Alignment and resonances in 12C+12C inelastic scattering

Volume 135B, number 4

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9 February 1984

ALIGNMENT AND RESONANCES IN 12C+12CINELASTIC SCATTERING W. TROMBIK, W. TRAUTMANN 1, F. KRUG, W. DUNNWEBER, D. KONNERTH, W. HERING, R. SINGH 2 and D. ZEPPENFELD Sektion Physlk, Umversitat Munchen, D-8046 Garching, West Germany Recmved 28 June 1983 Rewsed manuscript recmved 16 November 1983

Using the out-of-plane 0,-ray particle coincidence method we have measured the spin ahgnment Pzz of exmted 12C(2+) nuclei from 12C+12Cinelastic scattering m the energy range 16 MeV < Ecm < 33 MeV. Pzz vanes strongly as a function of energy and angle The correlatmn of resonant structures in the cross seclaon with maxmaa of the alignment is parttcularly clear m mutual inelastic scattering and m 0cm = 90 ° single melastm scattering.

The occurrence of pronounced resonance-like structures in the excitation functions o f many exit channels of the system 12C+12C is well known since many years, but in spite o f a large amount o f data and appreciable theoretical efforts the resonance mechanisms are far from being completely understood [1 ]. Usually it is assumed that the strong intermediate structures are caused by the coupling of the entrance channel to specific doorway states. In most o f the proposed models (e.g. Double Resonance Model [2], Band Crossing Model [3]), the single 2 + (4.44 MeV) or mutual 2 +, 2 + inelastic excitations in 12C+12C are considered as the most important coupling partners of the entrance-channel configuration. This was experimentally corroborated by the measurement o f the inelastic excitation functions [4]. Furthermore, in nearly all models the spin alignment, i.e. the coupling configuration o f the relative orbital angular momentum and the intrinsic spin o f the 2 + state, plays a crucial role for the explanation of the observed structures. The majority o f the resonance models, but also non-resonant conceptions (e.g. Austern-Blair Model, ref. [5]) predict [1,6] a strong and generally energy1 Present address' Brookhaven National Laboratory, Upton, NY 11973, USA. 2 Present address. North-Eastern Hill University, Shlllong, India. 0.370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

dependent dominance o f the aligned configuration. Consequently, the maxima o f the inelastic excitation functions should be associated with large ahgnment. Some indications of such a correlation in the case of 160(12C, 12C)160*(3-) were recently reported by Kato et al. [7]. From our earlier measurements [8] of the alignment in 12C+12C at a limited number o f energies and angles we concluded that in single inelast/c scattering large cross section and large alignment are not necessarily correlated. However, the need to have a more extended set o f data available was obvious. Here, we report on detailed measurements in the energy range 16 MeV ~< Ecru ~< 32.7 MeV in steps varying between 0.1 MeV and 0.4 MeV. The ahgnment is determined for both single and mutual inelastic scattering, and the results will be compared to the excitation functions measured by Cormier et al. [4,9]. Some o f our conclusions concermng the single inelastic channel are in qualitative agreement with the work o f Erb et al. [101. The principle o f the experimental method is the following: The reaction plane is defined by the beam and the particle detectors, and the reaction normal represents the quantlzation axis. Gamma radiation, in coincidence with inelasticaUy scattered particles, is detected by two cylindrical NaI crystals positioned on either side o f the reaction plane with their axes coin271

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ciding wlttt the reaction normal. One detector (Nail, 27 cm X 33 cm) was collimated to 0.y ~< 11 ° whereas the other detector (NaI2,36 cm X 20 cm) was placed 11 cm from the target without collimation. Because of the different radiation patterns of substates with different Im l, the probabilities to detect a coincident 4.44 MeV 7-ray depend on the orientation of the emitting 12C(2+) nucleus. The narrowly collimated Nail records almost exclusively radiation from Im I = 1 states whereas NaI2 is by factors between 2 and 3 less sensitive to [rn [ = 2 than to m = 0 or Im I = 1 radiation (the absolute detection efficiencies for Im I = 2, 1,0 radiation were found, see below, to be 0.0004, 0.0212, 0.0012, respectively, for Nail and 0.0823,0.1542, 0.1805 for NaI2). Thus with this detector arrangement, the three population probabilities PI m I can be determined from the comparison of the two measured -/-particle coincidence rates with the known m-substate detection probabihties including the normalization condition P121 + P I11 + P0 = 1. In single inelastic scattering to the 2 + state the Iml = 1 substates are not populated according to Bohr's theorem [11 ] and, therefore, the coincident counting rate measured with NaI2 is sufficient to determine P I2 I and P0 = 1 - P I2 t. The alignment Pzz, which for a 2 + state is defined [12] as 1

Pzz = 2 ~m m2Pm - l' results directly from the determined population probabilities P Im I" Since interference effects cancel because of the azimuthal detection symmetry no information on the polarization is obtained. The absolute detector response for the various Im I-radiation patterns was determined with the aid of Monte Carlo calculations [13]. The results for isotropic emission were checked in experiments with calibrated 3,-ray sources. This procedure is least accurate for the efficiency of NaI2 to Iml = 0,2 radiation because of the weight given to the edges of the detector where the calculations are presumably less reliable. In fact, it was found necessary to correct these numbers by 8% in order to guarantee that the deduced alignment stays within the allowed range - 1 <~Pzz <~ + 1. The corresponding changes of Pzz which are ZkPzz ~ 0.15 (for single-inelastic scattering and Pzz > O) up to ~3.30 (mutual-inelastic scattering and/or Pzz < 0) are considered as upper limits to the overall 272

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systematic error. The relative variation of Pzz with energy and angle, however, is little affected by this uncertainty. The experiments were performed at the Munich Tandem Van de Graaff accelerator. The thickness of the self-supporting 12C targets (50 gg/cm 2) caused an energy spread small enough to avoid averaging over the intermediate structures. For particle detection and identification of the inelastic channels the method of kinematic coincidences as described in ref. t8] was used. The angles of the four particle detectors (about 19 °, 26.5 °, 34 °, and 41.5 ° lab) were sightly changed with bombarding energy in order to keep the fourth detector close to 90 ° (CM). In a second set of experiments at selected energies we recorded kinematic coincidences between two positxon sensitive detectors, enabling the determination of Pzz in the continuous angular range 45 ° ~< 0cm ~< 110 °. In a few cases this angular average has been derived from an experiment with the Heidelberg crystal ball (performed in order to study the spin-spin correlations in mutual inelastic scattering [14]). In single inelastic scattering the measured alignment varies strongly with energy and angle: over the whole energy range pronounced structures of Pzz with different strength, width, and regularity are observed. Especially at lower energies, structures of intermediate width occur which resemble the observed fluctuations of the cross sections [4,9] without being directly correlated. The strength of the fluctuations ofPzz(E ) rises with increasing particle angle and, at 90 ° (cm), reaches a remarkable degree of regularity (fig. I b). Averaging the alignment over the four particle angles (weighted by do/d0) smears out some of the fluctuations but the overall variations of Pzz are still large (fig. 1d). Three characteristic features of the resulting average Pzz are noteworthy: (i) Except for the low energies the alignment is smaller than expected from the angular momentum matching condition. The average level is near Pzz = 0.33 which is the value obtained for equal population of the m = +2, 0, - 2 substates. (i 0 In contrast, the alignment is generally high below 20 MeV but not correlated to the finer structures observed in this region. The maximum value (Pzz ~ 0.9) is reached near Ecru = 19.3 MeV which is the energy of strong and correlated resonances in many exit channels [ 1]. The large alignment in this energy

Volume 135B, number 4

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range is in qualitative agreement with the predictions of the band crossing model [3]. (iii) The gross structures of the excitation function, e.g. the peaks near Ecru = 24 MeV and 30 MeV (fig. lc), are reflected in the alignment which, however, hardly attains values exceeding 0.6 at these energies. This agrees with the results of a recent analysis [15] of in-plane angular correlations which indicates con. siderable non.aligned contributions to the broad maxima. In addition, intermediate structures may also be connected with distinct relative maxima ofPzz. We

9 February 1984

note the peak near Ecru = 26 MeV which appears weakly in the excitation function and does not emerge from the Austern-Blair description [5]. The same general picture also arises from the individual study of gross and intermediate structures with the aid of smoothed or trend corrected excitation functions [6]. Recent theoretical calculations [16] based on different models (e.g. strong coupling, Austern-Blair, and band crossing model) also predict values of Pzz which are generally larger than the measured ones. Although some broad structures ofPzz(E ) are reflected in the calculations the variation of Pzz is considerably smoother than found experimentally. Moreover, many details of the observed structures of the alignment are clearly not reproduced. Therefore, we can conclude that most of the proposed concepts do not do justice to the complexaty of the reaction mechanism in 12C+12C. Regarding the angular dependence of Pzz we find that at forward particle angles the shapes of the maxima of the cross section do not resemble those of the alignment whereas at 0cm = 90 ° and Ecru > 21 MeV the correlated behaviour of excitation function and alignment is rather remarkable (figs. 1a, lb). This may be connected to the fact that the probabihty to ob. serve processes proceeding via long-lived doorway states is enhanced at this angle. The detailed angular distributions of Pzz exhibit regular oscillations with 15°-20 ° spacing at some energies, while at other energies a rather smooth behaviour is observed. The appearance of these patterns is not correlated with the gross structures of the excitation function. The averages of Pzz over the broader angular range, as covered by the position sensitive detectors employed at selected energies, are given in fig. 1d. They differ only little from the four angle average which, therefore, is expected to be representative, i.e. the structures ofPzz(E ) discussed above will appear similarly in the total angular average. Most of the features found in single inelastic scattering are also present in mutual inelastic scattering (fig. 2). Although at lower energies variations of Pzz with intermediate width are still present, it is obvious that above 23 MeV the gross structures of a and Pzz are strongly correlated. Even the doublet structure of the maxima in the excitation function seems to be reflected in the alignment. At the energies of the maxima (around Ecru = 25.5 MeV and 31 MeV)Pzz 273

Volume 135B, number 4

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ng. 2). It seems that the distinctly correlated behaviour of the mutual inelastic scattering should be related to a particularly favourable configuration o f the 12C+12C system. Classically, it may be viewed as the rigid rotation o f two 12C nuclei where, according to the sticking condition, 2/7 o f the incoming spin are transformed into internal excitation. Near Ecru = 25.5 MeV where l z = 14/i has been associated with the observed resonance [4] this would correspond to 2 h for each nucleus. This may perhaps explain why the strong gross 274

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structures are confined to this region o f angular momenta. More generally, the (2 +, 2 +) exit channel - because o f its s y m m e t r y - may be more strongly connected to other imaginable, highly symmetric configurations, which also couple strongly to the symmetric entrance channel. In summary, the single inelastic data show pronounced structures which at 90 ° (CM) correspond to the maxima of the excitation function. F o r the more forward angles the degree o f correlation is moderate. Even at the maxama o f the cross section the dominance of the aligned configuration is not very marked and all models proposed thus far are not able to explain the results satisfactordy. In the mutual inelastic scattering the maxama o f the cross sections above 25 MeV are reflected b y a clear preponderance o f lm I = 2 as compared to the small Pzz measured off-resonance. This finding seems to point to a favoured connection of this symmetric channel to rather simple configurations. The authors gratefully acknowledge valuable discussions with Dr. U. Mosel, Dr. O. Tanimura and Dr. K.A. Eberhard. This work was supported b y the BMFT.

References [ 1] See, e.g.K.A. Eberhard, ed., Lecture Notes in Physics, Vol 156 (Springer, Berlin, 1982). [2] H.J. Fink et al., Nucl. Phys. A188 (1972) 259. [3] Y. Abe et al., Prog. Theor. Phys. 59 (1978) 1393. [4] T.M. Cormler et al., Phys. Rev. Lett. 38 (1977) 940 [5] R.L. Phflhps et al., Phys. Rev Lett. 42 (1979) 566. [6] W. Tromblk, m Lecture Notes in Physics, VoL 156, ed. K.A. Eberhard (Springer, Berhn, 1982) p. 297. [7] N. Kato et al., Phys. Lett. 120B (1983) 314. [8] W. Tromblk et al., Z. Phys. A296 (1980) 187 [9] T M. Corm*er, prwate commumcatlon. [10] K A. Erb, Invited talk Intern. Conf. on Resonant behavior of heavy 1on systems (Aegean Sea, Greece, 1980), as quoted by D.A. Bromley, m: Lecture Notes m Physics, Vol. 156, ed. K.A. Eberhard (Springer, Berlin, 1982) p. 3. [11] A. Bohr, Nucl. Phys. 10 (1959) 486. [12] R.J. Bhn-Stoyle and M.A. Grace, in Handbuch der Physik, VoL 42, ed. S. Fliigge (Springer, Berlin, 1957) p. 555. [13] M. Glannmi et al., Nucl. Instrum. Methods 81 (1970) 104. [14] D. Konnerth et al., work m progress; Contnb. Intern. Conf. on Nuclear physics (Florence, Italy, 1983). [15] D.P. Balamuth et al., Phys. Rev. C23 (1981) 2492. [16] O. Tanmaura and U. Mosel, Phys. Lett. 114B (1982) 7.