Comparison of fusion cross sections for 12C+12C → 24Mg and 14N+10B → 24Mg

Nuclear Physics A348 (1980) 350- 364; @ Not to

North-Holland Publishing Co., Amsterdam

be reproduced by photoprint or microfilm without written permission from the publisher

COMPARISON OF FUSION CROSS SECTIONS FOR ‘2C+12C + 24Mg AND 14N $ l”B -_) 24Mg R. L. PARKS, S. T. THORNTON,

L. C. DENNIS t and K. R. CORDELL It

Department of Physics, Uniuevsity of Virginia, Charlottesville, Virginia 22901 USA

Received 10 March 1980 (Revised 7 July 1980) Abstract: The total fusion cross sections have been measured and compared for two light systems, “C-I- ‘*C and i4N+ “B, leading to the same compound nucleus at the same excitation energies, E*(24Mg) = 49, 50, 55 and 60 MeV. The critical angular momenta extracted for the formation of *%g via i2C + 12C and i4N + 1OBare different enough to clearly indicate the presence of an entrance channel effect (limitation). The Z-distributions of the evaporation residues are compared to each other and to Hauser-Feshbach calculations. The data are also fitted with and compared to theoretical models which predict total fusion cross sections.

E

NUCLEAR REACTIONS ‘tC(‘ZC, X), E = 52.1, 72.1, 82.1, 92.1 MeV; *‘B(i4N, X), E = 26.9, 50.9, 62.9, 74.9 MeV; measured i (fragment 0, E, Z); deduced critical angular momenta for fusion, entrance channel effects. Statistical model predictions of the residue cross sections. Macroscopic model fits of total fusion cross sections.

1. Introduction The role of angular momentum in the fusion cross section (gfUS)of heavy ions was first explored by Zebelman and Miller ‘) who employed three different targetprojectile combinations which led to the same relatively heavy compound nucleus (A = 170). They found that cfus was limited by the dynamical properties of the entrance channel, not by the unavailablity of high-spin yrast states. Many fusion measurements have been made for compound nuclei in the mass region A = 20-40 [refs. “-‘)I but only a few 4*6, ’ ) have examined the question of what limits oFuS, especially in the energy region near the characteristic bend in o,,,(E) versus E. In the case of the l”B -I-I60 and “C + 14N systems compared by Gomez de1 Camp0 et al. 4), cr;nu”s” for l”B + I60 was found to be surprisingly large, and the authors did not reach any definite conclusions about entrance channel effects. Moreover, + Present address: Department of Physics, Florida State University, Tallahassee, FL 32306, USA. tt Present address: Max-Planck Institut fur Kernphysik, 6900 Heidelberg, West Germany. 350

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we have extracted the critical angular momenta (1,,) from their measured ofus for both entrance channels for comparison at the same excitation energies in 26A1. This comparison shows that at the same E*(26Al), the I,, for the two entrance channels are nearly equal within uncertainties. Thus, no evidence for an entrance channel limitation is apparent. In the case of Horn et al. ‘j), the I60 + 26Mg and “F+ 23Na systems were compared but it should be noted that (i) the compound nucleus studied (A = 42) is at the upper limit of what is considered to be a light system and (ii) the conclusion concerning an entrance channel effect was based largely on one data point at %,. = 70 MeV for 160+26Mg whereas any such effect should be evident over a wider energy region. More recently, Saint-Laurent et al. ‘) studied the 160+ 160 and 12C+ 20Ne systems and found clear evidence that the cross section for the formation of 32S via these two reactions depends upon the entrance channel. In summary, the question of what limits crf=,in the lighter systems remains open. The choice to study’ the compound nucleus 24Mg via the 12C+ 12C and 14N+.loB entrance channels was prompted by practical and physical considerations such as availability of(i) targets and beams, (ii) previous measurements of ofus of 12C+ “C [refs. 2, “,“)] and (iii) yrast-line calculations for 24Mg. In order to effect the most explicit comparison of the two entrance channels, the 24Mg nucleus was excited to the same excitation energies via the two channels.

2. Experimental procedure The beams of “C and 14N ions were obtained from the Brookhaven National Laboratory MP-7 tandem Van de Graaff accelerator. The 12C beam was accelerated to 52.1, 72.1, 82.1 and 92.1 MeV while the 14N beam was accelerated to 26.9, 50.9, 62.9 and 74.9 MeV. Beam intensities varied from 10 to 100 nA depending on the angle of investigation. The natural, self-supporting 12C targets were 87 ,ug/cm2 thick. Carbon build-up was found to be small (N 2 % at the end of the experiment) and was not important since angular distribution measurements incorporated the use of three detectors at fixed angles to monitor the elastic scattering. The self-supporting l”B (enriched to 95 %) targets were 100 pg/cm2 thick and were also spared any appreciable carbon build-up through the use of liquid nitrogen traps and cryogenic pumps. Two BE-E telescopes were used for detection and identi~cation of the reaction products. The dE elements were ionization chambers in which P-10 gas (90 % argon, 10 % methane) was maintained at a pressure of 40 torr with a Cartesian manostat. The E-elements were surface-barrier detectors. One telescope with a very small (0.01356 msr) solid angle was positioned to the right of the beam for forward angle ~eas~ements (@,,, = 2-24O) while the other telescope with a relatively large (0.6433 msr) solid angle was positioned to the left of the beam for more backward angle measurments (Blab= 2244”). A region of overlap (f3,,, = 22-24*) was measured

352

R. L. Parks et al 1 Fusion cross sections

as a check to ensure that the method of norm~~ation between the two telescopes was consistent. The relative magnitudes of the telescope solid angles were checked by the use of an alpha source. Both ionization chambers had snouts incorporating cylindrical magnets to bend away any secondary electrons. Measurements were taken in N 2” steps so that each angular distribution consisted of N 20 points. The actual scattering angle was carefully determined to a precision of 0.04” by measuring elastic scattering with the first telescope at forward angles to the left and right of the beam direction. Aiding this precision was the use of three fixed-angle surface-barrier detectors to monitor the absolute position of the beam. Two of these were positioned above the beam at # = 9”, 8 = + 3”. The third one was positioned below the beam at (p = -3”, 8 =I 9” and thus any right/left, up/down deviation of the beam could be measured and taken into account. Even though the beam was highly collimated, such a precaution was needed in order to obtain the high-precision angular determination mentioned above., The E-signals from the telescopes and monitor detectors were stored in 1024 channel spectra while the LIE-E signals were binned into 128 x 128 channel arrays. All spectra were stored on magnetic tape and later analyzed off-line.

3. Experimental results A typical E-d E spectrum from the 12C+ 12C data is shown in fig. 1 for Eiab = 92.1 MeV and 6iab = 9”. The bands corresponding to the different elements are clearly separated and enclosed with solid lines for identification purposes. Angular distributions were obtained from the two-dimensional spectra such as that shown in fig. 1 in a systematic way. The elemental bands were projected onto the energy axis to give d20/dS2dE for each 2. The portions of the distributions which are attributed to the fusion process were then energy-integrated to obtain dc,,$dS2. The method used to separate fusion products from those due to direct or other reaction mechanisms was similar to that given in ref. ‘), where simple kinematic arguments were used. At the energies investigated in this experiment, the contribution to the energy spectra from processes other than fusion was typically less than 10 % except in the elastic band where direct components and slit-edge scattering (at very forward angles only) were evident but not separated from the fusion. Therefore, the fusion events could not be reliably extracted from the inelastic spectra in either reaction. Instead, this contribution was obtained using a statistical model calculation as explained later in this section. Absolute normalization could not be obtained reliably using target thickness and beam current integration because the Faraday cup was blocked at forward angles by one of the detector telescopes and the charge state of the beam after passing the target is not precisely known. Instead, a less direct but more precise method was used in order to minimize the ~certainty associated with the no~al~ation process.

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I

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‘2c +‘2c EL,.,B= 92.4 MeV e

LAB=

‘-’

90

z

80

1

70

d $ I 0

60

z

50

4

6 tj

F _

Ne

40

30

40

50

AE (CHANNEL

60 NUMBER)

Fig. 1. E versus AE spectrum for reaction products of “C+ lzC for I&,, = 92.1 MeV and Olab= 9“. The elemental bands, outlined by the solid curves, are projected onto the E-axis to obtain energy distributions.

This method is based on the fact that c-J,@)=

c-N,,(@ N lll0”

’

(1)

where N,,(0) is the number of elastic events from the 1024-channel energy spectrum at angle 0, N,,, is the sum of the number of elastic events from the three monitors which are fixed in angle and C is a normalization constant which is angle independent. The relative cross section N,r(@/N,,, was fitted with an optical-model potential using parameter sets from previous measurements lo- 12) as starting points. The fits were typically very good with reduced chi-squares close to unity. Using a,,(e)

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R. L. Parks et al. 1 Fusion cross sections

from these fits, eq. (1) was solved for C. Although the data at all angles (8,,, N 244”) were used in the fitting process, the constant C was obtained by averaging only the forward angle results (8,,, N 2-10”) where the statistics of N,i(G) were better than 1%. We then used an expression for the absolute fusion cross section analogous to eq. (l), i.e.,

where N,,,(B) is the total number of fusion events at angle 0. The constant C and N monare already known and thus, the absolute value of of,,(e) is obtained. The value of this process is that the uncertainty is derived mainly from the statistics and extraction of the values of 8, N,,(6), N,,,(e) and N,,, and the quality of the optical-model fit. Since N,,(6) and N,,, typically had better than 1 % statistics and the opticalmodel fits to N,i(Q)/N,,, were good, the normalization process alone (including the angular uncertainty) contributes only N 2 % to the overall uncertainty in the total fusion cross section. An additional uncertainty of N 3 % arises from statistics in N,,,(Q). In order to obtain ofus, one must first integrate do,,,/dSJ over all angles i.e., 0 fus

Xdofus =

~

so

de,

(3)

de

where all quantities are measured in the laboratory. Two typical angular distributions resulting from the sum of all fusion events (Z = 5-12) are shown in fig. 2 where the integrand on the r.h.s. of eq. (3) is plotted. In both cases the solid curve is the result of an interpolation routine which allows one to integrate the distribution using a very fine step size of A8 1: 0.02O.This method was also used for the elemental fusion yields, a,,,(Z). A valuable tool for deducing accurate fusion cross sections is the computer code LILITA “) which uses a Hauser-Feshbach, Monte Carlo model. In this experiment it was used as a check to see that the experimental energy and angular distributions of evaporation residues are consistent with the behavior predicted by the statistical model and to derive the contribution of the C and N evaporation residues to the “C+ “C and 14N+ l”B fusion cross sections, respectively. Fig. 3 shows two cases of experimental elemental yields compared to predictions of LILITA. Fig. 3a shows a case for which the agreement was better than average and fig. 3b shows the poorest agreement with the calculation. It should be noted that no attempt was made to fit the data with LILITA by variation of parameters. Undoubtedly better agreement could be obtained by line tuning of the exit channel level density parameters. The results shown are strictly predictions generated through the use of reasonable 13) parameters. The most important considerations were that the relative intensities of the isotopes produced and their behavior as a function of bombarding energy be reasonable. In an attempt to induce more confidence in the

355

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200

y .P B < 2

100

0

$ 400 -J CD P $

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_(b)

300

200

0

0

t0

20 LABORATORY

30

40

50

ANGLE (deg)

Fig. 2. (a) The angular distribution, (da,,,/d0),,,, for “C+ W at E,,, = 72.1 MeV. (b) The angular distribution for 14N + “B at I?,,, = 50.9 MeV. The solid curves are the results of interpolation.

predictions of LILITA for Z = 6 for the i2C+ “C reaction, the calculation was also done at lower energies and compared to the yields presented in ref. 3); agreement was found to be very good. Therefore, due to problems mentioned earlier, the LILITA predictions were decidedly more reliable for Z = 6 (for “C+ “C) and Z = 7 (for 14N+ “B) than any attempt to extract them experimentally. However, since the Z = 6 yield comprises from 4 to 40 % of orUSfor “C+ “C and the Z = 7 yield comprises from 2 to 18 % of dfus for 14N + “B, the uncertainties in orus are increased accordingly. The elemental yields for the two reactions are shown in fig. 4. These are experimental yields with the exception of Z = 6 in fig. 4a and Z = 7 in fig. 4b, both of which are LILITA predictions. As E*(24Mg) increases, the average Z of the residues decreases. These trends are consistent with the fact that increasing the excitation of the compound nucleus results in an increase in light-particle production. The LILITA predictions are in agreement with the trends displayed in the data in fig. 4.

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0

4

5

6

7

8

9

10

11

12

Fig. 3. Elemental abundances in a,,, for (a) 12C-I-‘*C at Elab = 92.1 MeV and (b) 14N + “B at E,=, = 50.9 MeV. The histogram represents a Hager-~~hbach, Monte Carlo calculation. The solid points are the data.

4. Analysis 4.1. TOTAL FUSION CROSS SECTION

The total fusion cross sections and the associated critical angular momenta (I,,) are presented in table 1. The sharp cut-off model was used to derive 1,, from ofus using d fus E 7rzP(E,,+ 1)2.

(4)

For the 12C+ IzC reaction, the uncertainties range from - 5 % to - 8 % while for the 14N+ l”B reaction, the uncertainties are below 5 %. The fusion cross sections are shown in fig. 5 as a function of E*(24Mg). The large drfference of the two qus at E*(24Mg) = 40 MeV is due largely to Coulomb barrier effects. This becomes clear upon exudation of the separation energies (S) of the “Mg. They are so dissimilar (S = 13.9 two systems from the compound nucleus MeV for the 12C+12C system while S = 28.9 MeV for the 14N+ l”B system) that

357

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I -

“N +“B

350

50

0 30

40

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60

70

ry

3n

40

50

60

Fig. 4. Experrmental elemental fusion cross sections versus E*(24Mg) from r4N + rOB. Note that the C yields in (a) and the N yields in (b) are not determined calculated

70

?4,,.;

as described

(a) “C + rzC and (b) experimentally but are

in the text.

TABLE 1 Fusion

52.1 72.1 82.1 92.1

cross sections

26.0 36.0 41.0 46.0

and critical

angular

40 50 55 60 r4N+

26.9 50.9 62.9 74.9

11.2 21.2 26.2 31.2

momenta

40 50 55 60

for “C+

“C

and r4N + rOB

839k40 768 k 40 930&75 873k40

13.1+0.3 14.9kO.4 17.7kO.7 18.2kO.4

576+25 896k40 961,40 903 + 40

6.6kO.2 12.0+0.3 14.OkO.3 14.8kO.4

rOB

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A ‘2c + ‘Q I

0

“N+‘oB

b

400 40

35

Fig. 5. Total

45

50 E” IN 24Mg (MeV)

55

60

65

fusion cross sections of rzC + ‘*C and r4N + rOB versus excitation energy in z4Jvig. Solid curves serve only to guide the eye in viewing the trend of the data points.

the&II.

needed to excite 24Mg to 40 MeV excitation energy are very different, being 26.0 and 11.2 MeV, respectively (see table 1). Another prominent feature seen in fig. 5 is the apparent continuation of the wellknown oscillations 2, 3, in ofus for i2C+ “C. It is interesting that the two grus are nearly equal at E*(24Mg) = 55 and 60 MeV, but the oscillations may be primarily responsible for this phenomenon. In fig. 6 it can be seen that the present work is in agreement with Argonne but not with Texas A & M for the low energy “C + “C data where all three data sets overlap. However, the two highest energy points from the present data do agree with the trend seen in the Texas A & M data. The Saclay data “) are not shown since their 1200

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+ I*C,ARG~NNE

‘*C + ‘*C,PRESENT

WORK

14N + l’B,PRESENT

WORK

1

I

40

I 60

I

I 100

E cm (MeV)

Fig. 6. qus versus I?,,,,. for “C+ r2C and r4N+ log. The data from Argonne *) and Texas A & M s) are also shown to be in general agreement with the present ‘*C + ‘*C data. The solid (dashed) curve is a Glas and Mosel calculation for “C+ 12C (r4N+ “‘B).

R. L. Parks et al. 1 Fusion cross sections

359

gross structure is much like that of Argonne. The broad oscillations as seen in the 12C+ 12C data seem to be fairly well understood. Tanimura 14) has employed the coupled channel method to reproduce the.&,, of the maxima in the Argonne data quite accurately. The maximum observed at E,,,. N 26 MeV is attributed to the J = 14 partial wave. The next two maxima predicted by this model are at E,.,, N 30-31 MeV (J = 16) and E,,,, 2: 36-37 MeV (J = 18) although indications are that the model becomes less reliable at higher energies. Abe et al. ’ 5, have also reproduced the maxima in the Argonne data using a band crossing model but they have not extended this calculation to higher energies. The present work shows a possible maximum near E,,,, N 41 MeV. In the region of E,,,, N 30-40 MeV, more data are are needed in finer energy steps in order to elucidate the oscillations. It is also evident in fig. 6 that the arsx for the two entrance channels are nearly the same if the Texas A & M data are excluded. They certainly agree within uncertainties for the present data since ofus max(12C+ 12C) = 930+75 mb while ort(14N+ is independent of the entrance “B) = 961 _t40 mb. This would indicate that o;“u”s” channel for these two systems. However, we point out that our 14N + l”B data contain only one point beyond the apparent orsx. 4.2. MACROSCOPIC

MODELS

The solid curve in fig. 6 is a calculation from the model of Glas and Mosel 16) using the parameters quoted in ref. 3). This curve tends to fit the Argonne data and those of the present work in an average way. Moreover, when extended to higher energies, the calculation is in good agreement with the Texas A & M data. The r4N+ l”B data were also fitted with the Glas and Mosel model as shown by the dashed curve in fig. 6, The 14N+ l”B data were rather easily fitted, due to their relative smoothness, using parameters which are similar to those needed to fit the ’ 2C + ’ 2C data. The ’ 2C + ’ 2C ( 14N + “B) parameters used are rcr = 1.050(1.035) fm, rB = 1.44(1.42) fm, V,, = -6.9( -9.5) MeV, I’,, = 6.6(6.6) MeV and hw = 2.0(2.0) MeV. The similarity is not surprising when examined closely. First of all, since this model is purely macroscopic, the same parameter sets give essentially identical results for the two reactions because the reduced mass (,u) and the nuclear radius dependence (Airoj + A&,) are similar for the two systems. Since the ’ 2C+ “C and 14N + l”B data are very similar (versus E _) at energies below the bend, the parameters related to the interaction barrier (i.e., rB and I$) should be and are similar. On the other hand, since the maximum fusion cross sections (ogsx) for the two reactions are different both in magnitude and energy, the parameters related to the critical radius (i.e., rcr and V,,) must be and are different. Another macroscopic theory has been reported by Birkelund et al. 17) which is based on a classical dynamical model employing different conservative and dissipative forces. The predictions of this model are shown with the present work in fig. 7. Although it does not fit the data well in either case, it seems to predict the energy of oK~*with reasonable accuracy.

(of

0.04

I

I

0.06

MODEL

0.42

PRESENT WORK

0

E;!,,, (MeV-‘1

-

l

ARGONNE A TEXAS ABM

Qc+ f2c

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E;.k (MeV-‘1

I 0.06

I 0.04

--

l

I

0.08

I

PRESENT WORK MODEL

+.J+loB

I

I

I

0.02

I

Fig. 7. (a) Fusion cross sections of ’ %Z+ “C with the solid curve showing the prediction of Birkelund ef al. 17). (b) Fusion cross sections of 14N + l”B with the dashed curve showing the prediction of Tubbs and Huizenga ‘*). The solid curve in (b) serves to guide the eye.

4000

1250

1500

361

R. L. Parks et al. 1 Fusion cross sections

More recently Lee et al. lg) have shown that a model incorporating the Q-values of a system fits most of the existing fusion fusion data at energies above the bend. They arrive at

where

R = r,,A* and p is the reduced mass. Using their parameters r0 = 1.2 fm and dQ = 10 MeV, we find that this model predicts cfus which are N 10 % higher than the 14N+ l”B data and N 25 % lower than the “C+ “C data above the bend in fig. 6. 4.3. ENTRANCE

CHANNEL

EFFECTS

Evidence for an entrance channel effect is most easily seen by comparing 1,, of the 12C+ 12C and 14N+ l”B reactions as shown in fig. 8. The Z,, deduced from the Argonne and Texas A & M data are included to show the low- and high-energy behavior, respectively, of the “C+ 12C channel. The solid curves show the grazing angular momenta (1,, or I,,,) calculated with the Wilczynski 20) formalism. The 120

r

100

>

!

_

80

_

.

‘2C + ‘2C,

TEXAS

0

‘2C+

ARGONNE

l

12C + 12C: PRESENT

WORK

A

14N + “B,

WORK

“C

,

-

I I

A8M

PRESENT

S ::g

60

z *w

40

I _

20

00 //

‘/’

,5’ _-

0 0

. __e+ 5

I

I

10

15

I 20

25

30

35

Fig. 8. Excitation energy in 24Mg versus I,,. The solid curves are the grazing angular momenta, I,,; the dashed curves are yrast-line calculations ‘I). The data shown are from refs. ‘r*) and from the present experiment.

362

R. L. Parks et al. / Fusion cross sections

two yrast line calculations shown as dashed lines are discussed elsewhere 21). The true yrast line is thought to lie between the two predictions. It is clear from fig. 8 that both fusion cross sections are limited at low energies by the angular momentum available (1,,) in the entrance channels since I,, N 1,, there. At higher energies, 1,, < 1,, for both reactions. This begins essentially near the bend m crfusbecause of dissipative frictional effects which come into play once the critical radius has been reached 16). Another obvious feature is that for a given excitation energy 1,, is well below the yrast angular momentum, implying that the availability of a compound nuclear state is not a limitation at these energies. The fact that the I,, for the two channels are quite different at the same excitation energies is important. It is an obvious result of the large separation energies of the two entrance channels from the compound nucleus 24Mg. However, the fact that 1,, for “C+ i*C is much larger than I,, for 14N+ l”B means that the compound nucleus formed via the ‘*C + ‘*C entrance channel must have a relatively higher spin distribution. If this premise is accepted, then one must expect to see a signature in the evaporation process of the compound nucleus. In fig. 9 the experimental evaporation residues of the two reactions are compared, except for Z = 6(7) for “C+ 12C(14N+ “B) which is the calculated result. The cross sections are shown for each Z as a percentage of the total ofus. Note the consistent production of lighter (heavier) fragments by the ‘*C+ ’ *C(14N + “B) reaction. Even disregarding the Z = 6 and 7 fragments which are in part calculated, the Z = 8-10 fragments are more populated by the 14N + l”B channel. These dissimilar Z-distributions are consistent with the statistical model prediction which shows that fusion residues resulting from a-decay are induced more strongly by the high J-values in the spin distribution of the compound nucleus while the n- and p-decays result most often from the low J-values. This implies that 24Mg formed via the ‘*C+ ‘*C reaction, with its relatively high-spin distribution, is more likely to evaporate into a+ a+ a+ ‘*C, for example, than 24Mg formed via 14N+ “B. Similarly, 24Mg formed via 14N+ 1°B, with its relatively low-spin distribution, is more likely to evaporate into, say, p+n+ **Na than 24Mg formed via ‘*C+ “C. Predictions by LILITA show this same effect, confirming the deduction that only angular momentum effects are responsible.

5. Summary Evaporation residues from the fusion of 12C+ ‘*C and 14N+ l”B have been measured over the same region of excitation energy in 24Mg and are found to differ significantly both in absolute magnitude and elemental abundance. The difference in magnitude of ofus at the lower energies is seen to be primarily a Coulomb barrier effect while the difference in the Z-distributions is shown to be a consequence of the differing spin distributions in the compound nucleus 24Mg. Both effects can be

R. L. Parks et al. / Fusion cross sections

c

Ex=40

(a)

MeV

363

E, =50

I

(6)

30

I

2

I

I

I

I

MeV

I

I

I

E, = 60 MeV

(d)

b” 40

30

20

IO

0 4

5

6

7

8

9

10 II

12

4

5

6

7

8

9

10 11

12

Fig. 9. Elemental fusion cross sections for ‘%+ “C (sohd histogram) and 14N + “B (dashed histogram) at excitation energies m ‘+‘Mg of (a) 40 MeV, (b) 50 MeV, (c) 55 MeV and (d) 60 MeV. Note the increased production of high-Z fragments by r4N+roB and low-Z fragments by ‘2C+‘2C. The experimental uncertainties for the measured a,,,(Z) are due mostly to statistics and range from 5 T0 for the more probable fragments to IO y0 for the less probable fragments.

traced to the large difference in the separation energies of the two entrance channels from 24Mg since both E*(24Mg) and I,, depend on S. The “C+ “C fusion data agree with previous work except for a few points. Together these data present a picture of the fusion of l ‘C+ 12C over a wide range of E c.m. = 10-100 MeV. More data in finer steps are needed in order to detect the possible continuance of the tine and broad oscillations seen at the lower energies. The best fits to the total fusion cross sections were those from the Glas and Mosel formalism. The fits to the two reactions are consistent with each other and with previous data. The parameter sets are similar and any differences are well understood. The predictions of the macroscopic models of Birkelund et al. “) and Lee et al. 18) are not in good agreement with the data although no parameter adjustments were attempted. The Hauser-Feshbach, Monte Carlo calculation produces Z-distributions which,

364

R. L. Parks et al. 1 Fusion cross sections

as a function of EC,,, and I,,, agree quite well with the data for both reactions. This is consistent with the statistical model assumption that a compound nucleus only remembers E* and J. We have shown that compound nuclei formed at the same E* but different J decay differently, just as the statistical model predicts. In conclusion, an entrance channel effect in the formation by fusion of 24Mg has been observed. It is seen both in the different I,, in the two entrance channels at the same E*(24Mg) and in the different Z distributions in the exit channels. The authors wish to thank J. Gomez de1 Camp0 for valuable discussions and for the use of LILITA. Thanks are also extended to L. E. Tubbs and J. R. Huizenga for performing the 14N+ l”B calculation seen in fig. 7b. Financial support from the National Science Foundation, the University of Virginia Computing Center, and the Oak Ridge National Laboratory, and the technical support of the staff at the Brookhaven National Laboratory are gratefully acknowledged.

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