Evaluation of neutron nuclear data on iodine isotopes

Abstract

Neutron nuclear data on six isotopes of iodine have been evaluated for the next version of Japanese Evaluated Nuclear Data Library (JENDL) general-purpose file in the energy region from 10⁻⁵ eV to 20 MeV. Unresolved resonance parameters were obtained by fitting to the total and capture cross sections calculated from nuclear models, while resolved resonance parameters remain unchanged from JENDL-4.0. A statistical model code was applied to evaluate the cross sections above the resolved resonance region. Coupled-channel optical model parameters were employed for the interaction between neutrons and nuclei. Compound, pre-equilibrium and direct-reaction processes were considered for cross-section calculation in high-energy region. Giant-dipole resonance parameters for γ-ray transition from iodine isotopes were determined so as to reproduce measured γ-ray spectrum for ¹²⁷I. The present results reproduce experimental data very well. The evaluated data are compiled into ENDF-formatted data files.

Keywords:

• neutron nuclear data
• evaluation
• iodine isotopes
• cross section
• JENDL
• optical model
• statistical model

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 of Z = 30–68. Although the resolved resonance parameters (RRPs) were examined by reviewing experimental data for all of these nuclides, the fast-neutron region above resolved resonances was re-evaluated for about 170 nuclides due to the deadline of the release. Hence, the fast-neutron cross sections for the rest of the fission-product nuclides may need improvements for the next version of JENDL general-purpose file. Under such circumstances, re-evaluations have been actually performed for the data on Er [2], Ga [3], Ru [4], Sb [5] and Te [6], after the release of JENDL-4.0. Iodine is the next target to be dealt with. Moreover, neutron-induced activation cross sections of iodine isotopes are important [7] for the decommissioning of light-water reactors.

The data of ^{127, 129}I were evaluated for JENDL-2 [8] in 1984. For JENDL-3.1 [9], the data on ^{127, 129}I were completely modified and those on ¹³¹I were newly evaluated in 1990. After that, these isotopic data were essentially carried over to JENDL-3.2 [10] and JENDL-3.3 [11]. In JENDL-4.0, the data on ^{130, 135}I were added to the library and the RRPs of ^{127, 129}I were renewed. Except for ^{130, 135}I in JENDL-4.0, no γ-ray production data were evaluated. The direct-reaction process, which is important for the inelastic scattering, was not considered in either evaluation.

The present work was undertaken to improve the evaluated data on iodine isotopes by considering the latest knowledge on experimental and theoretical nuclear physics. Moreover, the data on ¹²⁸I were newly evaluated, since the (n, γ) reaction on ¹²⁸I yields a long-life (T_1/2 = 1.57×10⁷ y) nucleus ¹²⁹I. 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), (n, 2np) reaction cross sections, the angular distributions of elastically and inelastically scattered neutrons, and the energy distributions of emitted particles and γ-rays in the energy region from 10⁻⁵ eV to 20 MeV are evaluated. The Q-values of the reactions were calculated from the 2012 version of the mass table (AME2012 [12]), and are listed in Table 1, together with abundance and half-lives [13]. The RRPs of ^{127, 129}I remain unchanged from JENDL-4.0. The unresolved resonance parameters (URPs) were obtained by fitting to the calculated total and (n, γ) cross sections.

Table 1. Isotopic abundance and reaction Q-values of iodine isotopes.

	^127I	^128I	^129I	^130I	^131I	^135I
Abundance (%)	100.0	24.99 m*	1.57$\times {{10}^7\mathrm{y}}^{*}$	12.36 h*	8.0252 d*	6.58 h*
Q-values (MeV)
(n, γ)	6.826	8.840	6.500	8.578	6.332	3.828
(n, p)	0.080	2.037	−0.720	1.199	−1.449	−5.279
(n, α)	4.284	6.164	3.533	5.410	2.834	1.493
(n, d)	−3.983	−4.521	−4.578	−4.996	−5.154	−6.317
(n, t)	−6.839	−4.552	−7.104	−4.821	−7.316	−7.735
(n, ^3He)	−7.588	−8.205	−8.668	−9.166	−9.673	−11.726
(n, 2n)	−9.144	−6.826	−8.840	−6.500	−8.578	−7.801
(n, np)	−6.208	−6.746	−6.802	−7.220	−7.379	−8.542
(n, nα)	−2.184	−2.543	−2.676	−2.968	−3.168	−4.232
(n, nd)	−13.097	−10.809	−13.361	−11.078	−13.574	−13.993
(n, 3n)	−16.289	−15.970	−15.666	−15.340	−15.078	−14.045
(n, 2np)	−15.321	−13.034	−15.586	−13.303	−15.798	−16.217

*Half-lives are given for ^{128, 129, 130, 131, 135}I which are unstable.

This paper presents how the evaluation was performed. Section 2 deals with the resonance region. In Section 3, the computational methods and procedures above the resonance region are described. Comparisons of the evaluated results with experimental and existing evaluated data are made in Section 4. Finally, Section 5 summarises the conclusion.

2. Resonance region

The resolved and unresolved resonance regions are given in Table 2 for each target nucleus. No RRPs are available for ^{128, 130, 131, 135}I. The RRPs of ^{127, 129}I remain unchanged from JENDL-4.0, since the JENDL-4.0 evaluation was based on the data obtained by Noguere et al. [14] and no newer measurements have been made available. Concerning ^{128, 130, 131, 135}I for which RRPs are unavailable, constant and 1/v energy dependencies are assumed for the elastic scattering and capture cross sections, respectively, up to the lower limit of unresolved resonance region. Normalisation of cross sections is done at thermal energy. The thermal scattering cross sections were calculated as 4πR², where R stands for the scattering radius that can be estimated from nuclear model calculations in the higher energy region. On the other hand, the thermal capture cross sections of these nuclides were estimated by using the simplified formula [5]. This formula gives rough estimates of thermal capture cross sections by using theoretical s-wave γ-ray strength functions. It is used only when no other options are available. The thermal capture and elastic scattering cross sections are listed in Table 3, together with the JENDL-4.0 data and the values recommended by Mughabghab [15]. There is a large difference in the capture cross sections of ¹³⁵I between the present and JENDL-4.0 evaluations. For ¹³⁵I, the JENDL-4.0 evaluation obviously adopted the same value that was recommended [15] for ¹³¹I. The s-wave level spacing of the compound nucleus ¹³⁶I is theoretically much larger than that of ¹³²I, because the separation energy of a neutron from ¹³⁶I (3.828 MeV) is considerably smaller than that from ¹³²I (6.332 MeV). Moreover, using the thermodynamical approach [16], the s-wave total radiative width for ¹³⁶I is found to be 36% smaller than that for ¹³²I. Thus, the capture cross section of ¹³⁵I is unlikely to be the same for ¹³¹I. However, it is not possible to judge which evaluation is reasonable, since no measurements are available.

Table 2. Resolved and unresolved resonance regions.

Target nuclei	Resolved resonance	Unresolved resonance
^127I	10^−5 eV–5.2 keV	5.2–200 keV
^128I	–	10 eV–100 keV
^129I	10^−5 eV–5.1 keV	5.1–200 keV
^130I	–	10 eV–40 keV
^131I	–	100 eV–200 keV
^135I	–	10–200 keV

Table 3. Thermal capture (C) and elastic scattering (E) cross sections at 300 K in units of barns.

Target				Mughabghab
nuclei	Reaction	Present	JENDL-4.0	[15]
^127I	C	6.403	6.403	6.15 ± 0.06
	E	3.255	3.255	–
^128I	C	6.028	–	–
	E	4.119	–	–
^129I	C	30.32	30.32	30.3 ± 1.2
	E	4.337	4.337	–
^130I	C	18.01	18.01	18 ± 3
	E	3.924	3.772	–
^131I	C	80.03	80.03	80 ± 50
	E	4.371	3.615	–
^135I	C	2.958 × 10^−3	80.03	–
	E	3.216	3.214	–

The ASREP code [17] was used to determine the URPs by fitting to the total and capture cross sections calculated in the energy region above 10 eV. It should be remarked that the URPs obtained are used only for self-shielding calculations, since the pointwise cross sections are given in the evaluated data files. As an example, the cross sections of ¹²⁷I reconstructed from the URPs presently obtained are compared with the total and capture cross sections calculated from the nuclear models in Figure 1. In the parameter fitting, 10% uncertainties in the nuclear model calculations were assumed. It is found from the figure that the reconstructed cross sections reproduce the nuclear model calculations very well.

Figure 1. Unresolved resonance region for n + ¹²⁷I.

3. Computational methods and procedures above resonance region

3.1. Nuclear models

The CCONE code (Version 0.8.4) [18] was used for calculating the neutron-induced-reaction cross sections of iodine isotopes. The code is based on the spherical and coupled-channel optical models, the two- component exciton pre-equilibrium model, the distorted-wave Born approximation (DWBA) and the multi-step statistical model. In order to simulate the direct and semi-direct effects on the radiative capture reaction, the pre-equilibrium capture was considered by using the γ-ray emission rate of Akkermans and Gruppelaar [19] extended [18] to the two-component exciton pre-equilibrium model.

3.2. Parameter determination

3.2.1. Optical-model potentials

As for neutrons, we employed the global optical-model parameters obtained by Kunieda et al. [20] using the coupled-channel method based on the rigid rotor model [21]. The potential V(r) is defined as (1) $$\begin{array}{ccc}\hfill V\left(r\right)& =& -V_R{f}_R\left(r\right)-i\left\{W_V{f}_V\left(r\right)-4W_D{a}_D\frac{d}{dr}{f}_D\left(r\right)\right\}\hfill \\ & & +{\left(\frac{\hslash }{m_{\pi }c}\right)}^2(V_{\text{SO}}+i{W}_{\text{SO}})\frac{1}{r}\frac{d}{dr}{f}_{\text{SO}}\left(r\right)\mathbf{APTARABOLDITALICL}·\mathbf{APTARABOLDITALIC}\mathbf{\sigma },\hfill \end{array}$$(1) where L and σ are the orbital angular momentum and the Pauli matrix, respectively. The form factor f_i(r) is of a Woods– Saxon shape, i.e., (2) $$f_i\left(r\right)=\frac{1}{1+exp\{(r-R_i)/a_i\}},i=R,D,V,\text{SO},$$(2) where R_i is written as (3) $$R_i=R_i^0\left[1+\sum _{l=2,4,...}{\beta }_l{Y}_l^0\left(\theta \right)\right].$$(3) The angle θ refers to the body-fixed system, and Y⁰_l and β_l denote spherical harmonics and a deformation parameter, respectively. The potential depths are given as follows: (4) $$\begin{array}{ccc}\hfill V_R& =& (V_R^0+V_R^1{E}^{†}+V_R^2{E}^{†2}+V_R^3{E}^{†3}\hfill \\ & & +V_R^{\text{DISP}}\text{exp}(-{\lambda }_R{E}^{†}))\hfill \\ & & \times \left[1-\frac{1}{V_R^0+V_R^{\text{DISP}}}{C}_{\text{viso}}\frac{N-Z}{A}\right],\hfill \end{array}$$(4) (5) $$\begin{array}{ccc}\hfill W_D& =& \left[W_D^{\text{DISP}}-C_{\text{wiso}}\frac{N-Z}{A}\right]\text{exp}(-{\lambda }_D{E}^{†})\hfill \\ & & \times \frac{E^{†2}}{E^{†2}+WI{D}_D^2},\hfill \end{array}$$(5) (6) $$\begin{array}{c}\hfill W_V=W_V^{\text{DISP}}\frac{E^{†2}}{E^{†2}+WI{D}_V^2},\end{array}$$(6) (7) $$\begin{array}{c}\hfill V_{\text{SO}}=V_{\text{SO}}^0\text{exp}(-{\lambda }_{\text{SO}}{E}^{†}),\end{array}$$(7) (8) $$\begin{array}{c}\hfill W_{\text{SO}}=W_{\text{SO}}^{\text{DISP}}\frac{E^{†2}}{E^{†2}+WI{D}_{\text{SO}}^2},\end{array}$$(8) where Z, A and N are the atomic number and mass number of a target and N = A − Z, respectively. The symbol E† is the incident-neutron energy (E) relative to the Fermi one (E_f), i.e, E^† = E − E_f. The Fermi energy E_f is calculated from neutron-separation energies of target and compound nuclei such as E_f = −{(S_n(Z, A) + S_n(Z, A + 1)}/2. From the neutron potentials, transmission coefficients are obtained together with total cross sections, shape-elastic scattering cross sections and the direct-reaction components of inelastic scattering cross sections for the CCONE calculation.

The parameters required in Equations (2(2) $$f_i\left(r\right)=\frac{1}{1+exp\{(r-R_i)/a_i\}},i=R,D,V,\text{SO},$$(2) )–(8(8) $$\begin{array}{c}\hfill W_{\text{SO}}=W_{\text{SO}}^{\text{DISP}}\frac{E^{†2}}{E^{†2}+WI{D}_{\text{SO}}^2},\end{array}$$(8) ) are listed in Table 4, and the coupling schemes and deformation parameters are given in Table 5. The deformation parameters were originally taken from the work of Koura et al. [22]. The calculated total cross sections of ¹²⁷I and ¹²⁹I are shown in Figures 2 and 3, respectively, together with the experimental data and the spherical optical-model calculations using the parameters of Koning and Delaroche [23]. In order to give a better fit to experimental data, the values of $W_D^{\text{DISP}}$, $W_V^{\text{DISP}}$ and WID_V were adjusted together with the β₂ values for ^{127, 129}I, while the rest of the parameters remain unchanged from the original ones [20]. Concerning charged particles, the spherical parameters of Koning and Delaroche [23] for protons, those of Lohr and Haeberli [24] for deuterons, those of Becchetti and Greenlees [25] for tritons and ³He, and those of Lemos [26] modified by Arthur and Young [27] for α-particles were used. The transmission coefficients, which are required by CCONE to calculate charged-particle emission, are obtained from the charged-particle parameters.

Figure 2. Total cross section of ¹²⁷I.

Figure 3. Total cross section of ¹²⁹I.

Table 4. Optical-model parameters for neutrons.

V^0R	= −34.40 − 6.18 × 10^−2A + 3.37 × 10^−4A^2 − 6.52 × 10^−7A^3 MeV
V^1R	= 0.027
V^2R	= 1.2 × 10^−4 MeV^−1
V^3R	= 3.5 × 10^−7 MeV^−2
$V_R^{\text{DISP}}$	= 94.88 MeV
Cviso	= 24.3 MeV
λR	= 1.05 × 10^− 2 + 1.63 × 10^− 4V^0R MeV^−1
$W_D^{\text{DISP}}$	= 9.8 MeV
WIDD	= 12.72 − 1.54 × 10^−2A + 7.14 × 10^−5A^2 MeV
Cwiso	= 18.0 MeV
λD	= 0.0140 MeV^−1
$W_V^{\text{DISP}}$	= 30.0 MeV
WIDV	= 80.0 MeV
$V_{\text{SO}}^0$	= 5.92 + 0.003A MeV
λSO	= 0.005 MeV^−1
$W_{\text{SO}}^{\text{DISP}}$	= −3.1 MeV
WIDSO	= 160.0 MeV
R^0R, D, V	= 1.21A^1/3 fm
aR, D, V	= 0.49 + 3.22 × 10^−3A − 2.07 × 10^−5A^2 + 4.47 × 10^−8A^3 fm
$R_{\text{SO}}^0$	= (1.18 − 0.65A^−1/3)A^1/3 fm
aSO	= 0.59 fm

Table 5. Coupling schemes used in the interaction between neutron and target.

Target	Coupled	Deformation
nuclei	levels*	parameters
^127I	5/2^+(g.s.), 7/2^+(0.058), 9/2^+(0.651), 11/2^+(0.717)	β2 = 0.070**
^128I	1^+(g.s.), 2^+(0.027), 3^+(0.085), 4^+(0.128)	β2 = 0.086
^129I	7/2^+(g.s.), 9/2^+(0.730)	β2 = 0.050**
^130I	5^+(g.s.), 6^+(0.594)	β2 = 0.079
^131I	7/2^+(g.s.), 9/2^+(0.852), 11/2^+(1.556)	β2 = 0.071
^135I	7/2^+(g.s.), 9/2^+(1.184)	β2 = 0.006

* The number in the parentheses indicates the excitation energy in MeV.

** The values were adjusted so as to reproduce measured total cross sections.

3.2.2. Discrete levels and level density

In the calculation, it was necessary to input the discrete levels and level-density parameters for 32 nuclei, i.e., ^{125 − 136}I, ^{125 − 131, 133 − 135}Te and ^{123 − 129, 131 − 133}Sb. The discrete levels were taken from the reference input parameters library RIPL-3 [28].

Concerning the level density, the composite formula of Gilbert and Cameron [29] 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, (9) $${\rho }_T\left(E\right)=\frac{1}{T}\text{exp}\left(\frac{E-E_0}{T}\right).$$(9) On the other hand, the a parameter, which characterises the Fermi-gas part of level density ρ_F, is defined as (10) $$a\left(U\right)=a(*)\left[1+\frac{E_{\text{sh}}}{U}(1-e^{-\gamma U})\right],$$(10) where E_sh is the shell-correction energy and γ a damping factor. The damping factor is given by γ = 0.40$A^{-1/3}{\mathrm{MeV}}^{-1}$. 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(*) and Δ were taken from the work of Mengoni and Nakajima [30]. The shell-correction energy E_sh is calculated as the difference between the experimental mass [12] and the theoretical mass [31]. The two parameters T and E₀ 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 6 for individual nuclei, together with the energies of the highest discrete levels $E_{\text{level}}^{\text{highest}}$.

Table 6. Level density parameters for each nucleus.

Nuclei	a(*)	Δ	Esh	T	E0	Em	E^highestlevel
	1/MeV	MeV	MeV	MeV	MeV	MeV	MeV
^136I	16.954	0.000	−5.076	0.807	−1.209	6.826	0.640
^135I	16.852	1.033	−5.872	0.818	0.259	7.770	2.421
^134I	16.749	0.000	−4.796	0.860	−1.935	8.381	0.316
^133I	16.646	1.041	−3.591	0.810	−0.980	8.302	2.136
^132I	16.543	0.000	−2.501	0.709	−1.417	5.235	0.278
^131I	16.441	1.048	−1.641	0.712	−0.761	6.597	1.925
^130I	16.337	0.000	−0.684	0.697	−2.022	5.498	0.642
^129I	16.234	1.057	−0.106	0.624	−0.365	5.340	1.401
^128I	16.131	0.000	0.637	0.659	−2.041	5.071	0.581
^127I	16.028	1.065	1.070	0.624	−0.704	5.595	1.413
^126I	15.924	0.000	1.622	0.630	−2.003	4.750	0.591
^125I	15.820	1.073	1.884	0.603	−0.677	5.389	1.392
^135Te	16.852	1.033	−6.047	0.941	−1.150	12.093	1.702
^134Te	16.749	2.073	−7.064	0.957	0.567	13.634	2.727
^133Te	16.646	1.041	−5.777	0.914	−0.845	10.899	2.024
^131Te	16.441	1.048	−3.424	0.829	−1.216	8.721	1.952
^130Te	16.337	2.105	−2.612	0.814	−0.401	9.583	2.878
^129Te	16.234	1.057	−1.463	0.737	−1.056	7.087	1.110
^128Te	16.131	2.121	−0.942	0.739	−0.223	8.303	2.749
^127Te	16.028	1.065	0.101	0.681	−0.999	6.360	1.568
^126Te	15.924	2.138	0.363	0.662	0.232	7.100	2.812
^125Te	15.820	1.073	1.248	0.664	−1.161	6.276	1.322
^133Sb	16.646	1.041	−8.466	0.948	0.962	12.103	4.650
^132Sb	16.543	0.000	−7.164	1.028	−2.408	14.543	0.529
^131Sb	16.441	1.048	−5.788	0.992	−1.871	13.685	2.166
^129Sb	16.234	1.057	−3.544	0.810	−0.812	8.053	2.263
^128Sb	16.131	0.000	−2.400	0.583	−0.291	2.828	0.833
^127Sb	16.028	1.065	−1.605	0.695	−0.435	6.077	2.325
^126Sb	15.924	0.000	−0.617	0.726	−2.249	5.894	0.128
^125Sb	15.820	1.073	−0.073	0.472	0.908	2.999	2.299
^124Sb	15.717	0.000	0.761	0.590	−1.233	3.766	0.804
^123Sb	15.613	1.082	1.086	0.541	0.216	4.154	1.896

3.2.3. Gamma-ray transition

The γ-ray transmission coefficients are related to the photoabsorption cross sections by the detailed balance. The photoabsorption cross section is usually approximated by various Lorentzian shapes. In the present calculation, the shape was determined by comparing with the gamma-ray spectra measured by Voignier et al. [32] at 500 keV. Three terms were needed to reproduce the spectra, i.e., a giant-dipole resonance (GDR), a pygmy resonance and a correction term, as in the analysis performed by Kim et al. [33]. A generalised Lorentzian (GLO), which was proposed by Kopecky and Uhl [34], was used for the GDR and the pygmy resonance, while the correction term was based on a standard Lorentzian (SLO). The resonance energy (E₀), resonance width (Γ₀) and peak cross section (σ₀) were fixed for all iodine isotopes, and they are given in Table 7. The calculated γ-ray spectrum is compared with the data measured by Voignier et al. at an angle of 90° in Figure 4, where the measurements are multiplied by 4π. When the three terms mentioned above are considered, agreement between the calculation and the experiment is satisfactory. For other nuclei, the GDR parameters for GLO are given [35] by (11) $$\begin{array}{c}\hfill E_0=31.2A^{-1/3}+20.6A^{-1/6}\mathrm{MeV},\end{array}$$(11) (12) $$\begin{array}{c}\hfill {\Gamma }_0=0.026E_0^{1.91}\mathrm{MeV},\end{array}$$(12) (13) $$\begin{array}{c}\hfill {\sigma }_0=1.2\times 120NZ/\left(A\pi {\Gamma }_0\right)\mathrm{mb}.\end{array}$$(13) The SLO form was used to describe the M1 and E2 radiations for which the parameters were taken from the work of Kopecky and Uhl [34].

Figure 4. Gamma-ray spectrum from n + ¹²⁷I at 500 keV.

Table 7. E1 parameters for iodine isotopes.

	$E_0\left(\mathrm{MeV}\right)$	${\Gamma }_0\left(\mathrm{MeV}\right)$	${\sigma }_0\left(\mathrm{mb}\right)$
GDR	14.9	4.8	270.0
Pygmy	6.0	1.6	4.5
Correction	1.4	1.0	0.1

In cases where the measured capture cross sections are available, the γ-ray strength functions are renormalised so that the calculated cross sections reproduce these data. The s-wave γ-ray strength functions are compared in Table 8 with the values recommended by Mughabghab [15] and those used in the JENDL-4.0 evaluation. The values of ^{128, 130}I were obtained after renormalisation using measurements.

Table 8. Gamma-ray strength functions for s-wave neutron in units of 10⁻⁴.

Compound	Present	Mughabghab
nuclei	work	[15]	JENDL-4.0
^128I	84.71	113 ± 14*	82.9
^129I	105.9	–	–
^130I	39.53	45.8 ± 4.6*	51.3
^131I	81.20	–	61.6
^132I	6.506	–	19.7
^136I	0.02065	–	0.0373

* Calculated from the s-wave average level spacing and the s-wave average radiative width given in [15].

3.2.4. Pre-equilibrium parameters

The Version 0.8.4 of CCONE incorporates pre-equilibrium process for the (n, γ) and first-step binary reactions such as (n, n′), (n, p), (n, d), (n, t), (n, ³He) and (n, α). In the two-exciton pre-equilibrium formalism, the single-particle state densities for protons and neutrons in a residual nucleus are described [36] by (14) $$\begin{array}{c}\hfill g_{\pi }=\frac{C_{0}Z}{15}{\mathrm{MeV}}^{-1},\end{array}$$(14) (15) $$\begin{array}{c}\hfill g_{\nu }=\frac{C_{0}N}{15}{\mathrm{MeV}}^{-1},\end{array}$$(15) respectively. The parameter C₀, of which the default value is unity, is changed so that the calculations reproduce measured neutron and proton emission data such as (n, 2n) and (n, p) in the present work. The (n, 2n) reaction is a ternary reaction, which proceeds from (n, n′) by sequential decay in the framework of the multi-step statistical model. Hence, the (n, 2n) cross section is sensitive to C₀ for the residual nucleus in the (n, n′) reaction. More experimental data are available for (n, 2n) than for (n, n′) in the nuclides presently concerned. In addition to the C₀’s, the pre-equilibrium parameters for complex-particle emission [37] were determined, i.e., those for the deuteron pickup reaction from the ¹²⁷I(n, t) reaction and those for the ³He pickup and the α knockout reactions from the ¹²⁷I(n, α) reaction. These parameters for the complex particles were used for all iodine targets. The pre-equilibrium parameters used are listed in Table 9, where C₀’s are given only for the residual nuclei in the (n, n′) and (n, p) reactions, and are assumed to be unity for those in the other first-step binary reactions.

Table 9. Pre-equilibrium parameters.

	C0		Knockout	Pickup	Pickup
Target nuclei	(n, n′)	(n, p)	for (n, α)	for (n, α)	for (n, t)
^127I	1.05	0.90	3.0	3.0	5.0
^128I	1.00	1.00	3.0	3.0	5.0
^129I	1.40	1.00	3.0	3.0	5.0
^130I	1.00	1.00	3.0	3.0	5.0
^131I	1.00	1.00	3.0	3.0	5.0
^135I	1.00	1.00	3.0	3.0	5.0

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

Comparisons are made with experimental data and other evaluated data. The experimental data are taken from the EXFOR database [38] that is compiled by the intentional data centres such as the IAEA Nuclear Data Section, the OECD NEA Data Bank and the National Nuclear Data Center at the Brookhaven National Laboratory. As for the general-purpose evaluated nuclear data, there exist three major libraries, namely JENDL-4.0 [1], ENDF/B-VII.1 [39] and JEFF-3.2 [40]. However, the fast-neutron cross sections of ^{129, 131}I in ENDF/B-VII.1 were actually taken from JENDL-3.3, which means that these data are almost the same as those in JENDL-4.0. Moreover, the ¹³¹I data in JEFF-3.2 are equivalent to those in JENDL-4.0. Identical evaluated data are not drawn in the following figures. Except ^{127, 128, 129}I in JEFF-3.2, the general-purpose libraries do not contain activation cross sections leading to the ground or isomeric state. The activation cross-section files JENDL/A-96 [41] and JEFF-3.1/A [42] are used for comparison with such activation data. We do not discuss most of the reactions where experimental data are unavailable, since it is difficult to judge whether the present evaluation is reasonable without measurements.

Capture cross sections of ¹²⁷I and ¹²⁹I are illustrated in Figures 5 and 6, respectively. As for ¹²⁷I, all the evaluations are in agreement with one another below several MeV. In the energy region from 500 keV to 3 MeV, the present evaluation is almost consistent with the data measured by Voignier et al. [32], while the measurements of Macklin [43], which the JENDL-4.0 evaluation was based on, are somewhat larger than the present values. In the case of ¹²⁹I, the present and JEFF-3.2 evaluations are smaller than the data measured by Macklin [43] between 30 and 500 keV. The ¹²⁹I data of JENDL-4.0 were normalised to the data of Macklin around 100 keV, and therefore, they are larger than the other evaluations in the 30–500 keV region. In either isotope, the present results agree very well with the measurements of Noguere et al. [14,44] below 100 keV. Although experimental data are unavailable for the capture cross sections of the remaining isotopes, they are shown in Figure 7, where the JENDL-4.0 cross sections are also indicated for ^{130, 131, 135}I. As for ¹³⁵I, the fast-neutron cross sections of JENDL-4.0 were connected at 15 keV with the 1/v cross sections having a big thermal value of 80.03 b, as seen from Table 3.

Figure 5. Capture cross section of ¹²⁷I.

Figure 6. Capture cross section of ¹²⁹I.

Figure 7. Capture cross section of ^{128, 130, 131, 135}I.

Figures 8 shows the (n, 2n) reaction cross sections of ¹²⁷I. There exist many experiments for ¹²⁷I. However, the data are divided into two groups, i.e., lower cross-section group and the higher one. Most of the evaluations, except ENDF/B-VII.1, belong to the higher group. The present evaluation is consistent with the data measured by Lu et al. [45,46]. The JENDL-4.0 evaluation rapidly decreases above 17 MeV. This can be explained by too large (n, 3n) cross section as seen in Figure 9, although the other evaluations are consistent with one another. Only two experimental data-sets are available for ¹²⁹I, as shown in Figure 10. The latest measurements of Nakano et al. [47] are smaller than all of the evaluations. The present evaluation, as well as JENDL-4.0, obviously places emphasis on the data measured by Kuhry and Bontems [48] by considering the result for ¹²⁷I.

Figure 8. ¹²⁷I(n, 2n)¹²⁶I reaction cross section.

Figure 9. ¹²⁷I(n, 3n)¹²⁵I reaction cross section.

Figure 10. ¹²⁹I(n, 2n)¹²⁸I reaction cross section.

Charged-particle emission cross sections of ¹²⁷I are illustrated in Figures 11–16. The measured (n, p) cross sections are well reproduced by the present evaluation. It is found from Figures 11 and 13 that the isomeric-state production of JEFF-3.2 is obviously overestimated. The ground-state production cross section measured by Bormann et al. [49] is larger than all of the evaluations, although their experimental uncertainties are also large. A single measurement [50] is available for the (n, t) reaction. In the present work, the pre-equilibrium parameter for triton emission was adjusted so as to reproduce it. There exist two measurements for the ¹²⁷I(n, α)^124m2Sb reaction, i.e., 18.4 ± 2.8 mb at 14.5 MeV measured by Paul and Clarke [51], and 1.5 ± 0.2 mb at 14.7 MeV measured by Qaim and Ejaz [52]. The present evaluation is based on the latter measurement, since the measured ground-state and isomeric-state production cross sections should be reproduced simultaneously.

Figure 11. ¹²⁷I(n, p)¹²⁷Te reaction cross section.

Figure 12. ¹²⁷I(n, p)^127gTe reaction cross section.

Figure 13. ¹²⁷I(n, p)^127mTe reaction cross section.

Figure 14. ¹²⁷I(n, t)^125mTe reaction cross section.

Figure 15. ¹²⁷I(n, α)^124gSb reaction cross section.

Figure 16. ¹²⁷I(n, α)^124m2Sb reaction cross section.

Angular distributions of neutrons elastically scattered from ¹²⁷I are shown in Figure 17. The experimental data of Gorlov et al. [53] and Cox and Cox [54] were corrected for the neutrons inelastically scattered from low-lying levels of ¹²⁷I, while such a correction was not made in the data of Begum et al. [55]. At an incident energy of 16.1 MeV, all the evaluations, except JENDL-4.0, are lower than the data measured by Begum et al. in the region from 40° to 90°. Even if the inelastic scattering is taken into account in the present evaluation, the resultant distributions are found to be somewhat smaller than the measurements. As a matter of fact, the angular distributions, which Begum et al. measured for several medium and heavy nuclei at 16.1 MeV, were found to be mostly larger than the optical-model predictions at angles ≥ 40°. More experiments would be needed to clarify the differences above an incident energy of 10 MeV.

Figure 17. Angular distributions of neutrons elastically scattered from¹²⁷I.

Double-differential neutron emission spectra at 14.5 MeV are illustrated in Figure 18. The present evaluation as well as ENDF/B-VII.1 and JEFF-3.2 is almost consistent with the data measured by Hermsdorf et al. [56], whereas the three evaluations deviate from the data of Sal’nikov et al. [57] with the increasing emitted-neutron energy. On the other hand, the JENDL-4.0 evaluation seems lower than the measurements above 6 MeV, although there is a systematic difference in the measured data in the high-energy region. In JENDL-4.0, the pre-equilibrium enhancement was considered for the normalised continuous (n,n’) spectra, which are the neutrons inelastically scattered from the overlapping levels of ¹²⁷I. However, their absolute cross sections were not enhanced by the pre-equilibrium effect. In fact, the 14-MeV continuous (n,n’) cross section of JENDL-4.0 amounts to 118 mb, while those for other libraries exceed 400 mb. Therefore, the underestimate of JENDL-4.0 is due to the contradictory treatment of the pre-equilibrium process in the evaluation.

Figure 18. Double-differential neutron emission spectra from¹²⁷I at 14.5 MeV.

5. Concluding remarks

The neutron nuclear data on iodine isotopes were evaluated in the energy region from 10⁻⁵ eV to 20 MeV. The RRPs of ^{127, 129}I remain unchanged from JENDL-4.0. In the low-energy region, the 1/v behaviour was assumed for the capture cross sections of ^{128, 130, 131, 135}I, and the thermal cross sections were normalised to the values calculated from the simplified formula. The URPs were obtained for self-shielding calculations by fitting to the total and capture cross sections calculated from the nuclear models.

In the present work, the statistical-model code CCONE was applied to the calculation of fast-neutron cross sections. 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 neutron potentials were found to be reliable by comparing with the measured total cross sections. The GDR parameters for iodine isotopes, which were needed to calculate γ-ray emission, were determined so as to reproduce the γ-ray spectrum for ¹²⁷I measured at 500 keV. On the whole, the presently evaluated cross sections are in good agreement with measurements. The data on ¹²⁸I, which were missing in JENDL-4.0, were newly evaluated. Moreover, γ-ray production data were evaluated for all nuclides, while these data were given only for ^{130, 135}I in JENDL-4.0. The evaluated data are compiled into ENDF-formatted data files for the next release of JENDL general-purpose file.

Acknowledgements

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