Jain, M.

Rad, F.N.

Saylor, D.P.

UNT Digital Library

, NOTICE This repori wu prepared is an account of work sponsored by the United States Government. Neither th'j United Ststei nor the United Stale* Atomic Energy Commission, not any of their employees, nor any of ihrlr contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, com-pleienesi or usefulness of any information, apparatus, product or piocess Cisctosed, OT represents that its n~ would not Infringe privately owned rights. FINAL STATE INTERACTION IN THREE NUCEEON .SYSTEM F . N. Rad Lawrc-nt'c B 'Tkv l^y L a b o r a t o r y , r rnivc-rHity of C a l i f o r n i a , B e r k e l e y , C a l i f o r n i a 94720 D. P . S a y l o r 39 Otsego, Worcestei, Massachusetts 01609 and Mahavir Jain^ Texas A S M University, College Station, Texas 77843 Vector to vector spin-transfer parameters for slightly inelastic p-d scattering are discussed in the context of rece.-.t theoretical and experimental developments. Work supported by the U. S. Atomic Energy Commission. Guest scientist, Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87544. INTERACTION A L'ETAT FINAL DANS LE SYSTEME A TROIS NUCLEONS F. N. Rad Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 D. P. Saylor 39 Otsego, Worcester, Massachusetts 01609 Texas A & M University, College Station, Texas 77843 Les parametres de transfert vectoriel de spin pcur la diffusion p-d faiblement inelastiqun seront discutes dans le contexte de recents developpements theoriques et experimentaux. Travail supporte" par U. S. Atomic Energy Commission. "S ̂  ? - '/ ' O-t - * *" •' *' \4 Scientifique invite, Los Alamos Scientific Laboratory, University of California, - . • \ '* g. Los Alamos, New Mexico 87544. «* -2-FINAL STATE INTERACTION IN THREE NUCLEON SYSTEM* F. 1 . Rad Lawrence Berkeley Laboratory, University of California, Rerkeley, California 94720 D. P. Saylor 39 Otsego, Worcester, Massachusetts 01609 and Mabavir Jain"*" Texas A £ M University, College Station, Texas 77843 The dynamics of three-nuclaon system, as well as the interaction between the parti­cles on and off the energy shell can be studied by the processes leading to three nucleons in the final st*.tc'. There are several approximate descriptions of the three-nucieon breakup process which are often used. Each is useful in providing an under­standing of and insight into the qualitative features of the breakup process in a limited part of phase space. The final stite interaction (FSI) mechanism is appropriate for understanding that part of the breakup sp3cti"um in which one of the three outgoing pairs of nucleons has a low relative energy. Typically, the cross sections are enhanced. The FSI theory of Watson and Higdal is often ased to describe these enhancements. Theoretical calculations ' based on separable S-wave potentials give results in good agreemeut with the Watson-Higdal form of the final state peak. These calculations also predict a rather complex angular dependence of the FSI which may prove to be sensitive to the energy shell behavior assumed in the model. Several attempts 2" 5' have been made to estimate the size of model dependent effects in N-d breakup reactions. The recent results of Brayshaw1*' and of Haftel and Peterson ' (HP) are of particular interest because these estimates were based on comparison of models which gave identical on-shell two-nucleon scattering. For E c m ^ 20 HeV Brayshaw and HP have found that significant model dependent variations were restricted to three-body 2S-waves. They also found that if i. J.S required that the N-d doublet scattering length, a 2 , is held fixed the remaining variability is much reduced. Brayshaw believes that his analysis indicates that the two nucleon observables and a 2 determine the low energy trinucleon reactions to high precision for any plausible interaction. It would be significant if this expectation were to be experimentally verified. The conclusions of HP are different from that of Brayshaw while they provide a basis for selecting experiments. HP have found substantial variability in the 2 S partial wave even with a fixed doublet scattering lenqth. The sensitive region is concentrated where singlet FSI dominates. The variability in the amplitude.? results in variations of the FSI angular distributions and spectra which are of sufficient magnitude to be significant experimentally. In regard to these HP expectations the experiment and analysis of Briickman e_t a_l_. 6' (BKMSW) should be particularly valuable. They found that the breakup cross section in the np FSI region could be fitted very accurately by whoro F and V are the singlet and triplet Watson-Migdai enhancement factors. Empiri­cally BKM5W have found that the triplet FSI angular distribution, X c O 3 ) , was the same as the experimental d-p elastic angular distribution and that the magnitude of the triplet FSI cross section could be successfully related to the elastic cross section. The if application of the Watson-Migdal analysis shows internal consistency with the np low-onergy parameters. Other experiments which should .ie particularly valuable in iso­lating the np singlut FSI are the measurements of the vtctor to vector spin transfer parameters iOj' in ^(d,?) and 2H(p,p) for siightly inelastic r—d scattering. These experiments when combined with kinematically incomplete cross section measurements should allow one to extract X^ (03) . Assuming the validity of the Watson-Migdal jn.ilysiB, -3-V ' X S (6,) F S <E._) + V X C (90J F C (E„> KY _ / np 3 np 45 y np 3 np 45 where Ki and K̂ , are the spin-transfer parameters for the singlet and triplet components respectively. Using the simplified structure of the breakup amplitudes, characteristic of the Amado model, it is ^asy to show that Kf, will depend on angle and energy but an implication oi BKMSW is that Ky is nearly the same as the K X parameters for elastic scattering. However in terms of the breakup .•mplitudes ' . f hi2- r lkj 2- jl*2l2- ! * A *^^\ +VJ*ey2 . . ; K = CO! H \ Q , p ; 2 | q | 2 + i | d l | 2 + | | d 2 | 2 - 1 f R e a ; d 2 V Y 3 k | 2 * j k 1 | 2 * | M 2 | 2 - ^ " K d 2 where q is the amplitude for breakup in the quartet state (S = 3/2), and di and dj are the doublet-state (S = 1/2) amplitudes in which the two identical nucleons are coupled to spin 1 or 0, respectively. To a first approximation the slightly inelastic Ky parameters can be computed on the basis of a decomposition of the breakup cross section similar to that of BKMSW and a measurement of the corresponding KiJ for elastic scattering. Thus a measurement of the K>j" parameters havo additional interest in that they provide additional checks of the final state interaction theory. We are currently worki ig on the theoretical predictions using a computer code which solves the three particle Faddeev equation for separable spin dependent s-wave nucleon nucleon interactions. ' REFERENCES *Work supported by the u. S. Atomic Energy Commission. Guest scientist, Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87544. 1. R. T. Cahil and I. H. Sloan, Nucl. Phys. A165 (1971) 161; W. Ebenhoh, Proceedings of the International Conference on Few Particle Problems in the Nuclear Interactions, Los Angeles, California, 1972, edited by Slaus et al. (North-Holland, Amsterdam, 19/2), pp. 325-328. 2. W. M. Kloet and J. A. Tjon, Nucl. Phys. A210 (1973) 3B0. 3. Mahavir Jain, J. G. Roger, and D. P. Saylor, Phys. Rev. Letters 31̂  (1973) 838. 4. D. D. Brayshaw, Phys. Rev. Letters 3_2_ (1974) 382. 5. H. I. Haftel and E. L. Peterson, Bull. Am. Phys. Soc. 19_ (1974) 505. 6. H. Bruckman, W. Kluge, H. Mattay, L. Schanzler and K. Wick, Nucl. Phys. A157 (1970) ,:09. 7. D. P. Saylor and F. N. Rad, Phys. Rev. C8 (1973) 507 8. Mahavir Jain and Gary D. Doolen, Phys. Rev. C8 (1973) 124. 

Final state interaction in three nucleon system

Jain, Mahavir.

eScholarship - University of California

Lawrence Berkeley National LaboratoryRecent WorkTitleFINAL STATE INTERACTION IN THREE NUCLEON SYSTEMPermalinkhttps://escholarship.org/uc/item/9v79v0zgAuthorsRad, F.N.Saylor, D.P.Jain, Mahavir.Publication Date1974-07-24eScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaTo be presented at the International Conference on Few Body Problems in Nuclear and Particle Physics, University of Laval, Quebec, Canada, August 27-31, 1974 FINAL STATE INTERACTION IN THREE NUCLEON SYSTEM F. N. Rad, D. P. Saylor, and Mahavir Jain ~ . ~ ~ .. . : ~,., July 24, 1974 Prepared for the U. S. Atomic Energy Commission under Contract W -7405-ENG-48 TWO-WEEK LOAN COPY LBL-29~~4" iJ.\'·.',;c:;:<CI.: This is a Library Circulating Copy which may be borrowed for two weeks. For a personal retention copy, call Tech. Info. Diuision, Ext. 5545 DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal 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 service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California. -1-FINAL STATE INTERACTION IN THREE NUCLEON SYSTEM* F. N. Rad Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 D. P. Saylor ~ 39 Otsego, Worcester, Massachusetts 01609 and Mahavir Jaint Texas A & M University, College Station, Texas 77843 Vector to vector spin-transfer parameters for slightly inelastic p-d scattering are discussed in the context of recent theoretical and experimental developments. * Work supported by. the u. S. Atomic Energy Commission. tGuest scientist, Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87544. INTERACTION A L'ETAT FINAL DANS LE SYSTEME A TROIS NUCLEONS* F. N. Rad Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 D. P. Saylor 39 Otsego, Worcester, Massachusetts 01609 et Mahavir Jaint Texas A & M University, College Station, Texas 77843 Les parametres de transfert vectoriel de spin pour la diffusion p-d faiblement inelastique seront discutes dans le contexte de recents developpements theoriques et experimentaux. * Travail supporte par u. S. Atomic Energy Commission. ~cientifique invite, Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87544. -2-FINAL STATE INTERACTION IN THREE NUCLEON SYSTEM* F.- N. Rad Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 D. P. Saylor 39 Otsego, Worcester, Massachusetts 01609 and Mahavir Jaint Texas A & M University, College Station, Texas 77843 The dynamics of three-nucleon system, as well as the interaction between the parti-cles on and off the energy shell can be studied by the processes leading to three nucleons in the final ·state. There are several approximate descriptions of the three-nucleon breakup process which are often used. Each is useful in providing an under-standing of and insight into the qualitative features of the breakup process fna limited part of phase space. The final state interaction (FSI) mechanism is appropriate for understanding that part of the breakup spectrum in which one of the three outgoing pairs of nucleons has a low relative energy. Typically, the cross sections are enhanced. The FSI theory of Watson and Migdal is often used to describe these enhancements. Theoretical calculations 1 ) based on separable S-wave potentials give results in good agreement with the Watson-Migdal form of the final state peak. These calculations also predict a rather complex angular dependence of the FSI which may prove to be sensitive to the energy shell behavior assumed in the model. Several attempts 2 -s) have been made to estimate the size of model dependent effects in N-d breakup reactions. The recent results of Brayshaw4 ) and of Haftel and Peterson 5 ) (HP) are of particular interest because these estimates were based on comparison of models which gave identical on-shell two-nucleon scattering. For Ecm ~ 20 MeV Brayshaw and HP have found that significant model dependent variations were restricted to three-body 2S-waves. They also found that if it is required that the N-d·doublet scattering length, a2, is held fixed the remaining variability is much reduced. Brayshaw believes that his analysis indicates that the two nucleon observables and a2 determine the low energy trinucleon reactions to high precision for any plausible interaction. It would be significant if this expectation were to be experimentally verified. The conclusions of HP are different from that of Brayshaw while they provide a basis for selecting experiments. HP have found substantial variability in the 2 s partial wave even with a fixed doublet scattering length. The sensitive region is concentrated where singlet FSI dominates. The variability in the amplitudes results in variations of the FSI angular distributions and spectra which are of sufficient magnitude to be significant experimentally. In regard to these HP expectations the experiment and analysis of Bruckman et al. 6 ) (BKMSW) should be particularly valuable. They found that the breakup cross section in the np FSI region could be fitted very accurately by dO where F~ and F~ are the singlet and triplet Watson-Migdal enhancement factors. Empiri-cally B~SW havepfound that the triplet FSI angular distribution, xt (83), was the same as the experimental d-p elastic angular distribution and that the m~~nitude of the triplet FSI cross section could be successfully related to the elastic cross section. Their application of the Watson-Migdal analysis shows internal consistency with the np low-energy parameters. Other experiments which should be particularly valuable in iso-lating the np singlet FSI are the measurements of the vector to vector spin transfer parameters ~· in 1H(d,p) and 2 H(p,p) for slightly inelastic p-d scattering. These experiments when combined with kinematically incomplete cross section measurements should allow one to extract Xs (8 3 ). Assuming the validity of the Watson-Migdal np analysis, .r, --.-y' K y xs (83) np xs (83) np -3-t • t t + Ky X (8 ) F (E y np 3 np 45 + Xt (83) Ft (E45) np np s y' t y' where KY and KY are the spin-transfer parameters for the singlet and triplet components respectively. Using the simplified structure of the breakup.amplitudes, 7 ) characteristic of the Amado model, it is easy to show that 1 1 3 for for 1 + + H(d,p) 2 + +. H(p,p) t y' t y' Ky will depend yo~ angle and energy but an implication of BKMSW is that Ky is nearly the same as the KY parameters for elastic scattering. However in terms of the breakup amplitudes7) - _/3 Red*d l'4 1 2 1 + + for H(d,p) 2 + + for H(p,p), where q is the amplitude for breakup in the quartet state (S = 3/2), and d1 and d2 are the doublet-state (S = 1/2) amplitudes in which the two identical nucleons are coupled to spin 1 or 0, respectively. To a first approximation the slightly inelastic K~· parameters can be computed on the basis of a decomposition of the breakup cross section similar to that of BKMSW and a measurement of the corresponding ~· for elastic scattering. Thus a measurement of the K~'parameters have additional interest in that they provide additional checks of the final state interaction theory. We are currently working on the theoretical predictions using a computer code which solves the three particle Faddeev equation for separable spin dependents-wave nucleon nucleon interactions. 8 ) REFERENCES *work supported by the U. S. Atomic Energy Commission. 'tGuest scientist, Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 8 7 5 44. ., .. . 1. R. T. Cahil and I. H. Sloan, Nucl.:Phys. Al65 (1971) 161; W. Ebenhoh, Proceed~ngs of the International Conference on Few Particle Problems in the Nuclear Interactions, Los Angeles, California, 1972, edited by Slaus et al. (North-Holland, ~jterdam, 1972)' pp. 325-328. 2. w. M. Kloet and J. A. Tjon, Nucl. Phys. A210 (1973) 380. 3. 4. 5. 6. Mahavir Jain, J. G. Roger, and D. P. Saylor, Phys. Rev. Letters~ (1973) 838. D. D. Brayshaw, Phys. Rev. Letters ~ (1974) 382. M. I. Haftel and E. L. Peterson, Bull. Am. Phys. Soc. 19 (1974) 505. H. Bruckman, w. Kluge; H. Mattay, L. Schanzler and K. wick, Nucl. Phys. Al57 (1970) 209. 7. D. P. Saylor and F. N. Rad, Phys. Rev. C8 (1973) 507 8. Mahavir Jain and Gary b. Doolen, Phys. 'Rev. C8 (1973) 124. t" r------------------LEGALNOTICE---------------------This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express 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. .... ' ~ .. TECHNICAL INFORMATION DIVISION LAWRENCE BERKELEY LABORATORY UNIVERSITY OF CALIFORNIA BERKELEY, CALIFORNIA 94720 ~· :~ 

Final state interaction in three nucleon system

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