Journal of Nuclear and Radiochemical Sciences,Vol. 3, No. 1, pp. 93–94, 2002

93

Evaluation of Prompt Neutron Spectra from Fission of Americium Isotopes
Takaaki Ohsawa∗
Department of Nuclear Engineering, Faculty of Science and Technology, Kinki University, 3-4-1
Kowakae, Higashi-osaka 577-8502, Japan
Received: November 13, 2001; In Final Form: March 12, 2002
Prompt neutron spectra for Am isotopes (241 Am, 242m Am, 243 Am) were calculated on the basis of a modified versionof the Madland-Nix model combined with multimodal fission model. The predicted spectra were found to be in fairagreement with recent data.
CSL = 0.01exp(0.46E ∗f ) ,AS1 = 141.0 − 0.053E ∗f ,AS2 = 82.3 + 0.293N f + 0.1Z f − 0.03E ∗f ,σ = 5.7 − 0.24(149.9 − N f ) + 0.12E ∗f ,µSL = 1.4 ,µS2 = 1.884 − 0.0094N f+ 0.267exp[−(N f − 142.5)2 ]+ 0.114exp[−|N f − 146.8| ] ,C = 100/(CS1 +CS2 +CSL /2) .

1. Introduction
With the development of extended burnup of nuclear fuel andincineration of long-lived actinide nuclides, the need for accurate nuclear data for transplutonium isotopes has been rising.
The prompt neutron spectra, among others, are required forshielding calculation of transportation casks and reprocessing
facilities as well as reactor core calculation. The authors haveproposed a method of calculation of the prompt neutron spectra based on the Madland-Nix model1 extended to consider themultimodal nature of the fission process. This method was applied to 235 U, 237 Np, and plutonium isotopes with satisfactory
results.2–4
The method was applied to americium isotopes (241 Am,242mAm, 243 Am) to obtain the spectra for incident neutron energies up to 5 MeV. Difficulties in applying the method to Am
isotopes lay in the fact that detailed multimodal analyses of fission have not been made for these nuclides. We solved these
problems by making the best use of systematics.
The calculated spectra were compared with experimental datawhen possible.
2. Method
2.1. Mass and Charge Distributions of Fission Fragments.
Wang et al.5 analyzed empirical data of primary mass distributions for fissioning systems ranging from Ac to Fm and foundthat the all the distributions were well represented with a superposition of five Gaussian functions with parameters varying
smoothly with the mass and excitation energy of the fissioning
system. The success of this analysis indicates possible existenceof three main modes in fission for the actinides.
The fragment mass distribution for each mode is expressed asa Gaussian function:
G(A, Ā, σ) = (2π)−1/2 σ−1 exp[−(A − Ā)2 /2σ2 ]

(3c)
(3d)
(3e)
(3f)
(3g)

(3h)
(3i)

The quantities Ci and Ai can be interpreted as the branchingratios and the average fragment masses for a fission mode i.
The charge distribution was assumed to be Gaussian with themost probable charge and standard deviation given by Wahl.6
The total energy release ER was calculated by using the TUYY
mass formula.7
2.2. Total Kinetic Energy of Fission Fragments. Systematics in the empirical data of total kinetic energy (TKE) of fragments for each mode were studied for nuclei in the actinide region on the basis of data analyzed by Fan et al.8 It was foundthat the TKEs for each mode for actinides vary linearly with theCoulomb parameter Z 2 /A1/3 of the fissioning nucleus (Figure 1).
These relations were used to estimate the TKEs for actinides forwhich the TKEs for each mode are not known.
3. Results and Conclusion
Calculations were made for 241 Am, 242m Am, 243 Am(n, f ) for
incident neutron energies from thermal to 5 MeV. The spectra
for each fission mode and the synthesized total spectrum for242m
Am are shown and compared with recent measurement byTh

(1)

U

Np Pu

Cf240

Y (A, A f , E ∗f ) = CS1 [G(A, AS1 , σ) + G(A, A f − AS1 , σ)]+CS2 [G(A, AS2 , µS2 σ) + G(A, A f − AS2 , µS2 σ)]+CSL G(A, A f /2, µSL σ)
(2)

220

Systematics of TKE for each mode
(Data from Fan et al.(1995))
<Er>

200

TKE (MeV)

where A is the fragment mass number, Ā the average fragment
mass number, σ the standard deviation of the mass distribution
for the fission mode. The total mass distribution Y (A, A f , E ∗f )for a fissioning nucleus with excitation energy E ∗f is written as asuperposition of five Gaussians each corresponding to standard1 (S1), standard-2 (S2) and superlong (SL) modes:

S2180

SL
160
140

where the parameters involved are given as follows for lowenergy fission of actinides5 :
CS1 =
CS2 =

2.66(169.9 − N f ) + 0.19(A f − 232.2)E ∗f ,59.3 − 0.263N f − 0.017(A f − 235.7)E ∗f ,∗E-mail: ohsawa@ned.kindai.ac.jp.

(3a)
(3b)

S1120

<TKE>exp: Viola et al.(1985)

1300

1400

1500
2

1/3

Coulomb parameter Z /A

Figure 1. The TKEs for each mode for actinides as a function of theCoulomb parameter Z 2 /A1/3 of the fissioning nucleus.

c 2002 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 6/30/2002

94J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

Ohsawa

1Am242m, En=thermal

0.1

Exp. data nomalized at 2MeV

Neutrons per MeV

0.01
1E-3
1E-4

Total
S1
S2
S3
Drapchinsky99

1E-5
1E-6
1E-7

05

101520

Neutron Energy (MeV)

Figure 2. The spectra for each fission mode and the synthesized total
spectrum for 242m Am together with recent measurement by Drapchinsky.9References

Ratio to χ(Am241)

1.3

1.2
Am242m/Am241Am243/Am241
1.1

1.0

0.9

0.01

Drapchinsky9 in Figure 2. It can be seen that the predicted total spectrum agrees fairly well with the measurement, although
there are some discrepancies in the region less than 1 MeV. This
discrepancy may be due to neutron emission before full acceleration of fission fragments, or neutron emission at the instant ofscission. This problem is under investigation at present.
The spectra for the three isotopes relative to that for 241 Am
for the incident energy En = 3 MeV are compared in Figure 3. It
can be seen that, although the differences are not considerable,
the spectrum for 242m Am is the hardest among them and thatfor 243 Am is slightly harder than that for 241 Am. This tendency
can be interpreted from energetics: the neutron binding energy
Bn = 6.77 MeV for the compound nucleus 243 Am is higher thanthose for other isotopes (5.53 MeV for 242 Am, and 5.36 MeV
244Am), and the average total energy release in fission increases
with mass number of the fissioning nucleus (207.51 MeV for242Am, 208.40 MeV 243 Am, and 208.42 MeV for 244 Am). Hencethe total excitation energy defined as TXE = ER +Bn +En − TKE
increases in the order of 241 Am < 243 Am < 242m Am.

0.1

1

10Neutron Energy (MeV)
Figure 3. The spectra for 242m Am and 243 Am relative to that for 241 Am
for the incident energy En = 3 MeV.

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