Evaluation of neutron nuclear data on xenon isotopes

ABSTRACT

Neutron nuclear data of Xe isotopes have been evaluated in the energy region, including the resolved resonance one, from 1 keV to 20 MeV by using the theoretical nuclear reaction models. The phenomenological optical model potential was employed to calculate the total cross section for natural Xe with the coupled-channels method. The cross sections for channels of capture, (n, 2n), (n, p) and (n, α) reactions were calculated and compared with available experimental results including recently measured data. The elastic scattering angular distributions and particle emission spectra were calculated, although there is no experimental information available. Reaction cross sections of evaluated libraries were considered for comparison with the calculated results. The presently calculated cross sections reproduce better the available experimental data.

Keywords:

• Neutron nuclear data
• evaluation
• xenon isotopes
• cross section
• JENDL-4.0
• coupled-channels optical model
• statistical model

1. Introduction

Natural element of xenon with atomic number Z = 54 is composed of nine stable isotopes whose number is the second largest one, following tin. The stable isotopes of natural Xe with mass numbers A = 129, 131, 132, 134 and 136 are significant fission products. In fission reactors, cumulative yields of ¹³⁴Xe, for instance, at thermal and fast neutron energies are 7.87 and 7.66% [1], respectively, for ²³⁵U. This notable yields have heightened urgency of data evaluation.

The neutron nuclear data evaluation of ^{131, 132, 133, 134, 135, 136}Xe was carried out first time in 1984 for JENDL-2 [2]. In this evaluation, the optical and statistical model code CASTHY [3] was utilized to calculate total, elastic and inelastic scattering cross sections. In 1990, the data of remaining isotopes of ^{124, 126, 128, 129, 130}Xe were evaluated and incorporated in JENDL-3.1 [4], where the pre-equilibrium and multi-step evaporation model code PEGASUS [5] was used for competing reactions. These data were eventually compiled into the subsequent revisions of JENDL-3.2 [6] and JENDL-3.3 [7]. These data were re-evaluated in the latest release of JENDL-4.0 [8], where total, elastic, inelastic, capture and particle emissions, as well as other competing reaction cross sections were calculated by nuclear reaction model codes POD [9] and OPTMAN [10]. Obviously, the evaluated data in JENDL-4.0 are expected to be better than those of previous evaluations due to the use of advanced nuclear reaction models. Nevertheless, JENDL-4.0 still has inconsistency with measured data for some reactions, and the experimental data after the release were not taken into account.

Integral test on activation cross sections of Xe isotopes was carried out in the liquid metal cooled fast reactors JOYO and YAYOI [11] to identify capsule rupture. These experiments were performed in the fast neutron energy region. There was discrepancy in data between the experiment in YAYOI and calculation with JENDL-3.2. The comparison revealed that the evaluated capture cross sections of ^{124, 126}Xe may be large in the keV energy region.

The work on large-scale searches for neutrinoless double-β decay experiments is currently operating in which ¹³⁶Xe is being considered as one of the most promising candidates. One of the experiments is named as “Kamioka Liquid Scintillator Antineutrino Detector Zero Electron Neutrino” (KamLAND-Zen) [12] at Kamioka mine in Japan and another one is called “Enriched Xenon Observatory” (EXO) [13] in USA. Although these experiments are being carried out in underground, neutron-induced background may have a severely influence on the detection events. Therefore, the relevant cross-section data such as capture and (n, 2n) reactions are required with a reliable accuracy.

Several neutron nuclear data evaluations [14–17] have been performed since the inception of nuclear reaction model code CCONE [18]. Those comprehensive works have given better prediction than those of previous results. It is noticed that the data evaluation of Xe isotopes is yet to be performed by the CCONE code. The aim of this work is to get further improvements in nuclear data of xenon by using the CCONE code.

In this paper, we performed evaluation of neutron nuclear data for Xe isotopes in which relevant nuclear reaction models were adopted to calculate cross sections for various reaction channels. Section 2 explains how the evaluation is performed by using nuclear reaction models with input parameters. The calculation results are compared with the experimental data and preceding evaluated ones in Section 3. Finally, the conclusion is drawn in Section 4.

2. Theoretical nuclear models and evaluation procedures

It is necessary to use several nuclear reaction models, in order to calculate cross-sections of different reaction channels and particle emission spectra induced by neutrons up to 20 MeV. The coupled-channels method [19] is employed for the calculation of total, shape elastic and direct inelastic scattering cross sections. Outgoing channels are delineated by other nuclear reaction models. The compound and pre-equilibrium processes are characterized by the statistical model, namely Hauser–Feshbach theory [20] and two-component exciton model [21], respectively. Moreover, the distorted wave Born approximation is employed to the direct reaction process for vibrational levels. The present calculation is performed by the theoretical nuclear reaction model code, CCONE, where all of these models are included.

2.1. Coupled-channels optical model

The coupled-channels optical model is based on the rigid rotator model [22] which is included in the CCOM code [23]. The CCOM code is used for Xe isotopes as a target and neutron as projectile in the incident channel. The code was utilized to evaluate the total cross section as well as to calculate the neutron transmission coefficients which are applied to statistical model calculation. The functional form of the optical model potential (OMP) is adopted from Kunieda et al. [24]. The real volume V_R and imaginary surface W_D terms of OMPs are given by (1) $$\begin{array}{ccc}\hfill V_R& =& \left(V_R^0+V_R^1{E}^{†}+V_R^2{E}^{†2}+V_R^3{E}^{†3}+V_R^{\text{DISP}}{e}^{-\lambda {}_R{E}^{†}}\right)\hfill \\ & & \times \left[1-\frac{1}{V_R^0+V_R^{\text{DISP}}}{C}_{\text{viso}}\frac{N-Z}{A}\right],\hfill \end{array}$$(1) (2) $$\begin{array}{c}\hfill W_D=\left[W_D^{\text{DISP}}-C_{\text{wiso}}\frac{N-Z}{A}\right]e^{-\lambda {}_D{E}^{†}}\frac{E^{†2}}{E^{†2}+WI{D}_D^2},\end{array}$$(2) where Z, N and A are the number of protons, neutrons and nucleons in the target nucleus, respectively. The imaginary volume and the real and imaginary spin–orbit terms are included in the same functional forms of Kunieda et al. The quantity E† is the projectile energy relative to the Fermi one. Symbols V^{(0 − 3)}_R, $V_R^{\text{DISP}}$, $W_D^{\text{DISP}}$, WID_D, C_viso, C_wiso, λ_{R, D}, nuclear radius r_{R, D, V, SO} and diffuseness a_{R, D, V, SO} are the OMP parameters. The values of these parameters were taken from global ones of Kunieda et al. Some values were, however, modified from the original ones for better agreement with the experimental data. The modified values are given in Table 1, together with the original ones. The coupling schemes used in the coupled-channels calculation along with the deformation parameters β₂ are listed in Table 2. The deformation parameters were originally taken from Raman et al. [25], although their values were adjusted so as to reproduce experimental total cross sections of natural Xe.

Table 1. Values of OMP parameters.

Parameter	Modified values	Original values
V^0R	−38.89 MeV	−34.40 MeV
$V_R^{\text{DISP}}$	98.767 MeV	94.88 MeV
$W_D^{\text{DISP}}$	11.00 MeV	11.08 MeV
WIDD	15.095 MeV	12.72 MeV
aSO	0.49 fm	0.59 fm

Table 2. Coupled levels and deformation parameters.

Nucleus	J^π (Ex in keV)	Modified β2	Raman β2
^124Xe	0^+ (g.s.), 2^+ (354.03),	0.192	0.212
	4^+ (878.92), 6^+ (1548.46)
^126Xe	0^+(g.s.), 2^+ (388.631),	0.1781	0.188
	4^+ (942.00), 6^+ (1634.98)
^128Xe	0^+(g.s.), 2^+ (442.911),	0.1636	0.184
	4^+ (1033.15), 6^+ (1737.26)
^129Xe	1/2^+(g.s.), 3/2^+ (39.578),	0.1563	0.177
	5/2^+ (321.711), 7/2^+ (518.70)
^130Xe	0^+(g.s.), 2^+ (536.068),	0.149	0.169
	4^+ (1204.61), 6^+ (1944.14)
^131Xe	3/2^+(g.s.), 5/2^+ (364.49),	0.1350	0.155
	7/2^+ (636.99), 9/2^+ (971.22)
^132Xe	0^+(g.s.), 2^+ (667.715),	0.1209	0.141
	4^+ (1440.32), 6^+ (2111.88)
^134Xe	0^+(g.s.), 2^+ (847.041),	0.099	0.119
	4^+ (1731.17), 6^+ (2136.61)
^136Xe	0^+(g.s.), 2^+ (1313.03),	0.102	0.122
	4^+ (1694.39), 6^+ (1891.70)

It is worth to be mentioned that the modified Kunieda potential is used only for neutron incident and corresponding decay channels. On the other hand, emission channel OMPs from nuclides other than targets are taken from Koning and Delaroche [26] for neutron and proton, Lohr and Haeberli [27] for deuteron, Becchetti and Greenlees [28] for triton and He-3, and Avrigeanu and Avrigeanu [29] for α-particle.

The calculated total neutron cross sections for natural Xe are shown in Figure 1. In this figure, the obtained result is compared with the experimental data of Vaughn et al. [30] and the evaluated data of JENDL-4.0 [8], JENDL-3.3 [7] and ENDF/B-VII.1 [31]. In addition, other OMPs, e.g., Kunieda et al. and Koning and Delaroche, are also used to calculate the total cross sections for comparison. It is observed that the present results and JENDL-4.0 show better agreement with the experimental data than the cross sections calculated with other OMPs, particularly, at the energy region below 2 MeV.

Figure 1. Comparison of the present total cross section of natural Xe with the evaluated and experimental data.

2.2. Pre-equilibrium model

It is well established that an intermediate process existing between direct and compound ones is referred to as the pre-equilibrium process which takes place after the first stage of the reaction and before statistical equilibrium of the compound nucleus. In the present calculation, the contributions of the pre-equilibrium process to the reaction cross section have been taken into account by using the two-component exciton model [21]. The global parametrization prescribed by Koning and Duijivestijn [32] is incorporated in the calculation of cross section for pre-equilibrium components. In the framework, the single-particle state densities are described by introducing the parameters C_ν for neutrons and C_π for protons as in the following equations: (3) $$g_{\nu }=C_{\nu }\frac{N}{15}\mathrm{for}\mathrm{neutrons},$$(3) (4) $$g_{\pi }=C_{\pi }\frac{Z}{15}\mathrm{for}\mathrm{protons},$$(4)

In order to fit the experimental data, these parameters were adjusted for Xe isotopes. The parameter values adopted are listed in Table 3. The default value of these parameters is unity.

Table 3. Pre-equilibrium parameters.

Isotopes	Cν	Cπ	Isotopes	Cν	Cπ
^124Xe	1.00	1.00	^131Xe	1.00	1.00
^125Xe	0.62	1.00	^132Xe	1.23	1.00
^126Xe	1.00	1.00	^133Xe	1.00	1.00
^127Xe	0.93	1.00	^134Xe	1.00	1.00
^128Xe	0.40	0.45	^135Xe	0.94	1.00
^129Xe	0.76	1.00	^136Xe	0.47	0.45
^130Xe	1.00	1.00	^137Xe	0.82	1.00

Furthermore, the particle pick-up and knock-out processes [33] were also considered in this evaluation. The knock-out process was employed only for α-particle.

2.3. Statistical model

The compound nuclear reaction was calculated on the basis of Hauser–Feshbach formalism [20] including width fluctuation correction. Neutrons, protons, deuterons, tritons, ³He, α-particle and γ-ray emission channels were included. It is noted that the neutron transmission coefficients for target Xe isotopes were imported from coupled-channels optical model calculation as mentioned in Section 2.1.

2.3.1. Discrete levels and level density

It is inevitable to provide input of the discrete levels and level density parameters for 47 nuclei, for instance, ^{122 − 137}Xe, ^{122 − 136}I and ^{120 − 135}Te. The discrete-level information was taken from the Reference Input Parameters Library, RIPL-3 [34].

The composite formula concerning nuclear level density introduced by Gilbert and Cameron [35] was adopted. The level density in constant temperature model can be expressed as (5) $$\rho \left(U\right)=\frac{1}{T}exp\left(\frac{U+\Delta -E_0}{T}\right),$$(5) where T is the nuclear temperature, E₀ is the energy shift and U is the corrected excitation energy obtained from excitation energy E_x and pairing energy Δ as U = E_x − Δ. The level density parameter a in Fermi-gas model has energy dependence, and is expressed by the following equation: (6) $$a\left(U\right)=a^{*}\left(1+E_{\text{sh}}\frac{1-e^{-\gamma U}}{U}\right),$$(6) where a* and γ are the asymptotic level density parameter and the shell correction damping factor, respectively. The shell correction energy E_sh was obtained from the difference between experimental mass and theoretical smoothed mass. The theoretical mass was derived from the empirical formula of Myers and Swiatecki [36] and the values of experimental mass were taken from the evaluated data of Audi et al. [37]. The parameter a* was determined so as to get better agreement with average level spacing of s-wave neutron resonances which was derived from experiments. On the other hand, the systematic value for a* was adopted from the work of Mengoni and Nakajima [38], if there were no experimental data available. The nuclear level density parameters used in this evaluation are tabulated in Table 4 for individual nuclei along with the energies of the adopted highest discrete levels E_max.

Table 4. Level density parameters for each isotope.

	a*	Δ	Esh	T	E0	Em	Emax
Isotope	1/MeV	MeV	MeV	MeV	MeV	MeV	MeV
^137Xe*	22.318	1.025	−3.896	0.566	0.082	5.078	2.230
^136Xe	16.954	2.058	−4.828	0.795	0.823	8.658	3.310
^135Xe*	21.617	1.033	−3.804	0.532	0.492	4.211	2.169
^134Xe	16.749	2.073	−2.819	0.804	−0.381	9.531	2.417
^133Xe*	18.344	1.041	−1.767	0.644	−0.608	6.043	1.071
^132Xe*	16.644	2.089	−1.151	0.689	0.251	7.428	2.670
^131Xe*	18.471	1.048	−0.177	0.604	−0.818	5.806	1.046
^130Xe*	16.037	2.105	0.153	0.670	0.163	7.205	2.705
^129Xe*	15.927	1.057	0.965	0.685	−1.349	6.617	1.089
^128Xe	16.131	2.121	1.122	0.676	−0.325	7.656	2.609
^127Xe	16.028	1.065	1.787	0.652	−1.288	6.277	1.119
^126Xe	15.924	2.138	1.762	0.654	−0.206	7.350	2.609
^125Xe	15.820	1.073	2.341	0.651	−1.401	6.325	1.126
^124Xe	15.717	2.155	2.177	0.596	0.418	6.391	2.625
^123Xe	15.613	1.082	2.645	0.656	−1.495	6.408	1.054
^122Xe	15.509	2.173	2.302	0.606	0.345	6.526	1.774
^136I	16.954	0.000	−5.030	0.797	−1.133	6.570	0.631
^135I	16.852	1.033	−5.872	0.872	−0.350	9.566	1.517
^134I	16.749	0.000	−4.810	0.876	−2.139	8.890	0.316
^133I	16.646	1.041	−3.591	0.807	−0.945	8.226	2.142
^132I	16.543	0.000	−2.498	0.743	−1.782	5.958	0.278
^131I	16.441	1.048	−1.642	0.712	−0.759	6.593	1.932
^130I*	17.362	0.000	−0.680	0.726	−2.837	6.660	0.296
^129I	16.234	1.057	−0.103	0.653	−0.675	5.862	1.292
^128I*	16.029	0.000	0.638	0.688	−2.361	5.579	0.554
^127I	16.028	1.065	1.071	0.632	−0.793	5.733	1.413
^126I	15.924	0.000	1.623	0.638	−2.089	4.878	0.591
^125I	15.820	1.073	1.885	0.607	−0.722	5.455	1.392
^124I	15.717	0.000	2.319	0.633	−2.207	4.887	0.497
^123I	15.613	1.082	2.416	0.577	−0.493	5.032	1.493
^122I	15.509	0.000	2.702	0.595	−1.829	4.270	0.458
^135Te	16.852	1.033	−6.146	0.948	−1.177	12.371	1.702
^134Te	16.749	2.073	−7.088	1.005	−0.173	15.817	2.727
^133Te	16.646	1.041	−5.789	0.948	−1.323	12.175	1.804
^132Te	16.543	2.089	−4.646	0.880	−0.099	10.951	3.015
^131Te*	20.931	1.048	−3.422	0.630	−0.458	6.229	1.207
^130Te	16.337	2.105	−2.610	0.790	−0.094	8.990	2.950
^129Te*	17.372	1.057	−1.461	0.712	−1.221	7.168	0.967
^128Te	16.131	2.121	−0.941	0.733	−0.148	8.175	2.762
^127Te*	16.635	1.065	0.102	0.649	−0.850	6.028	1.602
^126Te*	15.857	2.138	0.364	0.665	0.223	7.124	2.813
^125Te*	16.485	1.073	1.249	0.623	−0.912	5.813	1.358
^124Te*	15.194	2.155	1.308	0.715	−0.480	8.014	2.874
^123Te*	15.599	1.082	1.993	0.632	−0.967	5.826	1.446
^122Te	15.509	2.173	1.907	0.669	−0.263	7.501	2.996
^121Te	15.405	1.091	2.469	0.668	−1.502	6.493	1.177
^120Te	15.300	2.191	2.144	0.596	0.584	6.260	2.083

*Parameter a* was adjusted to experimental average level spacing of s-wave neutron resonances.

2.3.2. Gamma-ray strength function

The generalized Lorentzian form [39] was used for γ-ray strength function f_E1 of E1 radiation. The parameter values of the energy, width and peak cross section for resonances were taken from the systematics for spherical and deformed nuclei [40] with deformation value. In addition, the strength functions for M1 and E2 radiations were also incorporated from the work of Kopecky and Uhl [39]. It is to be mentioned that the calculated capture cross sections were adjusted to the experimental data by introducing a normalization factor f_γ which was just multiplied to the total strength functions. In this evaluation, the values of f_γ such as 1.43, 1.35, 2.15, 2.00, 1.15, 1.49, 0.58 and 1.55 were used for fitting to capture cross sections and Maxwellian-averaged ones of ¹²⁴Xe, ¹²⁶Xe, ¹²⁸Xe, ¹²⁹Xe, ¹³⁰Xe, ¹³²Xe, ¹³⁴Xe and ¹³⁶Xe, respectively. We found the fluctuation of f_γ values, when the γ-ray strength function with systematic giant dipole resonance parameters were consistently used. It is not confirmed whether these fluctuations have physical meanings. The Maxwellian-averaged cross section was averaged over an energy region including resolved resonance one. Lack of resonance contribution may be responsible for the fluctuation of f_γ values.

3. Evaluated results and discussion

The calculated neutron-induced reaction cross sections of ^{124 − 136}Xe for various channels, e.g., capture, (n, 2n), (n, p) and (n, α) reactions, were compared with the experimental data. In these comparisons, experimental data were retrieved from EXFOR database [41]. The present results are visualized with the currently available major evaluated data (JENDL-4.0, ENDF/B-VII.1 and JEFF-3.2 [42]) as well as measured data.

3.1. Capture cross section

The cross section of ¹²⁴Xe is compared with the recent experimental data measured by Bhike et al. [43] and data of evaluated libraries in Figure 2. The calculated cross section is in good agreement with the newly measured data. However, the cross sections of JENDL-4.0, ENDF/B-VII.1 and JEFF-3.2 are deviated from the measured data. The cross sections for ^{128, 129, 130}Xe were investigated by Reifarth et al. [44] as a function of neutron energy in the range from 3 to 225 keV by using time-of-flight method. The present cross sections are compared with those experimental results for the corresponding isotopes, and contrasted with major evaluated nuclear data as illustrated in Figures 3–5. In these figures, the calculated cross sections reproduce the experimental data satisfactory. Furthermore, JENDL-4.0 evaluation describes experimental data in this energy range well. However, the cross section of ENDF/B-VII.1 for ¹²⁸Xe and ¹³⁰Xe are slightly higher than experimental data except the energy below 35 keV for ¹²⁸Xe, where evaluation explains the experimental data. In addition, the data of ENDF/B-VII.1 for ¹²⁹Xe are estimated to be smaller cross section than experimental data.

Figure 2. Comparison of the present ¹²⁴Xe(n,γ)¹²⁵Xe reaction cross section with the evaluated and experimental data.

Figure 3. Comparison of the present ¹²⁸Xe(n,γ)¹²⁹Xe reaction cross section with the evaluated and experimental data.

Figure 4. Comparison of the present ¹²⁹Xe(n,γ)¹³⁰Xe reaction cross section with the evaluated and experimental data.

Figure 5. Comparison of the present ¹³⁰Xe(n,γ)¹³¹Xe reaction cross section with the evaluated and experimental data.

Figure 6 represents the comparison of calculated cross section of ¹³⁶Xe with the evaluated libraries (JENDL-4.0 and ENDF/B-VII.1) and experimental data. Obviously, the present calculation expresses better the recent experimental result obtained by Bhike et al. [45]. The experiment was performed by activation method in the incident neutron energy range of 0.4–14.8 MeV. In contrast, JENDL-4.0 and ENDF/B-VII.1 are unable to reproduce experimental results, while their cross sections agree with the results of Bhike et al. below 2 MeV. The cross sections for remaining Xe isotopes were calculated and depicted with the data of JENDL-3.2 for only ¹²⁶Xe and JENDL-4.0 as shown in Figure 7. The cross sections measured with Maxwellian neutron spectrum are only available for ¹²⁶Xe, ¹³²Xe and ¹³⁴Xe. The Maxwellian-averaged cross sections calculated with resolved resonance parameters in JENDL-4.0 well reproduce those data.

Figure 6. Comparison of the present ¹³⁶Xe(n,γ)¹³⁷Xe reaction cross section with the evaluated and experimental data.

Figure 7. Comparison of the present capture cross sections of ^{126, 131, 132, 134}Xe with the evaluated data.

In integral test of YAYOI reactor experiment, the analysis was done by using JENDL-3.2 [11]. A large discrepancy in C/E values of 2.2–2.6 and 2.1–2.3 was observed for the radioactivities of ¹²⁵Xe and ¹²⁷Xe, respectively, which were produced by the neutron capture reactions on ¹²⁴Xe and ¹²⁶Xe. It was considered that this result comes from their large capture cross sections. The present results for ^{124, 126}Xe are smaller than the data of JENDL-3.2 by about 40% at 500 keV, at which the neutron spectrum of YAYOI has the largest peak, as seen in Figures 2 and 7. Thus, they may improve inconsistency in the C/E values at the experimental analysis of YAYOI.

3.2. (n, 2n) reaction cross section

The measurements of cross section for (n, 2n) reaction on ¹²⁴Xe, ¹²⁶Xe, ¹²⁸Xe, ¹³⁴Xe and ¹³⁶Xe by activation method were done by Sigg and Kuroda [46] and Kondaiah et al. [47] at the incident neutron energies of 14.6 and 14.4 MeV, respectively. The calculated data are compared with those experimental data, evaluated libraries and other available experimental data as illustrated in Figures 8–12.

Figure 8. Comparison of the present ¹²⁴Xe(n,2n)¹²³Xe reaction cross section with the evaluated and experimental data.

Figure 8 shows that the present result for ¹²⁴Xe(n, 2n) reaction is in good agreement with the recent experimental data obtained by Bhike et al. [43] and gives smaller cross sections than those of Bazan [48] and the others. ENDF/B-VII.1 and JEFF-3.2 evaluations mostly agree with the original data of Sigg and Kuroda (open inverted triangle). In contrast, the data of JENDL-4.0 are much larger than those of Kondaiah et al. and Sigg and Kuroda, but marginally fitted to the data of Sigg and Kuroda (filled triangle) corrected by using up-to-date intensity I_γ = 48.9% for 148.9 keV gamma ray from the decay of ¹²³Xe.

In Figures 9–11, the calculated reaction cross sections reproduce well the data of Sigg and Kuroda for ¹²⁶Xe, ¹²⁸Xe and ¹³⁴Xe. For ¹²⁶Xe(n, 2n) reaction, JEFF-3.2 data agree with those of Sigg and Kuroda, and JENDL-4.0 is marginally accepted, while ENDF/B-VII.1 evaluation fitted to the data of Kondaiah et al. as in Figure 9.

Figure 9. Comparison of the present ¹²⁶Xe(n,2n)¹²⁵Xe reaction cross section with the evaluated and experimental data.

Figure 10. Comparison of the present ¹²⁸Xe(n,2n)¹²⁷Xe reaction cross section with the evaluated and experimental data.

Figure 11. Comparison of the present ¹³⁴Xe(n,2n)¹³³Xe reaction cross section with the evaluated and experimental data.

In ¹³⁴Xe(n, 2n) reaction, Reggoug et al. [49] and Sigg and Kuroda provided total reaction cross sections of 1.47 and 1.46 b at 14.7 and 14.6 MeV, respectively, whereas Kondaiah et al. reported the cross section 2.36 b at 14.4 MeV much larger than those of the former. Those cross sections might be incorrect, considering the systematics of (n, 2n) reaction cross section for ^{128 − 136}Xe (typically 1.8 b at 14.5–15 MeV). Sigg and Kuroda adopted I_γ = 14% for the 233.2 keV gamma ray from the internal transition of ^133mXe. The up-to-date value is 10.1%. This means that more plausible cross section for ^133mXe production is larger by 38% (open circle in Figure 11). The revision for the ^133gXe was also needed, but the measured data were not corrected due to their use of two gamma rays to derive activation cross section. Therefore, the revised ^133mXe production cross section was simply added to the original ^133gXe production one, in order to obtain the total ¹³³Xe production cross section (filled circle). The ^133mXe production data of Kondaiah et al. (open triangle) were also revised by the same way as the case of Sigg and Kuroda. It should be noted that the data of Reggoug et al. were not corrected since no information on decay monitors was available. The present data for ¹³³Xe total production cross section were fitted to revised data of Sigg and Kuroda, while ^133mXe cross section was marginally fitted to the revised data.

A recent experiment for ¹³⁶Xe(n, 2n)¹³⁵Xe reaction in the energy range of 9–14.9 MeV was performed by Bhatia et al. [50] which were done by using neutron activation method. In this experiment, they measured cross sections to 526.6 keV isomeric states of ¹³⁵Xe. Experimental data for total and isomer productions are depicted in Figure 12. It is found that the calculated cross sections for isomer are fairly fitted with the experimental data. The data of Kondaiah et al. and Sigg and Kuroda are smaller than the Bhatia cross sections. The cross sections of present calculation and JENDL-4.0 are consistent with the data of Bhatia et al. for total production cross section of ¹³⁵Xe. However, ENDF/B-VII.1 evaluation shows consistency with the data of Bhatia et al., particularly at energy below 10 MeV and at 14.9 MeV, at which ³H(d, n)⁴He reaction was employed as neutron sources, differing from the measurements at other energies by ²H(d, n)³He reaction. Furthermore, ENDF/B-VII.1 data agree with the work of Kondaiah et al.

Figure 12. Comparison of the present ¹³⁶Xe(n,2n)¹³⁵Xe reaction cross section with the evaluated and experimental data.

3.3. (n, p) reaction cross section

Figure 13 stands for the comparison of ¹²⁸Xe(n, p) reaction cross section of the present calculation with experimental data provided by Sigg and Kuroda along with those of the evaluated libraries. The data of Sigg and Kuroda were revised by using the up-to-date intensity I_γ = 12.6% for 442.9 keV gamma ray from the decay of ¹²⁸I (filled circle). The cross section increases by 62%. The present result reproduces well the revised data. The other evaluations, however, explain the original smaller cross section (open circle).

Figure 13. Comparison of the present ¹²⁸Xe(n,p)¹²⁸I reaction cross section with the evaluated and experimental data.

Figure 14 shows comparison of ¹³¹Xe(n, p) reaction cross section between the experimental data and calculated values. The cross sections of the present evaluation and ENDF/B-VII.1 agree with the data of Sigg and Kuroda. Although JEFF-3.2 is fairly consistent with the measured data, the shape of the excitation function is different compared to other libraries at energies above 15 MeV. In contrast, JENDL-4.0 evaluation is unable to reproduce the two data points.

Figure 14. Comparison of the present ¹³¹Xe(n,p)¹³¹I reaction cross section with the evaluated and experimental data.

3.4. (n, α) reaction cross section

The cross section of (n, α) reaction was calculated for natural Xe and compared with experimental data of Mack and Tornow [51] as shown in Figure 15. In addition to the statistical and pre-equilibrium α-emissions, the direct-like α-cluster emission by knock-out process was incorporated with a factor of 6.7 enhancement for all Xe stable isotopes, in order to better explain the energy dependence of cross section, while α-emission spectra have not been available. The presently calculated data and JENDL-4.0 reproduce well the measured cross section. In contrast, JEFF-3.2 and ENDF/B-VII.1 gave higher cross sections than the measured one, particularly at incident energy above 14 and 13 MeV, respectively.

Figure 15. Comparison of the present ^natXe(n,α) reaction cross section with the evaluated and experimental data.

3.5. Elastic scattering angular distribution

The angular distributions of elastically scattered neutrons were calculated at incident neutron energies 1 and 14 MeV as shown in Figure 16 and are compared with those of JENDL-4.0 and ENDF/B-VII.1. Unfortunately, there are no experimental data available. The differences among three data are not so large despite the use of different OMPs.

Figure 16. Comparison of the present elastic scattering angular distributions with the evaluated data for natural Xe.

3.6. Neutron-production double-differential cross section

Figure 17 illustrates the comparison between the calculated neutron-production double-differential cross sections (DDXs) and those of JENDL-4.0 for natural Xe. The DDX as well as γ-ray spectrum below for natural element was derived by considering their natural isotopic abundances. The discrete inelastic and elastic scattering contributions of emission DDXs were broadened by using Gaussian distribution with resolution proportional to emission energies multiplied by 0.02. It is to be noted that there is no experimental information available neither for natural Xe nor its isotopes. Furthermore, the DDX of natural Xe for other evaluated libraries is not available due to incomplete data of each isotope. In this comparison, the neutron energies of incident channels at 5 and 14 MeV were considered. It is observed that the calculated neutron emission DDX provides almost similar result with that of JENDL-4.0, except that the contribution of pre-equilibrium component in JENDL-4.0 is slightly smaller than that in the present results.

Figure 17. Comparison of the present neutron production double differential cross sections with those of JENDL-4.0 for natural Xe at emission angle 60 deg.

3.7. Gamma-ray spectrum

Figure 18 shows the comparison of calculated γ-ray spectra for natural Xe with those of JENDL-4.0 where the incident neutron energies of 0.5, 5 and 14 MeV were considered. This comparison tells that the present results are very similar in pattern to spectra of the evaluated library. It is to be noticed that there is no experimental data available so far for the γ-ray emission spectra of ^{124 − 136}Xe as well as of natural Xe. As is the case with the neutron emission DDX, it was not possible to get the γ-ray spectrum for natural Xe from other evaluated libraries because there was no other library which has complete information of spectra for all isotopes except JENDL-4.0.

Figure 18. Comparison of the present γ-ray emission spectra with those of JENDL-4.0 for natural Xe.

4. Conclusion

The neutron cross sections for nine stable Xe isotopes (^{124, 126, 128, 129, 130, 131, 132, 134, 136}Xe) were calculated by using theoretical nuclear reaction model code, CCONE, and then compared with the available experimental information to validate the calculated results. In addition, major evaluated data libraries were also included in the comparison to visualize the differences between the previous and present evaluations. The evaluation was made in the energy region from 1 keV to 20 MeV. The coupled-channels optical model code, CCOM, was used to calculate the total cross section with modifications of some OMP parameters given by Kunieda et al. in order to get the better agreement with the experimental data. The contributions of pre-equilibrium and direct processes in the statistical model calculations were considered to obtain reaction cross sections, gamma-ray and particle emission spectra. The present evaluation, indeed, can reasonably explain the experimental data of total, capture, (n, 2n), (n, p) and (n, α) reaction cross sections. The angular distributions of elastically scattered neutrons, neutron emission DDX and γ-ray emission spectra were calculated at particular incident neutron energies for natural Xe and compared with evaluated libraries where no experimental information was found.

The obtained capture cross sections for ^{124, 126}Xe are smaller than the data of JENDL-3.2 in the keV energy region where the neutron spectrum of YAYOI has a large contribution. Hence, this evaluation could be able to improve the overestimation of C/E value found by the analysis of YAYOI experiment. Moreover, the present capture cross section of ¹³⁶Xe, for instance, describes the latest experimental data better than all other evaluated libraries. In addition, the evaluated total (n, 2n) reaction cross section of ¹³⁶Xe is in good agreement with the experimental data. Therefore, the present data of ¹³⁶Xe could provide relevant cross-section data for KamLAND-Zen and EXO experiments.

Acknowledgement

This work has been supported by JSPS KAKENHI [grant number 22360429].

Disclosure statement

No potential conflict of interest was reported by the authors.