Differential recoil range measurements as a probe of heavy ion reaction mechanisms

Volume 116B, number 6

PHYSICS LETTERS

28 October 1982

DIFFERENTIAL RECOIL RANGE MEASUREMENTS AS A PROBE OF HEAVY ION REACTION MECHANISMS D.J. PARKER, J. ASHER, T.W. CONLON and I. NAQIB 1 Nuclear Physics Division, A E R E Harwell, UK

Received 5 April 1982 Revised manuscript received 8 July 1982

Comparison of measured differential recoil range distributions for radioactive residues from heavy ion reactions having the common compound nucleus 6aCu with those calculated assuming statistical evaporation confirms this mechanism for the entrance channel 12C + SlV, but reveals and quantifies pre-equilibrium processes in the channel 7Li + S6Fe. Measured excitation functions also show features consistent with these results.

For interactions of heavy ions at medium energies (up to 10 MeV/amu), the reaction cross section is expected to be dominated by statistical evaporation from a compound nucleus. Modern computer codes allow detailed calculations o f the statistical mechanism with explicit treatment of angular momentum. At the same time, deviations from predicted statistical behaviour have been observed and attributed to so-called preequilibrium processes. Such processes result in reduced momentum transfer to the product residues, and may also be revealed by discrepancies between observed cross sections and statistical model predictions. The recoil ranges of product residues have been used previously as an indication of reaction mechanism [ 1,2]. Although some differential range distributions have been measured, and their potential for discriminating between reaction mechanisms pointed out, quantitative analysis has been concentrated on the mean recoil ranges. The purpose of this letter is to report a series of measurements of differential range distributions from which the relative contributions o f statistical and pre-equilibrium reaction mechanisms are explicitly separated by Monte Carlo modelling. This analysis is applied systematically in combination with excitation function measurements, for two entrance channels to the same 1 Permanent address: Physics Department, University of Kuwait, Kuwait. 0 031-9163/82/0000--0000[$02.75 © 1982 North-Holland

compound nucleus. One of these shows behaviour entirely consistent with statistical evaporation, while for the other up to half of the reaction cross section is demonstrably diverted into non-statistical processes. We have chosen to study a particular compound system, 63Cu, formed with the same excitation energy through several different entrance channels. According to the statistical model, such reactions should differ only because o f the different angular momenta brought in through the various entrance channels - an effect accounted for in appropriate statistical model calculations - so that a single set of input parameters should be valid for all entrance channels. 63Cu can be formed in several different ways by fusion of a pair of stable nuclei and many of its product residues are radioisotopes that can be accurately quantified by off-line 3'ray spectrometry. In this letter we concentrate on the entrance channels 7Li + 56Fe and 12C + 51V. Firstly excitation functions for the production of various radioisotopes from these entrance channels were measured up to a 63Cu excitation energy of about 100 MeV and compared to the predictions of a recent and widely used statistical model code, CASCADE [3]. Secondly, recoil range distributions measured at selected energies in each entrance channel for particular products recoiling into aluminium catchers were compared with those calculated using a Monte Carlo program assuming statistical evaporation. 397

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In both sets o f measurements the 12C + 51V channel shows behaviour fully consistent with a true statistical mechanism, while the 7 Li. + 56 Fe channel shows anomalous behaviour attributable to pre-equilibrium processes. The measured distributions provide insight into these processes. Fig. 1 shows as histograms our excitation functions, measured by a stacked foil technique, for the production of seven radioisotopes from these two entrance channels and also from the entrance channel a + 59C0. Beams of a, 7Li and 12C from the Harwell Variable

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Energy Cyclotron (VEC) were used to bombard foil stacks of Co, Fe and V respectively (all o f natural isotopic abundance). The yield of each radioisotope in each foil was then determined by ")'-ray spectrometry. The experimental uncertainties on these measurements are typically + 10%. Also shown in fig. 1 at higher energies in the ct + 59Co channel are the published results o f Michel and Brinkmann [4] obtained in a similar way. Since there was uncertainty in the overall normalisation o f our results for this channel (but not for the other two) we have taken our normalisation from their data.

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28 October 1982

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Fig. 1. Excitation functions for the production of seven radioisotopes from three entrance channels as a function of excitation energy of the common compound nucleus 6aCu. 398

Volume 116B, number 6

PHYSICS LETTERS

compound nucleus formed must recoil with the full momentum of the incident ion. Subsequent particle emission perturbs the recoil velocity of the residue, but this simply broadens the velocity distribution without charging its mean, provided that such emission is due to statistical evaporation which is symmetric about 90 ° (CM). However, if pre-equilibrium processes are present, then a significant fraction of the initial momentum will be removed by fast forwardly-emitted light particles, reducing the recoil velocity and range of the residues. The recoil range distributions, projected parallel to the beam axis, were measured by irradiating a thin target of Fe or V, mounted in front of a stack of A1 catcher foils of measured thicknesses, with a 7Li or 12C beam respectively from the VEC. The distribution of product

The smooth curves in fig. 1 are the predictions of the statistical model code CASCADE of Piihlhofer [3], which treats angular momentum explicitly. The total fusion cross section was calculated as a function of incident energy for each entrance channel from the parametrisation of Horn and Ferguson [5]. Default values were used for all the other parameters required. The agreement between the CASCADE predictions and our measured cross sections for the 12C entrance channel is excellent, considering that no attempt was made to adjust the parameters of the calculation. For the other entrance channels there are features in the excitation functions that CASCADE cannot reproduce. Measurement of the recoil ranges of the product residues in a stopping medium gives a direct indication of their recoil velocity. If complete fusion occurs, the

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28 October 1982

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Fig. 2. Recoil range distributions for products of reactions (a) 12C + Sl V at a 6aCu excitation (Ex) of 43 MeV and (b) 7Li + 56Fe at E x = 51 MeV.

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radioisotopes through the stack of catchers was subsequently determined by "/-ray spectrometry. The resulting data are accurate to approximately -+10%. For the 12C + 51V entrance channel at all the energies studied, the measured recoil range distribution for each residue is approximately symmetric about its mean depth, and this agrees with the expected range of the compound nucleus. The set of measured distributions shown in fig. 2a (solid histograms) is typical and corresponds to a 12C incident energy of 36 MeV (a 63Cu excitation energy, Ex, of 43 MeV). The distributions for 58Co and 57Co, whose production involves emission of an a-particle from the compound nucleus, are broader than those for 61Cu and 6°Cu which involve only nucleon emission, reflecting the greater perturbation of momentum by a-emission. The dashed histograms in fig. 2a show the range distribution for each product calculated by Monte Carlo modelling of the statistical evaporation process from a 63Cu compound nucleus. The kinetic energy spectrum for each emitted particle was taken from the output of CASCADE, and the angular distribution assumed emission only in the equatorial plane of the emitting nucleus [da/d~2 cc (sin 0)-1]. An alternative angular distribution, isotropic in centre of mass, gave similar results by slightly poorer agreement overall. The calculations for 58Co represent the average of those with successive evaporation of a, n and n, a, and those for 57Co, the average of a, n, n and n, n, a. Full details of all experimental measurements, the Monte Carlo evaporation program and the CASCADE calculations appear elsewhere [6]. The good agreement between the measured and predicted range distributions, evident for all the evaporation residues measured from the 12C + 51 V entrance channel up to a 63Cu excitation energy of 83 MeV, is a convincing demonstration of the statistical nature of the reaction mechanism over this energy range. The fact that the CASCADE calculation for this channel also accurately reproduces the measured cross sections (fig. 1) confirms that this code is appropriate for this channel, and that the features it cannot reproduce in the other entrance channels are due to non-statistical behaviour. The measured range distributions for the 7 Li + 56Fe entrance channel differ dramatically from those described above. Many are asymmetrically peaked at very low ranges, corresponding to low momentum transfer 400

28 October 1982

to the produce residues, which confirms the presence of pre-equilibrium processes. At all energies this effect is seen consistently and exclusively for isotopes whose production may involve emission of an a-particle, suggesting that it is due to pre-equilibrium a emission; the other observed isotopes have range distributions consistent with purely statistical evaporation. A typical set of range distributions for the 7Li + 56Fe channel (E x = 51 MeV) is shown in fig. 2b. Just as the 60Cu distribution is statistical, the 58Co and 57 Co distributions must include a statistical contribution. The dashed histograms in this figure show the predictions of the statistical Monte Carlo program, normalised to the measured distributions over the upper quartile of the statistical distribution. In this way we can estimate what proportion of these cross sections is statistical with an uncertainty of about 15%. Comparison with the original CASCADE predictions suggests that

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Fig. 3. Difference between measured and calculated (statistical) range distributions from fig. 2b. Also shown is the equivalent CM angle of a-emission from an optimum Q-value transfer reaction.

Volume 116B, number 6

PHYSICS LETTERS

approaching half the expected fusion cross section has been diverted into a pre-equilibrium mechanism. Subtraction of this normalised statistical distribution from each measured range distribution gives the pre-equilibrium range distribution; the resulting distributions for 58Co and 57Co from fig. 2b are plotted in fig. 3. A possible pre-equilibrium mechanism in the 7 Li entrance channel involves the transfer reaction 56Fe(7Li, a)59Co *, forming an excited 59Co intermediate which then decays by particle evaporation. An alternative route, 56 Fe (7 Li, t)6°Ni *, is also possible, but comparison of the optimum Q-value for the transfer reaction with the excitation energy required by the intermediate to give the observed products suggests that the former route is more likely to be responsible for the production of 58Co and 57Co at these energies. Assuming that the first stage is the transfer reaction 56Fe(7Li, a)59Co * with a particular Q-value, there is a unique relationship between the angle of emission of the a-particle and the projected recoil range of 59Co. In fig. 3 the corresponding a-particle angle of emission (centre of mass) is also shown, assuming optimum Qvalue for the transfer reaction. This is only a general indication; the angular scale varies slightly according to the choice of Q-value. Subsequent neutron evaporation from 59Co* will broaden the range distribution, but if the mechanism is as described above it should be possible in principle to extract from fig. 3 the original aparticle angular distribution. This is clearly forward peaked as expected. In conclusion, a comparison of measured recoil range distributions with the predictions of a statistical evaporation calculation provides conclusive evidence of whether pre-equilibrium processes are present in a particular reaction. Although codes such as CASCADE accurately predict the results of pure statistical processes,

28 October 1982

comparison of isolated cross sections with statistical model predictions is insufficient to determine whether a particular cross section is entirely statistical. For example, in the 7 Li + 56 Fe entrance channel at E x = 51 MeV the superficial agreement between the statistical model prediction and the measured cross section for production of 57Co is fortuitous since the recoil range measurements indicate that half of this cross section is non-statistical. The presence of pre-equilibrium processes reduces the total cross section for purely statistical processes; although the production of 6°Cu under the same conditions is purely statistical, the cross section is significantly less than that originally predicted by the statistical model. The advantage of measuring detailed range distributions, rather than mean ranges, is that the statistical and pre-equilibrium components can be explicitly separated and quantified without making a priori assumptions as to the nature of the pre-equilibrium processes present. Moreover, the component of the range distributions corresponding to these processes contains information on their nature. It is planned to confirm the preliminary conclusions reached here by complementary measurements of the inclusive light particle spectra from these reactions.

References [1] J.M. Alexander and L. Winsberg, Phys. Rev. 121 (1961) 529. [2] J. Jastrzebski et al., Phys. Rev. C19 (1979) 724. [3] F. Piihlhofer, Nucl. Phys. A280 (1977) 267. [4] R. Michel and G. Brinkman, Nucl. Phys. A338 (1980) 167. [5] D. Horn and A.J. Ferguson, Phys. Rev. Lett. 41 (1978) 1529. [6] D.J. Parker et al., AERE R-10408 (1982), and to be published.

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