444	0.467	0.467	0.467	0.490	0.491	0.491	0.515	0.515	0.538
1.00	0.354	0.371	0.389	0.389	0.389	0.408	0.408	0.408	0.427	0.427	0.446

1.10	0.302	0.316	0.331	0.331	0.330	0.345	0.346	0.345	0.361	0.361	0.377
1.20	0.262	0.273	0.285	0.285	0.285	0.297	0.297	0.297	0.310	0.310	0.323
1.30	0.230	0.239	0.249	0.249	0.249	0.259	0.259	0.259	0.270	0.270	0.280
1.40	0.203	0.211	0.220	0.220	0.219	0.228	0.228	0.228	0.237	0.237	0.246
1.50	0.180	0.188	0.195	0.195	0.195	0.203	0.203	0.202	0.211	0.211	0.218

1.60	0.161					0.181					0.195
1.70	0.145					0.163					0.175
1.80	0.131					0.148					0.159
1.90	0.119					0.134					0.144
2.00	0.108					0.123					0.132

Element	Mn³⁺	Mn⁴⁺	Fe²⁺	Fe³⁺	Co²⁺	Co³⁺	Ni²⁺	Ni³⁺	Cu¹⁺	Cu²⁺	Zn²⁺
Z	25	25	26	26	27	27	28	28	29	29	30
Method	HF	HF	RHF	RHF	RHF	HF	RHF	HF	RHF	HF	RHF
(sin $[\theta]$ )/λ (Å⁻¹)
0.00			2.802	2.298	2.754		2.703		3.280		2.599
0.01			481.481	720.318	481.433		481.382		242.618		481.278
0.02			122.467	181.800	122.419		122.368		63.107		122.265
0.03			55.976	82.070	55.928		55.878		29.855		55.776
0.04	47.18	61.76	32.696	47.160	32.650	47.15	32.600	47.12	18.206	32.55	32.499
0.05	31.02	40.22	21.913	30.996	21.867	30.98	21.819	30.96	12.803	21.77	21.719

0.06	22.23	28.51	16.046	22.210	16.002	22.20	15.955	22.17	9.856	15.90	15.857
0.07	16.93	21.44	12.500	16.907	12.457	16.90	12.411	16.87	8.066	12.36	12.316
0.08	13.48	16.85	10.189	13.459	10.148	13.45	10.103	13.43	6.893	10.06	10.011
0.09	11.11	13.70	8.596	11.089	8.556	11.08	8.513	11.06	6.076	8.47	8.424
0.10	9.41	11.45	7.447	9.388	7.409	9.38	7.368	9.36	5.479	7.33	7.282

0.11	8.14	9.77	6.588	8.124	6.553	8.12	6.513	8.10	5.027	6.47	6.430
0.12	7.174	8.492	5.926	7.156	5.893	7.150	5.856	7.132	4.671	5.817	5.776
0.13	6.413	7.492	5.403	6.398	5.371	6.393	5.336	6.376	4.383	5.299	5.260
0.14	5.804	6.695	4.979	5.790	4.950	5.787	4.917	5.770	4.144	4.883	4.845
0.15	5.307	6.047	4.629	5.294	4.603	5.293	4.572	5.277	3.942	4.540	4.504

0.16	4.894	5.514	4.335	4.884	4.311	4.883	4.283	4.869	3.766	4.253	4.219
0.17	4.547	5.068	4.084	4.538	4.063	4.538	4.036	4.526	3.612	4.009	3.976
0.18	4.251	4.689	3.867	4.243	3.847	4.245	3.824	4.234	3.474	3.799	3.768
0.19	3.995	4.366	3.676	3.989	3.659	3.993	3.638	3.983	3.349	3.615	3.586
0.20	3.771	4.086	3.506	3.767	3.492	3.772	3.473	3.764	3.234	3.453	3.426

0.22	3.399	3.625	3.217	3.397	3.207	3.405	3.193	3.400	3.030	3.178	3.154
0.24	3.099	3.262	2.976	3.100	2.971	3.111	2.961	3.109	2.851	2.950	2.930
0.25	2.969	3.108	2.869	2.972	2.866	2.984	2.858	2.984	2.769	2.850	2.831
0.26	2.850	2.968	2.769	2.855	2.768	2.868	2.763	2.869	2.690	2.757	2.740
0.28	2.639	2.723	2.589	2.646	2.592	2.662	2.590	2.666	2.544	2.588	2.574
0.30	2.455	2.516	2.428	2.466	2.434	2.484	2.436	2.490	2.410	2.438	2.428

0.32	2.294	2.336	2.282	2.307	2.293	2.327	2.298	2.336	2.285	2.303	2.296
0.34	2.149	2.179	2.150	2.165	2.163	2.187	2.172	2.199	2.169	2.180	2.176
0.35	2.083	2.107	2.088	2.099	2.103	2.123	2.113	2.135	2.114	2.123	2.120
0.36	2.019	2.039	2.029	2.037	2.045	2.061	2.056	2.075	2.061	2.067	2.066
0.38	1.900	1.913	1.917	1.920	1.935	1.946	1.949	1.962	1.959	1.963	1.964
0.40	1.791	1.799	1.813	1.813	1.833	1.841	1.849	1.858	1.864	1.866	1.869

0.42	1.691	1.695	1.716	1.715	1.739	1.743	1.756	1.762	1.774	1.775	1.781
0.44	1.598	1.600	1.626	1.623	1.650	1.653	1.670	1.674	1.690	1.690	1.697
0.45	1.554	1.555	1.583	1.580	1.608	1.610	1.628	1.631	1.649	1.649	1.658
0.46	1.512	1.512	1.542	1.538	1.567	1.569	1.588	1.591	1.610	1.610	1.619
0.48	1.432	1.431	1.463	1.459	1.489	1.490	1.512	1.513	1.535	1.535	1.546
0.50	1.357	1.355	1.389	1.385	1.416	1.417	1.440	1.441	1.464	1.464	1.476

0.55	1.190	1.188	1.223	1.220	1.252	1.252	1.277	1.278	1.303	1.303	1.319
0.60	1.049	1.047	1.081	1.079	1.111	1.111	1.137	1.138	1.163	1.164	1.182
0.65	0.928	0.927	0.959	0.958	0.989	0.989	1.015	1.016	1.042	1.043	1.061
0.70	0.825	0.824	0.855	0.854	0.883	0.884	0.910	0.910	0.935	0.936	0.956
0.80	0.660	0.660	0.687	0.686	0.713	0.713	0.737	0.738	0.761	0.762	0.782
0.90	0.538	0.538	0.561	0.561	0.583	0.584	0.605	0.606	0.627	0.628	0.646
1.00	0.447	0.447	0.466	0.466	0.485	0.486	0.504	0.505	0.523	0.524	0.541

1.10	0.377	0.377	0.393	0.393	0.409	0.410	0.425	0.426	0.441	0.442	0.457
1.20	0.323	0.323	0.336	0.336	0.350	0.350	0.364	0.364	0.378	0.378	0.391
1.30	0.281	0.281	0.291	0.291	0.303	0.304	0.315	0.315	0.327	0.327	0.339
1.40	0.246	0.246	0.256	0.256	0.265	0.266	0.275	0.276	0.286	0.286	0.296
1.50	0.219	0.218	0.226	0.226	0.235	0.235	0.243	0.244	0.252	0.253	0.261

1.60			0.202	0.202	0.209		0.217		0.224		0.232
1.70			0.182	0.182	0.188		0.195		0.201		0.208
1.80			0.164	0.164	0.170		0.176		0.182		0.188
1.90			0.149	0.149	0.155		0.160		0.165		0.170
2.00			0.136	0.136	0.141		0.146		0.150		0.155

Element	Ga³⁺	Ge⁴⁺	Br¹⁻	Rb¹⁺	Sr²⁺	Y³⁺	Zr⁴⁺	Nb³⁺	Nb⁵⁺	Mo³⁺	Mo⁵⁺
Z	31	32	35	37	38	39	40	41	41	42	42
Method	HF	HF	RHF	RHF	RHF	*DS	*DS	*DS	*DS	*DS	*DS
(sin $[\theta]$ )/λ (Å⁻¹)
0.00			9.357	5.545	4.642
0.01			−230.004	244.880	483.320
0.02			−50.565	65.359	124.299
0.03			−17.431	32.090	57.798
0.04	47.03	61.67	−5.942	20.419	34.505	48.84	63.31	49.33	77.86	49.44	78.04
0.05	30.87	40.13	−0.738	14.987	23.704	32.67	41.74	33.15	50.92	33.26	51.09

0.06	22.09	28.43	1.978	12.005	17.816	23.86	30.02	24.34	36.28	24.45	36.45
0.07	16.78	21.37	3.508	10.176	14.246	18.54	22.95	19.01	27.45	19.11	27.61
0.08	13.34	16.78	4.399	8.957	11.907	15.07	18.34	15.52	21.70	15.63	21.87
0.09	10.97	13.63	4.917	8.091	10.283	12.68	15.17	13.12	17.76	13.23	17.92
0.10	9.28	11.38	5.202	7.442	9.101	10.95	12.90	11.38	14.92	11.49	15.09

0.11	8.02	9.71	5.335	6.932	8.206	9.66	11.20	10.07	12.82	10.18	12.98
0.12	7.057	8.437	5.367	6.516	7.506	8.658	9.898	9.062	11.212	9.170	11.369
0.13	6.305	7.442	5.331	6.166	6.942	7.867	8.874	8.257	9.952	8.364	10.105
0.14	5.703	6.650	5.248	5.863	6.477	7.227	8.052	7.601	8.945	7.708	9.094
0.15	5.213	5.818	5.132	5.595	6.084	6.696	7.378	7.057	8.124	7.163	8.269

0.16	4.809	5.481	4.996	5.352	5.746	6.249	6.817	6.596	7.444	6.702	7.586
0.17	4.470	5.041	4.846	5.130	5.449	5.867	6.343	6.200	6.873	6.304	7.012
0.18	4.182	4.669	4.688	4.925	5.186	5.534	5.936	5.853	6.388	5.957	6.523
0.19	3.934	4.351	4.527	4.733	4.949	5.242	5.582	5.548	5.969	5.650	6.101
0.20	3.719	4.078	4.365	4.552	4.734	4.981	5.273	5.275	5.605	5.376	5.733

0.22	3.364	3.631	4.046	4.218	4.352	4.535	4.751	4.805	5.002	4.903	5.123
0.24	3.081	3.281	3.745	3.914	4.021	4.161	4.327	4.410	4.520	4.505	4.634
0.25	2.960	3.133	3.602	3.773	3.871	3.995	4.143	4.233	4.313	4.327	4.424
0.26	2.849	3.000	3.465	3.638	3.729	3.841	3.972	4.069	4.124	4.162	4.232
0.28	2.654	2.769	3.208	3.384	3.466	3.560	3.668	3.771	3.791	3.860	3.892
0.30	2.487	2.574	2.975	3.151	3.228	3.311	3.403	3.507	3.505	3.592	3.599

0.32	2.340	2.407	2.765	2.938	3.012	3.088	3.168	3.269	3.255	3.351	3.344
0.34	2.210	2.262	2.576	2.744	2.815	2.886	2.957	3.054	3.034	3.132	3.117
0.35	2.150	2.195	2.488	2.652	2.723	2.792	2.860	2.955	2.933	3.031	3.013
0.36	2.093	2.133	2.405	2.565	2.635	2.702	2.768	2.859	2.837	2.934	2.915
0.38	1.986	2.018	2.252	2.403	2.470	2.534	2.596	2.681	2.659	2.752	2.732
0.40	1.888	1.914	2.114	2.254	2.319	2.381	2.439	2.518	2.497	2.585	2.566

0.42	1.798	1.819	1.990	2.119	2.180	2.240	2.295	2.369	2.350	2.432	2.414
0.44	1.714	1.732	1.877	1.996	2.053	2.111	2.163	2.231	2.215	2.292	2.276
0.45	1.674	1.691	1.825	1.938	1.994	2.050	2.102	2.167	2.152	2.225	2.211
0.46	1.635	1.652	1.775	1.883	1.937	1.992	2.042	2.105	2.092	2.162	2.148
0.48	1.562	1.577	1.682	1.780	1.831	1.883	1.931	1.988	1.978	2.042	2.031
0.50	1.493	1.507	1.598	1.686	1.733	1.782	1.828	1.881	1.872	1.931	1.922

0.55	1.337	1.351	1.415	1.483	1.522	1.564	1.604	1.647	1.643	1.690	1.686
0.60	1.201	1.216	1.266	1.318	1.350	1.385	1.419	1.454	1.453	1.491	1.489
0.65	1.082	1.098	1.140	1.182	1.208	1.237	1.266	1.295	1.295	1.326	1.326
0.70	0.977	0.994	1.034	1.068	1.089	1.113	1.137	1.161	1.163	1.188	1.188
0.80	0.803	0.821	0.860	0.887	0.902	0.919	0.937	0.954	0.955	0.973	0.974
0.90	0.667	0.684	0.725	0.749	0.761	0.775	0.788	0.801	0.802	0.815	0.816
1.00	0.559	0.575	0.616	0.640	0.651	0.662	0.673	0.684	0.685	0.696	0.696

1.10	0.474	0.489	0.528	0.551	0.562	0.572	0.582	0.591	0.592	0.601	0.601
1.20	0.406	0.419	0.456	0.478	0.488	0.498	0.507	0.516	0.516	0.525	0.525
1.30	0.351	0.363	0.396	0.417	0.427	0.436	0.445	0.453	0.453	0.462	0.462
1.40	0.307	0.317	0.347	0.366	0.376	0.384	0.393	0.401	0.401	0.408	0.408
1.50	0.271	0.280	0.306	0.324	0.332	0.340	0.348	0.356	0.356	0.363	0.363

1.60			0.272	0.288	0.296	0.303	0.311	0.318	0.318	0.325	0.325
1.70			0.243	0.257	0.265	0.271	0.278	0.285	0.285	0.292	0.292
1.80			0.219	0.232	0.238	0.244	0.251	0.257	0.257	0.263	0.263
1.90			0.198	0.209	0.215	0.221	0.227	0.232	0.232	0.238	0.238
2.00			0.180	0.190	0.196	0.201	0.206	0.211	0.211	0.216	0.216

Element	Mo³⁺	Ru³⁺	Ru⁴⁺	Rh³⁺	Rh⁴⁺	Pd²⁺	Pd⁴⁺	Ag¹⁺	Ag²⁺	Cd²⁺	In³⁺
Z	42	44	44	45	45	46	46	47	47	48	49
Method	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS
(sin $[\theta]$ )/λ (Å⁻¹)
0.00
0.01
0.02
0.03
0.04	92.49	49.53	63.83	49.53	63.87	35.30	63.89	21.21	35.23	35.15	49.41
0.05	60.17	33.34	42.27	33.35	42.31	24.50	42.32	15.77	24.43	24.36	33.23

0.06	42.61	24.54	30.54	24.55	30.58	18.61	30.61	12.79	18.54	18.47	24.43
0.07	32.01	19.21	23.46	19.22	23.50	15.03	23.52	10.96	14.97	14.90	19.11
0.08	25.13	15.73	18.85	15.74	18.89	12.69	18.92	9.73	12.63	12.56	15.65
0.09	20.40	13.33	15.68	13.34	15.72	11.06	15.75	8.87	11.00	10.94	13.26
0.10	17.02	11.59	13.39	11.61	13.44	9.87	13.46	8.22	9.82	9.76	11.53

0.11	14.50	10.29	11.69	10.31	11.74	8.97	11.76	7.70	8.92	8.87	10.24
0.12	12.585	9.281	10.381	9.301	10.430	8.259	10.458	7.287	8.217	8.169	9.249
0.13	11.086	8.480	9.351	8.502	9.399	7.687	9.431	6.935	7.652	7.608	8.463
0.14	9.891	7.827	8.521	7.853	8.571	7.214	8.603	6.631	7.184	7.146	7.826
0.15	8.919	7.286	7.840	7.313	7.891	6.813	7.924	6.361	6.789	6.756	7.299

0.16	8.118	6.827	7.271	6.858	7.322	6.467	7.357	6.117	6.448	6.419	6.856
0.17	7.449	6.432	6.788	6.465	6.841	6.163	6.877	5.894	6.149	6.126	6.476
0.18	6.881	6.088	6.372	6.124	6.426	5.892	6.464	5.687	5.883	5.865	6.147
0.19	6.395	5.784	6.011	5.822	6.065	5.647	6.105	5.494	5.643	5.629	5.858
0.20	5.975	5.511	5.692	5.553	5.747	5.423	5.788	5.312	5.424	5.416	5.600

0.22	5.283	5.042	5.153	5.087	5.211	5.026	5.255	4.975	5.036	5.036	5.158
0.24	4.739	4.646	4.712	4.695	4.771	4.679	4.818	4.667	4.697	4.705	4.786
0.25	4.508	4.469	4.519	4.520	4.578	4.521	4.626	4.522	4.541	4.553	4.621
0.26	4.297	4.304	4.340	4.356	4.400	4.370	4.449	4.383	4.394	4.410	4.466
0.28	3.931	4.003	4.020	4.057	4.080	4.090	4.130	4.120	4.121	4.142	4.184
0.30	3.620	3.733	3.738	3.789	3.799	3.836	3.850	3.876	3.871	3.898	3.930

0.32	3.352	3.490	3.488	3.547	3.548	3.601	3.601	3.649	3.640	3.672	3.701
0.34	3.118	3.269	3.263	3.327	3.323	3.385	3.376	3.437	3.427	3.463	3.490
0.35	3.011	3.166	3.158	3.224	3.218	3.284	3.271	3.336	3.327	3.363	3.390
0.36	2.910	3.067	3.058	3.125	3.118	3.185	3.171	3.239	3.230	3.268	3.295
0.38	2.725	2.882	2.872	2.939	2.931	3.000	2.984	3.055	3.046	3.086	3.115
0.40	2.557	2.711	2.702	2.768	2.759	2.828	2.812	2.883	2.875	2.917	2.947

0.42	2.406	2.553	2.545	2.609	2.601	2.668	2.653	2.723	2.716	2.759	2.790
0.44	2.267	2.408	2.400	2.462	2.454	2.520	2.505	2.573	2.567	2.611	2.643
0.45	2.202	2.339	2.332	2.393	2.385	2.450	2.436	2.502	2.497	2.541	2.574
0.46	2.140	2.273	2.266	2.326	2.319	2.382	2.369	2.434	2.429	2.473	2.506
0.48	2.024	2.148	2.143	2.199	2.193	2.253	2.242	2.304	2.300	2.343	2.378
0.50	1.916	2.033	2.028	2.082	2.077	2.133	2.124	2.182	2.179	2.222	2.258

0.55	1.682	1.779	1.776	1.823	1.820	1.869	1.863	1.913	1.912	1.953	1.989
0.60	1.487	1.568	1.567	1.607	1.606	1.647	1.644	1.687	1.686	1.725	1.760
0.65	1.325	1.392	1.392	1.426	1.426	1.461	1.460	1.496	1.496	1.531	1.564
0.70	1.189	1.244	1.244	1.274	1.274	1.304	1.304	1.335	1.335	1.367	1.397
0.80	0.975	1.014	1.015	1.036	1.037	1.059	1.060	1.083	1.083	1.107	1.132
0.90	0.817	0.846	0.846	0.863	0.863	0.880	0.880	0.898	0.898	0.917	0.936
1.00	0.696	0.719	0.720	0.732	0.732	0.745	0.746	0.759	0.759	0.774	0.789

1.10	0.602	0.621	0.621	0.631	0.631	0.642	0.642	0.653	0.653	0.664	0.676
1.20	0.525	0.542	0.542	0.551	0.551	0.560	0.560	0.569	0.569	0.578	0.588
1.30	0.462	0.477	0.477	0.485	0.485	0.493	0.493	0.501	0.501	0.508	0.516
1.40	0.409	0.423	0.423	0.430	0.430	0.437	0.437	0.444	0.444	0.451	0.458
1.50	0.363	0.377	0.377	0.384	0.384	0.391	0.391	0.397	0.397	0.403	0.409

1.60	0.325	0.338	0.338	0.344	0.344	0.350	0.350	0.356	0.356	0.362	0.368
1.70	0.292	0.304	0.304	0.310	0.310	0.316	0.316	0.322	0.322	0.327	0.332
1.80	0.263	0.275	0.275	0.280	0.280	0.286	0.286	0.291	0.291	0.296	0.301
1.90	0.238	0.249	0.249	0.254	0.254	0.260	0.260	0.265	0.265	0.270	0.274
2.00	0.216	0.227	0.227	0.232	0.232	0.237	0.237	0.241	0.241	0.246	0.251

Element	Sn²⁺	Sn⁴⁺	Sb³⁺	Sb⁵⁺	I¹⁻	Cs¹⁺	Ba²⁺	La³⁺	Ce³⁺	Ce⁴⁺	Pr³⁺
Z	50	50	51	51	53	55	56	57	58	58	59
Method	RHF	RHF	*DS	*DS	RHF	RHF	*DS	*DS	*DS	*DS	*DS
(sin $[\theta]$ )/λ (Å⁻¹)
0.00	6.144	3.971			13.835	9.035
0.01	484.819	961.330			−225.540	248.365
0.02	125.792	243.305			−46.145	68.827
0.03	59.280	110.331			−13.083	35.532
0.04	35.972	63.782	50.16	78.38	−1.690	23.823	37.64	51.70	51.62	65.94	51.53
0.05	25.152	42.227	33.97	51.44	3.399	18.344	26.81	35.49	35.42	44.36	35.34

0.06	19.242	30.510	25.14	36.81	5.981	15.307	20.87	26.65	26.59	32.62	26.51
0.07	15.646	23.435	19.81	27.97	7.365	13.414	17.25	21.30	21.23	25.51	21.15
0.08	13.280	18.833	16.32	22.22	8.103	12.124	14.86	17.78	17.72	20.87	17.65
0.09	11.625	15.668	13.91	18.28	8.462	11.180	13.17	15.34	15.29	17.66	15.22
0.10	10.411	13.395	12.16	15.45	8.586	10.448	11.92	13.57	13.51	15.34	13.45

0.11	9.484	11.703	10.85	13.35	8.560	9.851	10.96	12.22	12.17	13.60	12.11
0.12	8.750	10.407	9.825	11.743	8.437	9.345	10.185	11.163	11.119	12.258	11.064
0.13	8.152	9.388	9.010	10.486	8.249	8.903	9.547	10.313	10.275	11.185	10.224
0.14	7.653	8.571	8.344	9.480	8.021	8.506	9.003	9.610	9.576	10.312	9.531
0.15	7.227	7.902	7.790	8.660	7.767	8.143	8.531	9.016	8.987	9.586	8.947

0.16	6.856	7.345	7.319	7.982	7.500	7.806	8.113	8.505	8.482	8.972	8.446
0.17	6.528	6.875	6.911	7.413	7.228	7.491	7.738	8.056	8.038	8.441	8.008
0.18	6.234	6.473	6.555	6.928	6.955	7.193	7.395	7.658	7.645	7.979	7.619
0.19	5.968	6.124	6.239	6.512	6.685	6.911	7.080	7.300	7.292	7.569	7.270
0.20	5.725	5.818	5.955	6.149	6.423	6.643	6.787	6.974	6.970	7.202	6.954

0.22	5.293	5.304	5.464	5.548	5.925	6.143	6.256	6.398	6.403	6.568	6.396
0.24	4.918	4.886	5.050	5.067	5.468	5.688	5.785	5.900	5.912	6.033	5.914
0.25	4.747	4.703	4.864	4.860	5.255	5.475	5.568	5.674	5.690	5.794	5.695
0.26	4.586	4.535	4.691	4.671	5.054	5.272	5.362	5.461	5.480	5.570	5.489
0.28	4.289	4.232	4.375	4.336	4.681	4.893	4.980	5.069	5.094	5.163	5.109
0.30	4.021	3.967	4.094	4.048	4.348	4.549	4.633	4.716	4.745	4.800	4.766

0.32	3.778	3.730	3.840	3.793	4.049	4.237	4.318	4.396	4.429	4.474	4.454
0.34	3.556	3.516	3.611	3.567	3.782	3.954	4.032	4.106	4.142	4.179	4.170
0.35	3.452	3.416	3.503	3.463	3.658	3.823	3.899	3.971	4.008	4.042	4.037
0.36	3.352	3.320	3.401	3.363	3.541	3.698	3.772	3.843	3.880	3.911	3.910
0.38	3.164	3.140	3.208	3.177	3.325	3.466	3.536	3.602	3.640	3.667	3.673
0.40	2.991	2.973	3.031	3.006	3.129	3.255	3.321	3.383	3.422	3.444	3.455

0.42	2.830	2.817	2.867	2.848	2.951	3.064	3.124	3.183	3.221	3.240	3.255
0.44	2.680	2.672	2.716	2.702	2.789	2.890	2.946	3.000	3.038	3.054	3.072
0.45	2.610	2.604	2.644	2.632	2.714	2.808	2.862	2.914	2.952	2.967	2.986
0.46	2.541	2.537	2.575	2.565	2.641	2.731	2.782	2.832	2.870	2.883	2.904
0.48	2.412	2.410	2.444	2.438	2.505	2.586	2.632	2.679	2.715	2.726	2.749
0.50	2.290	2.291	2.322	2.319	2.379	2.452	2.495	2.538	2.573	2.582	2.606

0.55	2.020	2.023	2.050	2.051	2.103	2.163	2.197	2.232	2.264	2.268	2.295
0.60	1.791	1.794	1.819	1.822	1.871	1.923	1.951	1.980	2.010	2.011	2.038
0.65	1.594	1.597	1.622	1.625	1.673	1.721	1.745	1.770	1.797	1.796	1.823
0.70	1.426	1.428	1.453	1.455	1.503	1.548	1.570	1.592	1.617	1.615	1.641
0.80	1.157	1.157	1.181	1.182	1.227	1.269	1.288	1.307	1.328	1.326	1.349
0.90	0.956	0.956	0.976	0.977	1.017	1.055	1.072	1.090	1.108	1.107	1.126
1.00	0.805	0.804	0.821	0.821	0.855	0.888	0.904	0.920	0.936	0.935	0.952

1.10	0.688	0.688	0.702	0.702	0.729	0.757	0.771	0.785	0.799	0.799	0.813
1.20	0.597	0.597	0.608	0.608	0.630	0.654	0.666	0.678	0.690	0.690	0.702
1.30	0.525	0.524	0.534	0.533	0.551	0.571	0.581	0.591	0.602	0.602	0.612
1.40	0.465	0.465	0.473	0.473	0.487	0.504	0.512	0.521	0.530	0.530	0.539
1.50	0.416	0.416	0.422	0.422	0.435	0.448	0.456	0.463	0.471	0.471	0.478

1.60	0.374	0.374	0.379	0.379	0.391	0.402	0.409	0.415	0.421	0.421	0.428
1.70	0.338	0.338	0.343	0.343	0.353	0.364	0.369	0.374	0.380	0.380	0.386
1.80	0.306	0.306	0.311	0.311	0.321	0.330	0.335	0.340	0.345	0.345	0.350
1.90	0.279	0.279	0.284	0.284	0.293	0.301	0.306	0.310	0.314	0.314	0.319
2.00	0.255	0.255	0.259	0.259	0.268	0.276	0.280	0.284	0.288	0.288	0.292

Element	Pr⁴⁺	Nd³⁺	Pm³⁺	Sm³⁺	Eu²⁺	Eu³⁺	Gd³⁺	Tb³⁺	Dy³⁺	Ho³⁺	Er³⁺
Z	59	60	61	62	63	63	64	65	66	67	68
Method	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS
(sin $[\theta]$ )/λ (Å⁻¹)
0.00
0.01
0.02
0.03
0.04	65.86	51.44	51.35	51.26	36.99	51.17	51.08	51.04	50.92	50.83	50.74
0.05	44.30	35.25	35.15	35.07	26.17	34.97	34.90	34.85	34.72	34.64	34.55

0.06	32.55	26.42	26.33	26.25	20.26	26.15	26.08	26.02	25.92	25.83	25.74
0.07	25.44	21.07	20.98	20.90	16.67	20.81	20.74	20.68	20.58	20.50	20.41
0.08	20.81	17.57	17.49	17.41	14.30	17.32	17.25	17.19	17.09	17.01	16.93
0.09	17.60	15.14	15.06	14.98	12.65	14.90	14.83	14.77	14.68	14.60	14.53
0.10	15.29	13.38	13.30	13.23	11.44	13.15	13.08	13.02	12.94	12.86	12.79

0.11	13.55	12.04	11.97	11.90	10.51	11.83	11.76	11.71	11.62	11.55	11.48
0.12	12.210	11.003	10.937	10.870	9.770	10.802	10.739	10.681	10.604	10.538	10.469
0.13	11.141	10.167	10.106	10.044	9.167	9.979	9.919	9.863	9.792	9.728	9.664
0.14	10.272	9.480	9.422	9.366	8.663	9.305	9.248	9.194	9.128	9.068	9.007
0.15	9.550	8.901	8.849	8.796	8.229	8.740	8.686	8.634	8.574	8.517	8.460

0.16	8.939	8.405	8.357	8.310	7.850	8.257	8.207	8.158	8.102	8.049	7.995
0.17	8.413	7.972	7.930	7.886	7.511	7.838	7.791	7.746	7.694	7.645	7.594
0.18	7.955	7.589	7.551	7.512	7.206	7.468	7.425	7.383	7.335	7.290	7.242
0.19	7.549	7.245	7.212	7.177	6.927	7.138	7.099	7.059	7.016	6.974	6.930
0.20	7.187	6.932	6.904	6.874	6.669	6.839	6.804	6.768	6.729	6.690	6.650

0.22	6.561	6.384	6.364	6.342	6.204	6.316	6.289	6.258	6.227	6.196	6.162
0.24	6.033	5.910	5.899	5.884	5.792	5.865	5.845	5.822	5.798	5.773	5.745
0.25	5.797	5.695	5.687	5.677	5.601	5.661	5.645	5.625	5.604	5.582	5.557
0.26	5.577	5.492	5.488	5.481	5.419	5.469	5.456	5.439	5.421	5.402	5.380
0.28	5.176	5.118	5.121	5.120	5.080	5.115	5.107	5.096	5.085	5.071	5.055
0.30	4.818	4.780	4.789	4.793	4.768	4.794	4.792	4.787	4.780	4.772	4.760

0.32	4.496	4.473	4.486	4.496	4.482	4.501	4.504	4.504	4.502	4.498	4.492
0.34	4.205	4.193	4.210	4.224	4.218	4.233	4.240	4.244	4.247	4.247	4.244
0.35	4.069	4.061	4.081	4.096	4.093	4.107	4.116	4.122	4.126	4.128	4.128
0.36	3.939	3.936	3.956	3.973	3.973	3.987	3.997	4.005	4.011	4.014	4.016
0.38	3.697	3.700	3.724	3.743	3.748	3.759	3.773	3.784	3.793	3.799	3.804
0.40	3.476	3.484	3.509	3.531	3.540	3.550	3.566	3.579	3.590	3.600	3.607

0.42	3.273	3.285	3.312	3.335	3.347	3.356	3.374	3.389	3.403	3.414	3.423
0.44	3.087	3.103	3.130	3.155	3.168	3.176	3.196	3.213	3.228	3.241	3.253
0.45	3.000	3.017	3.045	3.069	3.084	3.092	3.112	3.130	3.146	3.160	3.172
0.46	2.916	2.934	2.962	2.988	3.003	3.010	3.031	3.049	3.066	3.081	3.094
0.48	2.759	2.779	2.807	2.833	2.850	2.856	2.878	2.897	2.915	2.931	2.945
0.50	2.614	2.636	2.664	2.690	2.709	2.714	2.736	2.756	2.775	2.791	2.807

0.55	2.299	2.324	2.351	2.376	2.397	2.400	2.423	2.444	2.463	2.481	2.498
0.60	2.040	2.065	2.091	2.115	2.137	2.138	2.160	2.181	2.201	2.220	2.237
0.65	1.823	1.848	1.872	1.895	1.917	1.917	1.939	1.959	1.978	1.997	2.014
0.70	1.639	1.664	1.686	1.708	1.730	1.729	1.749	1.769	1.788	1.806	1.823
0.80	1.347	1.369	1.389	1.408	1.428	1.427	1.445	1.463	1.480	1.497	1.513
0.90	1.125	1.144	1.162	1.179	1.197	1.196	1.212	1.228	1.244	1.260	1.274
1.00	0.951	0.968	0.984	0.999	1.015	1.014	1.029	1.044	1.058	1.072	1.086

1.10	0.813	0.827	0.841	0.855	0.869	0.869	0.882	0.895	0.908	0.921	0.934
1.20	0.702	0.714	0.727	0.739	0.751	0.751	0.763	0.775	0.787	0.798	0.810
1.30	0.612	0.623	0.634	0.644	0.655	0.655	0.666	0.676	0.687	0.697	0.708
1.40	0.539	0.548	0.557	0.567	0.576	0.576	0.585	0.595	0.604	0.613	0.623
1.50	0.478	0.486	0.494	0.502	0.510	0.510	0.519	0.527	0.535	0.544	0.552

1.60	0.428	0.435	0.442	0.449	0.456	0.456	0.463	0.470	0.478	0.485	0.492
1.70	0.386	0.392	0.398	0.404	0.410	0.410	0.416	0.423	0.429	0.436	0.442
1.80	0.350	0.355	0.360	0.366	0.371	0.371	0.377	0.382	0.388	0.394	0.399
1.90	0.319	0.324	0.328	0.333	0.338	0.338	0.343	0.348	0.353	0.358	0.363
2.00	0.292	0.296	0.301	0.305	0.309	0.309	0.313	0.318	0.322	0.327	0.331

Element	Tm³⁺	Yb²⁺	Yb³⁺	Lu³⁺	Hf⁴⁺	Ta⁵⁺	W⁶⁺	Os⁴⁺	Ir³⁺	Ir⁴⁺	Pt²⁺
Z	69	70	70	71	72	73	74	76	77	77	78
Method	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS
(sin $[\theta]$ )/λ (Å⁻¹)
0.00
0.01
0.02
0.03
0.04	50.67	36.30	50.58	50.50	64.91	79.42	94.00	65.56	51.44	65.65	37.41
0.05	34.47	25.49	34.40	34.32	43.35	52.47	61.68	44.00	35.25	44.09	26.60

0.06	25.67	19.61	25.59	25.52	31.63	37.84	44.11	32.26	26.43	32.36	20.68
0.07	20.34	16.03	20.27	20.19	24.54	28.99	33.51	25.17	21.09	25.26	17.09
0.08	16.86	13.68	16.79	16.72	19.93	23.24	26.62	20.55	17.60	20.64	14.72
0.09	14.46	12.05	14.39	14.32	16.76	19.29	21.89	17.36	15.18	17.45	13.06
0.10	12.72	10.86	12.65	12.59	14.47	16.45	18.50	15.06	13.42	15.15	11.84

0.11	11.42	9.95	11.35	11.29	12.77	14.34	15.98	13.34	12.10	13.43	10.91
0.12	10.406	9.243	10.343	10.282	11.463	12.727	14.051	12.019	11.071	12.108	10.170
0.13	9.603	8.669	9.542	9.484	10.432	11.460	12.545	10.971	10.248	11.061	9.567
0.14	8.950	8.191	8.891	8.835	9.600	10.443	11.341	10.122	9.571	10.211	9.058
0.15	8.405	7.788	8.349	8.296	8.918	9.613	10.361	9.421	9.006	9.510	8.623

0.16	7.943	7.436	7.890	7.839	8.348	8.924	9.550	8.833	8.523	8.919	8.241
0.17	7.545	7.128	7.495	7.447	7.863	8.343	8.870	8.330	8.104	8.415	7.902
0.18	7.196	6.852	7.150	7.104	7.445	7.847	8.292	7.895	7.734	7.978	7.595
0.19	6.888	6.601	6.843	6.801	7.081	7.418	7.795	7.512	7.404	7.594	7.314
0.20	6.610	6.372	6.569	6.529	6.760	7.042	7.364	7.172	7.107	7.253	7.055

0.22	6.128	5.962	6.093	6.058	6.214	6.415	6.650	6.591	6.585	6.668	6.587
0.24	5.717	5.601	5.688	5.659	5.765	5.907	6.080	6.107	6.138	6.181	6.173
0.25	5.532	5.434	5.505	5.479	5.566	5.687	5.836	5.893	5.936	5.965	5.981
0.26	5.358	5.276	5.334	5.310	5.382	5.485	5.613	5.693	5.745	5.764	5.799
0.28	5.038	4.980	5.019	5.000	5.049	5.124	5.220	5.331	5.395	5.398	5.458
0.30	4.748	4.708	4.734	4.720	4.754	4.809	4.882	5.009	5.078	5.072	5.145

0.32	4.484	4.456	4.474	4.464	4.489	4.530	4.586	4.719	4.789	4.779	4.857
0.34	4.240	4.221	4.234	4.228	4.247	4.279	4.323	4.456	4.524	4.512	4.590
0.35	4.126	4.110	4.122	4.117	4.134	4.162	4.201	4.333	4.400	4.387	4.464
0.36	4.015	4.003	4.013	4.010	4.025	4.051	4.086	4.215	4.280	4.267	4.343
0.38	3.806	3.800	3.807	3.807	3.821	3.843	3.872	3.994	4.055	4.042	4.114
0.40	3.612	3.609	3.616	3.618	3.632	3.650	3.675	3.789	3.845	3.834	3.900

0.42	3.431	3.432	3.437	3.442	3.455	3.473	3.495	3.599	3.651	3.641	3.702
0.44	3.262	3.266	3.271	3.277	3.291	3.307	3.327	3.423	3.471	3.462	3.518
0.45	3.182	3.187	3.191	3.199	3.213	3.229	3.248	3.340	3.385	3.377	3.430
0.46	3.105	3.110	3.115	3.123	3.137	3.153	3.172	3.259	3.303	3.295	3.346
0.48	2.958	2.965	2.969	2.979	2.993	3.009	3.027	3.106	3.146	3.140	3.186
0.50	2.820	2.829	2.833	2.844	2.859	2.875	2.892	2.963	3.000	2.995	3.036

0.55	2.514	2.526	2.528	2.541	2.557	2.573	2.590	2.646	2.675	2.672	2.704
0.60	2.253	2.267	2.269	2.283	2.299	2.315	2.331	2.375	2.399	2.398	2.423
0.65	2.031	2.046	2.047	2.061	2.077	2.092	2.108	2.144	2.164	2.164	2.184
0.70	1.839	1.855	1.855	1.870	1.885	1.900	1.914	1.945	1.962	1.962	1.979
0.80	1.529	1.544	1.544	1.558	1.572	1.585	1.598	1.623	1.636	1.636	1.649
0.90	1.289	1.304	1.303	1.317	1.329	1.341	1.353	1.375	1.386	1.386	1.397
1.00	1.099	1.113	1.112	1.125	1.137	1.148	1.159	1.179	1.189	1.189	1.199

1.10	0.946	0.959	0.958	0.970	0.981	0.992	1.002	1.021	1.031	1.031	1.040
1.20	0.821	0.833	0.832	0.843	0.854	0.864	0.873	0.892	0.901	0.901	0.909
1.30	0.718	0.728	0.728	0.738	0.748	0.757	0.766	0.784	0.792	0.792	0.800
1.40	0.632	0.641	0.641	0.650	0.659	0.668	0.677	0.693	0.701	0.701	0.709
1.50	0.560	0.569	0.569	0.577	0.585	0.593	0.601	0.616	0.624	0.624	0.631

1.60	0.500	0.507	0.507	0.515	0.522	0.529	0.537	0.551	0.558	0.558	0.565
1.70	0.449	0.455	0.455	0.462	0.469	0.475	0.482	0.495	0.502	0.502	0.508
1.80	0.405	0.411	0.411	0.417	0.423	0.429	0.435	0.447	0.453	0.453	0.459
1.90	0.368	0.373	0.373	0.379	0.384	0.389	0.395	0.405	0.411	0.411	0.416
2.00	0.336	0.341	0.341	0.345	0.350	0.355	0.360	0.370	0.374	0.374	0.379

Element	Pt⁴⁺	Au¹⁺	Au³⁺	Hg¹⁺	Hg²⁺	Tl¹⁺	Tl³⁺	Pb²⁺	Pb⁴⁺	Bi³⁺	Bi⁵⁺
Z	78	79	79	80	80	81	81	82	82	83	83
Method	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS	*DS
(sin $[\theta]$ )/λ (Å⁻¹)
0.00
0.01
0.02
0.03
0.04	65.73	23.52	51.50	23.84	37.35	24.11	51.46	37.98	65.83	52.12	80.28
0.05	44.16	18.07	35.32	18.38	26.53	18.65	35.29	27.15	44.27	35.91	53.34

0.06	32.42	15.05	26.49	15.36	20.63	15.62	26.48	21.23	32.54	27.09	38.69
0.07	25.33	13.19	21.15	13.49	17.04	13.74	21.15	17.62	25.45	21.74	29.85
0.08	20.71	11.94	17.67	12.23	14.67	12.47	17.67	15.24	20.83	18.23	24.09
0.09	17.52	11.04	15.25	11.31	13.03	11.54	15.26	13.57	17.65	15.81	20.13
0.10	15.22	10.35	13.50	10.60	11.82	10.83	13.51	12.34	15.35	14.04	17.29

0.11	13.50	9.80	12.18	10.04	10.89	10.26	12.20	11.40	13.64	12.70	15.17
0.12	12.178	9.341	11.153	9.565	10.165	9.775	11.178	10.642	12.316	11.663	13.539
0.13	11.130	8.946	10.331	9.156	9.569	9.356	10.362	10.024	11.272	10.827	12.262
0.14	10.281	8.599	9.660	8.795	9.072	8.983	9.696	9.500	10.427	10.138	11.234
0.15	9.579	8.285	9.097	8.466	8.644	8.645	9.139	9.049	9.730	9.559	10.392

0.16	8.988	7.997	8.617	8.166	8.271	8.335	8.664	8.653	9.144	9.061	9.690
0.17	8.484	7.731	8.201	7.887	7.940	8.045	8.253	8.297	8.644	8.629	9.097
0.18	8.047	7.480	7.834	7.624	7.640	7.773	7.890	7.975	8.211	8.245	8.587
0.19	7.662	7.243	7.506	7.376	7.367	7.516	7.567	7.679	7.830	7.901	8.144
0.20	7.320	7.018	7.211	7.141	7.114	7.272	7.275	7.406	7.492	7.589	7.755

0.22	6.735	6.598	6.693	6.703	6.658	6.817	6.765	6.912	6.913	7.040	7.100
0.24	6.246	6.210	6.247	6.301	6.253	6.400	6.326	6.472	6.429	6.566	6.564
0.25	6.029	6.028	6.046	6.112	6.065	6.205	6.127	6.268	6.214	6.351	6.329
0.26	5.827	5.852	5.855	5.930	5.886	6.017	5.939	6.075	6.014	6.148	6.111
0.28	5.459	5.519	5.505	5.587	5.550	5.664	5.591	5.714	5.647	5.773	5.721
0.30	5.131	5.209	5.186	5.270	5.240	5.337	5.275	5.383	5.320	5.433	5.377

0.32	4.385	4.921	4.895	4.975	4.953	5.035	4.985	5.078	5.023	5.123	5.069
0.34	4.565	4.652	4.627	4.702	4.686	4.756	4.718	4.797	4.751	4.838	4.790
0.35	4.439	4.525	4.501	4.573	4.560	4.624	4.591	4.664	4.623	4.704	4.660
0.36	4.318	4.402	4.379	4.448	4.437	4.497	4.469	4.536	4.501	4.576	4.535
0.38	4.090	4.170	4.149	4.212	4.206	4.257	4.238	4.295	4.269	4.333	4.300
0.40	3.880	3.953	3.936	3.993	3.990	4.034	4.022	4.072	4.053	4.108	4.083

0.42	3.684	3.752	3.737	3.789	3.788	3.827	3.821	3.864	3.851	3.899	3.881
0.44	3.502	3.564	3.552	3.599	3.600	3.635	3.633	3.671	3.663	3.705	3.692
0.45	3.416	3.475	3.464	3.509	3.511	3.544	3.544	3.579	3.574	3.613	3.603
0.46	3.333	3.389	3.379	3.422	3.424	3.456	3.457	3.491	3.488	3.524	3.516
0.48	3.176	3.225	3.218	3.258	3.260	3.290	3.293	3.323	3.323	3.355	3.351
0.50	3.028	3.073	3.068	3.104	3.107	3.134	3.139	3.166	3.168	3.197	3.197

0.55	2.700	2.735	2.733	2.762	2.765	2.790	2.795	2.819	2.823	2.847	2.850
0.60	2.422	2.449	2.448	2.474	2.476	2.498	2.502	2.524	2.528	2.549	2.554
0.96	2.184	2.206	2.206	2.227	2.229	2.249	2.252	2.272	2.276	2.295	2.300
0.70	1.980	1.998	1.998	2.017	2.017	2.036	2.038	2.057	2.059	2.077	2.080
0.80	1.650	1.663	1.663	1.678	1.678	1.693	1.694	1.709	1.710	1.726	1.727
0.90	1.397	1.408	1.408	1.420	1.420	1.432	1.432	1.445	1.445	1.458	1.458
1.00	1.199	1.208	1.209	1.218	1.218	1.229	1.228	1.239	1.239	1.250	1.249

1.10	1.040	1.048	1.048	1.057	1.057	1.066	1.066	1.075	1.075	1.084	1.084
1.20	0.909	0.917	0.917	0.926	0.925	0.934	0.933	0.942	0.941	0.950	0.949
1.30	0.800	0.808	0.808	0.816	0.816	0.824	0.824	0.831	0.831	0.838	0.838
1.40	0.709	0.717	0.716	0.724	0.724	0.731	0.731	0.738	0.738	0.745	0.745
1.50	0.631	0.638	0.638	0.645	0.645	0.652	0.652	0.659	0.659	0.665	0.665

1.60	0.565	0.572	0.572	0.578	0.578	0.585	0.585	0.591	0.591	0.597	0.597
1.70	0.508	0.514	0.514	0.520	0.520	0.526	0.527	0.532	0.533	0.538	0.538
1.80	0.459	0.465	0.465	0.470	0.470	0.476	0.476	0.482	0.482	0.487	0.487
1.90	0.416	0.422	0.422	0.427	0.427	0.432	0.432	0.438	0.438	0.443	0.443
2.00	0.379	0.384	0.384	0.389	0.389	0.394	0.394	0.399	0.399	0.404	0.404

Element	Ra²⁺	Ac³⁺	U³⁺	U⁴⁺	U⁶⁺
Z	88	89	92	92	92
Method	*DS	*DS	*DS	*DS	*DS
(sin $[\theta]$ )λ (Å⁻¹)
0.00
0.01
0.02
0.03
0.04	40.04	54.00	54.02	68.15	96.83
0.05	29.19	37.78	37.81	46.56	64.49

0.06	23.23	28.91	28.95	34.80	46.89
0.07	19.57	23.53	23.57	27.67	36.26
0.08	17.14	19.98	20.03	23.01	29.33
0.09	15.42	17.51	17.57	19.78	24.56
0.10	14.12	15.70	15.76	17.44	21.12

0.11	13.11	14.31	14.39	15.67	18.55
0.12	12.291	13.217	13.300	14.296	16.573
0.13	11.602	12.324	12.416	13.192	15.010
0.14	11.008	11.577	11.679	12.287	13.749
0.15	10.486	10.939	11.050	11.528	12.709

0.16	10.018	10.382	10.503	10.879	11.837
0.17	9.592	9.889	10.018	10.314	11.093
0.18	9.200	9.446	9.583	9.816	10.451
0.19	8.836	9.042	9.188	9.371	9.889
0.20	8.495	8.671	8.824	8.967	9.391

0.22	7.873	8.008	8.174	8.261	8.544
0.24	7.315	7.427	7.602	7.655	7.843
0.25	7.057	7.161	7.340	7.380	7.534
0.26	6.811	6.909	7.091	7.122	7.247
0.28	6.355	6.444	6.629	6.647	6.729
0.30	5.940	6.022	6.208	6.219	6.273

0.32	5.563	5.639	5.824	5.830	5.865
0.34	5.219	5.291	5.472	5.475	5.497
0.35	5.059	5.128	5.307	5.309	5.327
0.36	4.906	4.973	5.149	5.151	5.164
0.38	4.621	4.683	4.853	4.853	4.861
0.40	4.360	4.417	4.580	4.580	4.584

0.42	4.122	4.174	4.329	4.328	4.330
0.44	3.904	3.951	4.098	4.097	4.096
0.45	3.801	3.847	3.989	3.988	3.987
0.46	3.703	3.747	3.885	3.883	3.881
0.48	3.518	3.558	3.688	3.686	3.683
0.50	3.348	3.385	3.506	3.504	3.500

0.55	2.975	3.005	3.107	3.106	3.100
0.60	2.664	2.689	2.776	2.774	2.768
0.65	2.400	2.421	2.496	2.494	2.489
0.70	2.174	2.193	2.258	2.256	2.252
0.80	1.808	1.824	1.875	1.874	1.872
0.90	1.527	1.541	1.583	1.582	1.582
1.00	1.307	1.319	1.354	1.354	1.354

1.10	1.132	1.142	1.171	1.172	1.172
1.20	0.991	0.999	1.024	1.025	1.025
1.30	0.874	0.882	0.904	0.904	0.905
1.40	0.778	0.784	0.804	0.804	0.804
1.50	0.696	0.702	0.720	0.720	0.720

1.60	0.626	0.632	0.648	0.648	0.648
1.70	0.566	0.571	0.586	0.586	0.586
1.80	0.513	0.518	0.533	0.533	0.533
1.90	0.467	0.472	0.486	0.486	0.486
2.00	0.427	0.431	0.444	0.444	0.444

By the use of Poisson's equation relating the potential and charge-density distributions, it is possible to derive the Mott–Bethe formula for [f^B(s)] in terms of the atomic scattering factors for X-rays, [f_x(s)] : $[f^B(s)=2\pi{me^2\over h^2\varepsilon_0}\{Z-f_x(s)\}/s^2, \eqno (4.3.1.14)]$ where $[\varepsilon_0]$ is the permittivity of vacuum, or $[f^B(s)=0.023934\, \lambda^2\{Z-f_x(s)\}/\sin^2\theta \eqno (4.3.1.15)]$ [for λ in Å, [f^B(s)] in Å, and in electron units]. This was used for the other listed values.

References

International Tables for Crystallography (2006). Vol. C. ch. 4.3, pp. 259-260