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Pion-Pion interactions in particle physics
NUCLEAR
INSTRUMENTS
AND
METHODS
I37
(I976)
407-408;
©
NORTH-HOLLAND
PUBLISHING
CO.
BOOK REVIEWS Proc. 4th Int. Symp. o n Polarization phenomena in nuclear reactions (eds. W. Grtiebler a n d V. K6nig, Birkhiiuser Verlag, Basel, 1976). T h e s y m p o s i u m was held in A u g u s t 1975 in Ziirich, where almost thirty invited talks were given a n d m o r e t h a n 200 contributed papers b r o u g h t to the attention o f the participants. In addition to these papers the proceedings contain the s y m p o s i u m s u m m a r y talk a n d short reports f r o m a few discussion sessions. This m a k e s the b o o k a very large volume, the greatest value o f which lies in the general description it gives o f the 1975 status o f the field o f nuclear physics with polarized particles. T h e unifying feature o f the field is essentially the technical aspect, whereas
13. R. MARTIN, D. MORGAN, a n d G. SHAW, Pion-Pion interactions in particle physics (Academic Press, L o n d o n , 1975) pp. 460, $ 40.50. T h e pion is a f u n d a m e n t a l b u t slightly elusive creature in the elementary particle zoo. It was predicted by Y u k a w a in 1935 a n d definitely identified by Powell a n d collaborators in 1947. Fermi a m o n g others studied p i o n - n u c l e o n interactions in the early fifties. N o w a d a y s pion b e a m s o f very g o o d quality are obtained at the large particle accelerators; s o m e are even built as pion factories. It h a s therefore been possible to study the pion a n d its interactions in great detail. T h e pion owes its f u n d a m e n t a l i m p o r t a n c e n o t only to the fact that it is the basic glue that keeps nucleons together in a nucleus b u t also because it is the lightest elementary particle which has 'strong interactions. This m e a n s that, at least to s o m e extent, the p i o n - p i o n interaction can be studied by itself while any other hadronic interaction requires inclusion o f the pion. This was realized early a n d theoretical physicists developed schemes to discuss p i o n - p i o n scattering. In fact, this was a d o m a i n where basic postulates o f S-matrix theory (to be contrasted to those o f field theory, so successfully applied to electromagnetic interactions) could be tested. Analyticity properties, unitarity requirem e n t s a n d crossing relations are i m p o r t a n t in this approach. It
SCHMID a n d H. ZIEGELMANN, The quantum-mechanical three-body problem (Pergamon Press, Oxford/Friedr. V i e w e g +
E.W.
Sohn, Braunschweig, 1974) $21.00. Ever since the R u s s i a n m a t h e m a t i c i a n L. D. Faddeev in 1960 caused a b r e a k t h r o u g h in the q u a n t u m theoretical handling o f three-body systems by establishing the Faddeev equations and d e m o n s t r a t i n g that their solutions would be unique, the s t u d y o f three-body systems has been a very active field. It has turned o u t to be possible to solve these equations numerically with s o m e w h a t simplified two-body potentials even if large a m o u n t s o f c o m p u t e r time are needed. This has opened up new possibilities o f obtaining otherwise inaccessible information a b o u t the strong interaction, e.g., a b o u t the force between two n e u t r o n s and the properties o f three-body forces. A large n u m b e r o f review articles h a s been written on the subject, m a n y o f t h e m in connection with the rather frequently occurring conferences in the field. However, it is a rather laborious
otherwise the polarization effects are used to explore several rather different scientific p r o b l e m areas, such as s y m m e t r y principles, few-particle problems a n d spin-orbit potentials. A s a n up-to-date reference work to the various uses o f polarized particles, including b e a m s o f 3He a n d 6Li, a n d o f polarized targets the b o o k s h o u l d be quite valuable. However, it m i g h t in the future be a d v a n t a g e o u s to alter the topical pattern o f the s y m p o s i u m series towards m o r e specific scientific problems a n d away from the technical means. This would perhaps help to m a k e the proceedings m o r e useful, since a m o r e complete coverage o f one or two scientific topics would then be possible. A. JOHANSSON
was also realized early that the lack o f a target for pions could be substituted by scattering pions off the virtual pion cloud a r o u n d a nucleon. This so-called C h e w - L o w extrapolation procedure has by n o w m a t u r e d into a formidable industry o f helicity amplitudes, f o r m factor corrections, absorptive effects, etc. T h e b o o k u n d e r review is written by recognized experts o n the theory o f p i o n - p i o n interactions. It exhibits in great detail the state o f the art as of s u m m e r 1975; I say this because the field is still developing rapidly a n d new items continually enter it. There is a t h o r o u g h discussion o f h o w p i o n - p i o n scattering i n f o r m a t i o n m a y be extracted f r o m experiments as well as on theoretical approaches a n d models for p i o n - p i o n scattering. The b o o k h a s a true " H a n d b u c h " character a n d should be very valuable n o t only for specialists in the field b u t also for those theorists a n d experimentalists alike, w h o want to obtain information on all or part o f the field. It might even be possible to use the book as a textbook or as a c o m p l e m e n t to textbooks in university courses, the difference between an ordinary textbook a n d the present one being that the former usually develops the theoretical tools a n d applies t h e m to different experimental situations, while this textbook focuses on a definite experimental situation a n d applies all possible theoretical tools to investigate it. B. E. Y. SVENSSON
task for the theoretical s t u d e n t or for the experimentalist to learn the field f r o m the existing literature and, therefore, the book by Schmid a n d Ziegelmann fills a great need. The text requires o f the reader to have s o m e knowledge o f q u a n t u m scattering theory but s h o u l d nevertheless be quite easy to read also for experimentalists. It is a small b o o k (only slightly over 200 pages) a n d yet there are very few gaps o f any importance due to the inclusion o f a large n u m b e r o f detailed equations. The a u t h o r s only describe the abstract theory o f Faddeev although there n o w exist m a n y other approaches to the f u n d a m e n t a l theory. Instead they devote the m a j o r part o f the book to discuss the condition under which the Faddeev equations have been solved and to describe the m e t h o d s used to obtain the numerical solutions. This certainly m a k e s the book very useful as an introduction into the details o f this field where often a c u m b e r s o m e c o m p a r i s o n between precise numerical results a n d experimental data is essential for progress. A. JOHANSSON
INSTRUMENTS
AND
METHODS
I37
(I976)
407-408;
©
NORTH-HOLLAND
PUBLISHING
CO.
BOOK REVIEWS Proc. 4th Int. Symp. o n Polarization phenomena in nuclear reactions (eds. W. Grtiebler a n d V. K6nig, Birkhiiuser Verlag, Basel, 1976). T h e s y m p o s i u m was held in A u g u s t 1975 in Ziirich, where almost thirty invited talks were given a n d m o r e t h a n 200 contributed papers b r o u g h t to the attention o f the participants. In addition to these papers the proceedings contain the s y m p o s i u m s u m m a r y talk a n d short reports f r o m a few discussion sessions. This m a k e s the b o o k a very large volume, the greatest value o f which lies in the general description it gives o f the 1975 status o f the field o f nuclear physics with polarized particles. T h e unifying feature o f the field is essentially the technical aspect, whereas
13. R. MARTIN, D. MORGAN, a n d G. SHAW, Pion-Pion interactions in particle physics (Academic Press, L o n d o n , 1975) pp. 460, $ 40.50. T h e pion is a f u n d a m e n t a l b u t slightly elusive creature in the elementary particle zoo. It was predicted by Y u k a w a in 1935 a n d definitely identified by Powell a n d collaborators in 1947. Fermi a m o n g others studied p i o n - n u c l e o n interactions in the early fifties. N o w a d a y s pion b e a m s o f very g o o d quality are obtained at the large particle accelerators; s o m e are even built as pion factories. It h a s therefore been possible to study the pion a n d its interactions in great detail. T h e pion owes its f u n d a m e n t a l i m p o r t a n c e n o t only to the fact that it is the basic glue that keeps nucleons together in a nucleus b u t also because it is the lightest elementary particle which has 'strong interactions. This m e a n s that, at least to s o m e extent, the p i o n - p i o n interaction can be studied by itself while any other hadronic interaction requires inclusion o f the pion. This was realized early a n d theoretical physicists developed schemes to discuss p i o n - p i o n scattering. In fact, this was a d o m a i n where basic postulates o f S-matrix theory (to be contrasted to those o f field theory, so successfully applied to electromagnetic interactions) could be tested. Analyticity properties, unitarity requirem e n t s a n d crossing relations are i m p o r t a n t in this approach. It
SCHMID a n d H. ZIEGELMANN, The quantum-mechanical three-body problem (Pergamon Press, Oxford/Friedr. V i e w e g +
E.W.
Sohn, Braunschweig, 1974) $21.00. Ever since the R u s s i a n m a t h e m a t i c i a n L. D. Faddeev in 1960 caused a b r e a k t h r o u g h in the q u a n t u m theoretical handling o f three-body systems by establishing the Faddeev equations and d e m o n s t r a t i n g that their solutions would be unique, the s t u d y o f three-body systems has been a very active field. It has turned o u t to be possible to solve these equations numerically with s o m e w h a t simplified two-body potentials even if large a m o u n t s o f c o m p u t e r time are needed. This has opened up new possibilities o f obtaining otherwise inaccessible information a b o u t the strong interaction, e.g., a b o u t the force between two n e u t r o n s and the properties o f three-body forces. A large n u m b e r o f review articles h a s been written on the subject, m a n y o f t h e m in connection with the rather frequently occurring conferences in the field. However, it is a rather laborious
otherwise the polarization effects are used to explore several rather different scientific p r o b l e m areas, such as s y m m e t r y principles, few-particle problems a n d spin-orbit potentials. A s a n up-to-date reference work to the various uses o f polarized particles, including b e a m s o f 3He a n d 6Li, a n d o f polarized targets the b o o k s h o u l d be quite valuable. However, it m i g h t in the future be a d v a n t a g e o u s to alter the topical pattern o f the s y m p o s i u m series towards m o r e specific scientific problems a n d away from the technical means. This would perhaps help to m a k e the proceedings m o r e useful, since a m o r e complete coverage o f one or two scientific topics would then be possible. A. JOHANSSON
was also realized early that the lack o f a target for pions could be substituted by scattering pions off the virtual pion cloud a r o u n d a nucleon. This so-called C h e w - L o w extrapolation procedure has by n o w m a t u r e d into a formidable industry o f helicity amplitudes, f o r m factor corrections, absorptive effects, etc. T h e b o o k u n d e r review is written by recognized experts o n the theory o f p i o n - p i o n interactions. It exhibits in great detail the state o f the art as of s u m m e r 1975; I say this because the field is still developing rapidly a n d new items continually enter it. There is a t h o r o u g h discussion o f h o w p i o n - p i o n scattering i n f o r m a t i o n m a y be extracted f r o m experiments as well as on theoretical approaches a n d models for p i o n - p i o n scattering. The b o o k h a s a true " H a n d b u c h " character a n d should be very valuable n o t only for specialists in the field b u t also for those theorists a n d experimentalists alike, w h o want to obtain information on all or part o f the field. It might even be possible to use the book as a textbook or as a c o m p l e m e n t to textbooks in university courses, the difference between an ordinary textbook a n d the present one being that the former usually develops the theoretical tools a n d applies t h e m to different experimental situations, while this textbook focuses on a definite experimental situation a n d applies all possible theoretical tools to investigate it. B. E. Y. SVENSSON
task for the theoretical s t u d e n t or for the experimentalist to learn the field f r o m the existing literature and, therefore, the book by Schmid a n d Ziegelmann fills a great need. The text requires o f the reader to have s o m e knowledge o f q u a n t u m scattering theory but s h o u l d nevertheless be quite easy to read also for experimentalists. It is a small b o o k (only slightly over 200 pages) a n d yet there are very few gaps o f any importance due to the inclusion o f a large n u m b e r o f detailed equations. The a u t h o r s only describe the abstract theory o f Faddeev although there n o w exist m a n y other approaches to the f u n d a m e n t a l theory. Instead they devote the m a j o r part o f the book to discuss the condition under which the Faddeev equations have been solved and to describe the m e t h o d s used to obtain the numerical solutions. This certainly m a k e s the book very useful as an introduction into the details o f this field where often a c u m b e r s o m e c o m p a r i s o n between precise numerical results a n d experimental data is essential for progress. A. JOHANSSON