Experimental and theoretical results for 21Ne(6Li, d)25Mg

Volume 60B, number 2

EXPERIMENTAL

PtlYSICS LETTERS

AND THEORETICAL

5 January 1976

R E S U L T S F O R 21 Ne(6 Li, d) 25 Mg *

N. ANANTARAMAN, H.E. GOVE and J. TOKE Nuclear Structure Research Laboratory, University of Rochester, Rochester, N. Y, 14627, USA

and J.P. DRAAYER Department of Physics and Astronomy, Louisiana State University, Baton Rouge, La. 70803, USA

Received 19 November 1975 Alpha-particle spectroscopic strengths extracted from 21Ne(6Li, d) angular distributions agree in both magnitude and multipolarity with predictcd strengths. Secondly, strengths calculated using eigenfunctions determined in large shell-model computations are remarkably consistent with pure SU3 symmetry limit results.

A recent article [1] dealt with one of the first studies of tire (6Li, d) reaction on an odd-A target (25 Mg). It reported the striking result that, although angular momentum selection rules allowed a multiplicity of L-values for each transition, the observed angular distribution for each member of the ground-state band of 29Si, when compared with characteristic shapes from the 24Mg(6Li, d) reaction [2], was that corresponding to a single-L transfer. No explanation of this effect could be obtained in terms of a simple SU 3 model, probably because of the inadequacy of the assignment of a single (X~t) to the eigenstates of 29Si. The present letter reports the results of a (6Li, d) study on another odd-A target, 21Ne, in which experimental a-particle spectroscopic strengths S~ are compared with reliable theoretical predictions. Such predictions are possible because shell-model results for low-lying states of both 21Ne [3] and 25Mg [4] are available. Since 21Ne has a ground-state spin of 3/2 +, two L-values can contribute to the transitions to each J 4= 1/2 final state in 25 Mg. These contributions are separated using the characteristic shapes of pure-L angular distributions measured in the 20Ne(6Li, d) reaction [5]. The theoretical predictions for Sa have been made assuming a (0s) 4 a-particle transfer and using two different approximations for the wave functions of the initial and final states of the target and residual nuclei. Work supported by a grant from the National Science Foundation.

In the first approximation, they are states of pure SU 3 (oscillator)-SU 4 (supermultiplet) symmetry, and in the second, they are eigenstates generated in large shellmodel calculations and are consequently of mixed (X/I) symmetry. These approximations [6] lead respectively to what will be called the simple and the realistic predictions for S~. Thus a second purpose of this letter is to compare the simple and the realistic predictions for relative and absolute a-particle strengths and hence to study the effect of (X/I) symmetry mixing on S~. Two gas cells [7] containing 92% enriched 21Ne gas (with 5% 20Ne and 3% 22Ne) at a pressure of ~ 5 cm of Hg were bombarded with a 32 MeV 6 Li beam of 300 nA from the University of Rochester MP tandem accelerator. One of the gas cells was used in the angular range of 5 ° to 10 °, the other (which at the time of the experiment could not be used at very forward angles) was used in the range 17.5 ° to 60 ° , and both were used at 12.5 ° and 15 ° . Outgoing deuterons were momentum analyzed by an Enge split-pole spectrograph and detected in photographic emulsions with an energy resolution of about 70 keV. The 20Ne(6Li, d) reaction was also investigated at 32 MeV. That reaction is interesting in its own right [5], but here it is used merely to provide the characteristic pureL angular distribution shapes. Figs. 1,2 and 3 show the measured angular distributions for transitions to members of the ground-state band (K ~r = 5/2+), the first excited band (K" = 1/2 +) and the second excited band (K ~ = 1/2+), respectively, of 25 Mg. The 9/2 + member of the ground-state band 149

Volume 60B, number 2

PtfYSICS LETTERS

5 January 1976 i

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Fig. 1, (6El, d) angular distributions for the 5/2 + and 7/2 + members of the ground-state band of 25Mg, compared with solid and dashed fines which are smooth curves drawn through experimental points for two L = 2 transitions in the 2°Ne(6Li, d) reaction.

at 3.40 MeV excitation was not resolved from a 3 / 2 state 9 keV away, and so the angular distribution for that state is not shown in fig. I. The solid and dashed lines in figs. 1 and 2 represent two L = 2 shapes. They correspond to smooth curves drawn through experimental points in the 20Ne(6 Li, d) angular distributions for the two 2 + states at excitations of 1.37 and 4.24 MeV, respectively, in 24Mg. The difference in shape between the two is small compared to the difference of either from similarly determined characteristic L = 0 and 4 shapes and provides a measure for the degree o f precision with which one can expect to separate the contributions o f different L's in transitions to the 25 Mg states. The comparison in fig. 1 o f the experimental angular distributions for the 5/2 + and 7/2 + members o f the ground-state band o f 25Mg with the L --- 2 20Ne(6Li, d) curves indicates that the two states are populated predominantly by L = 2 transitions. Selection rules, o f course, allow L = 4 contributions as well. Fig. 2 similarly shows that the transitions to the first three members of the first K ~r = 1/2 + band are all predominantly L = 2 in character but that to the fourth member (7/2 +) is not. In particular, a small L = 0 contribution would result in a forward peaking o f the angular distri150

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+

bution for the 3/2 + state; such a peaking is absent in the data. The 1/2 + state of the second K ~ = 1/2 + band is excited necessarily by an L = 2 transition but, as shown in fig. 3, the 3/2 + and 5/2 + states are not excited by pure-L transitions. The dashed-dotted curves in figs. 2 and 3 are least-squares fitted curves for the measured angular distributions, using a mixture o f L = 0 and 2 experimental shapes for the 3/2 + (2.80 MeV) state and mixtures o f L = 2 and 4 shapes for the 5/2 + (3.90 MeV) and 7/2 + (2.74 MeV) states. These Lvalues are the ones allowed by angular momentum coupling and parity and the experimental L = 0, 2 and 4 shapes used are those measured in the 20Ne(6Li, d) reaction. The spectroscopic strengths for all the transitions, some of them with experimentally pure-L angular distributions and others with mixed-L shapes (as discussed above), have been obtained by fitting the curves with DWBA calculations using the finite-range code LOLA [8] with the assumption o f a cluster transfer mechanism. The 6 gi optical potential employed was the one used by Strohbusch et al. [9] and the deuteron potential was the average set determined by Newman et al. [10] ; the bound-state well had a radius of 1.30

Volume 60B, number 2

PIIYSICS LETTERS i

T

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t:ig. 3. (6Li, d) angular distributions for the second K n = 1/2 + band in 25Mg. The dotted line is a L = 2 LOLA fit; the dasheddotted lines are least-squares fitted curves.

A~/3 fm and a diffuseness of 0.65 fro. [This set of optical and bound-state parameters has proved sufficient to fit most of the measured angular distributions in our sd-shell (6Li, d) studies.] The dotted curve in fig. 3 is the LOLA fit for the L = 2 transition to the 1/2 + (2.56 MeV) state. Table 1 lists the measured and calculated spectro-

5 January 1976

scopic strengths for the 21Ne(6 Li, d) reaction for mem. bers of the first three bands of 25Mg, all normalized relative to unity for the L = 2 transition to the 5/2 + ground state. Sthy [SU(3)] is what was called above the simple prediction for S a, in which (~u) = (81) is assigned to the ground state of 21Ne and (34~) = (66) to members of the ground-state K " = 5/2 + band and first excited K ~r = 1/2 + band of 25Mg, and (~a) = (93) to members of the second excited K n = 1/2 + band. The simple predictions are taken from ref. [6]. The last two columns give our realistic predictions for Sa, with the ground state of 21Ne taken to be that determined by Strottman and Arima [3] using the KUO interaction [11 ] and the states in 25Mg to be those generated [4] using (a) the scalar interaction of Akiyama et al. [12] and (b) the Preedom-Wildenthal (PW) interaction [13]. First we compare the simple (pure symmetry) predictions with results from our more expanded calculations. From the table we see that they agree remarkably well, the simple prediction often lying between the more realistic ones. Now the structure of calculated eigenstates for members of the K ~r = 1/2 + excited bands is k n o w n to be sensitive to the effective interaction used [3, 14, 15]. lntraband B(E2) values, for example, apparently cannot be adequately reproduced using a simplified model. And indeed, as denoted by asterisks in table 1, a sensitivity to this uncertainty in the calculated eigenfunctions is in strong evidence

Table 1 Relative spectroscopic strengths measured in 21Ne(6Li, d)25Mg compared with three different theoretical predictions. E x (keV)

K 71-

j

l

S( 6 Li, d)

Sthy [SU(3) ]

Sthy(Scalar)

Sthy(PW)

0

5/2 +

5/2

2 4 2 4 2 0 2 2 4 2 4 2 0 2 2 4

1.00 -1.90

1.00 0.00 2.20 0.04 0.51 0.49 2.92 1.28 0.01 0.01 1.32 1.27 0.0l 0.54 0.14 2.53

1.00 0.05 1.81 0.00 0.48 0.64 3.26 0.63 0.03 0.08 2.78 0.70 0.27 0.19 0.34 0.70

1.00 0.03 2.32 0.02 0.73 1.01 5.19 1.42 0.02 0.23 4.66 0.90 0.15 0.01 0.49 0.13

1612 585 975

7/2 1/2 +

1/2 3/2

1965

5/2

2736

7/2*

2564 2801 3901

1/2 +

1/2 3/2* 5/2*

0.24 -1.94 1.45 0.98 1.17 0.37 2.12 0.88 0.42 0.26

* Calculated eigenstates do not correspond to well developed rotational bands. 151

Volume 60B, number 2

PHYSICS LETTERS

here as well. In general, however, the effect of (X/I) s y m m e t r y mixing on relative a-particle strengths is small. As regards the absolute strengths, the values predicted by the simple, scalar and PW calculations for the L = 2 transition to the ground state are 0.044, 0.064 and 0.048, respectively, relative to unity for the simple prediction for the 160(6Li, d)20Ne (g.s.) transition. Secondly, we compare the experimental strengths with the predicted ones. Again the agreement is good. The predictions as to which of the two L-transfers allowed for each J f 5/: 1/2 state dominates agree with the observed results and the relative magnitudes are also in good agreement with theory. In the groundstate band, the lower of the two allowed L-transfers is predicted to dominate for each state and it is observed to do so with the predicted strength. In the first K 7r = 1/2 + band, theory predicts the lowest three states to be populated mainly by L = 2 transfer, and that is what is observed. The transfer to the 7/2 + member o f this band is predicted to be by L = 4, but it is observed to be by a nearly equal mixture of L = 2 and 4. (The separation o f the two L-components in this case is achieved to a precision o f about 25%. This value was obtained by comparing the results of the least-squares fitting procedure using two different L = 2 angular distribution shapes measured in the 20Ne(6Li, d) reaction.) The experimental L = 2 strength for the groundstate transition is 0.03 relative to unity for the 160(6Li, d)2°Ne (g.s.) reaction, in reasonable agreement with the predicted theoretical strengths. Note that the scalar and PW interactions predict completely different L-admixtures for transitions to the 3/2 + and 5/2 + states o f the second K 7r = 1/2 + band. Tlfis selectivity suggests that observed (6 Li, d) strengths might serve to discriminate among various effective interactions. Unfortunately, in this particular case neither prediction corresponds to what is experimentally observed. This indicates, as discussed above, an even more fundamental inadequacy in the modeling probably related to the basis truncation imposed on the A = 25 system. One may also question why the simple SU 3 prediction works well for the 21Ne + a -+ 25Mg transitions but not for the 25Mg + a ~ 29Si transitions. Here a quantitative explanation can be offeted based on sum-rule strengths [16]. F o r 21Ne + a -+ 25Mg the (81) ~ (66) transitions exhaust 34% of the total (81) -~ all (X/a) strength whereas for 25Mg + a 152

5 January 1976

-~ 29Si the most obvious candidate, (66) -~ (1, 11), exhausts only 14% of the total (66) ~ all (X/I) strength. S y m m e t r y admixing should therefore be expected to be much more important in 29Si than in 25Mg insofar as a-particle transfer is concerned. Nonetheless, it is interesting to note that in both cases transitions to members o f the ground-state band are favored via the lowest allowed L-value. In conclusion, we have presented a-particle spectroscopic strength extracted from 21Ne(6Li, d) angular distributions measured for low-lying members o f the three lowest rotational bands in 25Mg. These are in very satisfactory agreement with theoretical predictions in regard to the magnitude and multipolarity of the transition for the five levels below 2 MeV excitation. In particular, for transitions to members o f the ground-state band, the lowest allowed L is predicted and observed to dominate. Moreover, absolute and relative strengths calculated using eigenfunctions determined in large shell-model computations are shown to agree well with the pure SU 3 symmetry limit predictions. We thank C.L. Bennett for help during the experiment.

[1] N. Anantaraman, J.P. Draayer, H.E. Gove and J.P. Trentelman, Phys. Rev. Lett. 33 (1974) 846. [21 J.P. Draayer et al., Phys. Lett. 53B (1974) 250. [31 D. Strottman and A. Arima, Nuclear Physics Theoretical Group Report no. 46, Nuclear Physics Laboratory, Oxford University, 1973. [4] J.P. Draayer, Nucl. Phys. A216 (1973) 457. [5] N. Anantaraman et al., to be published. [61 J.P. Draayer, Nucl. Phys. A237 (1975) 157. [7] H.W. Fulbright and J. T~ke, Nuclear Structure Research Laboratory Annual Report 1974, p. 191. [8] R.M. DeVries, Phys. Rev. C8 (1973) 951. I9] U. Strohbusch et al., Phys. Rev. C9 (1974) 965. [10] E. Ncwman et al., Nucl. Phys. A100 (1967) 225. [11] T.T.S. Kuo, Nucl. Phys. A103 (1967) 71. [12] Y. Akiyama, A. Arima and T. Sebe, Nucl. Phys. A138 (1969) 273. [13] B.M. Preedom and B.H. Wildenthal, Phys. Rev. C6 (1972) 1633. [14] B.J. Cole, A. Watt and R.R. Whitehead, Phys. Lett. 49B (1974) 133. [15 ] H. Feldmeier, private communication. [16] K.T. Hecht and D. Braunschweig, Nucl. Phys. A244 (1975) 365.