A. Nagl .V nahtanaveD .H llarebU o* Nuclear Pion noitcudorpotohP With 35 Figures galreV-regnirpS Berlin Heidelberg New kroY London Paris Tokyo Hong Kong Barcelona Budapest Professor Dr. Anton Nagl Department of Physics, The Catholic University of America, Washington, D. C., 20046, USA and Pailen-Johnson Associates, Vienna, VA 22182, USA Professor Dr. Varadarajan Devanathan Department of Nuclear Physics, University of Madras, Madras 600025, India and Crystal Growth Centre, Anna University, Madras 600025, India Professor Dr. Herbert {)berall Department of Physics, The Catholic University of America, Washington, D. C., 20046, USA Manuscripts for publication should be addressed :ot Gerhard H6hler Institut fi~r Theoretische Kemphysik der Universit~it Karlsruhe, Posffach 6980, W-7500 Karlsruhe 1, Fed. Rep. of Germany Proofs and all correspondence concerning papers in the process of publication should eb addressed :ot Emst A. Niekisch Haubourdinstral3e 6, W-5170 Jtilichl, Fed. Rep. of Germany ISBN 3-540-50671-3 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-50671-3 Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its current version, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. (cid:14)9 Springer-Verlag Berlin Heidelberg 1991 Printed in Germany The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Springer NET in-house system 57/3140-543210 - Printed on acid-free paper Preface Nuclear Pion Photoproduction has become a tool of investigation for (i) the finer details of the elementary photopion production amplitude from free nucleons, (ii) the pion-nucleus optical potential, and (iii) the nuclear structure of the target nucleus. The nuclear cross section involves various bilinear combinations of the different terms in the elementary amplitude and hence serves as an analyzer for the structure of the elementary amplitude. The produced pion undergoes strong interaction with the residual nucleus, and hence the nuclear photopion cross section depends sensitively on the pion-nucleus optical potential. The nuclear structure of the target nucleus plays a dominant role in determining the photopion cross section, and the charged pion photoproduction process with a T = 0 target nucleus selectively excites the T = 1 final states and hence offers us a powerful tool for investigating T = 1 isobar analogue states. In this monograph, all these aspects are considered in detail. In the near future, the experimental study of pion photoproduction will receive a new impetus with the improvement in the technology of pion spectrometers and the commissioning of 100% duty cycle electron accelerators at energies beyond the (3,3) resonance, and it is expected that the investigation of nuclear pion photoproduction will break new ground, and will realize its full potential as a powerful tool of nuclear research. This monograph should serve as an introductory guide as well as a reference manual for the graduate students and research scientists working in this important area of physics. In the course of writing this book, the authors had the benefit of discussions with numerous original contributors to the subject of nuclear photopion produc- tion; particular mention may be made of A. M. Bemstein, R. A. Eramzhyan, N. Freed, V. Girija, K. Shoda, F. Tabakin, L. Tiator and L. E. Wright. Thanks are due to R. Prasad and Reyna Tosta for preparing the manuscript with meticu- lous care and to S. Karthiyayini for proofreading. The authors acknowledge with thanks the keen interest of Prof. G. H6hler in the publication of this monograph. This work has been supported by the National Science Foundation and one of us (V. D.) acknowledges with thanks the financial support from the Council of Sci- entific and Industrial Research (India), the award of travel grants by the National Science Foundation and the hospitality at various centers during the preparation of the manuscript. Washington, D.C. and Madras, A. Nagl February 1991 .V Devanathan H. Oberall V Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. General Survey of Photopion Nuclear Physics ........... 4 2.1 Historical Overview ............................... 4 2.1.1 The First Phase (1947-1956) ................ 4 2.1.2 The Second Phase (1957-1976) ................. 4 2.1.3 The Third Phase (From 1977 Onwards) ........... 7 2.2 Experimental Charged Pion Spectroscopy ................ 8 2.2.1 The r+p+e+Method .......................... 9 2.2.2 The Activity Method ..................... 9 2.2.3 Pion Spectrometers .......................... 10 2.3 Theoretical Framework .............................. 11 3. Elementary Photopion Production Amplitude ............... 13 3.1 Introduction ....................................... 13 3.2 The Invariant Amplitude .............................. 18 3.3 Partial Wave Decomposition ...................... 23 3.4 Implications of Unitarity ............................ 26 3.5 The Born Approximation ............................. 28 3.6 Application of Dispersion Theory to Pion Photoproduction . . 37 3.7 The Effective Lagrangian Approach ................ 41 3.8 Elementary Photopion Production at Higher Energies ....... 49 4. Nuclear Transition Amplitude ........................... 58 4.1 The Impulse Approximation .......................... 58 4.2 Plane Wave Impulse Approximation (PWIA) .......... 60 4.3 Distorted Wave Impulse Approximation (DWIA) .......... 61 4.4 Formulation in Momentum Space ..................... 65 4.5 Beyond the Impulse Approximation .................... 67 5. Pion-Nucleus Optical Potential and Distorted Pion Waves .... 71 5.1 Solution of the Klein-Gordon Equation ............... 71 5.2 Pion-Nucleus Optical Potential ....................... 74 5.3 Pion-Nucleus Elastic Scattering ....................... 77 5.4 Distorted Pion Waves ............................... 79 VII 6. Nuciear Wave Functions and Nuclear Transition Densities D. . . 83 7. Charged Pion Photoproduction ...................... $8 7.1 Total Cross Section Measurements ..................... 88 7.2 Differential Cross Section ............................ 89 7.3 Discussion of Specific Reactions .................. 90 7.3.1 The Reactions 12C(y, rr-) 12N and i2C(y, r+) 12B m. . 90 7.3.2 The Reaction %(y, x’) 16N ................... 92 7.3.3 The Reaction 14N(y, nC)14Cs.s. .............. 95 7.3.4 The Reaction ‘“C(y, 7r’) 13Bg.s. ................. 100 7.3.5 The Reaction 13C(y,r -) 13Nss. ................. 103 7.4 Concluding Remarks ................................ 107 8. Neutral Pion Photoproduction ........................... 108 8.1 An Overview ................................ 108 8.2 The DWIA Method .... ............................ 110 8.3 The Isobar-Doorway Model .......................... 116 8.4 The Isobar-Hole Formalism ........................... 120 8.5 Concluding Remarks ................................ 123 9. Special Topics and Future Prospects .................. 126 9.1 Polarization Studies ............................... 126 9.2 Electroproduction of Pions ........................... 128 9.3 Photoproduction of K and q Mesons .................... 130 9.4 The Present Status and Future Prospects ............. 131 Appendix .............................................. 135 A* The Generalized Helm Model ......................... 135 References ~ e......l . ..D.............l....,,.......q........ 141 SubjectIndex .,~...S,.~l...O.~.........~.................. 151 Series Index (Springer Tracts in Modem Physics, Volumes 36-120) . . . 153 Author Index (Springer Tracts in Modem Physics, Volumes 36-120) . . 167 VII 1. Introduction The nuclear pion photoproduction reaction exhibits a number of unique features that make it a rewarding field of study 1.1-14 and a promising source of information on pion-nucleus interaction and nuclear structure. However, even though experimental and theoretical activity in this field started soon after the discovery of the pion and has never ceased ever since, it was a relatively stagnant area of research until recently. The major reasons for this were experimental difficulties and a lack of overlap between the experimentally and theoretically accessible areas of the field. The low beam intensity and/or low duty cycles of the accelerators available in the 1950~s and 1960's limited nuclear pion photoproduction experiments es- sentially to inclusive reactions in which only the final pion is observed. This meant that the final nucleus could be in a very large number of states, including those which lead to the emission of one or more nucleons. Theoretical predic- tions, on the other hand, are more likely to be reliable when the final state is well defined 1.15-17. Only with the commissioning of the high duty cycle, high in- tensity machines, starting in the mid-seventies,, and through the recent advances in detection and data processing equipment, has it been possible oc perform with sufficient accuracy pion photoproduction experiments in which transitions to in- dividual nuclear states can be reliably observed. This development has led to a sharp increase in both experimental and theoretical activity in the field, and it has opened the prospect of exploiting the particular characteristics of pion pho- toproduction, thus making finally accessible the possible benefits that a thorough study of this reaction may offer. As a source for nuclear structure information, pion photoproduction competes with a variety of other intermediate energy reactions, such as inelastic electron scattering, neutrino reactions, pion scattering, radiative pion capture, and muon capture 1,18-20. This is due to the fact that all these reactions proceed via similar nuclear transition operators. Studying all of these varioas reactions does, however, not simply lead to a large amount of redundant information. Rather, it generally leads to complementary information. Muon capture can provide information about transitions which are hard to study otherwise, but it suffers from the restriction that the momentum transfer is fixed. Electron scattering is free from this restriction, and moreover, it can induce both ~IT = 0 and TA_ = 1 transitions within the same nucleus. Charged pion photoproduction on the other hand connects only to the isobaric analogues of the states reached by the z~T = 1 transitions in electron scattering. It therefore allows to selectively investigate the isovector transitions. In electron scattering these are mixed up with the isoscalar transitions, and it is sometimes difficult to disentangle them. Pion photoproduction has, along with electron scattering, the advantage that the momentum transfer to the nucleus is not fixed as it is in muon capture or radiative pion capture, but that it is variable over a wide range, thus allowing to probe a considerable region of the form factors for the various nuclear transitions. Charged pion photoproduction has in addition the advantage that it proceeds predominantly via spin flip, unlike electron scattering, muon capture, and ineleas- tic pion scattering which excite transitions with and without spin flip. It therefore provides a tool for determining the degree of spin flip contained in the transition to a given level, or to separate out the spin flip components in an unresolved complex of closely spaced transitions. The interaction of pions with nuclei has thus far been studied mainly through elastic pion scattering and pionic atoms and more recently also through inelastic pion scattering. Here too, pion photoproduction provides an additional investiga- tive tool, complementing the applicatio n of the other reactions. The main advantage of pion photoproduction over elastic pion scattering as a probe of pion-nuclear interaction is that photoproduction provides a much more stringent test for pion wave functions, and hence for the pion-nuclear op- tical potential, than elastic scattering. The latter reaction is sensitive only to the asymptotic phase shifts. This causes a large ambiguity with respect to the pion wave functions in the nuclear interior, since all wave functions leading to the same phase shifts appear equivalent. Pion photoproduction on the other hand (as is the case with inelastic pion scattering), is very sensitive to the precise nature of the wave functions, particularly in the region in which the nuclear transition densities peak. Since the transition radii for the transitions to the different excited levels vary over a considerable region, it is in principle possible to selectively probe the pion-nucleus interacnon within different regions of the nucleus. The fact that in pion photoproduction, the pions can, in principle, be produced anywhere in the nuclear interior, since the photon can penetrate the whole nucleus essentially unattenuated, makes this reaction a potentially superior probe for pion- nuclear interactions -- except for the deep nuclear interior (where the nuclear transition densities tend to be small) and near the (3,3)-resonance region (where the nucleus appears essentially as a black sphere, and where other probes also fail). At energies sufficiently below the (3,3)-resonance, however, where the pion-nuclear interaction is relatively weak, i.e., where the nucleus is relatively transparent to pions, pion photoproduction promises to be an effective tool of pion-nuclear physics. With plonic atoms, the pion-nuclear interaction can only be studied at one energy (T~ = 0 MeV). Pion scattering experiments, on the other hand, can only be used for pion energies larger than about 30 MeV. The lower energy limit is imposed by experimental difficulties, stemming from the short distances the pions travel before decaying. In pion photoproduction experiments using spectrome- ters, a similar problem exists, although to a lesser extent. There are, however, other experimental techniques to measure photoproduction cross sections avail- able which do allow to extend the energy range all the way down to threshold, thereby completely filling the energy gap between pionic atom and pion scattering experiments. Moreover, in charged pion photoproduction, the pion interacts not with the target nucleus but with the residual nucleus which is usually an unstable isotope with N :/Z. Hence this reaction is extremely suited to test the pion-nucleus optical potential in such an unstable nucleus and study its isospin dependence. As the preceding discussion indicates, pion photoproduction has the potential of becoming a source of useful information in various parts of nuclear physics. In order to gain access to this source, a large number of experiments have been initiated, promising to yield rapidly increasing amounts of accurate pion photo- production data. In particular, there has been a growing number of experiments in which transitions to individual nuclear states have been resolved and differ- ential cross sections measured in recent years 1.211. Correspondingly, there has been a spurt of activity on the theoretical side investigating in detail the various inputs that go into the calculation of photopion cross sections. The purpose of this review is to outline the development, assess the progress and indicate the future prospects of the study of photopion reactions. This review deals with both the charged and neutral pion photoproduction from nuclei. The charged pion photoproduction takes place incoherently since in the r7 + production, a proton is converted into a neutron and in the ~r- production, a neutron is converted into a proton; thereby the final nucleus that is produced in the reaction is different from the initial nucleus. In the case of neutral pion photoproduction, the pion production can take place coherently when the final nucleus is left in the same state as the initial nucleus or incoherently when the nucleus makes a transition to an excited state. It is much easier to detect the charged pions rather than the neutral pions and hence the charged pion photo- production has received much greater attention. So, the major part of this review is devoted to the study of charged pion photoproduction save Chap. 8 which is devoted entirely to the neutral pion photoproduction. In Chap. 2, a general survey is made outlining the various phases of develop- ment of the subject of nuclear pion photoproduction. Chapters 3-6 deal with the various ingredients that go into the calculation of nuclear photopion cross sec- tions. The elementary amplitude, the construction of nuclear transition amplitudes using the impulse approximation, the final state interaction of the outgoing pion with the residual nucleus and the influence of nuclear wave functions/transition densities are discussed in sequence in successive chapters. In Chap, 7, the present status of the charged pion photoproduction is reviewed and the need for extending the photopion study beyond the (3,3) resonance region is stressed. In Chap. 8, a detailed study of the coherent r7 ~ photoproduction is:made, in Chap. 9, the prospects of the study of polarization phenomena, electroproduction of pions in double coincidence experiments and photoproduction Of more exotic mesons such as K and ~ are briefly discussed. 2. General Survey of Photopion Nuclear Physics The development of the subject of nuclear pion photoproduction can be broadly divided into three phases. In the first phase (1947-56), the gross features of the cross sections of photoproduction of pions from hydrogen and various nuclei have been studied. The second phase (1957-76) starts with the rigorous formu- lation of the elementary photopion production amplitude by Chew et al. using the dispersion theory. In this period, the study on nuclear targets has become more precise by measurement of exclusive total cross sections by observing the radioactivity of the low-lying final nuclear states that are stable against nucleon emission but decay by r-emission and to which the nuclear transition takes place. The third phase (from 1977 onwards) commences with the successful measure- ment of differential cross sections by Shoda et al. using pion spectrometers. It is during this period that major advances have been made, thus making the nuclear pion photoproduction a powerful tool to investigate the pionic interactions with nuclei and nuclear structure. In Sect. 2.2, different experimental techniques that are used in charged pion spectroscopy are also reviewed. In Sect. 2.3, an outline of the theoretical framework is given for calculating exclusive cross sections. 2.1 Historical Overview 2.1.1 The First Phase (1947-1956) Interest in pion photoproduction commenced even before the discovery of the pion in 1947 since it was in cosmic rays that the pion events were looked into, ever since Yukawa postulated the meson as the mediator of nuclear force. For a detailed account of photopion reactions during the first phase, the reader is referred to the review article of Bellamy 2.1, the book of Bethe and de Hoffmann 2.2, and other relevant references 2.3-14. 2.1.2 The Second Phase (195%1976) A major theoretical advance during this period was the application of dispersion theory to pion photoproduction, in which Watson's theorem played an important part. Based on the cut-off model, which they had already successfully applied to pion scattering, Chew et al. (hereafter referred to as CGLN) 2.15 used disper- sion relations to obtain a general amplitude for photoproduction of pions from nucleons. Even though a number of simplifying assumptions had to be made, the cross sections calculated with this amplitude compared well with the available data on reactions '3 + P ~ +rr + n and 7 + P *--- ~r7 + P. Applications to nu- clear photoproduction were made soon after by Devanathan and Ramachandran 2.16-19 to study charged and neutral pion production from deuterons and later from heavier nuclei. The first detailed claculations of nuclear pion photoproduction cross sections were attempted by Laing and Moorhouse 1.15. Despite the fact that crude approximations were made for the elementary amplitudes and the pion nucleus interactions, as well as for the nuclear transition probabilities, this calculation is important since it was the first attempt to calculate nuclear pion photoproduction cross sections under the assumption that the nucleus undergoes a transition to a discrete final state. This theoretical advance essentially coincided with an important experimen- tal innovation, due to Hughes and March 2.20. They introduced the activity method which allowed for the first time to investigate experimentally transitions to individual final nuclear states with pion photoproduction. Up to that time pho- toproduction experiments depended on the detection of mesons by determining their charges and energies. Such measurements do not distinguish between reac- tions in which the meson is the only particle emitted and those in which meson emission is accompanied by the emission of one or more nucleons. If instead of the produced pion, the residual nucleus is observed for some characteristic activity, it is possible to investigate separately reactions in which the nucleus undergoes a transition to individual states stable against particle emission. The reactions studied by Hughes and March 2.20 was B11 (7, r7 -) 11 C, wh ere the residual nucleus was identified by observing its positron activity, which has a half life of 20 minutes. Good agreement with theoretical results of Laing and Morehouse 1.15 was found if the surface production model was assumed to be valid, whereas strong disagreement was found if volume production was assumed (then the predictions were almost an order of magnitude too high). Soon, a large number of activity experiments were carried out, following the pioneering effort of Hughes and March. Notable among the activity experiments were those of Dyal and Hummel 2.21 on lIB, of March and Walker 2.22 on 6~ of Meyer et al. 2.23 on 160 and ,1A72 and of Nydall and Forkman 2.24 on 11B, 1A72 and SlV. A major advance on the theoretical side were the investigations by De- vanathan and his collaborators 2.16--t9,25-28. Starting in 1961, this group put the claculations of nuclear pion photoproduction cross sections on a more solid theoretical foundation. Their formalism was based on the impulse approximation, using the CGLN-amplitude for the photoproduction operator, and harmonic os- cillator wavefunctions for the nuclear states. Final state interactions between the pion and the nucleus were not considered explicitly. These effects, in particular absorption, were simulated in a phenomenological way by the surface produc- tion model, in which it is assumed that pions produced inside the nucleus are reabsorbed, and that therefore the contributions to the cross section come only