The fusion of 12C with 12C at projectile energies from 45 to 197 MeV

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Nuclear Physics A263 (1976) 491-499; (~) North-Holland Publishing Co., Amsterdam

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Not to be reproduced by photoprint or microfilmwithout written permission from the publisher

T H E F U S I O N O F t2C W I T H tZC AT PROJECTILE

E N E R G I E S F R O M 45 T O 197 M e W

M. N. NAMBOODIRI, E. T. CHULICK ,t and J. B. N A T O W I T Z Cyclotron Institute and Departmentof Chemistry, Texas A&M University, Colleoe Station, Texas 77843 Received 19 January 1976 AIma'act: Evaporation residues arising from the deexcitation of 2*Mg produced in the reactions of *zC with " C have been identified on the basis of energy and angular distributions measured with a semiconductor detector telescope. Excitation functions for the individual product elements have been obtained over the projectile energy range from 45 to 197 MeV. Evaporation residue cross sections for B and C were not directly measured because of interferences from other reaction mechanisms, but were determined from the systematics of the residue yields as a function of projectile energy and atomic number. Limiting angular momenta have been calculated from the summed yields of the evaporation residue cross sections. These limiting angular momenta are compared to limits predicted by several models.

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NUCLEAR REACTIONS *~C(*2C, X), E = 45, 75, 107, 155, 180, 197 MeV; measured o for product elements from Z = 1-12; deduced limiting angular momenta for fusion.

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1. Introduction M e a s u r e m e n t s o f fusion cross sections have been used to e x p l o r e the limits to the fusion process for a variety o f r e a c t i o n systems ~' 2). F o r light c o m p o u n d systems (A ~< 30) the technique has been e m p l o y e d o n l y at relatively low projectile energies because o f the difficulty e n c o u n t e r e d in s e p a r a t i n g the p r o d u c t s o f different reaction m e c h a n i s m s at h i g h e r energies. A n alternative technique, t h a t o f c o m p a r i n g the m e a s u r e d a n d c a l c u l a t e d yields o f light e m i t t e d species has been used in the light m a s s region 3 - 5 ) . This technique also becomes m o r e difficult to use at higher excitation energies because o f the d e c r e a s e d p r o b a b i l i t y o f p o p u l a t i n g a single, low-lying level in the e v a p o r a t i o n step a n d the increased p r o b a b i l i t y o f multiple particle emission. In the present w o r k we use m e a s u r e m e n t s o f the excitation functions for the p r o d u c t i o n o f e v a p o r a t i o n residues o f different a t o m i c n u m b e r s to derive the limiting a n g u l a r m o m e n t a for fusion o f t w o ' 2 C nuclei leading t o 24Mg nuclei with excitation energies as high as 113 MeV. Supported in part by US ERDA and the Robert A. Welch Foundation. tt Present address: Babcock and Wilcox, Lynchburg Research Center, Lynchburg, VA. 491

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2. Experimental procedure Solid-state counter telescopes employing three detectors were used to detect the products of the reactions of 12C projectiles with a 12C target which was 197/ag/cm 2 thick. The thicknesses of the three detectors in the telescope varied, depending upon the projectile energy and the ranges of the product elements to be identified. At the lower two projectile energies a first detector which was 4.9/~m thick was used. At the higher projectile energies, an 8.4/~m thick detector was used. Experiments were performed at six different projectile energies: 45, 75, 107, 155, 180 and 197 MeV. An IBM 7094 computer was used for data acquisition. Displays of the pulse height spectra from the individual detectors and of the correlated pulse heights from either the first and second or second and third detectors were employed to monitor the experiment. The pulse height data were simultaneously recorded, event by event, on magnetic tape. Data were taken at lab angles ranging from 4 ° to 165° relative to the direction of the incident beam. Following the experiment, the data were processed with the code BINIT 6) which identifies the detected ions using a table look-up technique. The identification tables are constructed using semi-empirical range energy tables 7) and pulse height defect CHANNEL 102

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data 8). Because the first detector was thin, isotopic resolution was not generally obtained. The data were binned in groups according to their elemental identity. As examples of the energy spectra observed in these experiments, we present in figs. 1 and 2, the spectra of N-ions and F-ions produced in the reactions with 107 and 197 MeV projectiles and detected at a lab angle of 6 °. The qualitative difference between the spectra of N-ions, differing in one atomic number from the target, and the F-ions, three atomic numbers removed from the target, is very apparent. The N-spectra have components extending almost to the full projectile energy. This component is absent in the F-spectra. The peaking of the forward-directed F-nuclei at energies close to 0.4 times the projectile energy is just what would be expected for F-evaporation residues with an average velocity equal to that of the recoiling composite 24Mg nucleus. Thus we take the entire spectrum of F-nuclei to represent evaporation residues of 24Mg. Those N-nuclei which are evaporation residues should have average energies of approximately 0.3 times the projectile energy at forward angles. The lower energy continua in the N-spectra do in fact consist of large bumps peaking at energies consistent with the average energy expected for N-evaporation residues. It is that

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portion of each of the N-spectra which we take to represent the yield of evaporation residues. Similar spectra observed for Be and O nuclei were treated in the same manner. Small corrections for losses due to detection thresholds were made to all the evaporation residue spectra. In fig. 3, the measured differential cross sections d¢r/d0 are plotted for N- and F-evaporation residues. Angular distributions obtained at 45, 107 and 197 MeV are presented. The dashed portions of the angular distribution curves indicates the extrapolation which was performed in order that the evaporation residue cross sections could be determined by integration over the angular distributions. In fig. 4 we present the excitation functions measured in this work for each of the product elements except carbon. The cross sections presented for those elements of Z = 3 and Z > 7 represent only the yields of products taken to be evaporation residues on the basis of the measured energy and angular distributions. Other cross sections are total elemental yields. As the projectile energy increases, the cross sections for the higher atomic number evaporation residues decrease. Over the same energy range the yields of the lighter elements (Z < 5) increase. Such a variation of excitation function with atomic number is consistent with increasing evaporation of light particles with increased excitation energy of the composite nucleus. However, contributions to the yields of the light nuclei from non-fusion processes are undoubtedly also present. A goal of this experiment was to obtain total fusion cross sections for the 12C+1zC reactions by measuring the fusion residue cross sections. At 45 MeV projectile energy, the fusion residue yields for Z > 7 give a summed cross section of 1020+ 100 mb. On the basis of the variation of the yield with Z, we estimate that the unmeasured fusion residue cross section for C is ~ 30 rob, much less than th: estimated experimental error of 10 % in the fusion cross section. However, as the projectile energy increases, the increased excitation energy of the composite system results in a shift of the residue yield distribution to lower atomic number. The unmeasured residue yields of C and B become increasingly significant. From our data we were unable to clearly separate B- and C-evaporation residues from the products of other reaction mechanisms. At the higher projectile energies it was possible to observe an apparent fusion residue component in the C-energy spectra observed at angles > 15 °. In order to estimate the residue yields of C at these higher energies, we have separated out that component and assumed that within 15° the angular distribution of the C-residues has the same shape as that of the N-residues. In this way we have arrived at cross sections for C-fusion residues of 287 mb at 155 MeV and 182 mb at 197 MeV. These cross sections are probably uncertain by + 25 %. In order to estimate the cross sections for C-fusion residues at the other energies, we have assumed that the C-excitation function has the same shape as that of N. To estimate the B-yields, we have plotted the yield distributions as a function of atomic number as shown in fig. 5. The B-yields have been obtained assuming a smooth variation of the yields with atomic number.

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Fig. 5. Yield distributions for evaporation residues produced in the fusion of ~zC with ~'C. Distributions are presented for projectile energie~ ranging from 75 to 197 MeV. Solid points with. error bars represent primary cross section data. Open circles represent the B and C cross sections determined from the interpolation method described in the text. The symbol × indicates residue cross sections determined by extrapolation of these yield curves. The cross-section scale on the left of the figure is for projectile energiea of 75, 155 and 197 MeV. The right-hand scale is for projectile energies of 107 and 180 MeV. Implicit in the procedure which we have employed is the assumption that the Be yield observed for projectile energies above 107 MeV represents evaporation residues rather than the light particles ejected from evaporation residues. Hanson and Stokstad 4,9) have calculated the cross sections for first and second chance evaporation of 7Be and 9Be in the deexcitation of 26A! produced in the fusion of I ' N with 12C at projectile energies of 90 and 157 MeV. Based upon these results we estimate that in the very similar system studied here, approximately 90 % of the Be yield measured at 155 MeV projectile energy and approximately 70 ~o of the Be yield measured at 107 MeV projectile energy corresponds to evaporation residues. We have summed the yields over the distributions indicated in fig. 5 to obtain total fusion residue cross sections. In table 1, these total fusion cross sections are

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Fig. 6. Limiting angular momenta for fusion in the reactions o f 12C with t2C. The limiting angular momenta (solid circles) derived from the evaporation residue cross sections reported in this paper are compared with various possible limits to the angular momentum o f the =*Mg nucleus. Data for the very similar systems I * N + t 2 C [ref. 3)] (open circles) and l a C + l ° B [ref. 5)] (open t~luar~) are also indicated. The long dashed line l a b e l e d / t , is the calculated maximum orbital angular momentum corresponding to a grazing collision. The two solid lines labeled Bass and CPS represent the theoretical fusion limits calculated by Bass lo) and by Cohen, Plasil and Swiatecki it). Three possible yrast lines for ='Mg are indicated. The dotted line represents the yrast line in 2*Mg as calculated by Cohen, Plasil, and Swiatecki. The short dashed line represents the yrast line o f a spherical rigid rotor assuming the moment of inertia is the same as that o f the 4 + level. The line composed o f dots and dashes represents a spherical rigid rotor with a moment o f inertia | m R 1. A radius parameter o f 1.25 fm was assumed.

presented together with limiting angular momenta which have been calculated assuming a sharp cut-off approximation, i.e.

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angular momenta as well as the angular momenta corresponding to the calculated yrast line in 24Mg. The latter has been calculated by using the moment of inertia indicated by the spacing of the lowest 2 + and 4 + levels of 2aMg. The experimental data, together with lines depicting the various predicted limits have been plotted in fig. 6. 3. Discussion

At the higher projectile energies the limiting angular momenta for the fusion of 12C+~2C into 24Mg are well below the maximum possible angular momenta for this reaction. The data are in good agreement with the prediction of the Bass model 10), a result which is entirely consistent with previous data obtained for the reactions of various projectiles with heavier targets 12). The possibility that in this mass region the limiting angular momentum reflects the energy dependence of the yrast line has been noted by several authors 1.3-5). As is apparent from fig. 6 the data are in fact very close to the yrast angular momenta which have been calculated for the 24Mg nucleus using the assumption of a rigid rotor. However, a 2*Mg nucleus deformed to the extent predicted by the LDM would be expected to have a significantly different yrast line. Very precise experiments employing different target projectile combinations to produce the same compound system might be used to distinguish between a dynamic entrance channel limitation and an intrinsic yrast limitation. At the highest kinetic energy, fused nuclei of 2~Mg have apparently been made with angular momenta equal to limits predicted using the liquid drop model. It is possible that a significant fraction of such fused nuclei eject relatively large fragments in the deexcitation step. In this mass region, the technique employed in this experiment does not allow us to separate such fission-like processes from other deexcitation modes. If such processes occur on a fast time scale, it might be that the fused composite system is not in fact a totally equilibrated compound nucleus. In such a case, these limiting angular

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momenta for fusion represent upper limits to the compound nucleus angular momentum.

We appreciate the assistance of R. Eggers, K. Geoffroy, P. Gonthier, K. Das, L. Webb and J. Bilbro with various portions of these experiments. We also thank the operations crew of the Texas A&M University Cyclotron Institute. References !) J. B. Natowitz, E. T. Chulick and M. N. Namboodiri, Phys. Rev. C6 (1972) 2133 2) J. Galin, D. Gucrreau, M. Lcfort and X. Tarra$o, Phys. Rev. C9 (1974) 1018 3) C. Volant, M. Conjeaud, S. Harar, A. Lepin¢, E. F. DaSilveira and S. M. Lee, Nucl. Phys. A238 (1975) 120 4) R. Stokstad, Proc. Int. Conf. on reactions between complex nuclei, Nashville, Tennessee, vol. 2 (North-Holland, Amsterdam, 1974) p. 327 5) H. V. Klapdor, H. Reiss and G. Rosncr, Phys. Lett. 58B (1975) 279 6) E. T. Chulick, J. B. Natowitz and C. Schnatterly, Nucl. Instr. 109 (1973) 171; E. T. Chulick, M. N. Namboodiri and J. B. Natowitz, Proc. Int. Conf. on the physics and chemistry o f fission, Rochester, New York, vol. 2 (1973) p. 365 7) L. C. Northcliff¢ and R. Schilling, Nucl. Data 7 (1970) 13 8) S. B. Kaufman, E. P. Steinberg, B. D. Wilkins, J. Unik, A. J. Groski and M. J. Fluss, Nucl. Instr. !15 (1974) 47 9) R. Stokstad, private communication 10) R. Bass, Phys. I.,¢tt. 4715 (1973) 139; Nucl. Phys. A231 (1974) 45 i !) S. Cohen, F. Plasil and W. J'. $wiatecki, Ann. of Phys. 82 (1974) 557 12) M. N. Namboodiri, E. T. Chulick, J. B. Natowitz and R. A. Kenefick, Phys. Rev. C I I (1975) 401