A study of neutron emission spectra and angular distribution of neutron from (p,n) reaction on some targets of heavy elements

For the design of ADS (Accelerator Driven System), it is important to study neutron spectra and details of nuclear reactions induced by neutrons. Furthermore, neutron energy and angular distribution data are important for a correct simulation of the propagation of particles inside a spallation target and the geometrical distribution of the outgoing neutron flux. Many experimental results are available for thin targets and massive targets additional studies of neutron spectra and neutron production were investigated to design target for ADS with incident proton energies up to 3 GeV. In our study, the angular distribution and the neutron energy spectra are reported for the (p,n) reaction on target nuclei such as Pb, U, W with energy from 50 MeV to 350 MeV calculated with database of JENDL-HE 2007. We obtain a set of data about the angular distribution and energy spectra of produced neutrons on some heavy targets with energy ranges as stated above. From the results of neutron spectra, the paper also gives many comments to recommend a choice of materials for target and energies for accelerating proton beam . From the angle distribution of neutrons generated in (p, n) reactions on the different targets with the different energies of proton, the solutions to arrange the reflection bars in reactor proposed. A comparison is also made to improve the reliability for calculation of the paper.


INTRODUCTION
The spallation reaction is caused by bombarding a target with particles having energies above a few hundred MeV. This reaction produces a great number of neutrons, and is applicable to produce an intense spallation neutron source or transmuting long-lived radioactive wastes [1,2].
The design of target is a key issue to be investigated when designing an ADS [3], and its performance is characterized by the number of neutrons emitted by (p, n) reaction. This paper describes the calculation of spatial distribution and energy spectra of produced neutron performed on the proton beam with the energy of 50 MeV to 350 MeV.
Based on the JENDL-HE library [4] we obtain a set data about energyangle spectra on Pb, U, W targets with ranges as stated above.

METHOD
We adopt the formula for calculating energyangle double differential cross section of neutron from (p,n) reaction: Where: E p is the incident energy (eV), E n is the energy of the product emitted (eV),  is the interaction cross section (barn), y is the product yield or multiplicity, f is the normalized distribution with units (eV unit cosine -1 ), energy-angle double differential cross section (barn/eV-sr).

Angular distribution of neutrons produced
For the proton induced reaction, we are interested in the neutron production. We use the data of JENDL-HE library to calculate for incident proton energies of 50, 100, 150, 200, 250, 350 MeV. Figures 1, 2, 3 show angular distribution of neutron produced from the (p,n) reaction on 238 U, 208 Pb, 186 W calculated at the energies from 50 MeV to 350 MeV: All the curves have the same behaviors but they have different values.
The angular distribution of emitted neutrons shows dominant forward angular emission with respect to the incident proton direction.
Production cross section is the highest for reaction induced on lead target and the lowest for reaction induced.
When the incident proton energy increases, production cross section does, too.

Comparison with the other published data
Up to now, we haven't found any papers studying about angular distribution of neutron in energy range of 50 MeV to 350 MeV. We use our model to calculate the angular distribution of neutron at 800 MeV and we make a comparison with the obtained result of P.K. Sarkar and Maitreyee Nandy [5] as following: We can see that there is a significant difference between the two models QMD (Quantum Molecular Dynamics) and SDM (Statistical Decay Model). Fig. 4A shows a dominant forward angle emission for the QMD process while the neutrons from the SDM calculations have isotropic angular distribution with respect to the incident proton direction. Fig.  4B shows that the curve in our result is similar to that of the QMD process. We do not mention several important effects, the result shows a significant difference in value.
We are interested in the form of the curve. It means that our calculation model is good.

CONCLUSION
We are interested in the cross section for the energic spectra and spatial distribution of neutron obtained for the incident proton energy of 50 to 350 MeV. We calculate the distribution of neutron escaped a heavy target at different angles from zero degree to 180 0 degree, so we know the dominant forward angular emission with incident proton direction and spatial distribution of produced neutrons to arrange fuel bars in ADS. Heavy nuclei as U, Pb, W were chosen as spallation target and obtained rather hard neutron energic spectrum (see Figures 4,5,6). This is the need to optimize the fission probability of Transuranic elements (TRU). Indeed, in the fast neutron flux provided by the ADS, all TRU can undergo fission, a process which eliminates them, while in a traditional reactor thermal neutron flux many TRU do not fission and thus accumulate as waste.
Acknowledgments: Author would like to thank to Nuclear Research Institute of Dalat for their support to finish this work.