Compound and precompound processes in (p, p′) and (α, p) reactions of even Zn isotopes

Nuclear Physics A277 (1977) 413--428; ~ ) North-HoUand Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

COMPOUND AND PRECOMPOUND

P R O C E S S E S I N (p, p')

A N D (~, p) R E A C T I O N S O F E V E N Z n I S O T O P E S c. R. LUX and N. T. PORILE Department of Chemistry, Purdue University, Lafayette, Indiana, USA 47907t Received 22 March 1976 (Revised 16 July 1976) Abstract: Energy spectra of protons emitted in the reactions of e4Zn, 66Zn, 6sZn, and 7°Zn with

12.5 MeV protons and 18 MeV 4He ions were measured between 30° and 150° to the beam. The contribution of the precompound process was determined on the basis of the asymmetry

in the angular distribution and by comparison of the spectra with calculations based on the compound and precompound models. Both methods indicate that the contribution of this process increases from ~ 5 Y. for e4Zn to ~ 20 ~o for 7°Zn. The ratio of proton to neutron evaporation widths is found to depend strongly on target neutron number and a correlation is established with the corresponding separation energies. NUCLEAR REACTIONS 6aZn(p, p'), 66Zn(p, p'), 68Zn(p, p'), 7°Zn(p, p'), E = 12.5 MeV; e4Zn(u, p), 66Zn(~, p), 68Zn(~, p), 7°Zn(~, p), E = 18 MeV; measured proton spectra between 30° and 150"; deduced relative contribution of compound and precompound processes.

1. Introduction

Nuclear reactions populating states in the c o n t i n u u m involve either c o m p o u n d nucleus f o r m a t i o n or preequilibrium decay. The properties o f c o m p o u n d nuclear reactions are fairly well understood and their description by the statistical theory has been the subject o f n u m e r o u s experimental tests 1-26). While this t h e o r y has been remarkably successful in accounting for a variety o f data it has generally been unable to explain the relatively large n u m b e r of energetic particles emitted in nuclear reactions. These particles are t h o u g h t to be emitted prior to the attainment of statistical equilibrium and the p r e e o m p o u n d model has successfully accounted for this feature o f the data 27). I n the present study we examine the interplay between these two types o f processes over a n a r r o w mass region and focus specifically on the effects o f binding energy variations. We have measured the energy spectra o f protons emitted in the reactions o f four even isotopes o f zinc w i t h 12.5 protons and 18 M e V 4He ions. The energies required to separate a p r o t o n or neutron f r o m the c o m p o u n d nucleus vary in a systematic way with target n e u t r o n n u m b e r and lead to large changes in the magnitude o f the c o m p o u n d nuclear cross sections. Binding energy differences play a m u c h t Work supported by the US Energy Research and Development Administration. 413

414

C.R. LUX AND N. T. PORILE

smaller role prior to the attainment of statistical equilibrium so that the precompound contribution should be much less affected by such a change. The spectra reflect the relative importance of these two mechanisms and vary in both shape and magnitude. The angular distributions also change in a regular way. We present both a phenomenological analysis of the data as well as a detailed comparison with theory. The spectra expected for compound nucleus formation are obtained by means of the spindependent statistical model 9, 28) while the preequilibrium spectra are based on the quasi-free scattering model 29). Cohen and collaborators 2, 7, 16, 2+, 25) have previously measured similar spectra from a series of isotopic targets. A comparison with their work is presented.

2. Experimental Targets of 64Zn, 66Zn, 6SZn, and 7°Zn were irradiated by 12.5 MeV protons and 18.0 MeV 4I-Ie ions and the energy spectra of the emitted protons were measured at 30 ° intervals between 30 ° and 150 °. The experiments were performed with beams from the Purdue tandem Van de Graaff. The experimental procedure has been described in previous reports from this laboratory 14, 15, 20, 23). Briefly, the emitted charged particles were detected by a counter telescope consisting of two surface-barrier detectors. Particle identification was based on the power-law method 30). The energy spectra were recorded with a two-parameter computer-based analyzer equipped with magnetic tape readout. Background was negligibly small in all cases. The beam intensity was determined by digitizing the current collected in a Faraday cup attached to the beam line and was also monitored by a detector located at a fixed angle to the beam. Targets were selfsupporting metallic foils having an isotopic enrichment > 98 ~o for all but 7°Zn, which had an 80 ~ enrichmentt. Target thicknesses ranged from 1.1 to 1.5 mg/cm 2 as determined by energy loss measurements performed with an 2+1Am ~-source.

3. Results The data were processed by computer in order to obtain energy spectra and angular distributions in the c.m. system and to remove lines due to light-element impurities 31). The differential cross sections obtained for each target were corrected for the contributions from the other zinc isotopes present on the basis of the known isotopic composition of the targets. This correction was only significant for 70Zn" As an example of the data fig. 1 shows the c.m. energy spectra obtained at 150° for 6#Zn and 7°Zn. All the spectra feature broad evaporation peaks followed by discrete lines at the higher energies. In addition, the spectra for 70Zn show the occurrence of a subsidiary peak at 2 MeV which can be ascribed to the emission of protons following low-energy neutron emission (~). * Obtained from Oak Ridge National Laboratory.

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The angular distributions of the evaporation-like protons are shown in fig. 2. In preparing these plots the energy spectra were integrated over the continuum but the small ~ peaks were excluded. The spectra were smoothly extrapolated at the highenergy end by following the envelope under the discrete peaks. The error bars in the angular distributions are a measure of the uncertainties, chiefly those in current integration, extrapolation to high energies, and impurity peak removal. It is seen that the (x, p) spectra are symmetric about 90 ° to the beam direction and, in fact, are nearly isotropic. On the other hand, the (p, p') spectra tend to peak at forward angles. A more detailed view of the angular distributions is shown in fig. 3 in terms of plots of dtr/df2 for successive 2 MeV energy intervals. The plotted data are for 68Zn but they are typical of all the targets. The (~e,p) angular distributions are indeed largely isotropic although some forward peaking may be noted for the highest energy protons. By contrast, the (p, p') angular distributions are forward-peaked for all energies. It is noteworthy in this case that while the lower energy protons do exhibit an isotropic component at large angles the values of da/dt2 for the highest energy protons decrease monotonically with increasing angle.

416

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418

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TABLE 1 Results for (p, p') and (g, p) reactions induced by 12.5 MeV protons and 18.0 MeV 4He ions on zinc isotopes Target

64Zn 66Zn

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The cross sections of the (p, p ' ) and (~, p) reactions were obtained by integration of the differential cross sections over energy and angle. In order to estimate the magnitudes of the differential cross sections below 30 ° and above 150 ° angular distribution curves such as those shown in fig. 3 were linearly extrapolated to 0 ° and 180 °. The results are summarized in table 1 where the uncertainties include in addition to the ones mentioned above those in target thickness, current integration, solid angle determination, and extrapolation to 0 ° and 180 °. Figs. 4 and 5 show the proton energy spectra integrated over angle. Both the energy spectra and the cross sections show that the probability for proton emission increases in a marked way with decreasing target neutron number. However this increase does not occur uniformly for all channel energies but appears to be concentrated in the region of the evaporation peak. The spectra for the heavier targets thus are considerably flatter and the yield of highenergy protons from 7°Zn is actually higher than from 68Zn. It m a y also be noted that the (~, p) cross sections decrease relative to the (p, p ' ) cross sections with increasing neutron number. These various features of the data will be considered in terms of the relative contributions from compound and precompound processes.

4. Phenomenological analysis of data 4.1. PREEQUILIBRIUM EMISSION FROM ANGULAR DISTRIBUTION MEASUREMENTS One possible way of distinguishing between compound and precompound processes is on the basis of the angular distribution of the emitted particles. Due to the long lifetime of the compound nucleus the angular distribution of evaporated particles must be symmetric about 90 ° to the beam direction. By contrast, precompound emission generally occurs before the directionality of the cascade initiated by the projectile has been dissipated and so tends to be predominantly at forward angles. This is particularly noticeable for the most energetic particles which, as shown in fig.

C O M P O U N D A N D P R E C O M P O U N D PROCESSES

419

3, exhibit the greatest degree of forward peaking. The extent of forward-backward asymmetry thus provides a measure of the contribution of the preequilibrium process. The result must be regarded as a lower limit since some precompound emission undoubtedly occurs at backward angles. Monte Carlo cascade calculations 32) indicate that at low energies cascade protons from (p, p') reactions are in fact predominantly emitted at forward angles. For instance, in 39 MeV proton bombardment of iron 95 Y/o of the protons are ejected into the forward hemisphere. The angular distribution may thus provide a reasonable way of estimating the precompound contribution at the energies of present interest. We have estimated the preequilibrium contribution to the (p, p') and (~, p) reactions on the assumption that only the excess forward protons are due to this process and show the results in fig. 6. It is seen that the preequilibrium contribution increases monotonically with target neutron number, varying from (7+4) ~ to (19+4) ~o for the (p, p') reaction and from (4+5) ~ to (27+5) ~o for the (~, p) reaction. It is of interest to note that while the precompound contribution can become quite significant under favorable conditions even at the rather low energies of present interest, the compound nuclear mechanism predominates in all cases. It may also be noted that while for the lighter Zn targets the precompound contribution to the (p, p') reaction is more significant than that to the (ct, p) reaction the opposite result is obtained for 7°Zn. The former result is understandable as a manifestation of precompound inelastic scattering and the latter may be a consequence of the enhancement in the compound nuclear (p, p') cross section due to isospin conservation, an effect that is discussed in a subsequent section. This enhancement, which does not occur for the (~, p) reaction, reduces the relative contribution of precompound emission below that observed for the (~, p) reaction on 7°Zn. To be sure these effects are only marginally significant since the uncertainties in the decomposition of the data are sizeable.

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420

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4.2. NUCLEAR TEMPERATURE ANALYSIS The constant temperature approximation to the spin-independent statistical theory allows a simple comparison of the various reactions. As suggested by the angular distribution data the temperature extracted from the 150 ° spectra should be indicative of compound nuclear processes while that obtained from the 30 ° data should in addition reflect the contribution of preequilibrium emission. The nuclear temperature may be obtained in the usualway from a plot of log [(d2cr/dedf2)/eainv] versus channel energy ,. The cross section for the inverse reaction, alnv, may be obtained from an optical model calculation. The nuclear temperature plots for the (p, p') reaction are shown in fig. 7. The 150° spectra yield plots of high linearity and the 30 ° spectra, while exhibiting considerably more scatter, are also reasonably linear. The results obtained from the (,e, p) spectra .3~

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COMPOUND AND PRECOMPOUND PROCESSES

421

are very similar. The temperatures may be obtained from the slopes of the lines through the points and the results are summarized in table 1 where the uncertainties include those in the input data as well as that arising from the least-squares fit. The (p, p') temperatures obtained from the 150° data are all in the vicinity of I. 1 MeV while those obtained from the 30 ° data are substantially higher. This difference reflects the fact that the spectra obtained at forward angles are composed of relatively more energetic protons as expected from the preequilibrium contribution at these angles. The uncertainty in the temperatures is unfortunately too large to show whether the previously noted mass dependence of the precompound contribution is also reflected in the present analysis. The (c,, p) temperatures exhibit a similar differnece between backward and forward angles. -Pp//~n The large decrease in the cross sections of the (p, p') and (~, p) reactions that occurs between 6#Zn and 7°Zn primarily reflects a decrease in Fp, the proton evaporation width, relative to Fn, the corresponding width for neutron evaporation. In this section we examine whether the relative magnitudes of the cross sections can be understood on this basis. We correlate the data by use of an equation for the ratio of these widths obtained from the constant temperature approximation 26): 4.3. SYSTEMATICS OF

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where S~ and S v are the neutron and proton separation energies, ~5n and cSp are the pairing energies of the residual nuclei, Beff is the effective Coulomb barrier to proton emission, and z is the nuclear temperature. Since all the targets are doubly even isotopes of zinc the pairing energy and barrier terms in the above expression are essentially equal in all cases. In order to focus on the important variable we thus restrict ourselves to examining the dependence of Fv/Fn on (S~- Sp). While the above equation should be directly applicable to Fv/F~ values extracted from the (0e, p) data a more detailed treatment has to be applied to the widths based on the (p, p') data because of the effect ofisospin conservation. Since the T> (analog) states of the compound nucleus populated in proton-induced reactions can virtually only decay by proton emission the value of ( S ~ - Sv) does not affect the deexcitation of these states. Strictly speaking the widths in eq. (1) should therefore be those for the decay of the T< (non-analog) states. In the absence of isospin mixing the ratio of (p, p') cross sections for the T> and T< states is related to the proton decay width of the T< states, F~, the total decay width of the T< states, F <, and the isospin of the target nucleus, T, by the expression aa) a(p, p')>/a(p, p')< = r~/ETr~. Since the proton evaporation probability decreases in going from 6*Zn to 7°Zn this ratio is expected to increase. Quantitative evaluation of the decay widths by means of the statistical theory described in the next section indicated that the ratio of T> to T< (p, p') cross sections increases from about 0.5 to 2 between 64Zn and 7°Zn. The effect of this increase is to enhance the value of Fv/Fn for the heaviest target nuclides over

422

C . R . LUX AND N. T. PORILE

that expected from eq. (1). Unfortunately isospin mixing complicates the situation. It has been established 1o, ~s, t 7, 22, 23) that mixing of the T> states into the 7'< states occurs to an appreciable extent and so reduces the enhancement in the (p, p') cross section. The mixing fraction for 6SZn has been determined t 7, 33) as g 0.3 but no data are available for the other nuclides. In view of this fact we shall ignore the complications due to partial isospin conservation except to point out their effect on the data and proceed with a consideration of the Fp/F, systematics. The quantity FD/F.is equal to the ratio of compound-nuclear (p,p') and (p, n), or (~, p) and (ct, n) cross sections. The (p, p') and (~, p) evaporation cross sections were obtained from the 150° differential cross sections by the expression tr = 47rJ'(d2a/ dedg2~so°)de which assumes that only evaporation contributes at this angle and that the angular distribution of evaporated protons is isotropic. A more complicated procedure had to be used to obtain the (p, n) and (~, n) evaporation cross sections. First, the total reaction cross section was obtained by means of an optical model calculation. The (p, p') or (~, p) cross sections, as well as the (p, ~) or (~, ~') cross sections, which were obtained in a companion study 34), were subtracted from the corresponding reaction cross sections to yield the (p, n) and (ct, n) cross sections*. The latter were finally corrected for a small contribution from preequilibrium emission on the basis of the calculation described in the next section. The resulting values OfTp[F.

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COMPOUND AND PRECOMPOUND PROCESSES

423

are plotted as a function of (Sn-Sp) in fig. 8 and are seento range from approximately 0.02 to 2. The ratios vary in exponential fashion with the difference in separation energy confirming the importance of this variable in determining the magnitude of the evaporation cross sections. Some of the scatter of the points reflects the effect of isospin conservation. For instance, the value of Fp/F,, for the 71Ga compound nucleus is almost equal to that for 69Ga in spite of the fact that there is a difference of over 2 MeV between the respective values of (Sn- Sp). This departure from the overall trend can be attributed to the relative importance of a(p, p')> for 7°Zn. This same effect presumably also accounts for the previously noted fact (fig. 6) that while the precompound contribution to the (p, p') reaction on 64Zn-6azn is larger than that to the (~, p) reaction the opposite result is obtained for 7°Zn. 5. Comparison of differential cross sections with compound and precompound emission models In this section we present a comparison between the energy spectra integrated over angle with calculations based on both the compound and precompound models. The angular distributions showed that the preequilibrium contribution ranged up to 25 ~ and in this section we determine the extent to which theory confirms this result. The contribution of the compound nuclear process may be evaluated by means of the spin-dependent statistical theory. Our specific formulation of the calculation has been described in detail elsewhere 9, 17). The calculated differential cross sections are determined by the optical model parameters 35-3s) required for the calculation of transmission coefficients 39) and by the parameters appearing in the spin-dependent level density expression. The most significant of these are the level density parameter, a, and the pairing energy, 6, of the residual nuclei resulting from neutron, proton, or ~-particle emission. The magnitudes of the differential cross sections of the (p, p') and (~, p) reactions are affected by the a- and 6-values of the residual nuclei resulting from neutron or ~-particle emission. On the other hand, the a- and ~-values of the nucleus formed by proton emission affect both the magnitude and shape of the differential cross sections in question. It has been shown 9, 12) that changes in a and ~5affect the spectra in opposite ways making a unique determination of these parameters difficult. This situation can be ameliorated by measurements of a variety of spectra all of which populate the levels of the same nuclide 9, 12, 20) over similar excitation energy intervals. An additional complication in the case of the (p, p') reaction arises from the effect of isospin conservation and mixing. In the absence of complete data on all the reaction channels and of measurements in which more than one entrance or exit channel leads to the same compound or residual nucleus it is impossible to uniquely determine a- and cS-values and to incorporate isospin effects in a meaningful way. Since we do not have such complete data in the present case we cannot extract a meaningful set of these parameters. We have instead started with the values compiled by Gilbert and Cameron 40) and varied them until a satisfactory fit to the evaporation

424

C . R . L U X A N D N. T. PORILE

peak was obtained. Our final parameters are by no means unique and other combinations of a and t~ could lead to comparable fits. The important point for the present comparison is that once the magnitude and energy of the evaporation peaks are fit, the shapes of the spectra are virtually independent of the specific parametrization. This fact permits a relatively unambiguous calculation of the compound nuclear spectra. The preequilibrium spectra were obtained from the recently developed quasi-free scattering model 29). According to this model the interaction of an incident proton or ~t-particle with the nucleus is treated as a series of successive quasi-free collisions with the target nucleons. Particle emission and internal transitions compete at each step and experimental ~-nucleon or p-nucleon differential cross sections modified for the effect of the Pauli exclusion principle are used to calculate the collision kinematics. The only important adjustable parameters in this calculation are the effective Fermi energy and, in the case of ~-induced reactions, an alpha breakup factor• The (p, p') calculations were performed assuming a Fermi energy corresponding to an average nuclear density 29), which is equivalent to the assumption that the incident proton can interact throughout the entire nuclear volume. For the (~, p) reactions we used a Fermi energy of 8 MeV corresponding to interactions in the nuclear surface 29). The alpha breakup factor was chosen on the basis of the best overall agreement wiht both

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COMPOUND AND PRECOMPOUND PROCESSES

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Fig. 10. Comparisonof angle-integrateddifferentialcross sections of (x, p) reactions with theory. See fig. 9 for details. the (~, p) and the (c~, C)[ref. 3,)] differential cross sections. A breakup factor of 0.5 was used for all four targets. The results of this comparison are shown in figs. 9 and 10. As expected, the preequilibrium spectra peak at substantially higher energies than the evaporation spectra and increase in relative magnitude with increasing neutron number. It may be noted that the inclusion of the precompound contribution improves the overall agreement of the calculated spectra with the data. This is particularly noticeable for the heavier targets where the precompound contribution is most significant. A careful examination of the spectra nonetheless reveals a number of discrepancies between experiment and calculation. All of the calculated (p, p') spectra and two of the (~, p) spectra predict an excessively large number of high-energy protons, an effect that is attributable to the preequilibrium calculation. In addition a number of individual discrepancies may be noted, the most serious of which occurs for the 7°Zn(,¢, p) reaction. The experimental spectrum appears to consist of two peaks whose energies correspond approximately to the peak energies of the calculated spectra. However, the magnitude of the calculated preequilibrium cross section is too low to account for the observed yield of energetic protons. The differential cross sections obtained from the quasi-free scattering model may be integrated and compared with the experimental cross sections in order to obtain the

426

C.R. LUX AND N. T. PORILE

fractional contribution of the precompound process. The results are given by the curves in fig. 6. It is seen that the relative importance of preequilibrium processes increases with target A. This trend is a consequence of the relative constancy of the precompound cross sections when compared to the sharply decreasing evaporation cross sections. It is of interest to note that the results obtained from the preequilibrium calculation are generally in very good agreement with those based on the asymmetry in the angular distribution. This agreement confirms the validity of the assumption that in low-energy reactions the vast majority of preequilibrium protons are emitted at forward angles. In a number of articles dealing with the energy spectra of protons and x-particles emitted in reactions induced in a series of isotopically pure targets by low-energy protons and ~-particles Cohen and collaborators 2. 7, 16, 24, 2 5) proposed a method of separating compound from precompound processesL As in the present study these workers noted that the cross sections for the emission of charged particles from a series of isotopic targets decreased with decreasing A. It was assumed that the protons emitted from the heaviest target nuclide could be entirely attributed to the precompound process. The compound nuclear contribution to reactions induced in the lighter targets was then obtained by direct subtraction of the spectrum from the heaviest target. This procedure was based on the further assumption that the precompound differential cross section is essentially the same for all isotopic targets. For instance, in a study of the (p, p') reaction on even Cd isotopes 7) these workers assumed that precompound emission accounted for the entire (p, p') cross section of 112, 11~, ~16Cd" The compound nuclear spectra of the lighter Cd targets were obtained by subtraction of the spectrum obtained for ~16Cd" As evidence for the validity of this procedure they cite the similarity of the spectra obtained from 112Cd ' 1t 4Cd ' and H 6Cd ' and the agreement of the compound nuclear proton emission probabilities obtained in this fashion for x°6Cd and ~1°Cd with statistical-model calculations. While this procedure may have some validity in the cadmium mass region, where the height of the barrier makes proton emission improbable even for neutron deficient targets, its application in the zinc region appears to be highly questionable. Nonetheless Rao et al. 7) used this method in an analysis of (p, p') spectra of Ni isotopes by assuming that only precompound emission contributed to the 6*Ni(p, p') reaction with 12 MeV protons. Although a direct comparison with the present results is not possible it does appear on the basis of the systematics developed in sect. 4 that their assumption is not supported by the present analysis. The value of (Sn-Sp) for the 65Cu compound nucleus, 2.46 MeV, thus lies between those of the 69Ga and 71Ga compound nuclei and the precompound contribution should be comparable. As indicated above we find on the basis of two different approaches that the precompound contribution to the (p, p') reaction of 6SZn and 7°Zn is less than 20 70. * Cohen and collaborators variously refer to the latter process as a direct interaction or as a noncompound process. Since these processes contribute to the evaporation-like region of the energy spectra they are in fact identical t o o u r precompound emission.

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427

A direct comparison can be made in the case of the (~, p) reaction since in a recent article Chan et al. 25) include data obtained in the bombardment of Zn isotopes by 15 MeV ~-particles. They conclude on the basis of the above analysis that the contribution ofprecompound emission to the (ct, p) reaction is ~ 95 ~ for 7°Zn, over 60 for 6SZn, and very small for 64Zn. Our analysis of the angular distribution as well as the comparison of the spectra with theory both indicate that the precompound process accounts for less than 30 ~o of the 7°Zn(~, p) cross section and for only ~ 10 ~ of the 6aZn(x, p) yield. Furthermore, their basic assumption forces these workers to some unreasonable conclusions about the properties of precompound reactions. For instance, since they find that the (~, p) spectra for 68Zn and 64Zn have similar shapes, they are forced to conclude that in this mass region both compound and precompound processes lead to similar spectra. The calculated spectra in figs. 9 and 10 show that this conclusion disagrees with theory. Similarly, they find that the angular distribution of protons emitted in the reactions of both 64Zn and 6SZn are essentially isotropic and so are forced to conclude that compound and precompound processes lead to a similar angular distribution. We feel that our interpretation of very similar data is more reasonable and leads to conclusions that are consistent with accepted formulations of the precompound process 27). 6. Conclusions

The energy spectra of protons emitted in the (~, p) and (p, p') reactions of 64Zn, 66Zn, 6SZn, and 7°Zn have been measured between 30 ° and 150° to the beam. The integrated cross sections decrease with increasing target neutron number and the ratios of proton to neutron evaporation widths vary exponentially with the difference between the neutron and proton separation energies. The contribution of preequilibrium processes has been evaluated from the forwardbackward asymmetry in the angular distribution and by comparison of the measured differential cross sections with values calculated by means of the quasi-free scattering model of precompound reactions. Both approaches yield essentially the same result: the precompound contribution increases with target neutron number but even for the most neutron-rich target it amounts to less than 30 ~. This result is butressed by a nuclear temperature analysis and by the agreement between the angle-integrated spectra with results obtained from both compound and preequilibrium models. Our analysis indicates that the assumption by Cohen and collaborators 2, 7, 16, 24, 25) that proton emission from reactions induced in the heaviest of a series of isotopic targets is exclusively due to precompound emission, is incorrect. The assistance of Drs. J. C. Pacer and J. R. Wiley throughout the Tandem runs is gratefully acknowledged. We would like to thank Drs. M. Blann and A. Mignerey for making the codes based on their quasi-free scattering model available to us and for instructing us in their use.

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References 1) D. M, Montgomery and N. T. Porile, Phys. Roy. (22 (1970) 595 2) B. L. Cohen, G. R. Rao, C. L. Fink, J. C. Vander Weerd and J. A. Penkrot, Phys. Rev. Lett. 25 (1970) 453 3) F. M. Lanzafame and M. Blann, Nucl. Phys. A142 (1970) 545 4) C. Birattari, E. Gadioli, A. M. Grassi-Strini, G. Stum, G. Tagliaferri and L. Zetta, Nucl. Phys. A166 (1971) 605 5) C. C. Lu, J. R. Huizenga, C. J. Stephan and A. J. Gorski, Nucl. Phys. A164 (1971) 225 6) S. M. Grimes, J. D. Anderson, J. W. McClure, B. A. Pohl and C. Wong, Phys. Rev. C3 (1971) 645 7) G. R. Rao, R. Balasubramanian, B. L. Cohen, C. L. Fink and J. H. Degnan, Phys. Rex,. C4 (1971) 1855 8) E. Gadioli, I. Iori, N. Molho and L. Zetta, Phys. Rev. C4 (1971) 1412 9) A. J. Kennedy, J. C. Pacer, A. Sprinzak, J. Wiley and N. T. Porile, Phys. Rev. C5 (1972) 500 10) L. C. Vaz, C. C. Lu and J. R. Huizenga, Phys. Rev. C5 (1972) 463 11) S. M. Grimes, J. D. Anderson, J. W. McClure, B. A. Pohl and C. Wong, Phys. Rev. C6 (1972) 236 12) C. C. Lu, L. C. Vaz and J. R. Huizenga, Nucl .Phys. A19"/(1972) 321 13) P. Decowski et al., Nucl. Phys. A204 (1973) 121 14) A. Sprinzak, A. J. Kennedy, J. C. Pacer, J. Wiley and N. T. Porile, Nucl. Phys. A203 (1973) 280 15) J. Wiley, J. C. Pacer, C. R. Lux and N. T. Porile, Nucl. Phys..6,212 (1973) 1 16) K. C. Chan, G. R. Rao, B. L. Cohen, J. M. Degnan and L. Shabason, Phys. Rev. C8 (1973) 1363 17) N. T. Porile, J. C. Pacer, J. Wiley and C. R. Lux, Phys. Rev. C9 (1974) 2171 18) S. M. Grimes, J. D. Anderson, J. W. McClure, B. A. Pohl and C. Wong, Phys. Rev. C10 (1974) 2373 19) K. Miyamo, M. Seikawa, T. Kaneko and M. Nomoto, Nucl. Phys. A230 (1974) 98 20) J. C. Pacer, J. Wiley, C. R. Lux and N. T. Porile, Nucl. Phys. A226 (1974) 413 21) F. Hermes, E. W. Jasper, H. E. Kurz and T. Mayer-Kuckuk, Nucl. Phys. A228 (1974) 165 22) N. T. Porilc, C. R. Lux, J. C. Pacer and J. Wiley, Nucl. Phys. A240 (1975) 77 23) C. R. Lux and N. T. Porile, Nucl. Phys. A248 (1975) 441 24) J. E. Alzona, K. C. Chan, L. Shabason and B. L. Cohen, Phys. Rev. C l l (1975) 1669 25) K. C. Chan, L. Shabason, J. E. Alzona and B. L. Cohen, Phys. Rev. C13 (1976) 1112 26) N. T. Porile, in Nuclear Chemistry, ed. L. Yaffe, vol. 1 (Academic, NY, 1968) p. 57; D. Bodansky, Ann. Rev. Nucl. Sci. 12 (1962) 79 27) M. Blann, Ann. Rcv. Nucl. Sci. 25 (1975) 123 28) T. Ericson, Adv. in Phys. 9 (1960) 425 29) A. Mignerey, P h . D . thesis, University of Rochester, 1975 (unpublished); M. Blann, A. Mignerey and W. Scobel, equilibration processes in nuclear reactions, presented at the Eight Summer School in Nuclear Physics, Warsaw University, 1975; Nucleonika, in press 30) F. S. Goulding, D. A. Landis, J. Cerny and R. M. Pehl, Nucl. Instr. 31 (1964) 1 31) A. J. Kennedy, J. Pacer, A. Sprinzak, J. Willey and N. T. Porile, Nucl. Instr. 101 (1972) 471 32) H. W. Bertini, G. D. Harp and F. E. Bertrand, Phys. Rev. CI0 (1974) 2472 33) C. R. Lux, N. T. Porile and S. M. Grimes, unpublished 34) C. R. Lux and N. T. Porile, unpublished 35) J. R. Huizenga and G. Igo, Nucl. Phys. 29 (1962) 462 36) F. G. Perey, Phys. Rev. 131 (1963) 745 37) D. Wilmore and P. E. Hodgson, Nucl. Phys. 55 (1964) 1673 38) P. E. Hodgson, in Proc. Conf. on direct interactions and nuclear reaction mechanisms, Padua, Italy, 1952, ed. E. Clementel and C. Villi (Gordon and Breach, New York, 1963) 39) E. H. Auerbach, Brookhaven National Laboratory Report no. BNL-6562 (unpublished) 40) A. Gilbert and A. G. W. Cameron, Can. J. Phys. 43 (1965) 1446