Evaluation of neutron nuclear data on platinum isotopes

ABSTRACT

Neutron nuclear data on 10 isotopes of platinum have been evaluated for the next version of Japanese Evaluated Nuclear Data Library general-purpose file in the energy region from 10⁻⁵ eV to 20 MeV. Resolved resonance parameters of naturally occurring isotopes were taken from a compilation work, while unresolved resonance parameters were obtained by fitting to the total and capture cross sections calculated from nuclear models. A statistical model code was applied to evaluate cross sections above the resolved resonance region. Compound, pre-equilibrium and direct-reaction processes were considered for cross-section calculation. Coupled-channel optical model parameters were employed for the interaction between neutrons and nuclei. Giant-dipole and pygmy resonance parameters for E1 γ-ray transition from platinum isotopes were determined so as to reproduce measured γ-ray spectrum. The present results reproduce experimental data very well. The evaluated data are compiled into Evaluated Nuclear Data File formatted data files.

KEYWORDS:

• Neutron nuclear data
• evaluation
• platinum isotopes
• cross section
• JENDL
• resonance parameter
• optical model
• statistical model

1. Introduction

Nuclear data are required for nuclear science and engineering. Especially, neutron-induced reaction data are important for nuclear energy applications. Japanese Evaluated Nuclear Data Libraries (JENDLs) have been developed by the Japan Atomic Energy Agency (JAEA) since 1977. The fourth version of the general-purpose file, JENDL-4.0, was released [1] in 2010. JENDL-4.0 contains neutron-induced reaction data for 406 nuclides in the atomic number of Z = 1–100. However, the data for 11 elements have never been evaluated due to the low priority for nuclear energy applications. Platinum is an element of which data are missing in JENDL-4.0. Recently, activation cross sections of various elements have been needed for the decommissioning of nuclear facilities. In addition to major elements, we have to pay attention to minor elements which could be contained as impurities in structural materials, since their radioactivity might be high. Hence, the platinum data should be evaluated in order to make JENDL a complete library.

The present work was undertaken to newly evaluate the data on platinum 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), (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. The Q-values of the reactions were calculated from the mass table AME2012 [2], and are listed in Table 1, together with abundances [3] and half-lives [4].

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

	^189Pt	^190Pt	^191Pt	^192Pt	^193Pt	^194Pt	^195Pt	^196Pt	^197Pt	^198Pt
Abundances(%)	10.87h*	0.012	2.83d*	0.782	50y*	32.86	33.78	25.21	19.8915h*	7.356
Q-values (MeV)
(n, γ)	8.911	6.448	8.662	6.261	8.352	6.105	7.922	5.846	7.555	5.556
(n, p)	2.754	0.213	1.792	−0.672	0.839	−1.446	−0.320	−2.427	−1.374	−3.302
(n, α)	12.163	9.542	11.084	8.343	9.874	7.281	8.734	6.396	7.662	5.252
(n, d)	−3.198	−3.933	−4.010	−4.646	−4.708	−5.289	−5.327	−6.017	−6.048	−6.704
(n, t)	−3.815	−5.852	−4.123	−6.415	−4.649	−6.803	−5.136	−6.992	−5.606	−7.346
(n, ^3He)	−2.124	−3.046	−3.573	−4.443	−4.945	−5.739	−6.260	−7.070	−7.770	−8.487
(n, 2n)	−6.728	−8.911	−6.448	−8.662	−6.261	−8.352	−6.105	−7.922	−5.846	−7.555
(n, np)	−5.423	−6.157	−6.235	−6.870	−6.933	−7.513	−7.551	−8.242	−8.273	−8.929
(n, nα)	3.899	3.252	3.095	2.422	2.082	1.522	1.176	0.812	0.549	0.107
(n, nd)	−10.072	−12.110	−10.380	−12.672	−10.907	−13.061	−11.394	−13.249	−11.863	−13.603
(n, 3n)	−15.943	−15.639	−15.359	−15.110	−14.923	−14.613	−14.457	−14.027	−13.768	−13.401
(n, 2np)	−12.296	−14.334	−12.605	−14.897	−13.131	−15.285	−13.618	−15.473	−14.088	−15.828

*Half-lives are given for ^{189, 191, 193, 197}Pt which are unstable.

The 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 the 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 listed in Table 2 for each target nucleus. In principle, resolved resonance parameters (RRPs) are obtained from the analyses of experimental data. RRPs are available for ^{190, 192, 194, 195, 196, 198}Pt, although the parameters were quite old and no new measurements have been reported. In the present work, the RRPs for these nuclei were taken from the compilation work of Mughabghab [5]. The neutron widths for the negative resonances of ^{190, 192, 194}Pt were adjusted so as to reproduce the thermal capture cross sections recommended by Mughabghab, while those of ^{195, 196, 198}Pt were modified by considering the data measured by Massarczyk et al. [6] for ¹⁹⁵Pt and by Farina Arboccò et al. [7] for ^{196, 198}Pt. Concerning ^{189, 191, 193, 197}Pt for which RRPs were unavailable, constant and 1/v energy dependencies were assumed for the elastic scattering and capture cross sections, respectively. Normalisation of these cross sections was done at thermal energy. The thermal scattering cross section was calculated as 4πR′ ², where R′ expresses 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 nuclei were estimated from a simplified formula used in the preceding work on antimony [8]. 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.

Table 2. Resolved and unresolved resonance regions.

Target nuclei	Resolved resonance	Unresolved resonance
^189Pt	–	0.3 eV–6.4 keV
^190Pt	10^−5–30.5 eV	30.5 eV–100 keV
^191Pt	–	0.7 eV–9.5 keV
^192Pt	10^−5 eV–5 keV	5–100 keV
^193Pt	–	4 eV–1.6 keV
^194Pt	10^−5 eV–1.3 keV	1.3–100 keV
^195Pt	10^−5 eV–900 eV	900 eV–100 keV
^196Pt	10^−5 eV–1.8 keV	1.8–100 keV
^197Pt	–	50 eV–53 keV
^198Pt	10^−5 eV–1.5 keV	1.5–100 keV

The unresolved resonance parameters (URPs) were determined with the ASREP code [9] by fitting to the total and capture cross sections evaluated with the nuclear models which will be described in the succeeding section. 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 average cross sections of ¹⁹⁷Pt reconstructed from the URPs are compared in Figure 1 with the total and capture cross sections calculated from the nuclear models. In the parameter fitting with the ASREP code, 10% uncertainties in the nuclear model calculations were assumed. The reconstructed cross sections reproduce the nuclear model calculations very well.

Figure 1. Unresolved resonance region for n + ¹⁹⁷Pt.

3. Computational methods and procedures above resonance region

3.1. Nuclear models

The CCONE code (Version 0.8.4) [10,11] was used for calculating the neutron-induced reaction cross sections of platinum 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, and the multistep 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 [12] extended 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. [13] using the coupled-channel method based on the rigid rotor model [14]. The potential forms are the same as those used in the previous work [15]. 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 parameter values are listed in Table 3, and the coupling schemes and deformation parameters are given in Table 4. The deformation parameters for ^{194, 196, 198}Pt were taken from the work of Deason et al. [16], while those for the remaining nuclei were based on the finite-range droplet model (FRDM) [17]. The calculated total cross section of elemental Pt is shown in Figure 2 together with experimental data and the spherical optical model calculations using the parameters of Koning and Delaroche [18]. In order to give a better fit to the experimental data, the value of W^DISP_D was adjusted, while the rest of the parameters remain unchanged from the original ones [13]. It is found from Figure 2 that the present calculations reproduce the measured data better than those using the parameters of Koning and Delaroche.

Figure 2. Total cross section of elemental Pt.

Table 3. 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^DISPR	= 94.88 MeV
Cviso	= 24.3 MeV
λR	= 1.05 × 10^− 2 + 1.63 × 10^− 4V^0R MeV^−1
W^DISPD	= 10.0 MeV
WIDD	= 12.72 − 1.54 × 10^−2A + 7.14 × 10^−5A^2 MeV
Cwiso	= 18.0 MeV
λD	= 0.0140 MeV^−1
W^DISPV	= 17.0 MeV
WIDV	= 105.05 − 14.13 × [1.0 + exp{(A − 100.21)/13.47}]^−1 MeV
V^0SO	= 5.92 + 0.003A MeV
λSO	= 0.005 MeV^−1
W^DISPSO	= −3.1 MeV
WIDSO	= 160.0 MeV
RR, 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
RSO	= (1.18 − 0.65A^−1/3)A^1/3 fm
aSO	= 0.59 fm

Note that the potential forms are given in [15]. The symbol A stands for the mass number of a nucleus.

Table 4. Coupling schemes used in the interaction between neutron and target.

Target nuclei	Coupled levels*	Deformation parameters
^189Pt	3/2^−(g.s.), 5/2^−(0.006), 7/2^−(0.238), 9/2^−(0.357)	β2 = −0.164, β4 = −0.021
^190Pt	0^+(g.s.), 2^+(0.296), 4^+(0.737), 6^+(1.288)	β2 = −0.156, β4 = −0.022
^191Pt	3/2^−(g.s.), 5/2^−(0.159), 7/2^−(0.488)	β2 = −0.156, β4 = −0.029
^192Pt	0^+(g.s.), 2^+(0.317), 4^+(0.785), 6^+(1.365)	β2 = −0.156, β4 = −0.029
^193Pt	1/2^−(g.s.), 3/2^−(0.002), 5/2^−(0.014), 7/2^−(0.599)	β2 = −0.156, β4 = −0.037
^194Pt	0^+(g.s.), 2^+(0.328), 4^+(0.811), 6^+(1.412)	β2 = −0.154, β4 = −0.046
^195Pt	1/2^−(g.s.), 3/2^−(0.099), 5/2^−(0.130), 7/2^−(0.450)	β2 = −0.148, β4 = −0.037
^196Pt	0^+(g.s.), 2^+(0.356), 4^+(0.877), 6^+(1.526)	β2 = −0.142, β4 = −0.049
^197Pt	1/2^−(g.s.), 3/2^−(0.072), 5/2^−(0.273), 7/2^−(0.483)	β2 = −0.148, β4 = −0.029
^198Pt	0^+(g.s.), 2^+(0.407), 4^+(0.985), 6^+(1.714)	β2 = −0.119, β4 = −0.042

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

Concerning charged particles, we utilised the spherical parameters of Koning and Delaroche [18] for protons, those of Lohr and Haeberli [19] for deuterons, those of Becchetti and Greenlees [20] for tritons and ³He, and those of Avrigeanu et al. [21] for α-particles. The transmission coefficients, which are required by CCONE to calculate charged-particle emission, were obtained from the charged-particle parameters.

3.2.2. Discrete levels and level density

In the calculation, it was necessary to input the discrete levels and level density parameters for 35 nuclei, i.e. ^{188 − 199}Pt, ^{188 − 198}Ir, and ^{185 − 196}Os. The discrete levels were taken from the reference input parameter library RIPL-3 [22].

Concerning the level density, the composite formula of Gilbert and Cameron [23] 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 (1) $${\rho }_T\left(E\right)=\frac{1}{T}\text{exp}\left(\frac{E-E_0}{T}\right),$$(1) where T and E₀ are adjustable parameters to fit the formula in measured discrete levels. On the other hand, the a parameter, which characterises the Fermi-gas part of level density ρ_F, is defined as (2) $$a\left(U\right)=a(*)\left[1+\frac{E_{\mathrm{sh}}}{U}(1-e^{-\gamma U})\right],$$(2) where E_sh is the shell correction energy and γ a damping factor. The damping factor is given by γ = 0.40A^{− 1/3}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 [24]. The shell correction energy E_sh was calculated as the difference between the experimental mass [2] and the theoretical mass [25]. 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 5 for individual nuclei, together with the energies of the highest discrete levels E^highest_level.

Table 5. Level density parameters for each nucleus.

	a(^*)	Δ	Esh	T	E0	Em	E^highestlevel
Nuclei	(MeV^−1)	(MeV)	(MeV)	(MeV)	(MeV)	(MeV)	(MeV)
^199Pt	23.228	0.851	−3.486	0.652	−1.577	7.628	0.474
^198Pt	23.131	1.706	−3.134	0.603	−0.154	7.247	1.944
^197Pt	23.033	0.855	−2.496	0.591	−1.093	6.292	0.965
^196Pt	22.936	1.714	−2.151	0.583	−0.239	7.037	1.992
^195Pt	22.839	0.859	−1.456	0.585	−1.366	6.400	0.875
^194Pt	22.741	1.723	−1.159	0.545	−0.056	6.437	1.992
^193Pt	22.644	0.864	−0.352	0.557	−1.327	6.020	0.692
^192Pt	22.546	1.732	−0.214	0.512	0.108	5.960	1.823
^191Pt	22.448	0.868	0.574	0.531	−1.227	5.657	0.613
^190Pt	22.351	1.741	0.575	0.473	0.405	5.356	1.915
^189Pt	22.253	0.873	1.275	0.491	−0.853	4.971	0.609
^188Pt	22.155	1.750	1.222	0.456	0.476	5.164	1.769
^187Pt	22.057	0.878	1.879	0.512	−1.272	5.494	0.621
^198Ir	23.131	0.000	−2.701	0.473	−0.605	2.953	0.116
^197Ir	23.033	0.855	−2.037	0.534	−0.541	5.142	0.654
^196Ir	22.936	0.000	−1.816	0.421	−0.373	2.287	0.522
^195Ir	22.839	0.859	−1.258	0.508	−0.450	4.793	1.107
^194Ir	22.741	0.000	−1.012	0.524	−1.561	4.307	0.524
^193Ir	22.644	0.864	−0.506	0.536	−0.987	5.523	1.038
^192Ir	22.546	0.000	−0.035	0.551	−2.203	5.097	0.320
^191Ir	22.448	0.868	0.290	0.525	−1.056	5.461	0.832
^190Ir	22.351	0.000	0.690	0.517	−1.927	4.514	0.386
^189Ir	22.253	0.873	0.866	0.504	−0.915	5.143	0.918
^188Ir	22.155	0.000	1.083	0.400	−0.682	2.450	0.354
^187Ir	22.057	0.878	1.431	0.522	−1.277	5.589	0.486
^196Os	22.936	1.714	−1.535	0.562	−0.197	6.749	0.300
^195Os	22.839	0.859	−1.132	0.435	0.242	3.509	0.439
^194Os	22.741	1.723	−0.995	0.553	−0.215	6.651	0.696
^193Os	22.644	0.864	−0.622	0.539	−0.998	5.571	0.456
^192Os	22.546	1.732	−0.347	0.516	0.102	6.001	1.895
^191Os	22.448	0.868	0.159	0.560	−1.500	6.171	0.748
^190Os	22.351	1.741	0.299	0.520	−0.098	6.205	1.824
^189Os	22.253	0.873	0.718	0.535	−1.280	5.726	0.736
^188Os	22.155	1.750	0.702	0.492	0.188	5.709	1.957
^187Os	22.057	0.878	0.987	0.532	−1.271	5.673	0.727
^186Os	21.959	1.760	1.013	0.481	0.285	5.532	2.031
^185Os	21.861	0.882	1.231	0.520	−1.144	5.454	0.729

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 γ-ray spectra measured by Voignier et al. [26] at 500 keV. As for the E1 radiation, 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. [27]. An enhanced generalised Lorentzian (EGLO) [28] was used for the GDR and the pygmy resonance terms, 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 platinum isotopes, and they are given in Table 6. The calculated γ-ray spectrum for ¹⁹⁴Pt is compared with the data measured by Voignier et al. at an angle of 90° in Figure 3, where the measurements are multiplied by 4π. Agreement between the calculated and measured shapes is satisfactory. In this comparison, much emphasis is placed on the spectral shape, since the 500-keV capture cross section of Voignier et al. is slightly larger than the present calculation, as seen in the succeeding section. For the other nuclei such as iridium and osmium isotopes, the GDR parameters for EGLO are given [29] by (3) $$E_0=31.2A^{-1/3}+20.6A^{-1/6}\mathrm{MeV},$$(3) (4) $${\Gamma }_0=0.026E_0^{1.91}\mathrm{MeV},$$(4) (5) $${\sigma }_0=1.2\times 120NZ/\left(A\pi {\Gamma }_0\right)\mathrm{mb},$$(5) where Z, A, and N are the atomic number and mass number of a nucleus, and N = A − Z, respectively. 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 [30].

Figure 3. Gamma-ray spectrum from n + ¹⁹⁴Pt at 500 keV.

Table 6. E1 parameters for platinum isotopes.

	$E_0\left(\mathrm{MeV}\right)$	${\Gamma }_0\left(\mathrm{MeV}\right)$	${\sigma }_0\left(\mathrm{mb}\right)$
GDR	13.72	4.99	512.00
Pygmy	5.50	2.40	2.50
Correction	1.40	1.60	0.50

In cases where measured capture cross sections are available in the keV region, 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 7 with the values recommended by Mughabghab [5]. In this work, the strength functions for ^{191, 196, 199}Pt were renormalised, whereas those for the rest of nuclei remained unchanged.

Table 7. Gamma-ray strength functions for s-wave neutron in units of 10⁻⁴.

Compound nuclei	Present work	Mughabghab [5]
^190Pt	1894	–
^191Pt	17.96^*	–
^192Pt	820.2	–
^193Pt	15.18	19.1 ± 0.9
^194Pt	153.9	–
^195Pt	8.030	8.78 ± 1.88
^196Pt	53.55^*	63.5 ± 11.7
^197Pt	3.537	4.06 ± 1.00
^198Pt	17.10	–
^199Pt	1.452^*	–

^* Renormalised, as mentioned in the text.

3.2.4. Pre-equilibrium parameters

The Version 0.8.4 of CCONE incorporates the pre-equilibrium processes 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 [31] by (6) $$g_{\pi }=\frac{C_{0}Z}{15}{\mathrm{MeV}}^{-1},$$(6) (7) $$g_{\nu }=\frac{C_{0}N}{15}{\mathrm{MeV}}^{-1},$$(7) 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 multistep 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 parameters for the knockout and pickup reactions [32] were adjusted for α emission. The pre-equilibrium parameters used are listed in Table 8, 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 8. Pre-equilibrium parameters.

	C0		Knockout	Pickup
Target nuclei	(n, n′)	(n, p)	for (n, α)	for (n, α)
^189Pt	1.00	1.00	1.00	1.00
^190Pt	0.90	1.00	1.50	1.50
^191Pt	1.00	1.00	1.50	1.50
^192Pt	0.85	1.00	3.00	3.00
^193Pt	1.00	1.00	3.00	3.00
^194Pt	1.00	0.95	5.00	5.00
^195Pt	1.00	1.00	5.00	5.00
^196Pt	1.00	0.80	8.00	8.00
^197Pt	1.00	1.00	8.00	8.00
^198Pt	1.10	1.00	8.00	8.00

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

The presently evaluated data are compared with experimental data and other evaluated data. The experimental data are taken from the EXFOR database [33] that is compiled by the international 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, i.e. JENDL-4.0 [1], ENDF/B-VII.1 [34], and JEFF-3.2 [35]. As for platinum, JEFF-3.2 contains the data on ^{190, 192, 194, 195, 196, 198}Pt, while no platinum data are included in JENDL-4.0 and ENDF/B-VII.1. The activation cross-section files JENDL/A-96 [36] and JEFF-3.1/A [37] are also used for comparisons. We do not discuss most of the reactions for which experimental data are unavailable, since it is difficult to judge whether the present evaluation is reasonable without measurements.

The capture cross sections of ^{192, 194, 195, 196, 198}Pt are illustrated in Figures 4–8. Except for ¹⁹⁸Pt, the measurements of Koehler and Guber [38] are useful for validating the evaluated data. In this work, the capture cross section of ¹⁹⁵Pt was renormalised by considering their data, although those of ^{192, 194, 196}Pt remained unchanged from the original calculations. The present evaluations well reproduce the data of Koehler and Guber for ^{192, 194, 195, 196}Pt. Concerning ¹⁹²Pt, the JENDL/A-96 evaluation is remarkably larger than the measurements and the other evaluations below 500 keV. As mentioned in Section 3, the 500-keV capture cross section of ¹⁹⁴Pt measured by Voignier et al. [26] (122 ± 9 mb) is slightly larger than the present evaluation (105.6 mb). This is why only the shape of their measured spectrum was considered for the determination of the γ-ray strength functions for the platinum isotopes. As for ¹⁹⁶Pt, the other evaluations obviously put emphasis on the data measured by Herman et al. [39] in the energy region from 0.5 to 1.3 MeV. An explanation is needed for the ¹⁹⁸Pt(n, γ) reaction. Renormalisation of the γ-ray strength function for ¹⁹⁹Pt was done so that the calculated Maxwellian-averaged cross section reproduced the cross section measured by Marganiec et al. [40] at kT = 30 keV, as shown in Figure 9. Figure 10 is illustrated in order to demonstrate that the Maxwellian averaging of ¹⁹⁶Pt(n, γ)¹⁹⁷Pt can also reproduce the data measured by the same authors. It should be noted that renormalisation of the γ-ray strength function was not done for the latter case. The capture cross section of ¹⁹⁰Pt was renormalised so as to reproduce the Maxwellian-averaged cross section measured by Marganiec et al. [41] at kT = 30 keV, as seen in Figure 11.

Figure 4. Capture cross section of ¹⁹²Pt.

Figure 5. Capture cross section of ¹⁹⁴Pt.

Figure 6. Capture cross section of ¹⁹⁵Pt.

Figure 7. Capture cross section of ¹⁹⁶Pt.

Figure 8. Capture cross section of ¹⁹⁸Pt.

Figure 9. Maxwellian-averaged capture cross section of ¹⁹⁸Pt.

Figure 10. Maxwellian-averaged capture cross section of ¹⁹⁶Pt.

Figure 11. Maxwellian-averaged capture cross section of ¹⁹⁰Pt.

Figures 12–17 show the (n, 2n) reaction cross sections of the naturally occurring isotopes. Experimental data are available only for ^{190, 192, 198}Pt. Concerning ¹⁹⁰Pt, the present evaluation is smaller than the data measured by Luo et al. [42]. The pre-equilibrium parameter C₀ for (n, n′) would become very small, i.e. less than 0.5, in order to fit the data of Luo et al. Such a small value is unreasonable by comparing with the values for ^{192, 198}Pt. In this work, further adjustment of the ¹⁹⁰Pt(n, 2n) cross section was not performed by considering the facts that the abundance of ¹⁹⁰Pt is extremely small and there exist no other measurements. The experimental data on the ¹⁹²Pt(n, 2n) reaction are well reproduced by the present evaluation, while the JEFF-3.2 evaluation is slightly smaller than the measurements. As for ¹⁹⁸Pt, all the evaluations are consistent with most of the measurements around 14 MeV except the one measured by Paul and Clarke [43] (2.77 b ± 50%) which would be outside Figure 17. However, the data of Bormann et al. [44], which were obtained by the β⁻ counting, are systematically larger than the evaluations in the region from 12 to 16 MeV. The presently evaluated ^{194, 195, 196}Pt(n, 2n) cross sections are almost consistent with the JEFF-3.2 evaluations. The (n, 2n) cross section of elemental Pt is illustrated in Figure 18, where the data of Frehaut et al. [45] were renormalised by the factor of 1.078 that was derived by Vonach et al. [46]. The present and JEFF-3.2 evaluations are in good agreement with the measurements, while the JEFF-3.1/A evaluation deviates from the former ones above 12 MeV.

Figure 12. ¹⁹⁰Pt(n, 2n)¹⁸⁹Pt reaction cross section.

Figure 13. ¹⁹²Pt(n, 2n)¹⁹¹Pt reaction cross section.

Figure 14. ¹⁹⁴Pt(n, 2n)¹⁹³Pt reaction cross section.

Figure 15. ¹⁹⁵Pt(n, 2n)¹⁹⁴Pt reaction cross section.

Figure 16. ¹⁹⁶Pt(n, 2n)¹⁹⁵Pt reaction cross section.

Figure 17. ¹⁹⁸Pt(n, 2n)¹⁹⁷Pt reaction cross section.

Figure 18. ^natPt(n, 2n) reaction cross section.

The charged-particle emission cross sections are depicted in Figures 19–26. As for the partial ¹⁹⁴Pt(n, p) reactions, the present and JEFF-3.1/A evaluations are consistent with the measurements. On the other hand, four evaluations of ¹⁹⁵Pt(n, p) are somewhat different from one another, although the measured data are reproduced by the present evaluation. Concerning the ¹⁹⁶Pt(n, p)^196mIr reaction, the pre-equilibrium parameter C₀ for (n, p) was adjusted so as to reproduce the cross sections measured by Filatenkov and Chuvaev [47]. They deduced the cross sections by measuring four γ-rays, i.e. 393.5, 447.1, 521.4, and 647.3 keV with high-energy resolution, while only the 355.9-keV γ-line was used for the determination of the cross section in the other experiments. The data of Filatenkov and Chuvaev were judged most reliable in this work, since it was indicated [47] that part of the 355.9-keV γ-ray peak could come from other reactions. The (n, α) cross sections of ^{194, 196}Pt, which were measured by Filatenkov and Chuvaev [47] and Coleman et al. [48], are reproduced by the present and JEFF-3.1/A evaluations.

Figure 19. ¹⁹⁴Pt(n, p)^194gIr (T_1/2 = 19.28 h) reaction cross section.

Figure 20. ¹⁹⁴Pt(n, p)^194mIr (T_1/2 = 31.85 ms) reaction cross section.

Figure 21. ¹⁹⁵Pt(n, p)^195gIr (T_1/2 = 2.5 h) reaction cross section.

Figure 22. ¹⁹⁵Pt(n, p)^195mIr (T_1/2 = 3.8 h) reaction cross section.

Figure 23. ¹⁹⁶Pt(n, p)^196gIr (T_1/2 = 52 s) reaction cross section.

Figure 24. ¹⁹⁶Pt(n, p)^196mIr (T_1/2 = 1.40 h) reaction cross section.

Figure 25. ¹⁹⁴Pt(n, α)¹⁹¹Os reaction cross section.

Figure 26. ¹⁹⁶Pt(n, α)¹⁹³Os reaction cross section.

5. Concluding remarks

Platinum data had never been considered in the JENDL general-purpose files due to the low priority. The present work was undertaken to make JENDL complete for various applications. The neutron nuclear data on platinum isotopes were evaluated in the energy region from 10⁻⁵ eV to 20 MeV. The RRPs of ^{190, 192, 194, 195, 196, 198}Pt were taken from the existing compilation work, since no new measurements were available. In the low-energy region, constant and 1/v energy dependencies were assumed for the elastic scattering and capture cross sections of ^{189, 191, 193, 197}Pt, since there exist no RRPs. The thermal capture cross sections of these nuclei were renormalised by using 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 this 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 and pygmy resonance parameters for platinum isotopes, which were needed to calculate γ-ray emission, were determined so as to reproduce the shape of the γ-ray spectrum for ¹⁹⁴Pt measured at 500 keV. The presently evaluated cross sections are in good agreement with measurements, and are much better than the other evaluations such as JEFF-3.2, JEFF-3.1/A, and JENDL/A-96. The evaluated data are compiled into ENDF-formatted data files for the next release of the JENDL general-purpose file.

Acknowledgments

The author would like to thank the members of the Nuclear Data Center, JAEA, for their helpful comments on this work. He is also grateful to Dr M. Ishikawa for reviewing the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.