"Methods for the Calculation of Neutron Nuclear Data for Structural Materials of Fast and Fusion Reactors" S. Chiba*, P.T. Guenther, R.D. Lawson and A.B. Smith Argonne National Laboratory Argonne, Illinois, U.S.A. ABSTRACT The calculation of neutron inelastic-scattering cross sections of vibrational nuclei is discussed, and it is shown that they are large for the yrast levels for A =: 110. It is shown that, in addition to common size and isospin effects, shell and collective effects are requisite to explanations of neutron elastic-scatering ratios. Explicit optical 58 potentials are presented for the interaction of neutrons with Ni (spherical and vibrational models), and with zirconium (spherical). It is shown that these potentials provide excellent descriptions of the results of recent comprehensive experimental results. I. PREFACE This Project has generally addressed generic issues, frequently at higher energies well above those of primary applied interest. As the Project draws to a close, it is proper to give focus to specific concepts suitable for the explicit calculation of structural—material nuclear data for applied purposes. This contribution is directed toward that end. Section II of this report briefly addresses two issues that arose at the prior meeting. New measurements and their interpretations have substantively contributed to resolving these issues. Section III presents two potentials explicitly suitable for use in the structural- CO material regions. The first is for Ni, and is formulated in the context of both the spherical optical model (SOM), and the coupled—channels model (CCM). The second potential is for elemental zirconium and its isotopes, formulated in the context of the SOM. These potentials are suitable for quantitative applied calculations and demonstrate certain physical properties generic to the respective mass regions. Some suggestions for future studies are given. H. ISSUES FROM PRIOR MEETING A. Inelastic Excitation of Vibrational Levels in the A = 100-110 Region At the previous meeting it was suggested that the inelastic neutron scattering cross sections of the first few vibrational levels of even isotopes in this mass region might be large (e.g., « 1.5 b) at relatively low incident—neutron energies (e.g., at s 1 MeVj. Of particular applied interest are the even isotopes of palladium and ruthenium. This issue was examined using high—resolution experimental measurements and complementary CCM *Visiting scientist from Japan Atomic Energy Research Institute interpretations. The results of the work are extensively described in the Laboratory report, ANL/NDM-112, and outlined in a journal paper (Ann. Nucl. Energy 16 637 (1989)). The abstract of the Laboratory report follows: ABSTRACT: The cross sections for the elastic-scattering of 5.9, 7.1 and 8.0 MeV neutrons from elemental palladium were measured at forty scattering angles distributed between » 15° and 160°. The inelastic-scattering cross sections for the excitation of palladium levels at energies of 260 keV to 560 keV Were measured with high resolution at the same energies, and at a scattering angle of 80°. The experimental results were combined with lower-energy values previously obtained by this group to provide a comprehensive database extending from near the inelastic-scattering threshold to 8 MeV. That database was interpreted in terms of a coupled-channels model, including the inelastic excitation of one— and two—phonon vibrational levels of the even isotopes of palladium. It was concluded that the palladium inelastic-scattering cross sections, at the low energies of interest in assessment of fast—fission—reactor performance, are large (s 50% greater than given in widely used evaluated fission—product data files). They primarily involve compound-nucleus processes, with only a small direct—reaction component attributable to the excitation of the one—phonon, 2+, vibrational levels of the even isotopes of palladium. B. Ambiguities in Elastic—Scattering Ratios At the past meeting it was shown that observed ratios of the differential elastic- scattering of 8 MeV neutrons from Co and Ni were not consistent with the predictions of either a "global" or "regional" SOM. This type of ratio ambiguity has been extensively investigated over the mass range A a 51 -• 209, and a number of possible physical contributions to the phenomena have been examined. This work is described in the Laboratory report, ANL/NDM—114, and a shorter version has been submitted to Nucl. Phys. The abstract of the Laboratory report is as follows: ABSTRACT: Ratios of the cross sections for the elastic scattering of 8 MeV neutrons from adjacent nuclei are measured over the angular range « 20°—160° for the target pairs 5lV/Cr, 59Co/58Ni, Cu/Zn, 89Y/93Nb, 89Y/Zr, 93Nb/Zr, In/Cd and 209Bi/Pb. The observed ratios vary from unity by as much as a factor of « 2 at some angles for the lighter target pairs. Approximately half the measured ratios (Cu/Zn, In/Cd and 209Bi/Pb) are reasonably explained by a simple spherical optical model, including size and isospin contributions. In all cases (with the possible exception of the 51V—Cr pair), the geometry of the real optical—model potential is essentially the same for neighboring nuclei, and the real—potential strengths are consistent with the Lane Model. In contrast, it is found that the imaginary potential may be quite different for adjacent nuclei, and the nature of this difference is examined. It is shown that the spin—spin interaction has a negligible effect on the calculation of the elastic—scattering ratios, but that channel coupling, leading to a large reorientation of the target ground state, can be a consideration, particularly in the 59Co/S8Ni case. In the A K 50—60 region the calculated ratios are sensitive to spin—orbit effects, but the exact nature of this interaction must await more definitive polarization measurements. The measured and calculated results suggest that the concept of a conventional "global", or even "regional", optical potential provides no more than a qualitative representation of the physical reality for a number of cases. III. EXPLICIT POTENTIALS FOR STRUCTURAL MATERIALS A. Potential for s*Ni A—1. Introductory Comments Nickel is a prominent component of radiation—resistant ferrous alloys. Sixty-eight percent' of the element consists of Ni, and the remainder is largely the fin *\R similar isotope Ni.. Ni is a relatively simple nucleus consisting of closed neutron and proton shells (N = Z = 28), plus two lPo/o neutrons. The fast—neutron interaction with 58 Ni shows characteristics of a direct process, but the details are not clear as the nucleus is neither a simple vibrator or rotator. It has recently been shown that SOMs in the 9 A = 50-60 region are very specific to the particular target. "Global", or even "regional", models fail to describe the interaction with a particular nucleus in quantitative detail. A comprehensive study of the fast—neutron interaction with 58Ni, including measurements and calculations, has been undertaken and is now nearing completion. The following remarks summarize the status of this work, particularly defining detailed SOM and CCM interpretations suitable for quantitative structural-material calculations. A-2. The Database A—2—a. Total Cross Sections Broad—resolution neutron total cross sections were measured from 1 -»10 MeV, with attention to self—shielding effects. These results are consistent with Fig. 1. Neutron total cross sections of -^Ni. ^g present broad-resolution results are indicated by "0" symbols, and the high-resolution results of Ref. 3 by the curve. energy averages of high—resolution measurements , as illustrated in Fig. 1, and provide a database consistent with the concept of an energy—averaged model. A—2—b. Elastic—Scattering Cross Sections Differential elastic—scattering cross sections were measured from 1.5 -• 10 MeV with sufficient energy—angle detail to define the energy—averaged behavior, with the results shown in Fig. 2. The results are in qualitative agreefhent with the few comparable distributions found in the literature. A—2-c. Inelastic—Scattering Cross Sections Cross sections for the inelastic excitation of the first 2* (1.454 MeV) level were measured concurrently with the above elastic scattering, with the results shown in Fig. 3. At lower energies the compound—nucleus process appears to dominate, while the direct reaction predominates at higher energies. High resolution measurements, illustrated in Fig. 4, gave additional information, particularly for the higher—lying levels. A—2—d. Strength Functions S— and p—wave strength functions were taken from the compilation of Ref. 4. 10.0 1.S7 0 180 G(deg) Fig. 2. Measured differential elastic-scattering cross sections. Symbols indicate the measured values, and the curves the results of Legendre-polynomial fits to the data. Data are in the laboratory coordinate system. 58 Ni 10-0 I 100 § 2.2 0 180 •a G(deg) Fig. 3. Measured cross sections (symbols) for the excitation of the 1.454 MeV level of 58Ni. Curves indicate the results of Legendre-polynomial fits. Data are given in the laboratory system. 10 o 160 2<° TIME CH. Fig. 4. Time-of-flight spectrum obtained by scattering 8 MeV neutrons from 58fli over a flight path of 14.65 m. Observed excitation energies are numerically given. 58 A-3. Ni Model Derivation A—3—a. Phenomenological Spherical Optical Model fSOM) The objectives of the SOM interpretation were: (i) to provide a basis for the subsequent CCM interpretation, (iij to gain some physical understanding of the interaction, and (iii) to obtain a simple SOM for applied use. The SOM interpretation was based upon explicit chi-square fitting of the elastic-scattering data, with supporting consideration of total cross sections and strength functions. The elastic-scattering database was taken from the present work to 10 MeV, with five additional distributions extending to 24 MeV taken from the literature.