1. INTRODUCTION

1. NUCLEAR REACTIONS ON COPPER INDUCED BY COSMIC PROTONSN.G. Chechenin*, T.V. Chuvilskaya, A.A. Shirokova, A.G. KadmenskiiSkobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119991 Russia

2. In continuation and development of our previous works where nuclear reactions of moderate energy (10 to 400 MeV) protons with Si, Al and W have been investigated, the results of nuclear reactions with Cu atoms are reported in this paper. Cu is a most important component in composition of materials in contact pads and pathways of modern and perspective ultra large-scale integration circuitry, especially in 3D topology. Nuclear reactions result in nuclear recoils with mass and charge spectra in the range from target nuclei down to helium and hydrogen. The formation cross-sections, mass, charge and kinetic energy spectra of the fragments produced in nuclear reactions, calculated using the TALYS program code, are reported here. The results of calculations, using our technique, are compared with calculation and experimental data reported by other authors.

3. 1. INTRODUCTION It is impossible to imagine a modern spacecraft without electronic integrated schemes with connecting and contact paths and areas, interlayer conducting connections, and other metallic components. Such interior components normally have a high concentration of Al, Fe, Ni, Cu, Mo, Ta, W, Pt, Au, and other chemical elements. The kinematical effect of the energy transfer in a head-on collision from incident proton to the target nucleus is weaker for heavier target nucleus, but the resulting recoil energy can be sufficient to cause a dangerous upset of the electronics in the case of a high energy of incident proton.

4. For example, 1 GeV proton encountering a head-on collision with a gold nucleus loses only about 2% of its energy but transfers an energy of about 20 MeV to the target gold nucleus. Head-on collisions are quite rare—elastic collisions occur predominantly at nonzero impact parameters, with the result that the kinetic energies of recoil nuclei form a spectrum associated with a specific angular distribution of recoil nuclei [1-2].

5. In addition to processes of elastic collisions between protons and target nuclei, it is necessary to consider the contribution of nuclear reactions, which result in the formation of the mass spectrum of recoil nuclei arising as nuclear-reaction products, which extends from the atomic mass of heavy target nuclei down to helium and hydrogen. Each nuclear-reaction product has its own kinetic-energy spectrum and its own angular distribution. Thus, the picture that arises upon the propagation of high-energy cosmic ray particles is quite complicated, so that, in order to estimate quantitatively radiative effects in the onboard electronics, it is necessary to invoke present day nuclear data, as well as modern models and code packages implementing them, which make it possible to compensate for missing nuclear data. Unfortunately, the presence of heavy elements is disregarded in the majority of the calculations, and this of course impairs the reliability of the respective forecasts.

6. The results of our present calculations make it possible to fill this gap. Special features of silicon fragmentation induced by high-energy cosmic-ray protons were explored in previous studies of our group [3-6]. In [5], it was shown that the results of the calculations performed on the basis of the preequilibrium model according to the EMPIRE code are sensitive to the choice of values for the parameters of the optical-model potential. In the present article, the results obtained by calculating for the 28Si + p, 27Al + p and 183W + p nuclear reactions, the cross-sections for elastic and inelastic scattering and the charge, mass, and energy distributions of heavy reaction products according to the TАLYS [7] codes are supplemented with the results of the calculations for the same features of the 63Cu + p reaction, and a comparative analysis of all these results is performed.

7. 2. COMPUTATIONAL METHODS 2.1. General Characterization of the TALYS Code Package The idea to create computer codes that would provide a simultaneous description of many nuclear reaction channels to a precision not poorer than the precision of the most detailed description of only one or several reaction channels is not new. Such codes known to date include the GNASH [8], ALICE [9], STAPRE [10], and EMPIRE [11] codes. The TALYS code [7] is a modern software facility for implementing the preequilibrium model and includes the coupled-channel method featuring a number of software procedures.

8. We will now highlight the most important special features of the TALYS code package. First of all, this is a tool for precisely calculating nuclear-reaction mechanisms such as direct and preequilibrium mechanisms of compound-nucleus formation and fission. The code in question makes it possible to construct a reliable description of various reaction mechanisms over a broad region of projectile-particles energies and mass numbers (0.001–200 MeV and 12 < A < 238, respectively).

9. An important special feature of the TALYS code is that it combines parameters of the modern optical model, both a phenomenological and a microscopic one, for many nuclei, as well as an integrated approach in describing nuclear reactions on the basis of the optical model and the ECIS-06 coupled-channel method [12]. The code involves various phenomenological and microscopic models for calculating the level density, as well as automated references to nuclear-structure parameters from the IAEA Reference Input Parameter Library [13] that include masses; discrete levels; resonances; and level density, deformation, fission-barrier, and gamma spectrum parameters.

10. 3. CALCULATION OF PROPERTIES OF RECOIL NUCLEI The possibility of calculating the kinetic-energy spectrum of recoil nuclei is one of the advantages of the TALYS codes, which we use to calculate radiation-induced failures that are due to the effect of high-energy cosmic-ray particles. 3.1. TALYS Code In calculating the properties of recoil nuclei, one usually takes into account only the recoil energy and a general angle θ, as well as the array P(Z,N,Ex,Er, θr), which is part of the total population P(Z,N,Ex) for a kinetic energy in the direction specified by the angle in accordance with the beam-axis direction in the laboratory frame; that is,

11. where Ep is the projectile kinetic energy in the laboratory frame, Mp is the projectile mass, and MC is the mass of the compound nucleus. In the calculations, we use the classical equation: which involves the velocity of the emitted particle in the laboratory frame, the particle velocity in the center of mass (c.m.), and the c.m. velocity. Further, the initial compound nucleus (ZC,NC) is taken for a specific case. Its kinetic energy in the laboratory frame is given by

12. It is necessary to relate the last one to ΔE (the energy difference between the initial and final nucleus). Thus we obtain the expression which corresponds to the classical expression for the c.m. velocity

13. 4. RESULTS OF THE CALCULATIONS AND DISCUSSION 4.1. Basic Mechanisms of Nuclear Reactions in Heavy Elements under an Impact of Cosmic-Ray Proton. Elastic scattering of protons on a target nucleus with a transfer of a recoil energy to this nucleus is not the most probable mechanism of formation of recoil nuclei. Figure 1 shows the calculated contributions of the dominant nuclear mechanisms, σ(Ep), in the p+63Cu reaction at proton energies between 10 and 200 MeV. The flux of space protons is strongest in this energy region [14]. The TALYS code package was used in this calculation. Without going into details of the formalism used, we note only that elastic proton scattering on a 63Cu nucleus is severely

14. suppressed by competing inelastic nuclear processes (curve 1). The degree of suppression is such that we can disregard elastic scattering. The probability of direct nuclear reactions is somewhat higher (curve 4). They include the direct knockout and pickup of nucleons from the target nucleus without excitation of other intranuclear nucleons. Figure 1 shows that, in the region of proton energies below 100 MeV, a significant contribution comes

15. Fig. 1. Cross-sections for nuclear processes, σ(Ep), in the interaction of protons with a 63Cu nucleus. The curves represent the contributions of (1) inelastic nuclear processes, (2) preequilibrium processes, (3) processes leading to compound-nucleus formation, (4) direct nuclear reactions and (5) elastic nuclear processes.

16. 4.2. Mass Distribution of Nuclear-Reaction Products Via the mechanisms discussed above, ever lighter products originate sequentially from a nuclear reaction upon the emission of light particles. It is necessary to consider that the emission of a light particle cascade proceeds within a very short time interval, so that the time of the whole process is less than 10−16 s. Within this time, the nucleus involved travels a short distance (smaller than one interatomic spacing in a target material) without causing any shift the excitation energy of the nucleus decreases to a level below the threshold for the emission of any particle, so that its further de-excitation is due to gamma ray emission. Such a nucleus is referred to as a residual nucleus. It moves owing to the recoil energy transferred in the collision with an incident proton and upon particle emission of reaction products.

17. The cross-sections calculated for the production of residual nuclei, σprod(A), on the basis of modern nuclear-physics models used in the TALYS code package are given in Fig. 2 for isotopes of eight residual nuclei. It can be seen that copper isotopes in the reaction 63Cu (p, 2p2n) 60Ni are formed with the highest probability.

18. Fig. 2. Cross-section for the production of residual nuclei, σprod(A) (mass spectrum), in the interaction of protons with a 63Cu nucleus at the proton energy of Ep = 150 MeV

19. 4.3. Kinetic-Energy Spectrum of Recoil Nuclei The generation of structural defects and electron–hole pairs is determined by the particle charge Z and velocity (energy). Thus, the calculation of the kinetic energy spectrum of a nuclear-reaction product is one of the most important problems in the code package used. As was indicated above, the kinetic energy of the residual nucleus is determined by the contribution of the momentum of the incident proton and by the recoil energy resulting from sequential evaporation of particles from an excited nucleus.

20. Fig. 3. The energy spectra σr(Er) are shown of (a) 53Mn and (b) 55Fe residual nuclei produced in the p+63Cu nuclear reaction for the incident proton energy Ep = 100 (dashed curve), 150 (thin solid curve), and 240 MeV (thick solid curve). The figure shows that the region of kinetic energies of residual nuclei depends both on the incident proton energy and on the mass of the target nucleus. The cross-section is maximal for the 55Fe nucleus at Ep =150 MeV which is an order of magnitude larger than the analogous cross-section for 53Mn. However, the maximum kinetic energy is observed for the residual nucleus 53Mn at Ep = 240 MeV.

21. 4.4. Comparison of the Results Obtained Using the TALYS and MEND Codes With the aim of testing the results of calculations based on the TALYS code, we have calculated the cross-sections for inelastic scattering in p+63Cu reactions. The cross-section for inelastic proton scattering, σinel(Ep), as calculated using the TALYS code is shown in Fig. 4 by the solid curve, while the results of calculations using the MEND code [15] is displayed by the dashed curve. Experimental results of [16] are plotted for comparison. One can see that our results describe somewhat better the experimental data than the results of [15].

22. The cross-section for inelastic proton scattering, σinel(Ep): TALYS code – the solid curve, MEND code [15] – the dashed curve. Experimental results of [16] are plotted for comparison.

23. Our calculations fit nicely the experimental data of [16] in the region of the peak at 40 MeV and give a reasonable agreement in the proton energy ranges of 10 to 40 MeV and 100 to 200 MeV. The results of MEND calculations give somewhat better description than TALYS ones in the proton energy range of 80 to 110 MeV, though the overall agreement between TALYS and MEND results is good. The MEND code is based on the statistical approach, including the exciton model, evaporation model of Hauser-Feshbach type and intranuclear cascade model. This approach is similar to that applied in TALYS. The difference is that TALYS program uses the global optical potential [17] while MEND program uses Thomas potential [15], which is calculated using subroutine APMN [18].

24. 5. CONCLUSIONS Most important contributions of various mechanisms to the cross-sections for nuclear reactions induced by 10 to 150 MeV protons by a collision with heavy nucleus 63Cu have been analyzed in the present study with the aid of the TALYS computer codes. We have found that a dominant contribution comes from inelastic scattering and pre-equilibrium processes. The contribution of the compound-nucleus mechanism prevails at low energies of about 10 MeV; it reaches a maximum at 50 MeV but decreases fast at higher energies. The above results of our calculations indicate that copper isotopes originating

25. from inelastic proton scattering followed by the emission of one to ten neutrons are residual nuclei that have the highest yield. The isotopes of Ni are also formed with a rather high probability, the maximum of the mass distribution being shifted toward smaller atomic masses in relation to the mass distribution of copper isotopes. The kinetic energy distribution of residual nuclei is also of great importance for possible radiation effects in the onboard spacecraft electronics. Our calculations have revealed that the recoil energy of residual nuclei may be as high as 1 to 3MeV, depending on the projectile-proton energy.

26. THANK YOU FOR YOUR ATTENTION!

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