A double-stripping study of 16O structure

Nuclear Physics A144 (1970) 473--480; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permission from the publisher

A D O U B L E - S T R I P P I N G S T U D Y O F 160 S T R U C T U R E J. L. HONSAKER, T. H. HSU *, W. J. McDONALD and G. C. NEILSON Nuclear Research Centre, The University of Alberta, Edmonton, Alberta, Canada tt

Received 23 January 1970 Abstract: Angular distributions of the reaction 14C(3He, n)160 have been measured at 6 MeV for the lowest states in 160. The ground state distribution has been analysed by double-stripping DWBA and the amplitudes of sd-shell transfer determined relative to lp 2 transfer. The results are smaller than the values predicted by shell-model calculations. The next higher level showing a direct-reaction distribution appears to be the 1 - level at 7.12 MeV. The 6.05(0 +) and 6.92(2 +) levels do not show strong direct formation, in agreement with their supposedly predominant 4p-4h nature. Excitation functions from 3.5 to 6 MeV for these lowest levels have a resonance at 4.1 MeV as the only outstanding feature. E I

NUCLEARREACTIONl*C(aHe'n)'E=3"5"6 MeV measuredtr(E;En'O)" 160 ground state deduced shell amplitudes. 170 deduced resonance.

I

1./ntrodnetion

The main incitement for the description o f nuclear states by the shell model comes f r o m experimental evidence concerning nuclei with closed and nearly-closed shell configurations. Recent calculations by Zuker, Buck and M c G r o r y ( Z B M ) l) o f energy levels in 160 and its nearest neighbors have indicated deviations f r o m the simple closed-shell picture. These are expressed as 2p-2h and 4p-4h c o m p o n e n t s in the wave functions. Since even the 160 g r o u n d state is assigned a sizable 2p-2h c o m p o n e n t , further study o f these levels by experiments sensitive to the higher configurations seems very desirable. One expects the 2p-2h c o m p o n e n t s to be formed strongly in the t w o - p r o t o n transfer reaction 14C(3He ' n)160. This reaction has been investigated previously 2) at b o m barding energies below 3.4 MeV. We have extended the excitation function up to 6 MeV, a n d measured an angular distribution at that energy. 2. Experiment W e have investigated the reaction using neutron time-of-flight spectrometer. T h e 3He beam f r o m the University o f Alberta Van de G r a a f f generator was pulsed and compressed with a M o b l e y bunching system. The detector was a 9 cm diameter x 1.9 cm thick N E 213 liquid scintillator on a X P 1040 photomultiplier, with constant fraction o f pulse-height timing 3) and ~-ray discrimination. * Present address: University of Ottawa, Ontario. ** Work supported in part by the Atomic Energy Control Board of Canada. 473

474

3. L. HON$AKERet aL

The carbon target t, of uncertain isotropic enrichment, was deposited on tantalum. The areal density of 14C was measured by a Geiger counter detecting fl-particles emitted through a 0.9 mm 2 mask from several spots on the target. The counting rate was compared with that from a calibrated 14C source. Counting statistics in this comparison, and uncertainty in the large (60 ~o) correction for backscattering from the heavy target backing limit the accuracy of the cross-section normalization to about 30 9/0. Absolute cross-section values were not used in the analysis, hence only the relative statistical errors of the measured points are shown in the figures.

3. DWBA analysis A detailed analysis of the ground state angular distribution (fig. 1) was made using double stripping DWBA calculations tt. The optical potential for 3He on 14C must be estimated from available data on elastic scattering of 3He from targets of similar mass. Two sets of potential parameters, from 160 and 14N, were chosen and are given in table 1. We consider them equally preferred. Note that the difference is primarily in the imaginary well. The potential for the neutron is that of Rosen 5). For the two-proton transfer between the two 0 ÷ ground states, the orbital angular momentum transfer is L = 0 if the spins of the protons are antiparallel. The shellmodel configurations which the protons can occupy are thus pairs coupled to 0 angular momentum. Following ZBM, we limit the analysis to the pairs (lp~r) z, (Idl) 2, and (2s~r)2 which will be designated p2, d 2 and s2. The differential cross section is obtained from the square of the coherent sum of transfer amplitudes to each of these configurations. If we take just two configuration pairs at a time, we would have for example da 1ratA(p2)+ 6e~A(d2)l 2. dr2 - -

oc

In the special case that only one of the amplitude coefficients S: t is not zero, it would be the double stripping analog to a spectroscopic factor in single stripping. The transfer amplitudes A include all angular momentum coefficients. By investigating the relative magnitude of two such factors, one can obtain significant structure information while avoiding the difficulties associated with determining an absolute magnitude for each. The largest component is expected to be the (lp÷) 2 part which completes the p-shell, so it is suitable to try to establish the ratios (rad/Sep) ~ and (S:,/Sap) ~. The calculated angular distributions with both ratios equal to zero, representing pure p2 transfer, do not agree well with the measurements for either potential I or II. No better fit can be obtained with potential I and s2 or potential II and d 2 transfer. For the remaining ? Supplied on loan by the Atomi c Energy of Canada Ltd., Chalk River. tt The program used was adapted from one written by Yates and uses the Rook-Mitra approximation.

160 STRUCTURE

475

combinations of potentials and transfer configurations, amplitude ratios can be found which produce good agreement with the experimental angular distribution, as shown in fig. 1. The "d" and "s" curves correspond to the ratios

\~-~./

o~'p/

- 0.26.

In order to express this information in terms of the 160 wave functions we must take the configuration of the 14C target into consideration. The mass-14 system has been studied intensitively 6), and it has been shown that the p-shell configurations are not sufficient to account for the properties of the 14C ground state. Although a 10

l a c (3He,n)160

5 q

d.__~ d~ 1

.5

.1 .05

0

30

60 90 120 C.M. ANGLE

150

180

Fig. 1. Ground state angular distribution at 6 MeV bombarding energy. The DWBA curve designations are: (p) p2 only, potential I; (d) p2 and d 2, potential I; (s) p2 and s 2, potential II.

TABLE 1 Woods-Saxon optical potentials 4) used in DWBA calculations Potential

Scattering

V (W) (MeV)

a (fro)

re (fro)

3He I

10.5 MeV on 160

real imaginary

170 20

0.893 0.51

1.03 2.06

aI-Ie II

29 MeV on X4N p bound state

real imaginary

169 32.1

0.675 0.566 0.60

1.14 1.82 1.25

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J.L. HONSAKERet aL

nuclear tensor force is required for a complete explanation of this state and its isobaric analogues, we consider here just the sd-shell mixing calculated without regard for the tensor force: ls 4 lp s x (0.95p 2-0.28d 2-0.12s2). These sd-components present in the initial state affect the p2 transfer amplitude by a small amount. When combined with a tensor force, they give satisfactory agreement with the mass-14 data. Normalizing the wave functions so obtained from the above amplitude ratios, representing the extreme cases of s2 transfer exclusion or d 2 transfer exclusion, we find the possible configurations for the 160 ground state: ls 4 lp 8 x

or 0.97p 4 - 0.26p2s 2

.

Since mixtures of the d 2 and s2 components in smaller amounts are also possible, these configurations represent limiting values of the d 2 and s2 amplitudes. No correction has been made for the projection of the p2 part of ~4C into LScoupled states as given in ref. 6). The 3P o term would not participate in the reaction because of the S = 0 selection rule in the proton-pair transfer. This would decrease the p2 transfer amplitude by about 10 ~, and a correction for it would decrease the s2-d 2 components by the same proportion. There may be partial compensation, however, due to an increase in the angular momentum coefficients when the (p~)2 component is included. 4. Discussion of results

We wish to compare these limits with some of the wave functions reported by other workers. Purser et al. ~) have measured the single neutron pickup in the 160(d, t)a 50 reaction and found 0.87 p4, 0.26 p2s2, 0.27 p2d2. Their combined s2-d2 components are thus somewhat greater than the limits given above. Results from the (3He, ~) reaction and from the (d, 3He) proton pickup discussed in that paper gave a larger portion of the wave function to the p2d2 component. The reasons for these discrepancies are not clear. The relative phases of the configuration would not be determined from the single pickup reactions. The ZBM shell-model calculations gave 0.71 p 4 + 0 . 5 8 p2d2 with possible amplitudes < 0.28 for p2s2 and higher configurations. Brown and Green [ref. 8)] give the result 0.874 ( 0 p - Oh) + 0.469 ( 2 p - 2h) + 0.130 ( 4 p - 4h)

477

t 6 0 STRUCTURE

based on Nilsson wave functions. Both of these theoretical results have s2-d 2 components larger than the above limits. 14C(aHe,A) =~0

2 0

I

I

0

I

6,05}MeV 6.13

_0 4

c 0 0

I

I

&

Levels

o 0

=

I

{..{-

O,0un° S , o , .

?g~."

:g

o

13

o •

s',s

41o

4',5

5'.0

s',5

6'.o

3He Energy, MeV Fig. 2. Excitation functions for the levels discussed in the text. The resonance behavior at 4.1 MeV is indicated by curves through the points.

Before discussing possible reasons for disagreement between the theoretical and experimental results, it is necessary to estimate the amount of cross section due to compound nuclear processes when analysing in terms of a direct reaction theory. In this case the 170 compound system would be formed at very high excitation and one would expect a large number of overlapping levels. The incoherent angular distribution from these levels should be nearly isotropic. From the deep minima observed in the ground state angular distribution, and the nearly isotropic compound-nuclear distributions expected from a 0 ÷ ~ 0 + reaction, the magnitude of the compound cross section seems to be very small relative to the

478

J . L . HONSAKER e t a l .

direct cross section. The compound effects were therefore ignored in the analysis and the errors thus incurred would require the DWBA calculation to have somewhat deeper minima than shown. The values for the resulting amplitude ratios would differ by an amount much smaller than their probable errors from other sources. It is commonly asserted that the compound nuclear part of a cross section is small relative to the direct reaction part when the excitation function is lacking in resonance behavior or fluctuations with energy. The conspicuous rise of the ground state cross section (fig. 2) up to 6 MeV seems, at first consideration, to indicate the contrary. However, the fact that the 12C(aHe, n)140 and 1aC(2He ' n)l s O reactions exhibit a similar rise at this energy to cross sections of comparable magnitude 9) suggests strongly that the rise is due to the 3He energy approaching that of the Coulomb barrier. The two doublets show a less pronounced rise and are free of resonant features near 6 MeV. There are three items which should be considered in any attempt to explain the difference between the theoretical and experimental results. (i) the ZBM shell-model calculations did not account for the effects of spurious states. These could make a significant change 1o) in the theoretical ratios. (ii) The wave functions of the present analysis are based on a Saxon-Woods potential, while the shell-model calculations used a harmonic-oscillator potential. The latter is not appropriate for DWBA calculations which are strongly dependent on the outer parts of the wave functions. Here also the shell-model ratios might be modified if a different potential were used. (iii) There are possible effects of higher configurations which were not included. One must also examine the assumptions made in the DWBA analysis: (i) We have assumed no interference between direct and compound reaction mochanisms. Such interference is often claimed to be the case of poor agreement in DWBA fits to data. There is no necessity to make this claim hero, and furthermore the incoherent compound cross section is evidently very small. (ii) We have assumed that the 3He+ 14C optical potential is close to the potential measured for 14N or 160. This can be justified by noting that the potentials for other nearby nuclei are similar. (iii) The DWBA program uses the zero-range approximation. It has been found that finite-range calculations give a different magnitude for the cross sections but the relative angular distribution shapes are about the same as for the zero-range case. Taking the ratios as we have done cancels out the effects on the magnitudes due to the finite range of interaction. 5. Excited state doublets

We have also obtained data on the first four excited states in the form of two unresolved doublets (fig. 3). The first of these consists of the closely spaced levels at 6.05 and 6.13 MeV with J~ reported as 0 + and 3-. This unresolved doublet peak shows a featureless cross section, both in the angular distribution and the excitation

16o STRUCTURE

479

curve. The 0 + level is expected to be formed with higher probability, requiring only s-waves where the 3 - level requires f- and s- or d- and p-waves in a compound nuclear reaction. I f the 0 + level is the major contributor to the doublet, the results show that it is fundamentally different in structure from the ground state, i.e. a 4p-4h or higher I

3

I

I

1

l

SECOND DOUBLET t

14 C ( 3 H e , n ) 1 6 0 "

2

1

b~

-o J'-o

6.92 MeV 2 +

I

I

I

I

FIRST DOUBLET

6.05MeV 0 + 6,13 MeV 30

"

0

I

I

1

I

I

30

60

90

120

150

180

C.M. ANGLE Fig. 3. Angular distributions of the doublets. The curve for the second doublet assumes an isotropic distribution for the 2 + level (dashed line) added to an L = 1 distribution for the 1 - level.

excitation must be present. This is in agreement with theories taking this level as the lowest of a rotational band. The shell-model calculations indicate a filled p-shell contribution half as large as that of the ground state. The present results show no evidence of such a contribution, which would have produced forward peaking. The 3 level wave function was given a large I p - l d component which would show up as an L = 3 transfer, but the measurements do not agree well with such a distribution either. The second doublet consists of the levels at 6.92 and 7.12 MeV. This 2 +, 1 - doublet contains the presumed 2 + member of the band based on the first excited state. It

480

J.L. HONSAKERet al.

s h o u l d exhibit the same featureless cross section as that level. T h e o b s e r v e d p e a k i n g (fig. 3) o f the a n g u l a r d i s t r i b u t i o n thus is likely d u e to the 1 - level. A c o m p a r i s o n with a D W B A calculation for a n L = 1, ( l p - 2 s ) transfer is shown. This is the transfer expected for the 1 - level on the basis o f the Z B M wave function. T h e 2 + level was given with a 1d-2s c o m p o n e n t a n d w o u l d have p r o d u c e d an L = 2 d i s t r i b u t i o n with m a x i m u m at 50 °, a p o o r m a t c h to the data.

6. Resonance A r e s o n a n c e at 4.1 M e V is o b s e r v e d in the 0 ° excitation function o f the g r o u n d state a n d the second d o u b l e t (fig. 2). T h e strength in the second d o u b l e t a n d lack o f reson a n c e in the first suggest t h a t the 2 + level is n o t involved, as it is s u p p o s e d l y a m e m b e r o f the b a n d b a s e d on the n o n - r e s o n a t i n g 0 + level at 6.05 MeV. This implies t h a t the 1 - level at 7.12 M e V is p a r t i c i p a t i n g strongly in the resonance. This r e s o n a n c e c o r r e s p o n d s to a level o r levels at 2 2 . 2 M e V in 170, which is higher t h a n levels previously r e p o r t e d . Since the first d o u b l e t shows n o signs o f the resonance, we suspect t h a t the 0+-2 + b a n d is n o t involved. T h e levels f o r m e d b y the r e s o n a n c e w o u l d then be the 7.12, 1 level a n d the g r o u n d state. T h e relative strengths o f the r e s o n a n c e s suggest t h a t s-wave n e u t r o n s can lead to the 1- level, thus i n d i c a t i n g a ½- o r ] - a s s i g n m e n t to the r e s o n a n c e level. F u r t h e r inf o r m a t i o n is n e e d e d to clarify this, a n d the ?-ray spectra should also be m e a s u r e d over the resonance. T h a n k s are due to V. K . G u p t a for clarifying some p o i n t s c o n c e r n i n g the theoretical calculations, a n d to the technical staff o f the N u c l e a r R e s e a r c h Centre for the assistance which m a d e this w o r k possible.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

A. P. Zuker, B. Buck and J. B. McGrory, Phys. Key. Lett. 21 (1968) 39 R. G. Johnson, L. F. Chase, Jr. and F. J. Vaughn, Proc. Rutherford Jubilee Conf. (1961) 591 W. J. McDonald and D. A. Gedcke, Nucl. Instr. 55 (1967) 1 J. C. Hiebert, E. Newman and R. I-L Bassel, Phys. Rev. 154 (1967) 898 L. Rosen, Proc. 2nd Int. Symp. polarization phenomena, ed. Huber and Schopper (1966) Rose, Hausser and Warburton, Rev. Mod. Phys. 40 (1968) 591 K. I-[. Purser et al., Nucl. Phys. A132 (1969) 75 G. Brown and A. M. Green, Nucl. Phys. 75 (1966) 401 T. H. Hsu, thesis and Hsu et aL, to be published P. J. Ellis and L. Zamick, Int. Conf. on properties of nuclear states (Montreal 1969) contribution 7.22