Evaluation of neutron nuclear data for erbium

Figures & data

Table 1. Isotopic abundances and reaction Q-values of erbium isotopes.

	^162Er	^164Er	^166Er	^167Er	^168Er	^170Er
Abundances (%)	0.139	1.601	33.503	22.869	26.978	14.910
Q-values (MeV)
(n, γ)	6.903	6.650	6.436	7.771	6.003	5.682
(n, p)	0.487	−0.180	−1.072	−0.228	−2.148	−3.088
(n, α)	8.477	7.758	7.101	8.323	6.268	5.468
(n, d)	−4.204	−4.630	−5.091	−5.284	−5.775	−6.376
(n, t)	−6.833	−6.781	−6.823	−5.271	−6.798	−6.926
(n, ^3He)	−3.524	−4.623	−5.818	−6.539	−7.267	−8.410
(n, 2n)	−9.205	−8.847	−8.475	−6.436	−7.771	−7.257
(n, np)	−6.429	−6.855	−7.316	−7.509	−7.999	−8.600
(n, nα)	1.645	1.304	0.830	0.665	0.552	0.051
(n, nd)	−13.090	−13.038	−13.080	−11.528	−13.056	−13.184
(n, 3n)	−16.427	−15.750	−15.125	−14.911	−14.208	−13.261

Table 2. Resolved and unresolved resonance regions.

Target nuclei	Resolved resonance	Unresolved resonance
^162Er	10^−5 eV – 250 eV	250 eV – 100 keV
^164Er	10^−5 eV – 800 eV	800 eV – 100 keV
^166Er	10^−5 eV – 3.0 keV	3.0 keV – 200 keV
^167Er	10^−5 eV – 591 eV	591 eV – 100 keV
^168Er	10^−5 eV – 3.5 keV	3.5 keV – 500 keV
^170Er	10^−5 eV – 3.0 keV	3.0 keV – 650 keV

Figure 1. Unresolved resonance region for n +¹⁶⁷Er.

Figure 2. Unresolved resonance region for n +¹⁷⁰Er.

Figure 3. Total cross section of elemental Er.

Table 3. Coupling schemes used in the interaction between neutron and target.

Target nuclei	Coupled levels*
^162Er	0^+(g.s.), 2^+(0.10204), 4^+(0.32962), 6^+(0.66668), 2^+(0.90072), 3^+(1.00206), 8^+(1.09670), 4^+(1.12811), 3^−(1.35677)
^164Er	0^+(g.s.), 2^+(0.09138), 4^+(0.29943), 6^+(0.61437), 2^+(0.86025), 3^+(0.94640), 8^+(1.02459), 4^+(1.05848), 3^−(1.43397)
^166Er	0^+(g.s.), 2^+(0.08058), 4^+(0.26499), 6^+(0.54546), 8^+(0.91121), 3^−(1.51374)
^167Er	7/2^+(g.s), 9/2^+(0.07932), 11/2^+(0.17797), 13/2^+(0.29495)
^168Er	0^+(g.s.), 2^+(0.07980), 4^+(0.26409), 6^+(0.54875), 8^+(0.92831), 3^−(1.43147)
^170Er	0^+(g.s.), 2^+(0.07860), 4^+(0.26015), 6^+(0.54072), 8^+(0.91502), 2^+(0.93403), 3^+(1.01054), 4^+(1.12732), 3^−(1.34021)
Note: *The number in the parentheses indicates the excitation energy in MeV.

Table 4. Deformation parameters in the coupled-channel calculation.

Target	Method	Deformation parameters*
^162Er	SRM	β20 = 0.250, β30 = 0.046, β4 = 0.050
^164Er	SRM	β20 = 0.213, β30 = 0.038, β4 = 0.045
^166Er	SRM	β20 = 0.262, β30 = 0.053, β4 = 0.040
^167Er	RRM	β2 = 0.294, β4 = 0.001, β6 =−0.023
^168Er	SRM	β20 = 0.260, β30 = 0.057, β4 =−0.04
^170Er	SRM	β20 = 0.264, β30 = 0.055, β4 =−0.03
Note: *For the definition of deformation parameters, see Ref. [16].

Table 5. Level density parameters for each nucleus.

Nuclei	a(*)	Δ	Esh	T	E 0	Em
	1/MeV	MeV	MeV	MeV	MeV	MeV	MeV
^171Er	20.616	0.918	1.520	0.517	−0.876	5.556	0.615
^170Er	20.165	1.841	1.740	0.579	−0.754	7.764	1.543
^169Er	19.931	0.923	1.659	0.517	−0.753	5.419	0.770
^168Er	19.559	1.852	1.843	0.560	−0.322	7.166	1.768
^167Er	19.951	0.929	1.916	0.564	−1.449	6.503	0.878
^166Er	19.758	1.863	2.177	0.540	−0.216	6.951	1.948
^165Er	19.721	0.934	2.568	0.545	−1.312	6.241	0.590
^164Er	19.554	1.874	2.668	0.555	−0.500	7.383	1.798
^163Er	20.272	0.940	3.040	0.510	−1.130	5.846	0.735
^162Er	19.349	1.886	3.006	0.527	−0.161	6.852	1.623
^161Er	19.842	0.946	3.339	0.531	−1.389	6.270	0.621
^160Er	19.144	1.897	3.217	0.527	−0.155	6.863	1.008
^170Ho	20.024	0.000	1.480	0.386	−0.390	2.209	0.140
^169Ho	19.261	0.923	1.801	0.553	−1.064	5.984	0.359
^168Ho	19.823	0.000	1.550	0.488	−1.290	3.868	0.193
^167Ho	19.065	0.929	1.863	0.546	−0.942	5.808	0.570
^166Ho	18.616	0.000	1.715	0.555	−1.814	4.856	0.597
^165Ho	18.868	0.934	2.069	0.556	−1.068	6.014	1.056
^164Ho	19.421	0.000	2.261	0.483	−1.333	3.882	0.343
^163Ho	18.671	0.940	2.668	0.578	−1.484	6.630	0.720
^162Ho	19.219	0.000	2.893	0.370	−0.399	2.119	0.766
^161Ho	18.473	0.946	3.157	0.527	−0.906	5.679	0.827
^160Ho	19.017	0.000	3.460	0.454	−1.210	3.565	0.170
^168Dy	19.962	1.852	1.924	0.494	0.366	5.992	0.873
^167Dy	20.440	0.929	1.843	0.585	−1.889	7.134	0.098
^166Dy	19.758	1.863	2.008	0.556	−0.373	7.221	1.351
^165Dy	19.645	0.934	1.905	0.561	−1.310	6.327	0.706
^164Dy	19.078	1.874	2.014	0.569	−0.344	7.275	1.303
^163Dy	19.156	0.940	2.163	0.569	−1.365	6.445	0.660
^162Dy	18.802	1.886	2.461	0.582	−0.575	7.638	1.767
^161Dy	19.464	0.946	2.764	0.563	−1.568	6.656	0.568
^160Dy	19.144	1.897	2.875	0.579	−0.774	7.872	1.708
^159Dy	19.642	0.952	3.162	0.543	−1.455	6.419	0.576
^158Dy	18.939	1.909	3.250	0.583	−0.894	8.056	1.559

Table 6. Gamma-ray strength functions for s-wave neutron in units of 10⁻⁴.

Compound nuclei	Present work	Mughabghab [37]
^163Er	86.41	145 ± 25*
^165Er	55.70	48 ± 8*
^167Er	15.92	24 ± 3
^168Er	211.7	220 ± 12
^169Er	7.162	9.2 ± 1.0
^171Er	3.979	4.32 ± 0.86**
Notes: *Calculated from the s-wave average level-spacing and the s-wave average radiative width given in Ref. [37]. **Calculated from the recommended D 0 in Ref. [37] and a theoretical prediction of <Γγ0> = 54 meV.

Figure 4. Relative capture gamma-ray spectrum from ¹⁶⁷Er at 27 keV.

Table 7. Pre-equilibrium parameters used in the present work.

Target nuclei	K(MeV^3)	K pickup	K knockout
^162Er	190	1.0	1.0
^164Er	100	1.5	1.5
^166Er	170	2.0	2.0
^167Er	180	2.0	2.0
^168Er	190	3.5	3.5
^170Er	100	5.0	6.0

Figure 5. Maxwellian-averaged capture cross sections of ^162,164Er.

Figure 6. Radiative capture cross section of ¹⁶⁶Er.

Figure 7. Radiative capture cross section of ¹⁶⁷Er.

Figure 8. Radiative capture cross section of ¹⁶⁸Er.

Figure 9. Radiative capture cross section of ¹⁷⁰Er.

Figure 10. Radiative capture cross section of elemental Er.

Figure 11. ¹⁶²Er (n, 2n)¹⁶¹Er reaction cross section.

Figure 12. ¹⁶⁴Er (n, 2n)¹⁶³Er reaction cross section.

Figure 13. ¹⁶⁶Er (n, 2n)¹⁶⁵Er reaction cross section.

Figure 14. ¹⁶⁸Er (n, 2n)^167m Er reaction cross section.

Figure 15. ¹⁷⁰Er (n, 2n)¹⁶⁹Er reaction cross section.

Figure 16. ¹⁶⁷Er (n, 2n′)^167m Er reaction cross section.

Figure 17. ¹⁶⁶Er (n, p)^166g Ho reaction cross section.

Figure 18. ¹⁶⁷Er (n, p)¹⁶⁷Ho reaction cross section.

Figure 19. ¹⁶⁸Er (n, p)¹⁶⁸Ho reaction cross section.

Figure 20. ¹⁶⁸Er (n, α)¹⁶⁵Dy reaction cross section.

Figure 21. ¹⁷⁰Er (n, α)¹⁶⁷Dy reaction cross section.

Figure 22. Angular distributions of neutrons in the energy region from 0.9 to 2.0 MeV.

Figure 23. Angular distributions of neutrons in the energy region from 2.5 to 3.5 MeV.

Figure 24. Neutron emission spectra for elemental Er at 90°.

Soukhovitski , E.S. , Chiba , S. , Iwamoto , O. , Shibata , K. , Fukahori , T. and Morogovskij , G.B. 2005 . Programs of OPTMAN and SHEMMAN Version 8 (2004) , Japan : Japan Atomic Energy Research Institute . JAERI-Data/Code 2005-002

 Google Scholar

Mughabghab , S.F. 2006 . Atlas of Neutron Resonance, Resonance Parameters and Thermal Cross Sections Z = 1–100 , Amsterdam : Elsevier .

 Google Scholar