Princeton, New J e r s e y 08540 1 I ABSTRACT Several a s p e c t s of deep i n e l a s t i c n e u t r i n o s c a t t e r i n g are discussed i n t h e framework of asymptotically f r e e f i e l d t h e o r i e s . W e f i r s t consider t h e growth behavior of t h e t o t a l c r o s s s e c t i o n s a t l a r g e energies. Because of t h e d e v i a t i o n s from strict s c a l i n g which are c h a r a c t e r i s t i c of such t h e o r i e s t h e growth need not b e l i n e a r .

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... ever, upper and lower bounds are e s t a b l i s h e d which r a t h e r c l o s e l y bracket a l i n e a r growth. \ W e next consider i n more d e t a i l t h e expected p a t t e r n of s c a l i n g d e v i a t i o n f o r t h e s t r u c t u r e functions and, correspondingly, f o r t h e d i f f e r e n t i a l c r o s s s e c t i o n s . The a n a l y s i s h e r e is based on c e r t a i n s p e c u l a t i v e assumptions. q u a l i t a t i v e e f f e c t s of s c a l i n g breakdown as they may show up i n t h e The focus is on x and y d i s t r i b u t i o n s . from t h e Callan-Gross r e l a t i o n . The l a s t s e c t i o n of t h e paper d e a l s w i t h d e v i a t i o n s * Work supported by t h e National Science Foundation under g r a n t GP-3078X; and by t h e U. S. Atomic Energy Commission under c o n t r a c t No. AT(11-1)-3072. / 'Alfred P. Sloan Foundation Fellow DECLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government Neither the Unittd States Government nor any agency thereof, nor any of their employets, makes any warranty, cxprcss or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or s m i c c by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement. m mmendation. or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not ncccssady state or reflect thwe of the United States Government or any agency thereof.