Neutron energy dependence of delayed neutron yields and its assessments

Figures & data

Table 1. Odd–even factors $C_{ee}^0$ and $C_{oe}^0$ taken from Madland and England’s evaluation [39]

	${ }^{233}$U	${ }^{235}$U	${ }^{236}$U	${ }^{238}$U	${ }^{239}$Pu	${ }^{240}$Pu	${ }^{241}$Pu	${ }^{242}$Pu
$C_{ee}^0$	0341	0344	0270	0100	0190	0210	0100	0140
$C_{oe}^0$	0197	0202	0170	0060	0098	0130	0100	0080

Table 2. Experimental data used for the least-squares fitting

Nucleus	References
${ }^{233}$U	Tuttle [16], Borzakov et al. [41], Piksaikin et al. [8], Cesana et al. [42]
${ }^{235}$U	Tuttle [16], Reeder et al. [43], Saleh et al. [44], Roshchenko et al. [45], Piksaikin et al. [5]
${ }^{236}$U	Roshchenko et al. [26], Bobkov et al. [53]
${ }^{238}$U	Tuttle [16], Piksaikin et al. [46], Meadows [51]
${ }^{239}$Pu	Tuttle [16], Piksaikin et al. [8]
${ }^{240}$Pu	Tuttle [16], Benedetti et al. [17], Cesana et al. [42]
${ }^{241}$Pu	Tuttle [16], Meadows [51], Benedetti et al. [17], Cesana et al. [42]
${ }^{242}$Pu	Krick and Evans [47], Bobkov et al. [53]

Table 3. Parameters used in Equation (6)(6) $Z_p(A,E_n)=\alpha Z_p^0(A)+\beta c(A)E_n+\gamma E_n^2.$(6) determined by the least-squares fitting to the experimental data (read text for more detail)

Nuclide	$\alpha$	$\beta$	$\gamma$	$\xi$
U-$233$	$1.00363$	$0.722$	$1.208\times {10}^{-4}$	$1.159$
U-$235$	$0.99980$	$0.929$	$-3.561\times {10}^{-4}$	$0.830$
U-$236$	$1.00146$	$-0.203$	$1.261\times {10}^{-3}$	$1.402$
U-$238$	$1.00384$	$-1.800$	$3.608\times {10}^{-3}$	$0.940$
Pu-$239$	$0.99997$	$-0.116$	$6.816\times {10}^{-4}$	$0.481$
Pu-$240$	$1.00149$	$0.400$	0	$0.475$
Pu-$241$	$0.99921$	$0.769$	0	$0.710$
Pu-$242$	$1.00350$	$0.734$	0	$1.608$

Figure 1. Delayed neutron yield of uranium isotopes from $A=233$ to $238$ For ${ }^{235}$U, the median of the result of Alexander and Krick (Figure 6 of Ref. [10]) is indicated by the dotted–dashed line.

Figure 2. Delayed neutron yield of plutonium isotopes from $A=239$ to 242.

Figure 3. Delayed neutron yields of ${ }^{238}$U and ${ }^{241}$Pu as a function of incident neutron energy with different pre-fission neutron energies. We have assumed ${ϵ}_n\equiv {ϵ}_n^{\prime }={ϵ}_n^{{ }^{\prime \prime }}$. The lines in the figure are the spline curves.

Figure 4. Fission yields of 10 most important precursors contributing the delayed neutron yields for ${ }^{235}$U and ${ }^{239}$Pu at thermal fission. The precursors are arranged in order of importance from left to right.

Figure 5. Fission yields of 10 most important precursors contributing the delayed neutron yields for ${ }^{238}$U and ${ }^{239}$Pu at fast fission. The precursors are arranged in order of importance from left to right.

Figure 6. Decay heats (the right panels) and delayed neutron activities (the left panels) multiplied by time $t$ for thermal neutron fission of ${ }^{235}$U and ${ }^{239}$Pu (bottom). We assume instant neutron radiation. The result of Keepin’s six group [55] are also shown with the delayed neutron activity. The experimental data for the decay heat are taken from Refs [56,57].

Table 4. Delayed neutron yields of the thermal and fast neutron fissions calculated with JENDL/FPY-2011 [20,21]. This work and the experimental data are listed

Nuclide	JENDL/ FPY-2011	This work	Experiment
${ }^{235}$U(thermal)	$0.01683$	$0.01603$	$0.0158\pm 0.0005$ [55]
			$0.0156\pm 0.0010$ [54]
			$0.0163$[43]
			$0.0159\pm 0.0004$ [44]
${ }^{239}$Pu(thermal)	$0.00781$	$0.00625$	$0.0061\pm 0.0003$[55]
${ }^{238}$(fast)	$0.04263$	$0.04402$	$0.0448\pm 0.0042$[55]
${ }^{239}$Pu(fast)	$0.00691$	$0.00658$	$0.0063\pm 0.0003$[55]

Figure 7. Same as Figure 6, but for fast neutron fission of ${ }^{238}$U and ${ }^{239}$Pu. The experimental data for the decay heat are taken from Refs. [58–60].

Madland DG, England TR. The influence of pairing on the distribution of independent yield strengths in neutron-induced fission. LA-6430-MS. New Mexico: Los Alamos National Laboratory; 1976. p. 1–21.

 Google Scholar

Tuttle RJ. Delayed-neutron yields in nuclear fission. INDC(NDS)-107/G+special, Proceedings of the Consultants’ Meeting on Delayed Neutron Properties, Vienna, 26-30 March 1979:29–67.

 Google Scholar

Borzakov SB, Andreev AN, Dermendjiev E, et al. Measurements of delayed neutron yields from thermal neutron induced fission of U-233, U-235, Pu-239 and Np-237. Phys Atomic Nucl. 2000;63:530.

 Web of Science ®Google Scholar

Piksaikin VM, Semenova NN, Mil’shin VI, et al. A method and setup for studying the energy dependence of delayed neutron characteristics in nuclear fission induced by neutrons from the T(p,n), D(d,n), and T(d,n) Reactions. Instrum Exp Techn. 2006;49:765–777.

 Web of Science ®Google Scholar

Cesana A, Sandrelli G, Sangiust V, et al. Absolute total yields of delayed neutrons in the fission of U-233, Np-237, Pu-238, 240, 241, Am-241. Energia Nucleare (Milan). 1979;26:542.

 Google Scholar

Reeder PL, Warner RA. Delayed neutron precursors at masses 97-99 and 146-148. Phys Rev C. 1983;28:1740–1751.

 Web of Science ®Google Scholar

Saleh HH, Parish TA, Shinohara N. Measurements of delayed neutron decay constants and fission yields from 235U, 237Np, 241Am, and 243Am. Nucl Sci Eng. 1997;125:51–60.

 Web of Science ®Google Scholar

Roshchenko VA, Piksaikin VM, Korolev GG, et al. Cumulative yields of delayed neutron precursors in neutron induced fission of 237-Np and 238-U in the energy range from 05 up to 5. MeV. Phys Atomic Nucl. 1999;62:1279.

 Web of Science ®Google Scholar

Piksaikin VM, Balakshev JF, Isaev SG, et al. Conference nuclear data for science and technology Trieste. Vol. 1, Italy: Italian Physical Society; 1997. p. 485–487.

 Google Scholar

Roshchenko VA, Piksaikin VM, Isaev SG, et al. Energy dependence of nuclear charge distribution in neutron induced fission of Z-even nuclei. Phys Rev C. 2006;74:014607/1–11.

 Web of Science ®Google Scholar

Yu BE, Gudkov AN, Dyumin AN, et al. Measurement of delayed-neutron group yields following the fission of 235U, 236U, 238U, 237Np, 242Pu by 147 MeV Neutrons. Atomnaya Energiya. 1989;67:408.

 Google Scholar

Piksaikin VM, Roshchenko VA, Korolev GG. Relative yield of delayed neutrons and half-lives of their precursor nuclei from U-235 fission by 142-179 MeV neutrons. At Energy. 2007;102:151.

 Web of Science ®Google Scholar

Meadows JW. The delayed neutron yield of 238 and 241Pu. Argonne Natl Lab Rep. 1976;18:1–24.

 Google Scholar

Benedetti G, Cesana A, Sangiust V, et al. Delayed neutron yields from fission of uranium-233, neptuniu-237, plutonium-238, −240, −241, and americium-241. Nucl Sci Eng. 1982;80:379–387.

 Web of Science ®Google Scholar

Krick MS, Evans AE. The measurement of total delayed-neutron yields as a function of the energy of the neutron inducing fission. Nucl Sci Eng. 1973;50:80.

 Google Scholar

Alexander DR, Krick MS. Delayed neutron yield calculations for the neutron-induced fission of uranium-235 as a function of the incident neutron energy. Nucl Sci Eng. 1977;62:627–635.

 Web of Science ®Google Scholar

Keepin GR, Wimett TF, Zeigler RK. Delayed neutrons from fissionable isotopes of uranium, plutonium, and thorium. Phys Rev. 1957;107:1044–1049.

 Web of Science ®Google Scholar

Dickens JK, Love TA, McConnell JW, et al. Fission-product energy release for times following thermal-neutron fission of 235U between 2 and 14000 s. Nucl Sci Eng. 1980;74:106–129.

 Web of Science ®Google Scholar

Dickens JK, Love TA, McConnell JW, et al. Fission-product energy release for time following thermal-neutron fission of plutonium-239 and plutonium-241 between 2 and 14000s. Nucl Sci Eng. 1981;78:126–146.

 Web of Science ®Google Scholar

Katakura J. JENDL FP decay data file 2011 and fission yields data file 2011. Tokai: Japan Atomic Energy Agency, JAEA-Data/Code 2011; 2011. p. 1–73.

 Google Scholar

Katakura J, Minato F, Ohgama K. Revision of the JENDL FP fission yield data. EPJ Web of Conferences. 2016;111:08004.

 Google Scholar

Synetos S, Williams JG. Delayed neutron yield and decay constants for thermal neutron induced fission of U-235. INDC(NDS)-107/G+Special. 1979.

 Google Scholar

Akiyama M, Furuta K, Ida T, et al. J Atom Ener Soc of Japan. 1982;24:709–722. in Japanese

 Web of Science ®Google Scholar

Akiyama M, An S. Measurements of fission-product decay heat for fast reactors. In: Proceedings of International Conference on Nuclear Data for Science and Technology; Antwerp, Belgium; 1982. p. 237–244.

 Google Scholar