: : ضعيفه . . . : . •. .. ( م * . | مهمه . - .. ,ا اد . ه ;} ست - . . " " ۲ .۲ | F سمیه . و * . . m . . Li. ji i * C I OF 1 ORNL P 2072 w $ : . T . TFEFE EFE 11:25 11.4 1.5 MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS - 1963 ., -p-2017 2 MASTEA CFSTI PRICES H.C. S/100 MN_.50 FILLING IN GAPS WITH CROSS SECTIONS CALCULATED FROM THEORY* MAY 5 1966 F. G. Perey Oak Ridge National Laboratory Oak Ridge, Tennessee ; RILASED FOR ANSCURIOSISIT IN NUCLEAR SCIENCE ABSTRAON LEGAL NOTICE This report was prepared as an account of Government sponsored work. Neither the United Statos, por the Commission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, expressed or implied, with respect to the accu- racy, completeness, or usefulness of the Information contained in this report, or that the use of any information, apparatus, molbod, or process disclosed in this report may not infringe printely owned righto; or B. Asrumos any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or proces disclosed in this report. As used in the above, "person acting on beball of the Commission" includes way em- ployee or contractor of the Commission, or employee of such contractor, to the oxtent that such employee or contractor of the Commission, or employee of such contractor prepares, disseminates, or provides acces lo, eny Information pursuant to his employment or contract with the Commission, or bio employment with such contractor. *Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. FILLING IN GAPS WITH CROSS SECTIONS CALCULATED FROM THEORY F. G. Perey Oak Ridge National laboratory Oak Ridge, Tennessee i. IATRODUCTION The title of my talk, given co me by the organizing committee, suggest to me that I should attempt to give a sort of progress report on the status of cal- culational methods of nuclear reaction cross sections for the benefit of people who are in need of cross sections for certain applications and no experimental data are available. I suppose that what is expected of me is a certain list of cross sections we believe we know how to calculate with the expected accuracy in the theoretical values. 'I am afraid that our knowledge of nuclear physics in general, and nuclear reactions in particular, is sucn that it is an impos- sible task in a 30-minute talk. We have certain models, not called theories any more, which have some parameters, the values of which ideally are uniquely determined when we analyze some data. Our models are gross approximations of what is supposed to take piace and the degree of enthusiasm, or lack of it, found in any one of us, for a given model is very much a function of how well he believes the model should work in a particular application. The judgment of the rits are very subjective and in any given situation may be called sood or baà, depending upon the degree of expectation. Every model has well-known failures and this is to be expected. Nuclei differ in structure; this is re- ziected in the data and sometimes in the theoretical calculations. The pre- äictive nature of a model cannot obviously be judged from the value of the x2 ootained on some nonexistent data. The quality on the fit to some data at dll- Terent energies or on different nuclei may be thought of as a measure of the quality of the predictions if one expects data in the gap to follow the trends of the godel. This kind of expectation can only be arrived at if we have simi- lar data that does so. The degree of confidence we have in a model and its : parameters is directly related to the number of times we have used it success- fully in the region where the gap exists. For instance, whenever a gap exists because of technological problems, it is obvious that we have very little, if any, data of its kind and the degree of confidence we have in the model and its parameters in this gap is low. Another example where little data of its kind can be said to exist is for light nuclei, which, for nuclear structure reasons, have often to be considered unique specimens. I will restrict mysell to a very limited aspect of the problem: elastic and inelastic scattering of neutrons from nuclei for energies below 16 Mev. In: these two areas, I believe that some theoretical calculations can be very success- Iully used to fill gaps in our present set of neutron cross-section data. I am aware of the limitations of the models to calculate cross sections at the present time. In the future, we will understand better the reaction mechanisms and will reprove our ability in ſitting data and thereby have a greater degree of con?i- aence in preäicting cross sections. However, I share the belief of many that ühe use or calculations to supplement existing data or to obtain cross sections at energies required for a particular case may not only be adequate but even better than some existing data. This is so because either the accuracy of same - - very old data may be poor or the very nature of the data is unsuitable in some applications. It is the aim of my talk to point out where I believe this may be so. I am aware that when a cross section is absolutely needed and it has not been measured, a theoretical estimate is better than nothing. But I would like to raise my sights to consider the possibility of calculating cross sections which are likely to be as good as most existing data. I will probably not tell anything which is new to some of you who have been associated with cross section calculations. It is not my purpose to discuss here the line points of the models or the subtleties of some parameter set. I would rather address myself to those om you who are in need of cross sections and try to convince you, if you are not aiready convinceà, that you may find it very expedient and adequate to use cal- culateà cross sections. II. ELASTIC SCATTERING . . The basic model used in such calculations is called the optical model. I assume that all of you have a certain degree of familiarity with it. But for cür purposes today it is only necessary to say that in order to perform an op- tical 1:odel calculation it is sufficient to know half a dozen parameters speci- . fying the potential. Once the potential is known, one can calculate an elastic ariguiar distribution (called the shape elastic cross section), the total cross section and the absorption cross section. In addition, one obtains certain cuantities frequently called transmission coefficients which are some of the basic ingredients needed in order to calculi e inelastic cross sections in some other models I will come to later. In the energy range of interest, up to 16 MeV, one has to consider two enery regions in order to discuss elastic scattering and the optical model. A practical way of finding the dividing energy is to look at the neutron total cross section curve as a function of energy schematically shown in Fig. I for a medium-weight nucleus. I realize that they do not all look like this, but we believe they would, more or less, if data of adequate energy resolution were avaiiable. There are two regions quite distinct: the lower part where there are resonances and the upper part where there are none. In practical cases there is ño sharp dividing line: one sees the oscillations die out gradually. I do not want to discuss the source of the resonances or whether a greater energy resclu- esclu. tion at higher energies would show some small resonances or not. These two points are receiving a great deal of attention at the moment and are not very relevant to our calculations as we perform them today. It is worth pointing out taat for light nuclei the energy scale is contracted so that we may still be in tae resonance region at 8 MeV and that it expands for heavier nuclei so that at I eV we may be out of it. Above the resonance region it is usually granted trat the optical model can be used to calculate elastic scattering, and comparison on the existing data with the shape elastic cross section gives very good agree- ment. The Neutron Cross Section Advisory Group (NCSAG) suggests that the optical model be used in the region where there are no resonances. Out of 37 requests zor dilferential elastic cross sections in the MeV region, the NCSAG feels that in 32 cases an optical model calculation could do for at least part of the energy range. The NCSAG gives the dividing energy as 6 MeV for elements below Si and 5 MeV for tãose above. There are at least five requests (three having a priority II and two havárie a priority III) that could be immediately completely satisfied. In fact, a report critically evaluating the available data and comparing them to a calculation has been published by Wilmore? and the three priority II cross sec- tions, Ca, Fe, and Po, are tabulated between 1 and 14 MeV in steps of 1 MeV and at 5-aeg intervals. In the resonance region, which is the lower energy part of our range, the shape elastic cross section alone should not be compared to the date directly. ORNL-DWG 66-2418. - -. . .... RESONANCES NO RESONANCES wymalon -- D . SHAPE ELASTIC ONLY : SHAPE ELASTIC i COMPOUND ELASTIC · · - 10 15 Én (MeV) Fig. 1. Typical Neutron Total Cross Section (Medium Weight Nuclei), Some of the incident neutrons have been absorbed to form a compound system and, due to the small number of decay channels open to the compound system, there is a non-negligibie probability that a neutron will be emitted leaving the residual rucleus in its ground state. This wili be measured as elastic scattering. We call it compound elastic scattering. The distributions of the neutrons emitted by the compound system can be calculated using what is called the Hauser-Feshbach theory and we use the penetrabilities from the optical model to make such calcu- lations. We also need to know the spins and parities of all the open channels for ine decay of the compound system. In some of the cases where this informa- tion is available, the calculations can be extended to the lower energy region. Figure 2 shows the comparison of a calculation with the available data2 for 2r. The optical parameters were not adjusted for a fit to the data and the full line includes the contributions due to compound elastic scattering up to 4.1 MeV. Above this energy only the shape elastic scattering was used. With this kind of üzreement one should not hesitate to use the calculation at intermediate energies. I müsü emphasize that the curves are not fits; they are predictions of the theory. I will come later to the very important subject of parameters at the risk car being too technical. Figure 3 gives the comparison of the data for total cross sections arā nonelastic cross sections. The full curves are the pre- dictions of the theory. The line labelled "o non" is the curve for the absorp- tion cross section. Below 4 MeV the conipound elastic cross section has to be suötracted from the absorption cross section to give the nonelastic cross sec- tion. The open triangles are the predictions for the nonelastic cross section below 4 MeV. I must apologize if the data for the total cross section does not lock like the one in Fig. 1, but I believe we do not have data of high enough resolution co exhibit the same behavior, I wi... give you another example of comparison of predictions with data, 2 This time i'or Ca, as given in Fig. 4. I have shown the contributions of the compound elastic scattering as a dasheä curve. Only the upper full curve is to be compared to the data. If the agreement below 3 MeV is not so good, it could ce attributeà to the fluctuations at these lower energies. Here again, I think I can convince most people that the predictions are just as good as the data for most applications. I now come to a very important question: are these two cases typical of wai To expect in the kind oſ agreement from 1 to 15 MeV for all nuclei? The answer is a qualified no, and I will now consider the various areas where a diiterent kind of agreement between data and such predictions is to be expected. a) Resorance Free Region. IH you compare the data from about 4 MeV up, then this is typical of the kind of agreement one expects for most nuclei. We have to exclude the light nuclei because we are still in the resonance region and must be cautious in the case of strongly deformed nuclei. The available data on deformed nuclei in general shows good agreement with the standard cal- culations using the same parameters es elsewhere. My personal conviction, based on various pieces of evidence which I do not want to go into here, is that the agreement is more likely to be fortuitous and in a large part due to the fact that inelastic scattering to the low-lying levels is not resolved in the experimental data. However, until we have better data, since the agreement is fairly good when you are not resolving the low-lying levels, I would still recommend the use of an optical model calculation using standard parameters ašove 4 MeV if in a particular application, such as shielding, it is not im- portant to distinguish between elastic scattering and inelastic scattering to very low-lying states o b) Resonance Region. This is below 4 MeV for most nuclei. As I have al- ready explained, we must then aiso calculate the compound elastic scattering. Vezy ołten we cannot do it, mostly because we do not know the epins and parities . . . . . ....... ORNL-LR-DWG 65053 10,000 5000 ZIRCONIUM 2.5 Mev ZIRCONIUM 14.6 Mev 2000 1000 olo) (mb/steradian) 5000 2000 1.5 Mev -7 Mev 1000 500 o(@) (mb / steradian) 2000 4 Mev 4.1 Mev 1000 500 200 o 25 50 125 150 175 0 25 50 125 150 175 75 100 OCM. (deg) 75 100 OC.M. (deg) Fig. 2. Zirconium Elastic Scattering Differential Cross Sections. -. ..commed...ou - ** qm .......-- ORNL-LR-DWG 65052 4047 o barns N ucts TOTAL Oo 2 4 6 8 ENERGY (Mev) 10 12 14 . Fig. 3. Zirconium Total and Nunelastic Cross Secticns. . . . . - . - - : - - . . ........ .... - II ORNL-OWO 63-2323 CE_1.0 MOV E 4.1 MOV DOEL/IN (mb/steradian) - En=2.0 MOV + .O MAN do ELINQ (mb/stercdian) No no no no 6 MOV IS.s FOE,=3.50 MOV Ene 3.65 MeV : 100 0 25 50 125 450 175 0 25 50 126 150 175 75 100 Oc.m. (deg) 75 100 c.m. (dog) ... Fig. 4. Calcium Elastic Scattering differential Cross-Sections. of the exit channels of the compound system, so that we are lacking sane nuclear strucüüre iaformation to perform the calculation. Kore fundamental is the problem for deformed nuclei. I believe that as we go down in eergy it becomes more and more crucial to take into account the e360° ci tie cicar deformation in elastic scattering and in the penetrabil- vies. I Tre what if the deformation is ignored, one has to juggle more and e une pe ters of the možel to try to account for it, and this becomes more and wore acicult as we go down in energy. If and when one succeeds in this Orain, one aas a way of interpolating and smoothing out the data, which in ise is a very valuable and useiul procedure. This method has only one draw- baci, nich I il consin later. The best way to treat the deformed nuclei is to unike dico account expiicitly the deformation in the calculation and this is 9 3 coure ir. some calculacioiis. The problem cf deformcd nuclei becomes then very Service to the one for other nuclei. 1. some cases the nuclei are not very deformed and we know the spins and cüw Oz the exit crannel, for example, in the lighter nuclei, and yet the opti- Ciri casi caicuiation does not give good agreement with most of the experimental dü.ve.. Wat can we ao at the moment to treat the problem of resonances in cross sections. The most widely reid oçinion is that calculations are of no help, and experimental data must be used. Here, I somewhat disagree and I believe I am row the only one to do so. It is very much a question of what kind of applica- tion the data are to be useä in. I think that it is better to discuss the prob- les with a specific example, for instance, a priority I request for the differen- üsal elastic cross section for neutrons on Si from 2 to 16 Mev. Let us look at üze toval cross section at the low-energy end as given in BNL-325 and shown in nis. 5. IC is evident that the cross section fluctuates strongly in this energy rarice. It is also certain that the amount of fluctuation one would obtain as a accion on energy in any given measurement in this energy range is very much ä municion o ühe energy resolution used unless it is of the order of 1 MeV or more. Il the particular application requires the cross section to be known at Huervals or 1 MeV or less, then at tæe moment a calculation is useless and I benicve thai most measurements which would not average the cross section by execmiy the required energy resolution would also be useless. The only proper way to tarile the problem is to measure the cross section with very high energy resolution, say of the order oſ 20 kev, over all the energy range and let the üser co the exact averaging required in the particular problem. Now if the problem does not require such detailed knowledge of the cross section, or is unable to use such knowledge if it is available, and an energy average of the order om 1 MeV or slightly more is sufficient, then the calculation we perform at these energies would very likely give this average value. Very many investi- gations concerning fluctuations in cross section have been performed in the last Two or three years, and, to my knowledge in almost all of them when the average was compared to results o Hauser-Feshbach calculations they have agreed very well. There is a äefinite possibility that the fluctuations here are different Irom those that were investigated but we have very little evidence that this migat be so.. At the position where the arrows are shown elastic differential Cross sections have been measured with the energy spread indicated. It is not surprising that the data do not agree very well with the calculations since a large enough energy average was not performed in the experiments. The request on Si asks for data of 1 MeV energy resolution or less; this data would seem to satiszy tre request between 3.4 and 4.9 MeV, but the result would probably be dey üillezeriü if the measurements were performed at slightly different ener- gies. So swearize, my point of view on the application of the optical model in the resonance reco02: unless cata. Oh nigh enough energy resolution at sufficiently ciose cura intervals are available, the only cross sections worth using in many applications are optical model cross sections. In view of the fluctuating nature - - UU NU I OF-BARNS 1.0 Lt 2.6 DIUUUULI IIINUDDI0000UIII 2.8 3.0 3.2 3.6 4,8 5.0 5.2 5.4 3.8 4.0 4.2 4.4 4.6 EN -MEV .....-- --.. ......... Fig. 5. Silicon Total Cross Section. .. . ........... ....: ... . ... -•• -••-. . .. . . ............-- ..... ..na . . . TF - - - of the cross section, it is a little bit difficult to talk of how accurate those calculations are and it is only through adequate data that we will eventually know. Below 1.5 MeV A. B. Smith and collaborators at Argonne have obtained much data of the kind I mentioned, high resolution at closely spaced intervals. It 18 usually not very difficult to fit the average behavior of the data with an optical model. Therefore, I believe that in the gap between 1.5 MeV and the end of the resonance region the optical model can be used to generate cross sections which are likely to be as good, if not better, than much of the data available in this energy range to date. I have carefully avoided talking about optical model paremeters until now. "Parameterology" 18 not a science and in order to do justice to this field of human endeavor, very close to numerology, I would have required much more time than I had available. The calculations I have just shown you were done with a nonlocal optical potential model.* This set of parameters has no great special virtue except that I happen to have used it a lot and I am satisfied with the over- all result I get for elastic scattering. There are some other sets of perfectly adequate parameters and some which are not so adequate. Since I am not going to recommend that the users do their own calculations, I shall not discuss them here. I will only raise a general problem which has to do with adjusting a set or parameters to fit data for a given nucleus and using a different one for nearby nuclei. In principle, this procedure should be the best since it could enable one to take into account various particular differences in nuclear struc- ture in an ad hoc fashion. In practice, one is faced with having to obtain a set of parameters from a very limited amount of data and although ultimately one might fit it better than by using a potential fitting a large class of data, there is no guarantee that the systematic errors in the data are not being extrapolated and that the data represent a suitable average over energy required for the optical model. However, if the set of data for a given nucleus is fairly complete, then this procedure would have a very definite advantage and from it we will learn how differences in nuclear structure affect the parameters of the potential. For instance, one has to modify rather strongly the parameters for deformed nuclei, if the deformations are not taken into account explicitly, whereas the parameters applying to spherice.I nuclei can be used if the deform- ations are included in the calculation. .--.. ---- --...- .. . -. III. INELASTIC SCATTERING Just as in elastic scattering, we recognize two main modes of excitation of levels by inelastic neutron scattering: excitation via a direct interaction mech- anism or via formation of a compound nucleus. We have various models for calcu- lating. inelastic scattering in the two cases. Inelastic scattering data are far more difficult to obtain experimentally than elastic data. As a result we have performed far fewer analyses of inelastic scattering than elastic scattering. One further difficulty with inelastic scattering analyses has to do with the nuclear structure aspect of the problem. In all the models for calculating in- elastic scattering we can divide the calculation in two parts: one I will call dynamical, usually derived from the optical model in various ways, and the other having to do with the structure of the target nucleus. This structure informa- tion takes different forms for various models. In Hauser-Feshbach calculations it is the spin and parity of the levels which must be known, not only for those you are interested in calculating inelastic scattering for, but for all the levels below the incident neutron energy. In another statistical theory it is the level density in the target nucleus. For direct interaction the information must be even more detailed, with knowledge of the nuclear wave function required. In same direct interaction calculations phenomenological models have been used as in the case of the excitation of collective levels. Since direct interactions are usually fairly selective in their reaction mechanism, we have a fairly good understanding of them, and particularly so because we can study them with charged particle reactions anů transfer this knowledge to the neutron-induced reactions, For compound nuclear reactions, because of the Coulomb barrier charged-article - ... --·. --...-.. .. . . - . - - . . . ........... . . . .. a ... ... .. studies are not as useful except in checking some general aspects of the . theory. Tras long introäuction to inelastic scattering calculation 18 in- var ei toetasize the fact that nowhere in the calculation of inelastic scüvüviting are we in as gooi a position to make calculations, and in parti- Cümnt, preactions of cross sections. However, we do have models and theories agricübie in any situations. Lack of proper complete data, 1.e. adequate 10x tre particular ceory in the energy range of interest, and lack of nuclear Sürücüne in ornauion have prevented us from vesting the..e theories adequately enouga to be able to make predictions. These theories are very useful to analyze cata und to make a certain amount of interpolation between measurements, but may ze unreliable to cover any sizable energy gap in the data. Let me now consider some of these theories and the problems we have in w them. The rauser-eshoach theory is the oldest one anå has been used evensively. I aiready mentioned that we need to have the spins and parities oihin te bevels to the garding energy. For many nuclei this is avail- aj se ozonych the lirst and second excited states and very seldom for as many ai Ve x leveis. As a result, most Hauser-Feshbach calculations to date Toivo not been used to test or rerine the model. Rather, they have been used to o ar. rucicar structure information, such as maki:18 spin and parity assign- merts. It is obvious that such assignments are considered by many people as un- selscore. In fact some compilations on nuclear levels do not report such assign- rienus vien they have been made. One other difficulty in doing Hauser-Feshbach calculations has to do with the mansmission coefficients from the optical model. We claim that we Lave a fair knowledge of the potential parameters as far as e scatering goes, but several sets of parameters may be equivalent for Cistic scattering and not be equivalent in Hauser-Feshbach calculations. Re- Sunris hanya mer by more than 30% due to differences in transmission coefficients. A Very Good example of this has to do with the imaginary part of the optical 3:06e potential at low ene.gy. Elastic scattering angular distributions at low exere in most cases are insensitive to the exact value of the imaginary poten- The because of condensating efIects in the shape elastic and campound elastic scavvenge. But this compensating effect is not present in inelastic scatter- no. cere is one ither dilliculty which is even more fundamental in the use of meuse-zeshbach theory. It is the fact that the use of this model is confined to ä esion oIº energy where we have fluctuations in the cross sections more often trar. 00. In order to resolve the various inelastic levels, it is not possible to use an experimental technique to average the data over energy. This average üsü be done on the data before & meaningful comparison with the theory can be made. It is possibie that one of the sources of difficulty found in analyzing some presently available data may be due to those resonances. To sum up my feelings or. Hauser-Feshbach calculations, I will say that it promises to be very useful in an important range of neutron energies when we have tested it weil and learned how to use it. In order to do so, we will need more data and more auciear structure information. as the inciäent neutron energy goes up, the number of levels increases and it is unreasonable to hope that many spin and parity assignments will be made in the rear suture i or many of the levels. This is a gap in energy where no theory can be usea in practice because of the lack of information on spins and parities. As the neutron energy goes up further, we enter a region where calculations can be periormed again because now the nuclear structure information required in the statistical theory used takes the foam of a nuclear level density formula, A. typical inelastic neutron spectrum looks like as shown in Fig. 6. The shape of The evaporation spectrum is a function of the optical model absorption cross seccion aná the nuclear level density, which is related to the nuclear temp- er mvuxe concert. Many nuclear temperatures have been measured and we have a y gooi dcä on the treras Oücnout the periodic table. But many questions Sun email to be bottled concerning nuclear level densities. If in a given appli- cacio. The exact wüail of the neutron evaporation spectrum is not too critical .. . .. , . . ....- . . . .. .. -.- - . is :) ORNL-DWG 66-2417 ELASTIC NUMBER OF COUNTS EVAPORATION SPECTRUM DIRECT INTERACTION En (MeV) . 7:5. 6. Inelastic Scuffering Spectrum. its shape can be airly well estimated and the value of the inelastic cross ceciico. Corary cases ...alized to the optical model eosorption cross section at that w.ver..cident neutron. energy, to provide a fairly reliable inelastic C oi special. The tocory can therefore lill an important gap in inelastic m.cat:.. lata in this region. Om energy by providing the evaporation spectrum. Com caraiso provide the most important neutron ine.lastic groups at the 2.0 - gye.. oi the neutron spectrum. There we have the phenomenological coniective .vaeis which are very successful in predicting the magnitudes and the arcular distributions of the most important neutron groups. Many charged Taici experiments have been performed and we have the necessary nuclear struc- de Oma02. in many cases. The few experimental inelastic neutron angular discutor:s in the range om 8 to 11; MeV agree very well with the predictions. IX. COUSCOUS on wouli .e to summarize now anà offer some suggestions to those of you VOUS C.sci. com elas vic ana inelastic cross sections. I believe that for manications the elasöic scattering can usefully be obtained from optical boiel cariculacions. The accuracy of the theoretical cross sections will be same- wiat uction on the nuclei under consideration and the energy range of in- tezest ut s oiten likely co be an adequate substitute for data which are not Evai ne. Zoon my own experience, I know that the answer for you does not lie 7 ceramide an appropriate set of optical model parameters for the potential. Put you wouid really need is a deck of cards which accepts only two numbers as Hou, he arget nucleus and the neutron energy of interest, and gives an angu- distribution. I have in fact, a few years ago, prepared such a deck of Casas era iu das received limited use at Oak Ridge. The usefulness of such a ..is very much a function of how sensitive the result of the calculation Svo viie ingut cross sections, in view of the approximation made in the par- ticular application. However, predictions of cross sections have the habit of caanging with time, as we achieve a better understanding of the reaction mech- arisons, and it is always best to check before any application, if the predic- tions which come out of the computer are still valid the day you want to use I would certainly not want the calculated cross sections to replace good üüa waen toey are available or when they become available. I am afraid that me emptation would be too great to use the above magic box as a substitute o cata. This magic box is nothing more than a computer equivalent to tabulated c3035 seciions in a report. The input card is scanned and if the nucleus, and wie e.cz y are not within certain limits for which the calculation has been desea, it reruses to give an answer. This solution I am afraid is not an omnes solution. The best solution would be one in which such calculat ed cross sections are evaluated, for given applications, by people very familiar with the state or the art and updated when new measurements become available, or when sig- minicant improvements in the model are made - essentially the kind of service provided io certain reactor calculations that was described by our first speaker tiis alternoon. I am not going to propose a very simple and easy way whereby This can be achieved, but is seems to me that some people believe they need some cross sections which some other people believe they know how to calculate and that it is conceivable that those two groups of people could communicate use- fully. As iaz as inelastic scattering of low-energy neutrons is concerned, there may be very iew cases wiere calculations could be useful. But the situation wili n ove criy when we have more adequate data and more nuclear structure mation on spins and parties of excited states to evaluate the models. Noit 203 cãe evaporation spectra tie situation is much better and in many cases can je cinculated to a degree oi accuracy which might be sufficient in many eiications. References: 1 1. D. Wilmore, The Calculation of Neutron Cross Sections from the Nonlocal Optical Model, British Report AERE-R4649, June 1964. 2. M. D. Goldberg, V. M. May, and J. R. Stehn, Angular Distribution in Neutron-Induced Reactions, USAEC Report BNL-400, Brookhaven National laboratory, October 1962. 3. R. J. Howerton, Tabulated Neutron Cross Sections, USAEC Report UCRL-5226, University of California, October 1959. 4. F. G. Perey and B. Buck, Muc. Phys. 32 353 (1962). END DATE FILMED 6 / 3 / 66 .. .