

ORIGINAL ARTICLE 

Year : 2016  Volume
: 39
 Issue : 4  Page : 212221 


ISOGEN: Interactive isotope generation and depletion code
Kamatam Venkata Subbaiah
Manipal Centre for Natural Sciences, Manipal University, Manipal, Karnataka, India
Date of Web Publication  13Feb2017 
Correspondence Address: Kamatam Venkata Subbaiah Manipal Centre for Natural Sciences, Manipal University, Manipal  576 104, Karnataka India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09720464.199976
ISOGEN is an interactive code for solving first order coupled linear differential equations with constant coefficients for a large number of isotopes, which are produced or depleted by the processes of radioactive decay or through neutron transmutation or fission. These coupled equations can be written in a matrix notation involving radioactive decay constants and transmutation coefficients, and the eigenvalues of thus formed matrix vary widely (several tens of orders), and hence no single method of solution is suitable for obtaining precise estimate of concentrations of isotopes. Therefore, different methods of solutions are followed, namely, matrix exponential method, Bateman series method, and Gauss–Seidel iteration method, as was followed in the ORIGEN2 code. ISOGEN code is written in a modern computer language, VB.NET version 2013 for Windows operating system version 7, which enables one to provide many interactive features between the user and the program. The output results depend on the input neutron database employed and the time step involved in the calculations. The present program can display the information about the database files, and the user has to select one which suits the current need. The program prints the “WARNING” information if the time step is too large, which is decided based on the builtin convergence criterion. Other salient interactive features provided are (i) inspection of input data that goes into calculation, (ii) viewing of radioactive decay sequence of isotopes (daughters, precursors, photons emitted) in a graphical format, (iii) solution of parent and daughter products by direct Bateman series solution method, (iv) quick input method and context sensitive prompts for guiding the novice user, (v) view of output tables for any parameter of interest, and (vi) output file can be read to generate new information and can be viewed or printed since the program stores basic nuclide concentration unlike other batch jobs. The sample problems are chosen to serve two purposes, namely to validate the results of the code against problems where the analytical solution is possible, and the other is to demonstrate the use of particular solution method adopted for solving the problem. Besides spent fuels, results are validated for many of the useful deduced parameters of practical interest such as radioactivity, thermal power, alpha activity, neutron emission rate, and photon emission spectrum. These parameters are of utmost important in handling spent fuels, in waste disposal, in fuel management, in radiation shielding and many other areas of nuclear fuel cycle facilities. Keywords: Bateman solution method, burnup, fission, fuel cycle, Gauss–Seidel iteration method, isotopes, matrix exponential method, neutron transmutation, nuclear reactor, radioactivity, spent fuel
How to cite this article: Subbaiah KV. ISOGEN: Interactive isotope generation and depletion code. Radiat Prot Environ 2016;39:21221 
Introduction   
Nuclear energy is produced in nuclear reactors, by the process of fission in fissionable nuclides such as U235 and Pu239, wherein a large amount of energy is released and two (three in rare instances) fission fragments are generated. The fission fragments thus produced vary widely in mass, as well charge resulting in the formation of several hundreds of new nuclides or isotopes. Many of the fission products produced are radioactive, and consequently, they decay till a stable nuclide is formed, producing series of new isotopes. Likewise, actinides (U, Pu) used in reactors for producing power, produce a wide variety of fission fragments, further they undergo various modes of radioactive decay leading to the generation of several hundreds of new isotopes. The stable structural materials and others employed in nuclear reactors undergo neutron transmutation producing several other new radioactive isotopes. As a result of all the above processes, several thousands of isotopes are present in the reactor core. The estimation of precise quantities of all these nuclides as a function of time is important in the safe operation of reactor and also required at the front and back end of nuclear fuel cycles. The rate of change concentrations of isotopes can be written in the form of coupled first order linear differential equations with constant coefficients (approximating slowly timevarying variables with average values). The same equation can be written in a matrix notation and this matrix generally called transition matrix since it denotes for the formation of one isotope from another. In general, the size of matrix is very large (nuclides under consideration) demanding for computer memory space. However, due to limited number of nuclear transmutations possible, the matrix is a triangular (around the diagonal element decay constant) of nuclide. The range of decay constants (exp [−20] to exp [+20]), which form the elements of the matrix, whose eigenvalues are wide apart (several orders of magnitude). Direct solution method pose convergence problems since the norm of the matrix is very large.^{[1]} To overcome this problem, an alternate method of solving by the Chebyshev rational approximation method was proposed by Pusa et al.^{[2]} From the attempts of earlier workers, it is inferred that no one method of solution is suitable for all the nuclides. Therefore, nuclides are classified into two categories namely long and shortlived, and then different solution methods can be adopted. The ORIGEN code ^{[3]} employs matrix exponential method for longlived isotopes and Bateman series or Gauss–Seidel iteration method for shortlived ones. ORIGEN code package contains general data libraries, and one group crosssection libraries for pressurized water reactors (PWR), boiling water reactors (BWR), liquid metal fast breeder reactor core and blanket fuel, Canada deuterium–uranium (CANDU)
reactors as well as recycled fuel constants. At Oak Ridge National Laboratory (ORNL), sustained efforts were made over the years to improve on the code.^{[4],[5],[6],[7],[8]} Further, they updated the reactor models, crosssections, fission product yields, decay data, decay photon data.^{[9]} ORIGEN2 code has been extensively used for fuel management, waste analysis, shielding studies, and safeguard investigation. Consequently, numerous benchmark studies both experimental and calculated have been performed to illustrate the code's ability to predict uranium, plutonium, and fission product concentrations in spent fuels of PWR and BWRs. Charlton et al.,^{[10]} have made a comparison of Am241 and Am243 concentrations with measurements and the calculated with three different codes HELIOS (lattice physics code), ORIGEN2 (burnup code), and MONTEBURN (MCNP/ORIGEN2 linked code) codes. It was concluded from this study all the codes performed well and the ORIGEN2 libraries are not adequate for VVER spent fuel analysis.
The ORIGEN code runs in DOS mode and produces the specified results based on the concentration of nuclides. The output results produced by ORIGEN code is voluminous and difficult to look for the results required. The code has to be rerun to get another parameter of interest for the same problem. To circumvent these difficulties, in the present work a code “ISOGEN” has been developed based on the same algorithms as used in ORIGEN2 but a modern computer language, namely, VB.NET, version Microsoft Visual Studio 2013 VB.NET, Visual Studio 2013, Microsoft, USA. This code is interactive and userfriendly and developed for novices. The paper presents the brief description of mathematical methods, components design, and interactive features results and validation and conclusions.
Description of Mathematical Method   
A general expression for the formation and disappearance of a nuclide by nuclear transmutation and radioactive decay may be written as follows:
Where X_{i} is the atom density of nuclide i; λ_{i} is the radioactive disintegration constant; σ_{i} is the spectrum averaged neutron absorption crosssection of nuclide i; l_{ij} and f_{ij} are the fractions of radioactive disintegration and neutron absorption by other nuclides which lead to formation of species i, and ϕ̄… is the position and energy averaged neutron flux, which is also assumed to be constant over short intervals of time, since its variation with time is slow.
Nuclide decay constants, abundance, recoverable energy, and photon emissions are read from general data libraries. One group crosssections and fission product yields are read from predetermined reactor specific libraries. The data libraries of decay and neutron crosssections undergo revisions based on the current developments in this field. Therefore, users are expected to use the best available databases. Equation 1 is a homogenous set of simultaneous firstorder differential equation with constant coefficients, which may be written in matrix notation:
Equation 2 has the general solution of the form:
Where X (0) is a vector of initial atom densities and A is a transition matrix containing the rate coefficients for radioactive decay and neutron capture. In constructing the transition matrix for the problem, the following are accounted. In radioactive decay, the modes of decay considered are β^{−}, β^{−'}, β^{+}, β^{+'}, α, isomeric transition and spontaneous fission process. Moreover, in the neutron interaction reactions considered are (n, γ), (n, α), (n, p), (n, 2n), (n, 3n), and (n, fission). The computation scheme followed in the present code is same as that followed in ORIGEN code ^{[4]} and is described in brief below.
First, the nuclides are classified as three kinds namely:
 Activation products
 Actinides and daughters, and
 Fission products.
Further classification is made as short or longlived ones based on the halflife and time duration.
Present WorkDesign of Components and Interactive Features   
VB.NET of Microsoft Visual Studio provides an integrated development environment for easy design of attractive screens embedded with interactive components. Various Visual Basic (VB) tools and components used and their functional role in the code are described in sequel.
The screen shot of design layout of various VB.NET components employed in the form frmISOGEN, with opening of Sample_Inputs menu item is shown in [Figure 1]. Generic names of the VB.NET components given in the form list numbering 1–15 and the location of the components are indicated by the nearby circle inscribed with the corresponding numeral.  Figure 1: Design layout of VB.NET components in the form frmISOGEN, with opening of sample inputs menu item
Click here to view 
All the components are common windows features and are explained in the online help file as well as in the/user's manual of the code. The areas marked with numerals 3 and 15 are important, which contain the textual information of input and output, respectively.
Results and Discussions   
The results of ISOGEN code is the concentration of nuclides at the time steps specified in the input. Based on this coupled with nuclear properties, many parameters of practical interest can be generated and are given in [Table 1].
The program ISOGEN is developed in VB.NET language of Microsoft Visual Studio version 2013 under Windows operating system, version 7. The algorithms used in the present code are same as that employed in ORIGEN2 code ^{[4]} for solving a first order linear differential nuclide rate equation with constant coefficients. Since the magnitudes of coefficients vary widely, the solutions contain terms of differences of these coefficients which may result in unphysical solutions. To circumvent this problem, the nuclides are divided into two kinds, namely, longlived or shortlived. This is done based on the halflife (T_{½}) of the nuclide and the time duration (T_{i}) of irradiation/decay. If T_{i} <9.97*T_{½}, then the isotope is considered to be long else shortlived. This would limit the number of terms used to approximate the exponential and expected to yield a result in the accuracy of nuclide concentration of 0.1% for longlived nuclides. All the isotopes which are stable are considered to be longlived. For longlived nuclides matrix exponential solution method is employed and for shortlived ones Bateman series solution method or Gauss–Seidel method is selected depending on the nature of precursors. The coding of ISOGEN is tested against sample problems, which are chosen where the analytical solution possible. The sample problems are chosen to demonstrate the solution methodology adopted in code for any given situation. The abbreviations used in the text below denote the following:
L = Longlived nuclide, S = Shortlived nuclide, D = Daughter nuclide, P = Precursor/Parent nuclide, T_{½}= Halflife of radioactive nuclide, T_{i} = Time duration of irradiation or decay, GA = GramAtom or mole of a nuclide, GWd = Gigawatt days, MTU = Metric ton of uranium.
Validation of ISOGEN code with analytical solutions
Problem1: LP ==> LD solution method: Matrix exponential method
Estimate the concentration of Na24 and Mg24 after time interval (Ti) of 15 h?
Initial data concentration = 1.0 GA, T_{½} of Na24 = 15 h (5.400E + 04 s and Mg24 is stable).
Answer: Na24 = 0.5 GA and Mg24 = 0.5 GA.
Solution:
Since T_{i} = 15 h ≤ 9.97*T_{½} (Na24 [15 h]), Na24 and Mg24 (stable) are considered to be longlived in this case and hence matrix exponential method is used by the code to solve this problem. From the norm of matrix (At) = 0.693, it is estimated the number of terms required is 7. The progress of the solution with each addition of term in exponential series is shown in [Table 2]. In [Table 2], N corresponds to the term number in the exponential series.  Table 2: Variation concentration in moles (GramAtom) in matrix exponential solution method
Click here to view 
It can be observed that the term alternating sign with decreasing magnitude (Column 3 and Column 5) and converges rapidly in about six terms to the analytically expected value.
Problem2: LP ==> LD test of convergence: Matrix exponential method
Estimate the concentration of Na24 after Ti of 148.5 h?
Initial data concentration = 1.0 GA, T_{½} of NA24 = 15 h (5.400E + 04 s).
Answer: Concentration of Na24 = 1.043E02 GA.
Solution:
Since T_{i} = 148.5 h ≤ 9.97*T_{½} (Na24 [15 h]), Na24 and Mg (stable) are considered to be longlived in this case and hence matrix exponential method is used by the code to solve this problem. From the norm of matrix (At) = 6.861, it is estimated that the number of terms required is 29. The progress of the solution with each addition of term in exponential series is shown in [Table 3]. In [Table 3] also, the terms alternate in sign however the magnitude of term is not decreases with the increase in term number. As one can notice, the magnitude of the sixth term (1.450E+02) is maximum and thereafter decreases. However, actual solution converges at about 28^{th} term closer to the true value of 1.043E03. Therefore, sample problems 1 and 2, at extreme ends of the norm of transition matrix, establishes that the matrix exponential method converges to the expected accuracy.  Table 3: Variation concentration in moles (Gram.Atom) in matrix exponential solution method
Click here to view 
Problem3: SP ==> LD solution methods (Bateman for parent and matrix exponential method for daughter)
Estimate the concentration of Na24 and Mg24 after Ti of 150 h?
Initial data concentration = 1.0 GA, T_{½} of NA24 = 15 h (5.400E + 4 s).
Answers:
Concentration of Na24 from Bateman's method = 1.0*exp (−0.693*Ti/T_{½}) =9.765E04 GA.
Concentration of Mg24 from matrix exponential method = 9.990E01 GA.
Solution:
Since T_{i} = 150 h > 9.97*T_{½} (Na24 [15 h]), Na24 (15 h) and Mg (stable) considered to be short and longlived respectively in this problem. The computed results are displayed in the [Table 4].  Table 4: Variation concentration of Mg24 in moles in matrix exponential solution method
Click here to view 
Problem4: LP ==> SD solution methods (matrix exponential method for parent and Gauss–Seidel method for daughter)
Estimate the concentration and radioactivity of Ra226 (1.6 ky) and Rn222 (3.8D) after decay of (T_{i}) of 40 days? Given: Initial concentration of Ra226 = 1.0 GA.
Answers:
Concentration of Ra226 matrix exponential method after 40D decay ~1.0 GA.
Concentration of Rn222 from Gauss–Seidel method = 6.544E06 GA.
Solution:
Since T_{i} = 40D ≤ 9.97*T_{½} (Ra226 [1.6 ky]), Ra226 (1.6 ky) is considered to be longlived and T_{i} = 40D >9.97*T_{½} (Rn222 [3.8D]) is considered to be shortlived in this problem.
Solution methodology is matrix exponential method for Ra226 (LP, demonstrated in problems 1 and 2) and daughter is (SD) in secular equilibrium with the parent, solved by Gauss–Seidel iteration method. [Table 5] presents the results of Gauss–Seidel iteration method. It is to be noted here since the parent and daughter in secular equilibrium and hence their radioactivities are equal. This can be noticed from the entries of the last two columns of bottom row in [Table 5].  Table 5: Variation concentration in moles and activity in Ci in GaussSeidel iteration method
Click here to view 
Problem5: SP ==> SD solution methods (Bateman series method for both)
Estimate the concentration and radioactivity of Rn222 (3.8D) and Po218 (3.1M) after decay of (T_{i}) of 40 days? Given: Initial concentration of Rn222 = 1.0 GA.
Answers:
Concentration of Rn222 from Bateman's method = 1.0*exp (−0.693*Ti/T_{½}) =7.099E04 GA.
Concentration of Po218 from Bateman's series method = 3.934E07 GA.
Solution:
Since T_{i} = 40D > 9.97*T_{½} (Rn222 [38.1D]), Rn222 (3.81D) is considered to be shortlived and T_{i} = 40D >9.97*T_{½} (Po218 [3.1M]) is considered to be shortlived in this problem. [Table 6] shows the solution obtained.  Table 6: Variation concentration in moles and activity in by Bateman's method
Click here to view 
Problem4: Am242M decay – All three methods are employed in solving series decay
Estimate the total radioactivity and alpha activity (Ci) of Am242M over a period of 1MY and display the results graphically. Given: Initial concentration of Am242M = 1.029E09 g (0.1 µCi).
Solution:
The decay series of Am242M (one linear chain Ignoring branching) is shown in [Figure 2]. In general, it is expected that radioactivity decreases with the time. This is not true when the daughter products are also radioactive. Results are obtained from the ISOGEN code at regular intervals of 2, 5, and 10 in a decade over 1 million years. The values thus obtained are compared with literature values.^{[5],[11]} Both total activity and alpha activity over the entire period is in excellent agreement with the published values [Figure 3].  Figure 2: Am242M decay series (linear chain and branching is not shown)
Click here to view 
Validation of ISOGEN code for irradiation and decay
Problem1: Comparison of nuclear material characteristics of spent fuel of Canada deuterium–uranium type
ORIGEN2 has been extensively used for fuel management, waste analysis, shielding studies, and safeguard investigation. A number of benchmark studies have been carried out to illustrate the code's ability to predict concentrations of nuclides in spent fuels. Here, ORIGEN2 code is employed to generate results for CANDU reactor fuel irradiated to 7000 MWd/MTU over a period of 1 year and cooled 10 years. The sample input file is prepared for this case. The same input data are used for the ORIGEN2 and ISOGEN codes. The results obtained are compared for radioactivity of fission products, actinides, and daughters, concentration of uranium and plutonium vectors, thermal power and photon spectrum (α, n) and spontaneous neutron sources for the case of 7000 MWd/MTU burnup and 10 years cooled spent fuel. All the results found to be in good agreement except last digit numerical truncation error. A portion of results is given in [Table 7], [Table 8], [Table 9].  Table 8: Actinide masses of U and PU isotopes of 7000 MWd/MTU 10 years cooled spent fuel
Click here to view 
 Table 9: Neutron emission rate of 7000 megawatt days/metric ton of uranium 10 years cooled spent fuel of typical Canada deuteriumuranium type reactor
Click here to view 
From the close agreement of results for burnup case and the reproduction of analytical solution results for decay problems, establishes that the ISOGEN code is functioning reliably.
Problem2: H.B. Robison reactor spent fuel calculationsextended burnup 72 gigawatt days/metric ton of uranium
It is curious to analyze the results of ISOGEN code with published values. ORIGEN2 code produces voluminous amount of results and hence many of the published values limited to comparing integral quantities. However, detailed calculated results for H.B. Robinson reactor (PWR) have been reported by Sandia National Laboratory for various irradiation and cooling times using ORIGEN2 and ORIGENARP codes.^{[12]} The reported data in this document serves the purpose of testing the validity of existing crosssections to the extended burnup situations and the magnitude of deviations expected between the two results. The details of modeling of reactor fuel compositions, irradiation and decay times are taken from the above report (given in Appendix A ^{[12]} of that report). The same input is used for ISOGEN code. The output results generated with the ISOGEN code are compared with the reported values. All the quantities compared here corresponds to the irradiation of fuel for 72 GWd/MTU and 8 years cooled spent fuel. [Table 10] gives the comparison of total radioactivity in Curies for three kinds of nuclides.  Table 10: Comparison of total radioactivity in curies for three kinds of nuclides of 72 gigawatt days/metric ton of uranium spent fuel of H.B. Robinson reactor
Click here to view 
From the values of ratios in [Table 11], it can be observed that the agreement is excellent between the present and reported values for activation products and fission products. However, the difference of about 7% appears between them for actinide and daughters case. Although the agreement appears to be very good, it is necessary to identify nuclides that contribute significantly to the radioactivity.  Table 11: Comparison of radioactivity of significant activation product nuclides of 72 gigawatt days/metric ton of uranium spent fuel of H.B. Robinson reactor
Click here to view 
[Table 11] gives the nuclides which contribute significantly to the radioactivity of activation products. Although 684 nuclides are present in this kind, nearly, 97% of the total activity comes from tritium H3 (81%), which gets formed through activation of lithium, which is present as impurity in the fuel and Co60 (16%), which gets formed due to impurities present in the fuel (structural materials given as impurities in the fuel). Since tritium emits, soft beta radiation does not pose a spent fuel handling problem, unlike Co60 which emits hard gamma rays. Comparison of the magnitudes in [Table 12] shows the excellent agreement between the two.  Table 12: Comparison of radioactivity in curies for few actinide nuclides (which contribute to 97% of activity) of 72 gigawatt days/metric ton of uranium spent fuel of H.B. Robinson reactor
Click here to view 
Similarly, [Table 12] compares the actinide nuclides which contribute significantly (97%) to the total radioactivity. Out of the three nuclides, it is Pu241 which contributes 71% of the total activity. The ISOGEN has overestimated the activity for all the significant nuclides. However, the relative percentages seem to agree well as shown in brackets in [Table 12].
This can be ascribed to the differences in the crosssection libraries used especially for burnup dependent crosssections. This point is to be recalled when the comparison is made on the concentration of actinides in grams.
[Table 13] presents the comparison of few fission product nuclides which contribute nearly 96% of the total fission products activity. The agreement is very good between the present and reference values. There are about seven isotopes which contribute to the total fission product activity. Cs137 (30 y) and Ba137m (150 s) are in secular equilibrium, and its contribution is maximum, and it is 59% of the total fission product activity. It is the Cs137 isotope which has long halflife and emits 662 keV gamma ray needs attention while designing radiation shield.  Table 13: Comparison significant fission products radioactivity (Ci) (which contribute to 96% of activity) of 72 gigawatt days/metric ton of uranium spent fuel of H.B. Robinson reactor
Click here to view 
[Table 14] shows the comparison of actinide masses for the spent fuel of H.B. Robinson reactor of 8 years cooled 72 GWd/MTU spent fuel. In particular, uranium and plutonium elements, which are responsible for power generation, are included along with total actinides and its daughters mass. Total mass of actinides and its daughters in both cases is same. However, there are differences in isotopes U and Pu concentrations. For example, ISOGEN code under predicted fissile isotopic (U235, Pu239, and Pu241) masses by about 2.5% and seems to be reasonable. However, a large difference in Pu240 has occurred, and it is about 32.5%. This could have arisen due to in burnup dependent crosssections used in IGOGEN code, which accounts up to 50 GWd/MTU, whereas actual burnup of spent fuel is 72 GWd/MTU.  Table 14: Comparison of actinide mass in grams of 72 gigawatt days/metric ton of uranium spent fuel of H.B. Robinson reactor
Click here to view 
In handling or design of transportation flask or storage of spent fuel, the gamma rays emitted and the neutron source term are the two important parameters. Therefore, total photons and integral energy emitted by 72 GWd/MTU spent fuel, cooled for 8 years is given in [Table 15]. The photon library includes bremsstrahlung photons emitted in the fuel matrix by the betas and positrons. Therefore, the number photons/s is different in both cases. However, the energy emitted MeV/s matches well with the present values except for actinides and daughters. The argument given in support of actinide mass over prediction holds good for this case also.  Table 15: Comparison of gamma rays emitted by 72 gigawatt days/metric ton of uranium spent fuel of H.B. Robinson reactor, cooled for 8 years
Click here to view 
Based on the tabulated values of [Table 15], average energy parameter has been deduced (Column 4/Column 2) for the three kinds of nuclides and is given in [Table 17]. There is a good agreement for activation products and actinide and daughters case. However, a marked difference in the average energy of photons emitted in the fission products is observed. The reference 0.387 MeV appears to be low. From the [Table 8] on the radioactivity of nuclides, it was observed that Cs137 is the major contributor. This isotope emits 0.662 MeV gamma photons, and this value is closer to the value shown [Table 16] against ISOGEN code value of 0.548 MeV.  Table 17: Comparison of alpha activity of few actinide nuclides of 72 gigawatt days/metric ton of uranium spent fuel of H.B. Robinson reactor
Click here to view 
 Table 16: Comparison of gamma photons emitted for three kinds of nuclides of 72 gigawatt days/metric ton of uranium spent fuel of H.B. Robinson reactor, cooled for 8 years
Click here to view 
Alpha activity is the parameter is used in the segregation of nuclear wastes and its subsequent disposal. Most of the Alpha emitters are actinides and often they are longlived isotopes. Therefore, [Table 18] provides a comparison of present values with that reported in a study by Naegeli ^{12]} for some of the significant contributors. From [Table 18], it can be seen that the most of the alpha activity (92% of total) comes from the Pu238 and Cm244 nuclides. The values are different and are consistent with respect to their masses given in [Table 17].  Table 18: Comparison of α, n neutrons for few actinide nuclides of 72 gigawatt days/metric ton of uranium spent fuel of H.B. Robinson reactor
Click here to view 
Neutrons per se cond (n/s) emitted in the spent fuels need to be considered in the estimation of hazards associated with the radioactivity. There are two types of neutron sources present in the spent fuels namely (α, n) sources and spontaneous fission neutron sources. The first source is linked to the alpha activity of the nuclide and the energy of the emitted alpha. For seven isotopes of oxide fuels experimentally measured values are used and for other empirical relation is used in arriving at the neutron source term for (α, n) source. [Table 18] presents the comparison of (α, n) source term for significant nuclides. It can be observed that 98% (α, n) source is contributed by three nuclides, namely, Pu238, Am241, and Cm244. There is a nearly a factor of two present, and the ISOGEN code values are higher.
Spontaneous fission process occurs in higher actinides, and the neutrons are emitted. The spontaneous neutron source term is deduced from the radioactive decay. There are three important isotopes which produce significant spontaneous neutrons namely Cm244, Cm246, and Cf252 are shown in [Table 19].  Table 19: Comparison of spontaneous fission for few actinide nuclides of 72 gigawatt days/metric ton of uranium spent fuel of H.B. Robinson reactor
Click here to view 
It can be inferred from comparison of tabular values in [Table 19] that the magnitude of present values computed from ISOGEN code higher due to prediction higher actinide masses.
The crosssection library is of particular importance to the calculation since the crosssections will vary with burnup due to depletion and buildup of nuclides in the fuel during the burnup. For accurate calculations, one must employ burnup dependent crosssection libraries.
Conclusions   
The code ISOGEN is written in VB.NET version 2013 for Windows operating system. This code solves the firstorder differential rate equation for nuclide buildup and decay with time due to radioactive decay or due to neutron transmutation.
The ISOGEN program thus developed is tested for its accuracy by formulating sample problems where the analytical solution exists. The problems presented as examples demonstrate that the solution method adopted in code for radioactive decay problems gives the precise expected answers. Extensive comparison made with the reported values and the discussions presented there in validates the suitability of the code for estimation of concentration of nuclides in spent fuel as well as many of the derived useful parameters radioactivity, neutron production rate and alpha activity, which are essential in handling of reactor spent fuels.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
References   
1.  Pusa M, Leppanen J. Computing the matrix exponential in burnup calculations. Nucl Sci Eng 2010;164:1407. 
2.  Pusa M, Leppanen J. Solving linear system with sparse Gaussian elimination in the Chebyshev rational approximation method. Nucl Sci Eng 2013;175:2508. 
3.  Bell MJ. ORIGENThe ORNL Isotope Generation and Depletion Code. ORN4628. Oak Ridge National Laboratory, Oak Ridge, TN; 1973. 
4.  Croft AG, ORNL. A User's Manual for the ORIGEN2 Computer Code. ORNL/TM7175. Oak Ridge National Laboratory, Oak Ridge, TN; 1980. 
5.  
6.  Rearden BT. SCALE: A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluation, ORNL/NUREG/CSD2/R4. Rev. 4. Vol. 3. Oak Ridge National Laboratory, Oak Ridge, TN; 1995. 
7.  Leal LC, Hermann OW, Bowman SM, Parks CV. ARP: Automatic Rapid Process for the Generation of ProblemDependent SAS2H/ORIGENS CrossSection Libraries. ORNL/TM13584, Prepared by Oak Ridge National Laboratory for the U.S. Nuclear Regulatory Commission, Washington, DC; April, 1998. 
8.  Longmire P, Smith JD, Ross KW, Gauntt RO. Radionuclide Inventories: ORIGEN2. 2 Isotopic Depletion Calculation for High Burnup LowEnriched Uranium and WeaponsGrade MixedOxide PressurizedWater Reactor Fuel, SAND20086997; Sandia National Laboratories, New Mexico 87185, California, April,2010. 
9.  Croff AG, Haese RI, Gove NB. Updated Decay and Photon Libraries for the ORIGEN Code. ORNL/TM6055. Oak Ridge: Oak Ridge National Laboratory; 1979. 
10.  Charlton W, Stanbro WD, Perry RT. Comparison of HELIOS, ORIGEN2 and Monteburns calculated Am241 and Am243 concentrations with measured values of PWR, BWR and VVER spent fuel. J Nucl Technol 2000;37:61523. 
11.  
12.  Naegeli RE. Calculation of the Radionuclides in PWR Spent Fuel Samples for SFR Experiment Planning, Sandia Report, SAND20042757; June, 2004. 
[Figure 1], [Figure 2], [Figure 3]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6], [Table 7], [Table 8], [Table 9], [Table 10], [Table 11], [Table 12], [Table 13], [Table 14], [Table 15], [Table 16], [Table 17], [Table 18], [Table 19]
