Ascuitto, R.J.

Glendenning, Norman K.

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Lawrence Berkeley National LaboratoryRecent WorkTitleON THE SYSTEMATICS OF THE INTERFERENCE BETWEEN DIRECT AND INDIRECT MODES IN TWO-NUCLEON PICKUP AND STRIPPING REACTIONS BETWEEN HEAVY-IONSPermalinkhttps://escholarship.org/uc/item/3sq793dzAuthorsAscuitto, R.J.Glendenning, Norman K.Publication Date1973-09-01eScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaSubmitted to Phys. Letters LBL-1987 Preprint ~,d.__ ON THE SYSTEMATICS OF THE INTERFERENCE BETWEEN DIRECT AND INDIRECT MODES IN TWO-NUCLEON PICKUP AND STRIPPING REACTIONS BETWEEN HEAVY -IONS R. J. Ascuitto and Norman K. Glendenning September 1973 RECEIVED LAWRENCE RA;)IATION LABORATORY OC1221973 LIBRARY AND DOCUMt;::NTS SECTION Prepared for the U. S. Atomic Energy Commission under Contract W -7405-ENG-48 TWO-WEEK LOAN COPY ·This is a Library Circulating Copy which may be borrowed for two weeks. For a personal retention copy, call Tech. Info. Division, 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 conect 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 wananty, 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- LBL-1987 ON THE SYSTEMATICS OF THE INTERFERENCE BETWEEN DIRECT AND INDIRECT MODES IN TWO-NUCLEON PICKUP AND STRIPPING REACTIONS BETWEEN HEAVY-IONS* R. J. Ascuitto Wright Nuclear Structure Laboratory Yale University New Haven, Connecticut 06520 and Norman K. Glendenning Lawrence Berkeley Laboratory University of California Berkeley, California 94720 September 1973 The interference between direct and indirect modes of excitation of vibrational states in two-nucleon transfer reactions a:r·e of opposite sign for stripping as compared to pickup reactions. If the indirect modes are sufficiently strong, destructive interference gives rise to a dip in the angular distribution at the grazing angle, compared to the normal shape when the interference is constructive. The absolute sign of the interference may change through a string of isotopes thus revealing details of the structure of vibrational states not accessible through other experiments~ The effect of indirect transitions on two-nucleon transfer reactions involving light projectiles was calculated to be strong for spherical vibrational nuclei [1], and in the case of deformed nuclei, the experimental confirmation of the effect was very striking [2,3]" Such effects must therefore be anticipated in heavy ion reactions. Unfortunately, our knowledge.of the strength of inelaotic cross sect.ioll!:l is not so complete a!; yet for heavy ions dS to make * Work performed under the auspices of the u. s. Atomic Energy Commission. -2- LBL-1987 the magnitude of the effect so certain. Nonetheless, there is an indication that the deformation constant, B, deduced from proton and heavy ion scattering ~ are nearly the same [4]o We use this literally in fixing the strength of the inelastic branch in our calculations, but there is an uncertainty at this point. In this note, we point out the possible existence of systematics in the interference between direct and indirect modes that would reflect on intimate details of the structure of vibrational stateso d 1 . h 120 (180 160) .. h' h h' • We reporte ear 1er on t e Sn , react1on w 1c ex 1b1ted a strong destructive interference between the direct and indirect modes of . . h + . 122 [ 5] exc1t1ng t e 2 state 1n Sn " Here we point out that the interference is of opposite sign in the stripping and pickup reactions to vibrational states. This is illustrated in figs. 1 and 2 for both heavy and light tin isotopes. Since both direct and indirect modes have cross sections which are peaked near the grazing angle [5], the interference can actually produce a dip at the grazing angle if the indirect amplitudes are sufficiently close in magni-tude to the direct. This is calculated to be the case for the 2+ state of the heavy tin isotopes, fig. 1, where the dip is readily apparent for the stripping reactiono This is in contrast to the pickup reaction where the interference is constructive and the resultant cross section therefore has the "normal" shape. The indirect modes are calculated to be unimportant for the ground state transitiono They are not as strong in the light isotopes even for the 2+ and consequently no interference dip occurs there, figo 2. At this p9int'we note that the details of our results depend upon the structure of the nucleio These calculations employed a two-quasiparticle description of the vibrational state [6]o An R.P.A. calculation could have .-3- LBL-1987 produced quantitatively different results. However, both descriptions would have led to an opposite sign of the interference for stripping.and pickup though they would not necessarily agree on the absolute sign. The parentage amplitudes connecting the four states shown in fig. 3 are given by [7,8} = 1 ( 2J+l ) T l+cab = ( 1 ) ! - l+oab , where S is defined in general as 1 = r <2J +1) (l+o b> ] 2 P a (1) (2) (3) (4) (5) where d+ creates a particle in the state n t j • In the production of the a a a a I ground state in both stripping and pickup reactions, transitions 1 and 4 are indirect~ while 2 is the direct amplitude for pickup and 3 is the direct amplitude for stripping. The opposite sign of these amplitudes, 2 and 3, is what determines their opposite interference characteristics with the direct modes. -4- LBL-1987 The situation is different for production of the ground states. Both 2 and 3 are the lo·west order indirect modes and since they are of opposite sign they tend to cancel each other accounting for the weak indirect " I contribution to the ground state transitions. we have so far remarked on the opposite signs of the two parentage amplitudes. For two quasiparticle states {TDA) the <P are zero and the lj;ab are to be identified with the quasiparticle amplitudes nab of our earlier paper [B). In this case the absolute sign of the interference is that illustrated by our figures, and is destructive for stripping. However 6 the form of the parentage amplitudes admits a more complex behaviour. For example, through a series of isotopes the relative importance of ljJ and <P could change. At the same time the U and V factors are changingo It could then happen that the absolute sign of i:he 8's would be opposite for light and heavy members of an isotopic series, and that in the neighborhood of the change, the two amplitudes would not necessarily have opposite signs. A systematic study of pickup and stripping reactions throughout a series of isotopes {or isotones for proton transfer) is therefore likely to yield structural details that have not been accessible in other experiments. APPENDIX The parameters and nature of the calculation reported here were described in refo 5 except that here we generated single-particle states in a Woods-Saxon potential, all having a binding of one-half of the two.neutron separation energyo These are used as the basic states from which the nuclear states are built. Earlier we had used an average potentiaL The difference I in the final ~esults is slight. •./ -5- LBL-1987 REFERENCES 1. N. Ko Glendenning, Proc o International Confo on Properties of Nuclear States, ed. by Mo Harvey, (University of Montreal Press 1969) 245: Ro J. Ascuitto and N. Ko Glendenning, Physo ReVo C 2 (1970) 1260; ibid 181 (1969) 1396 2o Ro J. Ascuitto, No Ko Glendenning and Bo Sorensen, Phys. Rev. Letters 34B (1971)_ 17; Nucla Phys. ~ (1972) 60 3o T. Tamura, D. Ro Bes, Ro Ao Broglia and s. Lansdowne, Phys. Rev •. Letters 25 (1970). 1507 and errata 26 (1971) 156 4. F. Da Becchetti, D. Ga Kovar, Bo Ga Harvey, J;, Mahoney, B • Mayer and .. F. Ga Puh1hofer, Physa Rev a C6 (1972) 2215 -5. Ra J. Ascuitto and No Ko Glendenning, Physa Letters 45B (1973) 85 and -Symposium pn Heavy-Ion Transfer Reactions, Argonne, Ill. (1973) 513a Figure 9 in the Symposium also shows the effect of changing the sign of the interference 6. Ra Arvieu and Mo Veneroni, Campt. Rendo ~ (1960) 992; Ra Arvieu, Annales dE:! Physique (Paris) ,!! (1963) Series 13 7. So Yoshida, Nucla Physo ~ (1962) 685 So Ra Jo Ascuitto and No Ko Glendenning, Physo Revo C2 (1970) 415 ..... ~ ·' : •. ~(. ' > .·•· -6- LBL-1987 Figure Captions Figo 1. The stripping and pickup cross sections for the ground state and 2+ state, c~puted with direct and indirect transitions (CCBA)o The indirect ·transitions almost cancel each other for the ground stateo However, for the 2+, they interfere destructively with the direct, for the stripping reaction, producing the dip at the grazing angl~o For the pickup reaction, they interfere constructively and preserve the characteristic peak at the grazing angle. The two ground state cross sections would be time reversed reactions,except for the finite Q-value and the use of the 100 MeV incident energy for·. each. Figo 2. This figure contains material analogous to fig. 1 for the light end of the tin isotopeso Here the indirect transitions are weaker compared to the direct than was the case for the heavy isotopes of figo lo Consequently the difference in the 2+ sta_tes is smaller o Cross sections are in mb,/s!:"~ The top scale refers to the o+ and the bottom to the 2+ stateo Fig. 3. The parentage amplitudes, Eqso 1, o•o 4, correspond to the four connections shown hereo The transitions 2 and 3 have opposite signo Since they are each a segment of the two second order transitions!to the ground in both pickup and stripping, they tend to cancel each other, yielding a ffinall second order contribution to the ground stateo For the 2+ state ~owe"·er, 2 is direct for a pickup reaction and 3 is direct for stripping, while 1 and 4 are segments of the second order routes. The opposite sign of 2 and 3 implies opposite interference of direct and indirect transitions in stripping compared to pickup~ j • '·' 0 -7-120Sn+180 ~122Sn+ 160 E=100 MeV ...... ··. 0 ··,· .. 2 ...... .. ·. . . . .. ·· .,_ · ... . . . . . . .. .... . . ..... ····· •··· ... .... .... r . .: .· '!:'\:. , .. Stripping Pick- up 10 ao 30 40 50 e Fig. 1 eo LBL-1987 CCBA TO 80 80 . XBL 738-1086 0 -8-112 s . 18 ~ 114 s + 160 ·. n+ 0 .,__ n Stripping Pick-up tO ao E=100MeV ...... ... .. 0 .. .. 2 ·,. ··· ..• . . ········. . ·. ·· .. · .. ·. .......... 30 40 50 0 Fig. 2 . . . . . . . . . '.. eo . . . \ . . CGBA . . . TO 80 eo XBL 738-108 7 LBL-1987 I '" I -9-4 ~ ~ I (A+ 2) Fig. 3 LBL-1987 J ---0 (A) XBL 739-1244 .------------------LEGAL NOTICE---------------------. 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 ,.. .. ~ 

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ON THE SYSTEMATICS OF THE INTERFERENCE BETWEEN DIRECT AND INDIRECT MODES IN TWO-NUCLEON PICKUP AND STRIPPING REACTIONS BETWEEN HEAVY-IONS

https://escholarship.org/uc/item/3sq793dz

ON THE SYSTEMATICS OF THE INTERFERENCE BETWEEN DIRECT AND INDIRECT MODES IN TWO-NUCLEON PICKUP AND STRIPPING REACTIONS BETWEEN HEAVY-IONS

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