Evaluation of neutron nuclear data for erbium

Abstract

Neutron nuclear data on ^{162,164,166,167,168.170}Er have been evaluated for the next version of JENDL general purpose file in the energy region from 10⁻⁵ eV to 20 MeV. The resolved resonance parameters remain unchanged from JENDL-4.0, while the unresolved resonance parameters were revised. The statistical model was applied to calculate the cross sections above the resolved resonance region. In the calculations, coupled-channel optical model parameters were used for neutrons. Pre-equilibrium and direct-reaction processes were taken into account in addition to the compound process. A modified Lorentzian was employed for E1 gamma-ray strength functions. The present evaluation is consistent with available experimental data. The evaluated data are compiled into an ENDF-formatted data file.

Keywords:

• neutron nuclear data
• evaluation
• erbium isotopes
• resonance parameter
• cross section
• JENDL
• coupled-channel optical model
• statistical model

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Erratum

1. Introduction

The fourth version of the Japanese Evaluated Nuclear Data Library (JENDL-4.0 [1]) was released in May 2010. In this library, 215 nuclides are regarded as fission products in the region from Z = 30 to 68. Although the resolved resonance parameters were examined by reviewing experimental data for all of those nuclides, the fast neutron region above resolved resonances was re-evaluated for 174 nuclides due to time limit. Therefore, the fast-neutron cross sections for the remaining 41 nuclides may need improvements for the next version of JENDL general purpose file. Erbium isotopes are among the 41 nuclides. More importantly, erbium is a candidate for burnable poisons in fission reactors. It is required to re-examine the cross sections of erbium.

Erbium data were evaluated [2] for JENDL-3.3 [3] in 2000. Since then, minor modifications were done for JENDL-4.0 in the resonance region. In the 2000 evaluation, the statistical-model code CASTHY [4] was used to calculate the total, elastic and inelastic scattering and capture cross sections, while the cross sections for the competing reactions such as (n, 2n) and (n, p) were obtained from the Hauser-Feshbach [5] code GNASH [6]. The direct inelastic scattering was considered only for the first excited states of even–even isotopes, while it was taken into account for five excited states of ¹⁶⁷Er.

This study was undertaken to improve the evaluated data on erbium isotopes by considering the latest knowledge on experimental and theoretical nuclear physics. Evaluated are the total, elastic and inelastic scattering, (n, γ), (n, p), (n, d), (n, t), (n,³He), (n, α), (n, np), (n, nd), (n, nα), (n, 2n), (n, 3n) reaction cross sections, the angular distributions of emitted neutrons and charged-particles, and the energy distributions of emitted particles and γ -rays in the incident-neutron energy region from 10⁻⁵ eV to 20 MeV. The Q-values of the reactions were calculated from the latest version of the mass table (AME2003) obtained by Audi et al. [7] and are listed in Table 1, together with isotopic abundances [8]. The unresolved resonance parameters were obtained by fitting to the calculated total and (n, γ) cross sections.

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

This article presents how the evaluation was performed. Section II deals with the resonance parameters. In section 3, the computational methods and procedures are described. Comparisons of the evaluated results with available experimental data and evaluated data are made in section 4. Finally, section 5 summarizes the conclusion.

2. Resonance parameters

The resolved and unresolved resonance regions are given in Table 2 for each target nucleus. After the compilation of JENDL-4.0, new resolved resonance parameters for ^{166,167,168,170}Er were published by Wang et al. [9] from the analyses of their transmission measurements on elemental erbium. Using their parameters for ¹⁶⁷Er, however, the calculated thermal capture cross section of ¹⁶⁷Er is about 10% larger than the value of JENDL-4.0 (644.2 b at 300 K). This large change is unacceptable by considering the results of the sample worth analyses [10] of Er₂O₃. As a result, the resolved resonance parameters remain unchanged from JENDL-4.0.

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

The ASREP code [11] was used to determine the unresolved resonance parameters (URPs) by fitting to the total and capture cross sections evaluated by the nuclear model calculations described in the following section. It should be noted that the URPs obtained are used only for self-shielding calculations, since the point-wise cross sections are given in the evaluated data files. As examples, the cross sections of ¹⁶⁷Er and ¹⁷⁰Er reconstructed from the URPs presently obtained are compared with the total and capture cross sections calculated from the nuclear models in Figures 1 and 2, respectively. In the parameter fitting, 10% errors of the nuclear model calculations were assumed. It is found from the figures that the reconstructed cross sections reproduce the nuclear model calculations very well.

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

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

3. Computational methods and procedures above resonance region

3.1. Nuclear models

The POD code [12] was used for calculating the neutron-induced reaction cross sections of erbium isotopes. The code is based on the spherical optical model, the one-component exciton pre-equilibrium model, the distorted-wave Born approximation (DWBA) and the multistep statistical model. In order to simulate the direct and semidirect effects on the capture reaction, the pre-equilibrium capture was considered by using the γ-ray emission rate derived by Akkermans and Gruppelaar [13]. The original POD code was modified to allow for options of γ-ray strength functions, i.e. generalized, extended generalized and modified Lorentzians [14,15] (GLO, EGLO and MLO, respectively) for E1 radiation, in addition to the standard Lorentzian (SLO).

The POD code is not capable of calculating direct reaction cross sections and transmission coefficients by the coupled-channel method. These two kinds of data are supplied to POD by a separate coupled-channel code if the use of the coupled-channel method is preferable. In the present study, the coupled-channel optical model code OPTMAN [16] supplied those values to the POD code.

3.2. Parameter determination

3.2.1. Optical-model potentials

We employed the global neutron optical-model parameters obtained by Kunieda et al. [17] using the coupled-channel method based on the rigid-rotator model (RRM) [18] with a slight modification. The values were changed to −38.0 MeV for ^{162,164,166,167}Er and to −38.4 MeV for ^168,170Er, which amount to changes less than 1% as compared with the original values. The coupled-channel method based on the soft-rotator model (SRM) [16] was applied to calculate the transmission coefficients, and the total and direct-reaction cross sections of even–even targets, since the SRM could consider vibrational modes in addition to rotational ones. The coupling schemes and deformation parameters are listed in Tables 3 and 4, respectively. The calculated total cross section of elemental Er is illustrated in Figure 3, together with experimental data and the spherical optical model calculations using the parameters of Koning and Delaroche [19]. It is found from the figure that the present calculations are in good agreement with the experimental data in the entire energy region. The spherical optical model parameters of Koning and Delaroche yield large cross sections in the low energy region. Built-in values in POD were used for charged-particle optical-model parameters, i.e. the values of Koning and Delaroche [19] for protons, those of Lohr and Haeberli [20] for deuterons, those of Becchetti and Greenlees [21] for tritons and ³He, and those of Lemos [22] potentials modified by Arthur and Young [23] for α-particles. The values of Lohr–Haeberli and Becchetti–Greenlees potentials were actually taken from the compilation of Perey and Perey [24].

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].

3.2.2. Discrete levels and level density

In the present calculation, it was necessary to input the discrete levels and level density parameters for 34 nuclei, i.e. ^160–171Er, ^160–170Ho and ^158–168Dy. The discrete levels were taken from the reference input parameter library RIPL-3 [25].

Concerning the level density, the composite formula of Gilbert and Cameron [26] was used in the present work. In the region of low excitation energy E, the level density is described by the constant temperature formula ρ _T , namely,

On the other hand, the a parameter, which characterizes the Fermi-gas part of level density ρ _F , is defined as:

where E _sh is the shell correction energy and γ a damping factor. The energy U is expressed by E and the pairing energy Δ, i.e. U = E −Δ. In the above equations, the values of a(*), E _sh, γ and Δ were taken from the work of Mengoni and Nakajima [27,28]. The two parameters T and E ₀ were determined so as to connect ρ _F and ρ _T smoothly at an appropriate matching energy E_m . The parameters used in this work are listed in Table 5 for individual nuclei, together with the energies of the highest discrete levels .

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

3.2.3. Gamma-ray transition

The SLO γ -ray strength function is solely available in the original POD code. The options for GLO and EGLO were added for E1 radiation in the previous work [29–31]. Recently, further modification was done to allow for a new option MLO, which is recommended to use in RIPL-3 [25]. The MLO form was used in the present work. The giant resonance parameters for E1 were taken from RIPL-3, where the parameters were obtained by a fit of theoretical photo-absorption cross sections to experimental data. Unless the parameters are available for particular nucleus in RIPL-3, one can use the systematics given in Ref. [25]. Moreover, a pygmy resonance was considered for E1 radiations of the compound nuclei. The parameters of the pygmy resonance were determined from the systematic trend obtained by Igashira et al. [32], namely, a peak cross section of 0.5 mb, a resonance energy of 3.5 MeV and a width of 1.0 MeV. The resonance energy and width parameters for M1 and E2 are also obtained from another systematics [33] and given by

The symbol A stands for the mass number of a nucleus. The contributions of M1 and E2 relative to E1 were estimated [6] such as

Figure 4 shows the relative capture gamma-ray spectrum for ¹⁶⁷Er at an incident neutron energy of 27 keV. The present calculations reproduce the data measured by Harun-ar-Rashid [2,34] satisfactorily, which indicates that the present choice of gamma-ray strength functions is reasonable. As for the compound nuclei ^{167,168,169,171}Er, the strength functions are normalized so as to reproduce measured capture cross sections of the corresponding target nuclei around several tens of keV. For ^163,165Er, Maxwellian-averaged capture cross sections [35,36] at kT = 30 keV were used for the normalization, since the data measured using mono-energetic neutrons are very scarce above the keV region. The s-wave γ-ray strength functions S_γ0 obtained are compared in Table 6 with the values recommended by Mughabghab [37]. Except for ¹⁶³Er, the present values are almost consistent with the ones given by Mughabghab. Using a theoretical value [37] of the average total radiative width <Γ_γ0> = 71 meV for ¹⁶³Er, the gamma-ray strength function would be equal to 103 ± 18, which is not far from the present value. Normalization factors for other nuclei were obtained by using the calculated average level spacing D ₀ for s-wave neutrons and the thermodynamical formula of <Γ_γ0> for s-wave neutrons. The latter quantity is expressed [38] by

where S_n is the separation energy of a neutron from a compound nucleus. These two quantities lead to

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.

3.2.4. Pre-equilibrium parameters

For pre-equilibrium capture, SLO-shaped photon absorption cross sections are required [13] to calculate the γ -ray emission rate. The peak cross section, resonance energy and resonance width are calculated from the systematics [25]. If the experimentally-determined parameters are available in RIPL-3, the systematics is replaced with them. The single-particle state density g, which is required to describe the pre-equilibrium state density for a residual nucleus, is set to A/13 MeV⁻¹ for all nuclei but ^167,168,169Ho and ^165,167Dy. Comparing with measured charged-particle emission data, the g values were adjusted for these residual nuclei, i.e. 10.0, 10.5, 10.5, 15.5 and 14.5 MeV⁻¹ for ^167,168,169Ho and ^165,167Dy, respectively. There remain three kinds of normalization parameters for pre-equilibrium particle emission in the POD code: K, which determines the absolute square of the average matrix element for the residual two-body interaction and the scale factors for a pickup reaction and α-particle knockout, K _pickup and K _knockout. These parameters were determined so as to fit to the measured cross sections. The values obtained are listed in Table 7.

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

4. Comparison with experimental and other evaluated data in fast neutron energy region

The presently evaluated data are compared with experimental and other evaluated data. The experimental data are taken from the EXFOR database [39], which is available in the international data centres such as the OECD/NEA Data Bank. As for the general-purpose nuclear data, there are three major libraries, i.e. JENDL-4.0 [1], ENDF/B-VII.1 [40] and JEFF-3.1.2. [41] As for JEFF-3.1.2, the whole data of erbium isotopes were taken from JENDL-3.3. The resonance parameters of ^{166,167,168,170}Er for ENDF/B-VII.1 were independently evaluated, although the other data for ENDF/B-VII.1 were taken from JENDL-3.3. As described in section 1, the erbium data of JENDL-4.0 are based on those of JENDL-3.3 with modifications of resonance regions. Thus, in the fast neutron energy region, JENDL-4.0, ENDF/B-VII.1 and JEFF-3.1.2 are all equivalent as far as erbium is concerned. Therefore, the JENDL-4.0 data are solely drawn in the following figures as existing evaluated data. It should be noted that the general-purpose libraries do not contain any partial activation cross sections leading to the ground or isomeric state.

As mentioned in the previous section, experimental data on the radiative capture cross sections of ^162,164Er are very scarce above the keV region. The Maxwellian-averaged data [35,36] were used to normalize the present statistical model calculations, as shown in Figure 5. It is found from the figure that the JENDL-4.0 evaluations deviate from the measurements. The radiative capture cross sections of ^{166,167,168,170}Er are illustrated in Figures 6–9, respectively. The present evaluations are almost consistent with available experimental data. Concerning ¹⁷⁰Er, the JENDL-4.0 evaluation reproduces the experimental data better than the present one in the region from 30 to 80 keV. As a matter of fact, the statistical model calculations done for JENDL-3.3 were almost the same as the present ones, and could not reproduce the experimental data. Finally, the calculations were modified by following the data measured by Igashira [42]. In the present work, we tried to solve the discrepancy between the measured and calculated data in this particular energy region by changing model parameters such as optical model and level-density parameters. However, none of these efforts were successful. Therefore, we gave up fitting the calculations to the measurements, and adopted the calculations as the evaluated data. More new measurements might be needed to solve the discrepancy. There is a difference between the present evaluation and JENDL-4.0 in the MeV region, although no measurements are available except for ¹⁷⁰Er. According to the radiative capture cross sections of elemental Er shown in Figure 10, the present calculations almost reproduce the experimental behaviour in the MeV region.

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.

The (n, 2n) reaction cross sections are illustrated in Figures 11–15. The present evaluations are somewhat smaller than the JENDL-4.0 cross sections in the high energy region, although the ¹⁶⁸Er (n, 2n)^167m Er cross section is not contained in JENDL-4.0. Figure 16 shows the cross section for the activation reaction ¹⁶⁷Er (n, n′)^167m Er. In order to enhance the activation cross section particularly above 10 MeV, the vibrational excitation was considered by using DWBA for several low-lying levels of ¹⁶⁷Er, since the OPTMAN code [16] is not capable of taking account of vibrational levels for odd nuclei with the RRM.

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.

The charged-particle emission cross sections are shown in Figures 17–21. It is found from these figures that the presently evaluated cross sections are in good agreement with the measured data. It should be noted that the pre-equilibrium mode was enhanced in order to reproduce the measured composite-particle emission data for ^168,170Er, as seen in Table 7. In all cases, the JENDL-4.0 evaluations differ from the measurements.

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.

Figures 22 and 23 show the angular distributions of neutrons elastically scattered from elemental erbium. The figures include the contributions of the neutrons inelastically scattered from the first excited states of individual isotopes, since the energies of the first excited states are mostly less than 100 keV, which is smaller than typical experimental resolutions. The present evaluation is in good agreement with the measured data. The evaluated neutron emission spectra for elemental erbium are compared in Figure 24 with the experimental data measured by Owens and Towle [43] and the JENDL-4.0 evaluation. The present evaluation agrees with the measurements, while the JENDL-4.0 evaluation is smaller than the measured data below 2 MeV. The difference in the evaluated spectra comes from the neutrons inelastically scattered from continuum levels of the target nuclei.

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°.

5. Concluding remarks

The neutron nuclear data of erbium isotopes were evaluated in the energy region from 10⁻⁵ eV to 20 MeV. It was found that the new resolved resonance parameters, which were obtained from the analysis of transmission measurements, yielded large thermal capture cross section of ¹⁶⁷Er. Therefore, it was decided that the resolved resonance parameters remained unchanged from JENDL-4.0. On the other hand, the unresolved resonance parameters were revised by fitting to the total and capture cross sections calculated from the nuclear models.

Above the resolved resonance region, the present evaluation is mainly based on the statistical model using the POD code. The neutron transmission coefficients were obtained by the coupled-channel method, together with the total cross sections, the shape elastic scattering cross sections and the direct-reaction components of the inelastic scattering cross sections. The E1 gamma-ray strength functions were determined by comparing with measured gamma-ray spectra. The presently evaluated cross sections are in good agreement with available experimental data. The evaluated data are compiled into an ENDF-formatted data file.

Acknowledgement

The author would like to thank the members of the Nuclear Data Center, Japan Atomic Energy Agency, for their helpful comments on this work.