Inelastic scattering of heavy ions

2.L

[ [

Nuclear P h y s w s 3 0 (1962) 3 7 3 - - 3 8 8 ,

( ~ ) North-Holland Pubhshing Co , A m s t e r d a m

Not to be reproduced by photoprmt or macrofflm without written permlssmn from the publisher

I N E L A S T I C S C A T T E R I N G OF H E A V Y I O N S D J. W I L L I A M S t a n d F. E. S T E I G E R T Sloane Physics Laboratory, Yale Umvers~ty, New Haven, Connecticut tt R e c e i v e d 15 M a y 1961 A b s o l u t e inelastic e x c i t a t i o n cross sections h a v e b e e n o b t a i n e d in t h e r e a c t i o n s (C1., C1'), (C l*, Ole), (O is, O is) a n d (N 1., C1'). T h e h e a v y i o n b e a m s u s e d were t h e full e n e r g y (10.54 MeV p e r nucleon) b e a m s f r o m t h e Yale U m v e r s i t y h e a v y i o n accelerator. T h e d a t a were a n a l y s e d w i t h t h e diffraction m o d e l of inelastic s c a t t e r i n g a n d i n t e r a c t i o n radii, d e f o r m a t i o n p a r a m e t e r s a n d t h e p a r i t y of t h e t r a n s i t i o n s were d e t e r m i n e d . T h e r e s u l t s i n d i c a t e t h a t t h e inelastic r a d n a r e s h g h t l y larger t h a n t h e c o r r e s p o n d i n g elastic radii T h e a n a l y s i s also s h o w s t h a t t h e o x y g e n e x c i t a t i o n is m a i n l y one of odd p a r i t y a n d verifies t h e 2 +, 4 433 M e V e x c i t a tion m C 1.. I n t h e N 1., C 1. r e a c t i o n t h e 2.312 MeV level of N 1. is f o u n d to be s t r o n g l y s u p p r e s s ed relative to o t h e r e x c i t a t i o n s seen.

Abstract:

1. I n t r o d u c t i o n

During the past several years there has been an accumulation of data which display a marked oscillatory structure characteristic of the surface direct category of interactions. The bulk of these data tit are interactions of fight (p, n, d, a) particles with light to medium targets (C, O, A). More recently, the work of Newman 4), Roll 5) and Smith 6) on the elastic scattering of heavy ions from light nuclei has also shown oscillations characteristic of surface reactions. Attempts at analyzing some of the earlier data were based on a plane wave Born approximation of the surface interaction 7). This had the disadvantage of approximating the scattering with plane waves although it was recognized that strong distortions took place at the nuclear surface. Attempts s) to include these effects led to the use of a distorted wave Born approximation where the exact wave functions for the motion of the projectile with respect to the nucleus were employed *. One of the earlier successes of the distorted wave theory was the explanation of the filling in of the valleys in deuteron stripping angular distributions 9). Good agreement also has been obtained for t N a t i o n a l Science F o u n d a t i o n Fellow, 1960---61. P r e s e n t address" J o h n H o p k i n s Applied P h y s i c s L a b o r a t o r y , Silver Springs, M a r y l a n d . t t Tins w o r k h a s b e e n s u p p o r t e d b y t h e U S A t o m i c E n e r g y C o m m i s s i o n . T h i s p a p e r is b a s e d m p a r t o n a d i s s e r t a t i o n s u b m i t t e d b y D J. W l l h a m s in p a r t i a l f u l f i l l m e n t of t h e r e q u i r e m e n t s for t h e degree of D o c t o r of P h i l o s o p h y in Yale U n i v e r s i t y . tt* See for e x a m p l e refs. l-s) $ A c o m p i l a t i o n of references c o n c e r n i n g t h e d i s t o r t e d w a v e B o r n a p p r o x i m a t i o n m a y be f o u n d in f o o t n o t e 4) of ref. s). 373

~74

D. J. WILLIAMS AND F. E. STEIGERT

the light particle reactions b y using optical model wavefunctions in the distorted wave theory and with further refinements even better agreements are expected 8). Other more simplified approaches have also been extensively used in the analysis of the data. These are the sharp cutoff model 1o) and the diffraction calculations based on the adiabatic approximation 8,11,1,). The earlier form of the sharp cutoff model assumes that all partial waves with angular momenta up through the cutoff value are completely absorbed b y the nucleus while all above the cutoff experience no nuclear interaction. Refinements in this approach have been to employ the "crossover point" method rather than the "quarter point" method of determining interaction radii 10). Also, in relatively high angular momentum reactions a "rounded" cutoff is employed s, 13). In the diffraction model, the nucleus is replaced by a black absorbing disk (as it is in the sharp cutoff model) and the diffraction scattering of the impinging wave is calculated. Here it is assumed that the coordinates of the nucleus can be considered fixed because of their long period in comparison to the collision time. The elastic scattering data of refs. i--e) have been fitted by both the above methods. Good agreement is obtained in relation to the peak positions for both models, the diffraction model giving somewhat more consistent results. However, the absolute magnitude predictions do not show agreement. While it is usually argued that these discrepancies are due to Coulomb effects, the present data would seem to indicate that these corrections alone are insufficient. The discrepancies appear to be too large to be accounted for solely b y the usual Coulomb terms. The diffraction calculations have been extended to inelastic excitations 11,1~,14) by assuming the target to have a small deformation with radius defined by n ~ R 0 ( l + ]~ o~,~Y,,~(O, ~)), where the g,~ are the vibrational parameters employed b y Inopin 1,). Assuming the adiabatic hypothesis and expanding to terms of first order in the g,~,, Blair 1,) has obtained very useful closed form expressions for the inelastic excitations. The data presented are analysed in terms of these diffraction calculations. It is felt that this type of analysis t is useful in view of the equivalence of the diffraction calculations and the distorted wave calculations at small angles 8). The angular range of the present experiments is from about 9 ° to 23 ° in the centre-of-mass system. With the available kR values (25 ~ kR ~ 37), this range is sufficient to observe several of the theoretical maxima. t Elastic a n d inelastic h e a v y ion scattering a t lower energies h a s been previously considered b y Zucker a n d H a l b e r t . See ref. 11).

INELASTIC SCATTERING OF HEAVY IONS

375

Sect. 2 gives a discussion and description of the experimental apparatus and procedure; sects. 3 and 4 are a presentation of the experimental results and the data analysis; sect. 5 is a discussion of the conclusions drawn from the analysis.

2. Experimental Apparatus and Procedure 2.1. A P P A R A T U S

The scattering apparatus used in these experiments was t h a t described by Newman in refs. 4, 6). The magnetically analysed and focused beam from the Yale University heavy ion accelerator was used to initiate the reactions studied. The scattered beam was detected with an RCA solid state detector and an R I D L 400-channel analyser was used to analyse the pulse-height spectra obtained. A TMC 256-channel analyser was used on some of the later runs and use was made of its equivalent 1024-channel property. The detector output was fed to a standard cathode follower and then to an integrating circuit. (Because of the rise time acceptance characteristics of the R I D L 400-channel analyser it was necessary to integrate the detector pulses before analysing them. This feature was not necessary with the TMC unit.) The integrated output was then run to a TMC Model AL-2A amplifier whose output was fed directly to the 400-channel analyser. The amplifier was selectively chosen on the basis of noise considerations. Noise problems were also reduced with the use of a cathode follower rather than a preamp at the detector output. This was possible due to the large output pulses at these energies ( ~ 0.2 V for 120 MeV C1~). The beam monitoring system was the same as t h a t used in ref. *) except t h a t a Tullamor pulser was now used to check for drifts in the monitoring electronics. A typical operating voltage for the detector was 50 V. This bias voltage was obtained from a regulated L a m b d a power supply and a 10 K~2 precision helipot. The experimentally observed resolution of the detector system was from 1 % to 2 % . The target gas was flowed continuously through the scattering volume. The pressure was maintained constant with a manostat. Pressure and ambient temperature readings were regularly made and were used to correct the yield at each angle. These corrections in no case amounted to more than 1 % . 2.2. P R O C E D U R E

The pertinent data recorded for a run at a given angle were as follows: the 400-channel spectrum, the monitor scaler reading, the elapsed live time and clock time and the pressure-temperature readings at the scattering centre both before and after t~e run. Also, at the end of each run the pulser was used to check for drifts in the monitor electronics. Pressure-temperature corrections and dead time corrections were then

~76

D. J . WILLIAMS AND F. E . S T E I G E R T

applied to the data. In the worst cases the dead time corrections amounted to as much as 10 ~o- The probable error due to this effect has been estimated as + 3 ~/o, assuming an uncertainty of 30 ~/o in these corrections. The differential cross section was then calculated from the yield in the manner described b y Critchfield and Dodder 16). The geometric corrections were in all cases less than 0.3 %. The true zero of the apparatus was obtained b y taking a series of runs at positive and negative angles. The zero so obtained was consistently within 10' of the zero obtained from the optical alignment of the apparatus. During some of the previous elastic scattering runs it was observed that the incident beam direction through the slit system varied slowly with time. Because of this effect, a short run at a predetermined calibration angle was taken before and after each data run. The variation of yield at the calibration angle was then used to obtain the beam drift and this correction was applied to the data. Typically the range of this correction remained within 10' of the initial calibration run during a 64 h running period. The continuous checks on the monitor electronics gave no indication of an electronic drift of magnitude necessary to produce the angle shifts indicated above. The angular resolution of the entire system is calculated to be 35'. The accuracy in the angle determination is estimated to be ± 5 ' . The beam energy entering the scattering apparatus was the full energy beam of 10.54 MeV per nucleon. The incident energy at the scattering centre and the energy at the detector were then obtained from the range energy curves of Roll and Steigert 1~) and MartiniS). It is felt that this energy determination is good to better than 2 %. The absolute magnitude of the inelastic excitations was obtained by taking their ratio to the elastic scattering. The absolute value for the elastic scattering cross section was obtained in a separate series of runs employing a F a r a d a y chamber. The counting statistics varied from point to point, depending upon the angle being taken and the time available. Typical values are from 3 % to 9 %.

3. E x p e r i m e n t a l Results Sample spectra of the reactions studied are shown in fig. 1. The labelled arrows indicate the positions of various levels of excitation as determined from the known Q values and the elastic peak position. A full discussion of these and other levels seen is presented under the appropriate reaction titles below. As the spectra of fig. 1 show, one problem in all of these reactions is that of background. All the results presented in this paper were obtained with no attempt at making a background subtraction. It is felt that the method of obtaining the absolute inelastic cross sections minimizes the effect of this back-

I N E L A S T I C SCATTERING O F H E A V Y IONS

377

ground and th at these inelastic cross sections are known to nearly the same accuracy as the elastic cross sections at these angles• The absolute inelastic excitations are obtained b y assuming t hat a small but constant background extends through both the inelastic and elastic peaks. C t z C It ~'lob=l13 2 MeV

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spectra of the reactions studied. Arrows indicate the positaons of the various discussed in the text. Angles shown are laboratory angles•

levels

378

D. J. WILLIAMS AND F. E. STEIGERT

The inelastic excitations are then normalized to the known absolute elastic cross sections at an angle where the two yields are nearly equal. The absolute elastic cross section is obtained at a small angle where the background effects are thought to be negligible. Although the assumption of a constant background through the elastic peak is unjustified it can be seen that some background will exist under the elastic peak with the resolutions available in these reactions. An example of this is the reaction Ols(O le, CIg)Ne 2° Which has a ground state Q value of - 2 . 4 MeV. Because of their lower energy loss, the C 12 products would fall well within the base of the elastic 0 zs peak. Preliminary results zg) indicate that at forward angles the differential cross section for this reaction is ~ 10 rob. As a rough check on background effects, the 4.433 MeV excitation in the C n, Cn reaction was analysed twice; first with a background subtraction and then with no background corrections. The resulting relative angular distributions agreed well within the limits of error for these experiments. A reasonable estimate for the uncertainty in the absolute values of the excitations studied is ± 1 5 % . Figs 2, 3 and 5 through 10 present the differential cross sections obtained in these experiments. Fig. 4 is a (C14, Cz2) spectrum which shows some of the higher excitations which were present. Fig. 11 shows (N 14, Clz) spectra which emphasize the expected position of the 2.312 MeV level in N 14. These figures will be discussed in more detail in the appropriate sections below. 3 1. T H E

CI=(C z2, CIz)C TM R E A C T I O N

Fig. 1 (a) and (b) present two sample spectra from the (C1=, C1=) reaction. The arrows indicate the expected positions of the following levels: (a) Q -- o, (b) Q = - 4 . 4 3 3 MeV, (c) Q = - 7 . 6 5 6 MeV, (d) Q = - 1 0 . 1 MeV. These spectra clearly show the out of phase character of the 4.433 MeV level with ~ O 0 1 l l l l l n l l l t l l l 160

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F i g 2 C e n t r e - o f - m a s s d i f f e r e n t i a l c r o s s s e c t i o n of t h e 4 . 4 3 3 M e V i n e l a s t m e x c i t a t i o n i n t h e (C lz, C 12) r e a c t i o n a t Ecru = 56.6 M e V S o l i d c u r v e s h o w n is t h e p r e d i c t e d q u a d r u p o l e d i s t r i b u t i o n for k R o = 25.5, i n a r b i t r a r y u n i t s .

INELASTIC

SCATTERING

OF

HEAVY

379

IONS

respect to the elastic peak. The differential cross section for the excitation of this level is shown in fig. 2. Also in fig. 1 (a) and (b) an excitation is seen between the 7.656 and 10.1 MeV levels. This peak was seen in all the spectra and an attempt was made to anaJyse it. The resulting angular distribution is shown in fig. 3. Due to the poor statistics an arbitrary error of 25 % has been assigned to all the data on this peak. Contributions to this excitation could come from double excitation of the 4.433 MeV level, excitation of the 9.63 MeV level or nucleon exchange collisions. Transfer of a single nucleon or of a group of nucleons enters at a I

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Fig. 4. S p e c t r u m showing higher exitations prese n t in the (C12, C 12) reaction (Ellb = 113.2 MeV and

01&b =

9°33').

much lower Q value. It is to be noted t h a t although we have identical bosons in the incoming channel, any excitation is possible due to the structure inherent in each nucleus. Fig. 4 shows a spectra in which an excitation around 14 MeV is present. This excitation was seen at several of the larger angles but was sufficiently weak t h a t no a t t e m p t was made to analyse it. It is interesting to note that a 4 + rotational level is predicted to lie at about 14.7 MeV in C12and this level m a y be contributing to the observed peak at 14 MeV. However, it is also recognized t h a t neutron transfer takes place with a Q value of - 1 3 . 9 MeV. 3.2. T H E Ola(C 1|, Cl|)O 16 R E A C T I O N

Fig. 1(c) and (d) present two sample spectra from the Clz, O le reaction. The arrows show expected level positions as follows: (a) Q = 0, (b) Q = - 4 . 4 3 3

380

D.J.

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WILLIAMS

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Fig 5. C e n t r e - o f - m a s s differential cross section for (Cis, O I8) elastic s c a t t e r i n g a t Eer a = 63.4 M e g . T h e r e s u l t of a diffraction a n a l y s i s for k R o = 30 3 is also s h o w n

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o~m Fig 6 C e n t r e - o f - m a s s differential cross section of t h e 4.433 M e V level of C ts in t h e (Cis, O 16) reaction a t Ecru = 63 4 MeV (inelastic excitation). Solid c u r v e is t h e predicted q u a d r u p o l e d i s t r i b u t i o n for h R e = 30.4, in a r b i t r a r y u n i t s .

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8~m F i g 7. Centre-of-mass d i f f e r e n t i a l cross section o f t h e o x y g e n inelastm e x c i t a t i o n i n t h e (C 1=, 0 Ie) r e a c t i o n (Q = - - 6 t o - - 7

MeV). Solid c u r v e is p r e d i c t e d octupole distributxon for k R a ~ 31 5 in a r b i t r a r y umts

INELASTIC SCATTERING OF HEAVY IONS

381

MeV; (c) Q = - 6 . 0 6 MeV, (d) Q = - 6 . 9 2 MeV, (e) O = - 7 . 6 5 6 MeV. As can be seen from the figure the oxygen levels from 6 to 7 MeV could not be resolved. This excitation will simply be termed the oxygen excitation in what follows. The spectra of fig. 1 (c) and (d) show that the 4.433 MeV excitation and the oxygen excitation exhibit an out of phase behaviour. This is interpreted as signifying that the oxygen excitation is mainly one of odd parity. This will be borne out in greater detail in the analysis of sect. 4 concerning the (Caz, 016) and the (01S, O 1") reactions. Figs. 5, 6 and 7 present the differential cross sections for the (C12, O is) elastic scattering, the excitation of the 4.433 MeV level in C12 and the oxygen excitation. Weak excitations were also seen in the regions of 11--12 MeV and 14--16 MeV. Again these higher excitations were too weak to attempt an analysis. 3 3. T H E

O l s ( O le, Otd)O xs R E A C T I O N

Fig. l(e) presents a typical spectrum from the (0 xe, 016) reaction. The arrows indicate expected level positions as follows: (a) Q = 0, (b) Q = - 6 . 0 6 MeV, (c) Q = --6.92 MeV, (d) Q = - - 9 . 8 MeV. As in the (C1~, O le) reaction it was not possible to resolve the levels from 6 to 7 MeV. This excitation was thus analysed as a single level (see sect. 4). too

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~ m ----bF i g 8. C e n t r e - o f - m a s s d i f f e r e n t i a l c r o s s s e c t i o n for (O xd, O le) e l a s t i c s c a t t e r i n g a t Eem = 70 2 MeV. T h e r e s u l t o f a d i f f r a c t i o n a n a l y s i s a t k R o = 36 0 is a l s o s h o w n

382

D . J.

WILLIAMS

A N D F . ]~. S T E I G E R T

Figs. 8 and 9 show the differential cross sections for the (0 is, O is) elastic scattering and the oxygen excitation, respectively. The absolute value for the elastic scattering ~v~s obtained from an extrapolation from the work of Roll s) at 154 MeV. A very broad excitatior, group was seen in the region from 11 to 15 MeV. Again no analysis was possible. 340[

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Fig 9. Centre-of-mass differential cross section for the o x y g e n inelastic excitation in the (OTM, O le) reaction (Q = - - 6 to --7 MeV). Results of an octupole (kR u = 37.0) a n d a quadrupole (kR o = = 31.8) fit are also s h o w n in a r b i t r a r y units.

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---

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Fig. 10. Centre-of-mass differential cross section of the inelastic g r o u p s observed in the (N 'l, C1') reaction a t Ecru = 61.8 MeV.

INELASTIC

SCATTERING.

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HEAVY

383

IONS

3.4. T H E CI=(N x4, NI*)C 1= R E A C T I O N

Fig l(f) shows a sample spectra from the (N 14, C12) reaction. The arrows show the expected level positions as follows: (a) Q = 0, (b) Q = --2.312 MeV, (c) Q = --3.945 MeV, (d) Q = --4.433 MeV, (e) Q = --5.69 MeV, (f) Q = --7.656 MeV, (g) Q = - 8 . 9 MeV, (h) Q = - 9 . 6 3 MeV. All levels from 3.9 to 5.8 MeV could contribute to the first excitation seen and all levels from 7 through 10 MeV could contribute to the second peak. Thus it is not surprising that these excitations show a very structureless angular distribution (fig. 10). 400

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Chonnel Number

Fig. 11. (N 1*, Cit) s p e c t r a illustrating t h e e x p e c t e d position of t h e 2.312 MeV level in N I ' (Els b = =

133.8 MeV).

Fig. 11 is presented to show, as does fig. l(f), the positioning of the 2.312 MeV level of N 14. In all the spectra the expected position for this level falls consistently at the lowest point in the valley between the elastic peak and the first excitation. It is estimated from these spectra that the amount of the 2.312 MeV level present is not greater than ~ 5 % of the first excitation group. The suppression of this level in this reaction m a y be accounted for b y either the isobaric spin forhiddenness or the single particle nature of the level. 4. A n a l y s i s The differential excitation cross sections as presented b y Blair 14)have the form da (0 ~ l ) = (kRoS) =

d-b

4=

(

× Jl,~t ~ (2kR 0 sin {O),

[(l--m)!!(l+m)l!]*

384

D,

J.

WILLIAMS

AND

F.

E,

STEIGERT

where the approximations used are the adiabatic hypothesis, the Fraunhofer limit, small deformations and k t = k t ---- k. The small deformation assumption allows the projection of the nuclear surface to be considered the same as the area within the sharp radius R = R 0 [ l + • ~,mY,m(½z, 4)]. Zm

The choice of the argument 2kR sin ½@ corresponds to the choice of a shadow plane perpendicular to ~r+~l. Making the substitution (2Z+1) G

-+/32,

the quadrupole and octupole rotational transitions can be expressed as /322 da (0 -+ 2) ---- (kRo2)2 ~ {-~Jo2(2kRo sin ½0)+-~J22(2kRo sin ½0)}, dE2 da (0 -+ 3) : d~2

f132 (kRo2) 4 ~ {sJ12(2kR° sin ½0)+~Js2(2kRo sin ½0)}.

For the above choice of the shadow plane, the elastic d /fraction scattering is given by da J~l (2kR o sin 16)~ dQ e -- (kR02)2 cos 2 ½0 (2kR ° sin ½0) 3 The above expressions were used to analyse the data. From this analysis, interaction radii, deformation parameters and the parity of the transitions were determined. The theoretical distributions shown with the elastic scattering data are in absolute units and those shown with the inelastic data are in arbitrary units. The latter curves were normalized to the data at each peak and an average value of the deformation parameter was obtained. Fig. 2 shows the quadrupole fit to the excitation of the 4.433 MeV level in the (C12, C12) reaction. Only the angle dependent term J02+ 3J22 is plotted and is in arbitrary units. The fit shown is for k R o ---- 25.5, which yields R o = 6.34 fro. Using R o = r o (Alt+A2]), a value of r 0 = 1.38 fm is obtained. The values for the deformation parameter/32 and their average fie, obtained by normalizing to each observed peak separately are /33 = 0.204, 0.146 and /~2 = 0.175. A diffraction analysis of the (C12, Cle) elastic scattering results yields 6) R o = 6 . 2 2 fro, r o - - 136 fm. Fig. 5 shows the diffraction fit to the (CTM, 016) elastic scattering. Unfortunately, only one peak is observed and the fit is subject to somewhat more uncertainty than in the cases where several maxima are observed. However,

INELASTIC

SCATTERING

OF

HEAVY

IONS

385

the corresponding m a x i m u m of the theoretical distribution is easily obtained and the best fit determined to be k R o ----30.3. This yields R o ----6.66 fro, ro ----1.38 fro. T h e quadrupole fit to the observed excitation of the C Is, 4.433 M c V level in the (C 12, O le) reaction is s h o w n in fig. 6. T h e curve s h o w n is for k R o = 30.4 and yields R o = 6.68 fro, ro = 1.39 fro. T h e deformation parameter values and their average as determined from the above normalization procedure are fls = 0.160, 0.I19; fls = 0.140. Fig. 7 shows the oxygen excitation in the (C is, O le) reaction as fit b y an octupole distribution. Again only one m a x i m u m is seen and the same remarks apply here as in the elastic scattering. T h e values obtained from the octupole fit are k R o = 31.5, R e ----6.92 fm, r0 -= 1.44 f m and f13 = 0.122. O n thc assumption that the oxygen excitation is a quadrupole transition, the best curve obtained is for k R o = 26.0, giving R 0 = 5.71 f m and ro = 1.19 fro. Fig. 8 shows the diffraction fit to the O is, O Is elastic scattering. T h e plot s h o w n is for k R o = 36.0 and yields R 0 = 6.96 fro, ro = 1.38 fro. T h e inelastic excitation in the (0 Is, 0 Is) reaction is s h o w n in fig. 9 as it is fit b y both a quadrupole a n d an octupole distribution. T h e parameters obtained from the octupole fit are k R o = 37.0, R o = 7.15 fro, ro = 1.42 fro, f13 = 0.172, 0.095, 0.088; /~3-----0.118. T h e quadrupole fit gives k R o = 31.8, R o = 6.15 fro,

r 0 = 1.22 fro. The curves in fig. 9 show that the oxygen excitation is best fitted b y an octupole distribution. It is also observed that the inelastic excitation is roughly in phase with the elastic scattering. In the (Ct2, 016) reaction the angular distributions, figs. 6 and 7, and the spectra of fig. 1 (c) and (d) showthe two inelastic excitations to be roughly out of phase. These arguments support the view that the oxygen excitation is an odd parity transition. However, it is recognized TABLE I

Diffraction analysm results

Reaction C is, C TM

C ~s, 0 ~6

0 ~s, 0 's

level observed

parity

Ro fm

r0 fm

Q = 0 --4 433

+

6 225=0 12 6 345=0 12

1 365=0 03 1 385=0.03

0 175

0 - - 4 433 --6 to --7

~--

6 66=}=0 11 6 685=0 11 6925=0.11

1.385=0 02 1.394-0.02 1.445=0 02

0 140 0122

0 - - 6 to --7

--

6 964-0 10 7.155=0 10

1 385=0 02 1.424-0 02

0118

Col. 1 s h o w s t h e reaction studied. I n col. 2 t h e level (or levels) observed, consistent w i t h t h e energy resolution attainable, a r e listed. T h e p a r i t y of t h e excitation as determined b y t h e b e s t fit to t h e d a t a is listed in col. 3. Cols. 4, 5 a n d 6 give the values of

Ro,

r 0 a n d ~t obtained.

S86

D . J . WILLIAMS AND F. "~. STEIGERT

that the clarity of the phase relationships is somewhat obscured b y allowing the interaction radius to vary. Also, the octupole fits in both the (CTM, 0 TM) and (0 TM, 0 is) reactions yield interaction radii which are consistent with the (C TM, C TM) and (C TM, 016) quadrupole analysis of the 4.433 MeV level of CTM, i.e., the inelastic interaction radii appear to be slightly larger than the corresponding diffraction elastic radii. The quadrupole fits to the oxygen excitation in (CTM, O TM) and (0 TM, O TM) yield radii which are much smaller than any so far observed in these experiments. Table 1 summarizes the results obtained from the above analysis. The errors listed have been obtained b y determining the change in the "best fit" k R o value required to produce a readily observable change in the angular distribution and b y estimating the error due to possible incorrect positioning of the experimental peaks. If the magnitude of the outgoing wave vector k r is used in the computations, the resulting radii are increased b y about 4 %. This effect does not alter the preceding interpretation of the inelastic excitation in oxygen being one of odd parity. However, the slight trend of the inelastic radii being larger than the corresponding elastic radii is then magnified. The validity of the approximation k r ----kl is subject to the criterion 14) (kt--kt)RO << 1. The range of this parameter in the present experiments is 0.15 ~ ( k t - - k t ) R O ~ 0.7, where the larger values occur in the large angle excitations of the oxygen levels in the (CTM, 0 TM) reaction. At these points the above criterion is very poorly satisfied. The above restriction is related to the adiabatic criterion that ~o~/E << 1. The present range of this quantity is 0.08 ~ tio)/E < 0.12. The simplifications obtained from the assumption of small deformations are open to question in view of the magnitude of the deformation parameters obtained. It has been suggested that these magnitudes could be reduced b y employing a larger value of R 0 in the sealing factor (kRo~) ~ than is obtained from the theoretical fit to the data. The justification for this procedure would be that the "fuzziness" of the nuclear surface would be observed as a scaling factor whereas the "sharp" radius of the core would determine the angular distribution. From the expressions for the excitation cross sections it is seen that to reduce the deformation parameter b y a factor 2 in this manner, a "fuzzy" edge of the order of a R 0 is required.

INELASTIC SCATTERING OF HEAVY IONS

387

5. C o n c l u s i o n s

The preceding diffraction analysis results indicate that the inelastic interaction radii are slightly larger than the corresponding diffraction elastic radii. This trend has been noted in the ~ scattering work of Yavin and Farwell 1). In their results on Ole(~, ,¢') O le*, the assumption that the 1- and 3- levels of the low lying doublets in O le are being excited, leads to interaction radii larger than the elastic values. The assumption of 0 + and 2 + excitations yields inelastic radii smaller than the elastic radii. Unfortunately in their work it is not possible to distinguish between even and odd parity fits to the data. It should be noted that in the present experiments the absolute k R o values are subject to the uncertainty of the energy determination. However, the relative Ro values within a given reaction will be independent of this error. On the basis of fitting the data, it is not possible to distinguish between a dipole (l ~-- 1) and an octupole (l = 3) fit to the oxygen excitation in the present experiments. A monopole fit will require a somewhat larger value of R o ( R o = 7.40 fm for 1 = 1 excitation). The octupole analysis was used mainly because the alpha particle model of C12 and 018 predicts that the 2+, 4.433 MeV level of C1~ and the 3% 6.14 MeV level of O le are the first levels excited in those nuclei b y a purely rotational transition. Other neighbouring levels require excitation of vibrational modes in addition to a rotational transition. The values of the deformation parameters obtained serve only to indicate that the deformations present are quite large. Due to the ground state symmetries of these nuclei, the deformations are viewed as a measure of the distortions produced b y the Coulomb and nuclear fields. These distortions in turn, influence the scattering. The authors would like to thank Mr. G. Garvey for many stimulating discussions, particularly in the original statement of the problem, and Mr. A. M. Smith for his invaluable assistence throughout the experiment, particularlyin the experimental set up. References 1) 2) 3) 4) 5) 6) 7) 8) 9)

A. I. Yavin and G W. Farwell, Nuclear Physics 12 (1959) 1 R. Sherr and M. Rickey, Bull Am. Phys Soc. 2 (1957) 29 H J. Watters, Phys. Rev. 103 (1956) 1763 E . Newman, P. G. Roll and F. E. Steigert, Phys. Rev 122 (1961) 1842 P. G. Roll, E. Newman and F. E. Stelgert, Nuclear Physics 29 (1962) 544 A. M. Smith, Phys. Rev. (to be pubhshed Febr. 1, 1962) N. Austern, S T. Butler and H. McManus, Phys. Rev 92 (1953) 350 E. Rost and N. Austern, Phys. Rev. 120 (1960) 1375 J P. Martin, Technical Report No. 1, Sarah Mellon Scaafe Radiation Laboratory, University of Pittsburg (Oct 1959) 10) J. S. Blair, Phys Rev. 95 (1954) 1218, 107 (1957) 1343 11) S. I. Drozdov, J E T P (Soviet Physics) 1 (1955) 591, 588

388 12) 13) 14) 15) 16) 17) 18) 19)

D J. WILLIAMS AND F. E. STEIGERT E. V. Inopm, J E T P (Soviet Physics) 4 (1957) 764 J. A. McIntyre, K. H. Wang and L. C Becker, Phys. Rev. 117 (1960) 1337 J. S. Blair, Phys. Rev. 115 (1959) 928 A. Zucker and M. L. Halbert, Proc. Second Conf. on Complex Nuclei, May 2 --4 1960, Gatlinburg Tenn., pp. 144--160 and 164--166 C. L. Cntchfield and D. C. Dodder, Phys. Rev. 75 (1949) 419 P. G. Roll and F. E. Steigert, Nuclear Physics 16 (1960) 534 F W. Martin, private communication P G. Roll and F. E. Steigert, Nuclear Physics 29 (1962) 565