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MONK10: A Monte Carlo Code for Criticality Analysis - 14574

The MONK{sup R} code, if we include its predecessor GEM, has now been in use for 50 years. It is a Monte Carlo code for nuclear criticality and reactor physics analyses which is used extensively in the UK nuclear industry and worldwide. In 2014 a major new version of the code, MONK10A, was released introducing many new features; these are described with example applications presented where appropriate. Experience with MONK9A models indicates that MONK10A has increased run-time performance for all cases and on average runs 2.4 times faster. New geometry options include the direct import of CAD generated models using the new IGES body, POLY body, TETMESH Hole and TETMESH Zone features. Example calculations for a selection of CAD import options are presented and compared with the intrinsic MONK geometry representation, with relative merits discussed. New Features are included to assist with the modeling of distributed parameters; such features include Unified Tally (UT), Action Tallies (AT) in UT and Shannon entropy. The latter is useful in assessing the convergence of distributed parameters, such as scalar neutron flux. As such it is an important tool in determining the appropriate point to stop settling and begin scoring stages in a Monte Carlo simulation. The utility of UT, AT-in-UT and Shannon entropy is demonstrated using calculations employing the new CAD import geometry options. Runtime Doppler broadening is included to allow accurate representation of temperature distributions within models. Example calculations which further demonstrate UT and AT-in-UT are presented for different bodies at different temperatures to evaluate the effects of temperature differences on k-effective and reaction rates. The MONK10A code was issued with a new set of continuous energy and group nuclear data libraries. These include JEFF3.1, JEFF3.1.1, JEFF 3.1.2, ENDF/B-VII.0 and CENDL 3.1 libraries. The inclusion of a range of libraries allows the user to evaluate the impact of different international nuclear data evaluations on their results and an example is provided to illustrate the differences that can arise from the use of different nuclear data evaluations. The code was also issued with a new version of the VisualWorkshop IDE to allow easy construction and editing of input decks, running of calculations and display of geometry and results. Examples are provided of the geometry and results display and showing how results can be superimposed upon the geometry. (authors)

42 ENGINEERING↗

TU-AB-BRC-10: Modeling of Radiotherapy Linac Source Terms Using ARCHER Monte Carlo Code: Performance Comparison of GPU and MIC Computing Accelerators

Purpose: (1) To perform phase space (PS) based source modeling for Tomotherapy and Varian TrueBeam 6 MV Linacs, (2) to examine the accuracy and performance of the ARCHER Monte Carlo code on a heterogeneous computing platform with Many Integrated Core coprocessors (MIC, aka Xeon Phi) and GPUs, and (3) to explore the software micro-optimization methods. Methods: The patient-specific source of Tomotherapy and Varian TrueBeam Linacs was modeled using the PS approach. For the helical Tomotherapy case, the PS data were calculated in our previous study (Su et al. 2014 41(7) Medical Physics). For the single-view Varian TrueBeam case, we analytically derived them from the raw patient-independent PS data in IAEA’s database, partial geometry information of the jaw and MLC as well as the fluence map. The phantom was generated from DICOM images. The Monte Carlo simulation was performed by ARCHER-MIC and GPU codes, which were benchmarked against a modified parallel DPM code. Software micro-optimization was systematically conducted, and was focused on SIMD vectorization of tight for-loops and data prefetch, with the ultimate goal of increasing 512-bit register utilization and reducing memory access latency. Results: Dose calculation was performed for two clinical cases, a Tomotherapy-based prostate cancer treatment and a TrueBeam-based left breast treatment. ARCHER was verified against the DPM code. The statistical uncertainty of the dose to the PTV was less than 1%. Using double-precision, the total wall time of the multithreaded CPU code on a X5650 CPU was 339 seconds for the Tomotherapy case and 131 seconds for the TrueBeam, while on 3 5110P MICs it was reduced to 79 and 59 seconds, respectively. The single-precision GPU code on a K40 GPU took 45 seconds for the Tomotherapy dose calculation. Conclusion: We have extended ARCHER, the MIC and GPU-based Monte Carlo dose engine to Tomotherapy and Truebeam dose calculations.

60 APPLIED LIFE SCIENCES↗

SU-E-T-521: Investigation of the Uncertainties Involved in Secondary Neutron/gamma Production in Geant4/MCNP6 Monte Carlo Codes for Proton Therapy Application

Purpose: A major concern in proton therapy is the production of secondary neutrons causing secondary cancers, especially in young adults and children. Most utilized Monte Carlo codes in proton therapy are Geant4 and MCNP. However, the default versions of Geant4 and MCNP6 do not have suitable cross sections or physical models to properly handle secondary particle production in proton energy ranges used for therapy. In this study, default versions of Geant4 and MCNP6 were modified to better handle production of secondaries by adding the TENDL-2012 cross-section library. Methods: In-water proton depth-dose was measured at the “The Svedberg Laboratory” in Uppsala (Sweden). The proton beam was mono-energetic with mean energy of 178.25±0.2 MeV. The measurement set-up was simulated by Geant4 version 10.00 (default and modified version) and MCNP6. Proton depth-dose, primary and secondary particle fluence and neutron equivalent dose were calculated. In case of Geant4, the secondary particle fluence was filtered by all the physics processes to identify the main process responsible for the difference between the default and modified version. Results: The proton depth-dose curves and primary proton fluence show a good agreement between both Geant4 versions and MCNP6. With respect to the modified version, default Geant4 underestimates the production of secondary neutrons while overestimates that of gammas. The “ProtonInElastic” process was identified as the main responsible process for the difference between the two versions. MCNP6 shows higher neutron production and lower gamma production than both Geant4 versions. Conclusion: Despite the good agreement on the proton depth dose curve and primary proton fluence, there is a significant discrepancy on secondary neutron production between MCNP6 and both versions of Geant4. Further studies are thus in order to find the possible cause of this discrepancy or more accurate cross-sections/models to handle the nuclear interactions of protons with energy ranges used for therapy. NSERC-CRSNG’ CREATE Medical Physics Research Training Network compute calcul CANADA; McGill University health center research institute the fast foundation; LM acknowledges partial support by the CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering; Research Council Grant number 432290.

60 APPLIED LIFE SCIENCES↗

Preparatory Verification of a New Monte Carlo Code cosRMC based on VERA Core Physics Benchmark

To promote nuclear power plant system design and simulation software self-reliance development, DOE of China approved a R and D key project to develop an integrated engine for pressurized water reactor core and system design and analysis, referred as COSINE hereafter. The scope of this code package includes reactor physics, thermal hydraulics, safety analysis, severe accidents, probability safety assessment and etc. Many universities, research institutes and nuclear related corporations in China are involved in the code development, among which the State Nuclear Power Software Development Center (SNPSDC) plays the leading role. With the requirement of accurate three-dimensional modeling of the advanced, special or new complex core in reactor neutronics and shielding analysis, Monte Carlo method is becoming a more powerful tool for reactor analysis. Thus, a new Monte Carlo transport code named cosRMC (abbreviation for COSINE Reactor Monte Carlo) has been developed jointly by SNPSDC and Department of Engineering Physics, Tsinghua University, the main developer of RMC code. The cosRMC now has many functions as criticality calculation, fixed-source calculation, burnup calculation, and etc. Some techniques for geometry treatment, new burnup algorithm, source convergence acceleration, massive tally and parallel calculation have been implemented in cosRMC to improve the efficiency. In order to ensure its reliability, several types of V and V work have been and are being carried out for cosRMC. In this paper, some preparatory verification results based on VERA Core Physics Benchmark are presented. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Comparison of the Performance of Various Correlated Fission Multiplicity Monte Carlo Codes

When measuring special nuclear material for a large array of national security needs, it is often important to accurately predict outcomes of the physical experiment using Monte Carlo radiation transport codes. Historically, radiation transport codes have uncorrelated fission emissions. In reality, both spontaneous and induced fissions release particles that are correlated in time, energy, and multiplicity. This work investigates the performance of various current Monte Carlo codes that take into account the correlated physics of fission neutrons. Only fission neutrons are of interest and the physics of gamma production in fission is ignored. Because of their large impact on correlated neutron results, underlying fission neutron multiplicity distributions utilized by the different codes are also compared. The codes currently being compared include MCNP{sup R}6, MCNP{sup R}6/FREYA, and MCNPX-PoliMi. By default, MCNP{sup R}6 uses a bounded integer treatment to sample the number of neutrons emitted from each fission event. The FMULT card, an optional input in MCNP that allows for user definition of spontaneous and induced fission parameters, can be utilized to call either built-in or user-specified multiplicities to replace the bounded integer treatment. Similarly, MCNPX-PoliMi utilizes one of a few different built-in multiplicity sets. MCNPX-PoliMi also models the multiplicity dependence of emitted neutron energy in spontaneous fission. It is possible to use an anisotropic model for emitted fission neutrons in MCNPXPoliMi, but this option was not used. For MCNP{sup R}6/FREYA, the FREYA fission event generator determines the number of particles emitted for each fission event and gives the results to MCNP{sup R}6 for transport. The fission event generator uses fission fragment mass and kinetic energy distributions, unbounded statistical evaporation models, and conservation of energy and momentum to generate the number, energy, and direction of neutrons released by each fission event. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

VERIFICATION OF THE SHIFT MONTE CARLO CODE

Shift is a new hybrid Monte Carlo/deterministic radiation transport code being developed at Oak Ridge National Laboratory. At its current stage of development, Shift includes a fully-functional parallel Monte Carlo capability for simulating eigenvalue and fixed-source multigroup transport problems. This paper focuses on recent efforts to verify Shift s Monte Carlo component using the two-dimensional and three-dimensional C5G7 NEA benchmark problems. Comparisons were made between the benchmark eigenvalues and those output by the Shift code. In addition, mesh-based scalar flux tally results generated by Shift were compared to those obtained using MCNP5 on an identical model and tally grid. The Shift-generated eigenvalues were within three standard deviations of the benchmark and MCNP5 values in all cases. The flux tallies generated by Shift were found to be in very good agreement with those from MCNP

42 ENGINEERING↗

Analysis of the track- and dose-averaged LET and LET spectra in proton therapy using the GEANT4 Monte Carlo code

Purpose: The motivation of this study was to find and eliminate the cause of errors in dose-averaged linear energy transfer (LET) calculations from therapeutic protons in small targets, such as biological cell layers, calculated using the GEANT 4 Monte Carlo code. Furthermore, the purpose was also to provide a recommendation to select an appropriate LET quantity from GEANT 4 simulations to correlate with biological effectiveness of therapeutic protons. Methods: The authors developed a particle tracking step based strategy to calculate the average LET quantities (track-averaged LET, LET{sub t} and dose-averaged LET, LET{sub d}) using GEANT 4 for different tracking step size limits. A step size limit refers to the maximally allowable tracking step length. The authors investigated how the tracking step size limit influenced the calculated LET{sub t} and LET{sub d} of protons with six different step limits ranging from 1 to 500 μm in a water phantom irradiated by a 79.7-MeV clinical proton beam. In addition, the authors analyzed the detailed stochastic energy deposition information including fluence spectra and dose spectra of the energy-deposition-per-step of protons. As a reference, the authors also calculated the averaged LET and analyzed the LET spectra combining the Monte Carlo method and the deterministic method. Relative biological effectiveness (RBE) calculations were performed to illustrate the impact of different LET calculation methods on the RBE-weighted dose. Results: Simulation results showed that the step limit effect was small for LET{sub t} but significant for LET{sub d}. This resulted from differences in the energy-deposition-per-step between the fluence spectra and dose spectra at different depths in the phantom. Using the Monte Carlo particle tracking method in GEANT 4 can result in incorrect LET{sub d} calculation results in the dose plateau region for small step limits. The erroneous LET{sub d} results can be attributed to the algorithm to determine fluctuations in energy deposition along the tracking step in GEANT 4. The incorrect LET{sub d} values lead to substantial differences in the calculated RBE. Conclusions: When the GEANT 4 particle tracking method is used to calculate the average LET values within targets with a small step limit, such as smaller than 500 μm, the authors recommend the use of LET{sub t} in the dose plateau region and LET{sub d} around the Bragg peak. For a large step limit, i.e., 500 μm, LET{sub d} is recommended along the whole Bragg curve. The transition point depends on beam parameters and can be found by determining the location where the gradient of the ratio of LET{sub d} and LET{sub t} becomes positive.

60 APPLIED LIFE SCIENCES↗

Computation of a Canadian SCWR unit cell with deterministic and Monte Carlo codes

The Canadian SCWR has the potential to achieve the goals that the generation IV nuclear reactors must meet. As part of the optimization process for this design concept, lattice cell calculations are routinely performed using deterministic codes. In this study, the first step (self-shielding treatment) of the computation scheme developed with the deterministic code DRAGON for the Canadian SCWR has been validated. Some options available in the module responsible for the resonance self-shielding calculation in DRAGON 3.06 and different microscopic cross section libraries based on the ENDF/B-VII.0 evaluated nuclear data file have been tested and compared to a reference calculation performed with the Monte Carlo code SERPENT under the same conditions. Compared to SERPENT, DRAGON underestimates the infinite multiplication factor in all cases. In general, the original Stammler model with the Livolant-Jeanpierre approximations are the most appropriate self-shielding options to use in this case of study. In addition, the 89 groups WIMS-AECL library for slight enriched uranium and the 172 groups WLUP library for a mixture of plutonium and thorium give the most consistent results with those of SERPENT. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

AEOLUS: A MARKOV CHAIN MONTE CARLO CODE FOR MAPPING ULTRACOOL ATMOSPHERES. AN APPLICATION ON JUPITER AND BROWN DWARF HST LIGHT CURVES

Deducing the cloud cover and its temporal evolution from the observed planetary spectra and phase curves can give us major insight into the atmospheric dynamics. In this paper, we present Aeolus, a Markov chain Monte Carlo code that maps the structure of brown dwarf and other ultracool atmospheres. We validated Aeolus on a set of unique Jupiter Hubble Space Telescope (HST) light curves. Aeolus accurately retrieves the properties of the major features of the Jovian atmosphere, such as the Great Red Spot and a major 5 μm hot spot. Aeolus is the first mapping code validated on actual observations of a giant planet over a full rotational period. For this study, we applied Aeolus to J- and H-band HST light curves of 2MASS J21392676+0220226 and 2MASS J0136565+093347. Aeolus retrieves three spots at the top of the atmosphere (per observational wavelength) of these two brown dwarfs, with a surface coverage of 21% ± 3% and 20.3% ± 1.5%, respectively. The Jupiter HST light curves will be publicly available via ADS/VIZIR.

79 ASTRONOMY AND ASTROPHYSICS↗

Calculation of neutron flux spectra of the VVER-1000 mock-up shielding benchmark with Monte Carlo code MCS utilizing mesh-based weight window

The measurements of neutron spectra compiled inside the NEA-1517/82 package from the Shielding Integral Benchmark Archive and Database (SINBAD) are chosen as benchmark cases to validate the variance reduction technique based on weight window in Monte Carlo Code MCS. A full 3D model for fixed source mode calculation with hexagonal lattice source definition is developed to simulate total of 6 points of measurements at the vicinity of the reactor and the reactor pressure vessel region. A code/code comparison against MCNP6 code is first conducted as verification element for the mesh-based weight window capability in MCS. Finally, the validation results are presented against measurements. The verification against MCNP6 code gives good agreement in addition of the insight to the importance of user understanding to determine proper reference point and reference lower weight bound for scaling which is not required in MCS code due to its capability of automatic scaling. The comparison of neutron spectra between MCS and measurements shows good agreement within 3 standard deviations for all of six detector positions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Preliminary TRIGA fuel burn-up evaluation by means of Monte Carlo code and computation based on total energy released during reactor operation

Aim of this work was to perform a rough preliminary evaluation of the burn-up of the fuel of TRIGA Mark II research reactor of the Applied Nuclear Energy Laboratory (LENA) of the Univ. of Pavia. In order to achieve this goal a computation of the neutron flux density in each fuel element was performed by means of Monte Carlo code MCNP (Version 4C). The results of the simulations were used to calculate the effective cross sections (fission and capture) inside fuel and, at the end, to evaluate the burn-up and the uranium consumption in each fuel element. The evaluation, showed a fair agreement with the computation for fuel burn-up based on the total energy released during reactor operation. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Benchmarking Monte Carlo codes for the modelling of low-energy neutron production target reactions

The increasing adoption of accelerator-based neutron sources (ABNS) for applications including neutron capture therapy (NCT) research has highlighted the need for accurate simulation tools. Precise modelling of the neutron production target is crucial to ensure that simulated predictions of neutron beam characteristics used for subsequent beam shaping assembly design are reliable. This work presents a comprehensive benchmarking of four widely-used Monte Carlo codes - Geant4, PHITS, FLUKA (CERN), and MCNP - for modelling low-energy neutron production target reactions. Using their recommended physics models and cross-section libraries, we evaluate each code’s performance in simulating four beam-target reactions: 7 Li(p,n) 7 Be, 9 Be(p,n) 9 B, 9 Be(d,n) 10 B, and C(d,n)N. Predictions of neutron yield, angular distributions, and energy spectra are compared against available thick target experimental data. Results show varying levels of agreement between the codes depending on the reaction type, energy range, and beam characteristics. Geant4, MCNP and PHITS are the overall best performing codes for the simulation of total neutron yield and yield in the forward direction across most reactions. Across energies where experimental benchmarks exist, inter-code discrepancies in total and forward-directed yield are typically 10 to 30%, with larger deviations at near-threshold incident ion energies. PHITS provides the best overall reproduction of experimental spectra, particularly for the 9 Be(p,n) 9 B reaction. Additionally, PHITS demonstrates superior computational performance for most reactions. These findings provide valuable guidance for ABNS design, highlighting the strengths and limitations of each code for the simulation of low-energy neutron production reactions.

43 PARTICLE ACCELERATORS↗

First application of the massively-parallel Monte Carlo code ERO2.0 for plasma-wall interaction and 3D local impurity transport at JET ILW

Here, estimating erosion for plasma-facing components (PFCs) is one of the key issues for ITER. Effective sputter yields can be obtained experimentally e.g. by estimating flux ratios with S/XB ratios. The interpretation of such experiments and extrapolation to ITER conditions is not straightforward, because the effective yields result from a complex interplay of plasma conditions, wall geometry and impurity transport. This makes modelling tools like the Monte Carlo code ERO necessary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Using the FLUKA Monte Carlo Code to Simulate the Interactions of Ionizing Radiation with Matter to Assist and Aid Our Understanding of Ground Based Accelerator Testing, Space Hardware Design, and Secondary Space Radiation Environments

Designing hardware to operate in the space radiation environment is a very difficult and costly activity. Ground based particle accelerators can be used to test for exposure to the radiation environment, one species at a time, however, the actual space environment cannot be duplicated because of the range of energies and isotropic nature of space radiation. The FLUKA Monte Carlo code is an integrated physics package based at CERN that has been under development for the last 40+ years and includes the most up-to-date fundamental physics theory and particle physics data. This work presents an overview of FLUKA and how it has been used in conjunction with ground based radiation testing for NASA and improve our understanding of secondary particle environments resulting from the interaction of space radiation with matter.

Reddell, Brandon↗

Interpretation of 3D void measurements with Tripoli4.6/JEFF3.1.1 Monte Carlo code

The present work details the first analysis of the 3D void phase conducted during the EPICURE/UM17x17/7% mixed UOX/MOX configuration. This configuration is composed of a homogeneous central 17x17 MOX-7% assembly, surrounded by portions of 17x17 1102 assemblies with guide-tubes. The void bubble is modelled by a small waterproof 5x5 fuel pin parallelepiped box of 11 cm height, placed in the centre of the MOX assembly. This bubble, initially placed at the core mid-plane, is then moved in different axial positions to study the evolution in the core of the axial perturbation. Then, to simulate the growing of this bubble in order to understand the effects of increased void fraction along the fuel pin, 3 and 5 bubbles have been stacked axially, from the core mid-plane. The C/E comparison obtained with the Monte Carlo code Tripoli4 for both radial and axial fission rate distributions, and in particular the reproduction of the very important flux gradients at the void/water interfaces, changing as the bubble is displaced along the z-axis are very satisfactory. It demonstrates both the capability of the code and its library to reproduce this kind of situation, as the very good quality of the experimental results, confirming the UM-17x17 as an excellent experimental benchmark for 3D code validation. This work has been performed within the frame of the V and V program for the future APOLL03 deterministic code of CEA starting in 2012, and its V and V benchmarking database. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Monte Carlo code G3sim for simulation of plastic scintillator detectors with wavelength shifter fiber readout

A detailed description of a compact Monte Carlo simulation code ''G3sim'' for studying the performance of a plastic scintillator detector with wavelength shifter (WLS) fiber readout is presented. G3sim was developed for optimizing the design of new scintillator detectors used in the GRAPES-3 extensive air shower experiment. Propagation of the blue photons produced by the passage of relativistic charged particles in the scintillator is treated by incorporating the absorption, total internal, and diffuse reflections. Capture of blue photons by the WLS fibers and subsequent re-emission of longer wavelength green photons is appropriately treated. The trapping and propagation of green photons inside the WLS fiber is treated using the laws of optics for meridional and skew rays. Propagation time of each photon is taken into account for the generation of the electrical signal at the photomultiplier. A comparison of the results from G3sim with the performance of a prototype scintillator detector showed an excellent agreement between the simulated and measured properties. The simulation results can be parametrized in terms of exponential functions providing a deeper insight into the functioning of these versatile detectors. G3sim can be used to aid the design and optimize the performance of scintillator detectors prior to actual fabrication that may result in a considerable saving of time, labor, and money spent.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Verification of the shift Monte Carlo code with the C5G7 reactor benchmark

Shift is a new hybrid Monte Carlo/deterministic radiation transport code being developed at Oak Ridge National Laboratory. At its current stage of development, Shift includes a parallel Monte Carlo capability for simulating eigenvalue and fixed-source multigroup transport problems. This paper focuses on recent efforts to verify Shift's Monte Carlo component using the two-dimensional and three-dimensional C5G7 NEA benchmark problems. Comparisons were made between the benchmark eigenvalues and those output by the Shift code. In addition, mesh-based scalar flux tally results generated by Shift were compared to those obtained using MCNP5 on an identical model and tally grid. The Shift-generated eigenvalues were within three standard deviations of the benchmark and MCNP5-1.60 values in all cases. The flux tallies generated by Shift were found to be in very good agreement with those from MCNP. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Development of a Monte Carlo code for the data analysis of the {sup 18}F(p,α){sup 15}O reaction at astrophysical energies

Novae are astrophysical events (violent explosion) occurring in close binary systems consisting of a white dwarf and a main-sequence star or a star in a more advanced stage of evolution. They are called 'narrow systems' because the two components interact with each other: there is a process of mass exchange with resulting in the transfer of matter from the companion star to the white dwarf, leading to the formation of this last of the so-called accretion disk, rich mainly of hydrogen. Over time, more and more material accumulates until the pressure and the temperature reached are sufficient to trigger nuclear fusion reactions, rapidly converting a large part of the hydrogen into heavier elements. The products of 'hot hydrogen burning' are then placed in the interstellar medium as a result of violent explosions. Studies on the element abundances observed in these events can provide important information about the stages of evolution stellar. During the outbursts of novae some radioactive isotopes are synthesized: in particular, the decay of short-lived nuclei such as {sup 13}N and {sup 18}F with subsequent emission of gamma radiation energy below 511 keV. The gamma rays from products electron-positron annihilation of positrons emitted in the decay of {sup 18}F are the most abundant and the first observable as soon as the atmosphere of the nova starts to become transparent to gamma radiation. Hence the importance of the study of nuclear reactions that lead both to the formation and to the destruction of {sup 18}F. Among these, the {sup 18}F(p,α){sup 15}O reaction is one of the main channels of destruction. This reaction was then studied at energies of astrophysical interest. The experiment done at Riken, Japan, has as its objective the study of the {sup 18}F(p,α){sup 15}O reaction, using a beam of {sup 18}F produced at CRIB, to derive important information about the phenomenon of novae. In this paper we present the experimental technique and the Monte Carlo code developed to be used in the data analysis process.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗