The 26Mg(d,n)27Al reaction

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Nuclear Physics A90 (1967) 311--320; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

T H E 26Mg(d, n)27AI REACTION B. L A W E R G R E N

A.E.R.E., Harwell, Berks., UK Received 17 A u g u s t 1966 Abstract: N e u t r o n time-of-flight technique has been used to resolve m o s t o f the k n o w n lcvels below

6 McV excitation in 2TA1. T h e a n g u l a r distributions o f n e u t r o n groups to levels below 3.7 MeV s h o w typical stripping patterns which imply /-values in accord with previous J~ assignments; in particular, j n = :~, and .~- for the 2.97 a n d the 3.68 MeV states respectively. T h e spectroscopic factors for levels up to 3 MeV excitation resemble, within experimental uncertainties, the predictions o f both the s t r o n g a n d the weak coupling models but refute the "centre-of-gravity" model. T h e 3.68 MeV level is a n o m a l o u s l y weakly populatcd however. A m o n g levels above 3.7 MeV excitation, only those at 5.75 a n d the 6.83 McV s h o w u n a m b i g u o u s stripping patterns (l = 0). T h e latter state is the lowest T ~ ~ analogue to 27Mg. E

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N U C L E A R R E A C T I O N 2eMg(d, n), E ~ 3 MeV; measurcd o'(En, 0). °-~AI deduced levels, J, :'r, spectroscopic factors. Enriched target.

I. Introduction

Recent inelastic nucleon scattering experiments t) suggest that the core excited model of de-Shalit 2) (the centre-of-gravity model) may be applicable to the six lowest levels of the nucleus of 27A1. Thankappan 3) has also applied the model to positions and transition rates for the same levels. The model only involves one shell model configuration, namely the ld÷ proton hole state. If furthermore the ground state of 26Mg is entirely two d~ holes in the closed 2SSi core, only l = 2 transitions should be present in the 26Mg(d, n) reactions. From the observed / = 0 and / = 2 patterns in the 26Mg(d, t) and 28Si(3He, d) reactions one concludes 3) that there are < 20 % admixtures of s~ and d~ orbitals in the ground states. The stripping of s~ and d,~ is therefore permitted by the core excited model but only in small amounts (S < 0.1). If, on the other hand, one applies the weak coupling collective model, comprising ld~. and higher configurations, we expect both l = 2 and l = 0 transitions. This result is also given by the rotational model as can be seen in, for example, the 24Mg (d, p) reaction. The (d, n) reaction was studied in order to elucidate the role of the possible 2s~ admixtures in transitions to 27A1 levels. In fact, the fairly low bombarding energy of the available accelerator ( < 3.1 MeV) does not permit reliable measurements of transitions with / > 0, since penetrability factors in DWBA calculations become very sensitive to the optical parameters. However, stripping reactions leading to the 27AI nucleus have never been reported before and even fairly inaccurate measurements of I = 2 and 3 may be of interest. 311

B.

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LAWERGREN

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26Mg(d, n)~?Al

REACTION

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2. Experimental procedure The target, a 150 pg/cm 2 26Mg deposit on a thick Ta backing, was bombarded with ,-- 2/~A o f 3 M e V deuterons from the Harwell IBIS accelerator 4) and the detector had a time spread o f 2 nsce for the gamma-ray peak. The fast plastic neutron detector was biased at about 200 keV neutron energy. It was necessary to use a flight path o f

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12 m to resolve the neutron groups leading to the 0.84/1.01 MeV levels but it was felt that a complete resolution was o f little interest and only some angles were run at this distance while angular distributions covering angles between 0 ° and 150 ° were recorded at 6 m flight path. N o attempt was made to resolve the 2.97/3.00 MeV doublet since one assume negligible contribution from the 3.00 MeV level with l = 4. In the experiment one seeks - by trial and error - the highest bombarding energy where the contribution from the c o m p o u n d nucleus formation was small and where it interfered little with the direct reaction component. Angular distribtutions were

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ISO

315

Z6Mg(d, n)gTAl REACTION

measured at several bombarding energies and the ones at Eo = 3.0 MeV were found to give good stripping patterns to levels of known spins and parities. The neutron time spectrum is shown in fig. 1. Most of the known low lying levels in AI are, in fact, resolved. In doubtful cases, a careful line shape analysis was applied as in fig. 2. Fig. 3 il

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Fig. 4. Angular distribution of '-'TAl(d, d) at E D ~ 3.32 MeV. The data points are taken from Slaus and Alford 7). The solid curve shows the optical model prediction using the quoted parameter values.

shows 16 angular distributions, many of which shows characteristic forward peaking, as required, and for which quite good fits are obtainable with DWBA calculations. In order to establish the error limits of the cross sections some excitation functions (in 50 keV intervals between 2.6 and 3.1 MeV) were measured. The l = 0 and / = 2 transitions were measured at 0 ° and 30 °, respectively. The yields oscillated by approx-

316

S. LAWERGREN

imately a factor of two but the ratios l(g.s.)/l(2.73) and 1(0.84)/1(3.68) remained constant within the statistical uncertainties ( g 30 ~o) across this bombarding energy range. In the later discussion we shall consider these ratios which probably determine the ratios of S-factors to within 50 ~ error. The absolute magnitude of the direct interaction is considered to be determined only within a factor of two because of inadequate knowledge of compound nucleus formation and of target thickness. Uncertainty about the parameters in the DWBA calculations add some further uncertainties in the estimate of absolute S-factors. One can hardly justify an elaborate study of the DWBA cross section as a function of input parameters. There are no published optical-model parameters of a required 6) depth of ~ 100 MeV, for .~ 3 MeV deuteron scattering on 26Mg. The set of parameters of fig. 4 is obtained by fitting the aluminium scattering at ED = 3.32 MeV by Slaus and Alford 7) of 1959. TABLE 1

Results o f measurements Ex

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S (within a factor

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of two) 0 0.84 1.01 2.73 2.97 3.68

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of two) 3.95 4.40 4.58 5.75 6.83

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0.1 0.03 0.03 0.02 0.6

The neutron potential was U = 50 MeV (Saxon Woods) and W = 8 MeV (Gaussian) with r o = 1.42 fro, au = 0.65 fm and aw = 0.98 fm. The bound state potential depth was ~ 50 MeV with ro = 1.3 fm and a = 0.7 fm (Saxon Woods). The DWBA code used the zero range approximation and a cut-off radius of 4 fm was introduced to obtain the best angular distribution fits. In general these fits are reasonable. It appears impossible to generate the large backward peaking of the transition to the 5.75 MeV level. It is not likely to be due to interference between direct interaction and compound nucleus formation. If it is caused by the heavy particle stripping mechanism the absence of such a stripping contribution in the transition to the 6.83 MeV level * can be understood a) in terms of the latter having 5) T = 3. The spectroscopic factor S and the associated /-values are contained in table 1. The S-factors here are defined in the isospin formulation aexp(d, n) = S 2-Jfq-. i (1½1--½ITf½)2trDWSA. 2J'+ 1 t The value o f Ex = 6.83 :t=0.02 MeV given for the T = ] state, supersedes that given in ref. 6).

26Mg(d, n) ~TAI REACTION

3 17

3. The consistency of the S-value

In this (d, n) reaction, where the s t transitions proceed to states of two different isospins, one can apply a number of checks on the model independent consistency of the spectroscopic factors. (i) The S-factors, in isospin notation, of the analogue reactions 26Mg(d, po)27Mg and 26Mg(d, n)27A]r=~ should be equal. The spectroscopic factor of the (d, p) reaction has been given by Glover 9). The experimental ratio of S(d, po)/S(d, n6.s3) is 1.4_+0.8. (ii) A more sensitive test of the relative S-factors (where some experimental uncertainties cancel) of the 1 = 0 transitions can be obtained by comparing the two T-states in the (d, n) reaction involved. French and Macfarlane 10) define G(T f) = ~(2Jf+ l)(2J i+ 1)- 1(1~ 1 -½[Tf½)2S, where the summation extends over all states of a particular l- and T-value. In our case only one (T>)-state is excited. The total G(T>) strength was estimated from a comparison with the distribution of / = 0 transitions in the analogous 26Mg (d, p) reaction. The only sizable transitions proceed to the ground state and the 3.47 MeV state in 27Mg with a ratio of spectroscopic factors 9) of 1.65. We obtain G(T<) = 1.5 and G(T>) = 0.64 for s~ transfer in the 26Mg(d, n) reaction. Let (holes)j denote the average number of holes in the complete j-shell. French and Macfarlanc i o) show that

G(T> ) = ( N - Z + 1)-1 (neutron holes)s G(T< ) = (proton holes)j- ( N - Z + 1)- t (neutron holes)/, where N, Z refer to the target nucleus. We put (neutron holes), = (proton holes)½ ~ 2 for the ground state wave function of 26Mg. This assumption is consistent with nuclear models for this mass region. There is, for example, no admixture of st in Nilsson orbit 5 for any value of deformation. We obtain table 2. The sum relationship is, of course, merely stating that Z S = I for each isospin state. In a later paper 1i) these relationships will be applied to other (d, n) reactions involving the transfer of the s~ orbit. Considering their good behaviour, the spectroscopic factors may be discussed with a high degree of confidence. TABLE 2 Experimental and theoretical values Experiment

G(T< )G-t(T> ) G(T<)+G(T>)

2.3 2.1

Theory 2 2

318

B. LAWERGREN 4. Discussion

4.1. THE /-VALUES The spins and parities of ground state and the four lowest excited states in 27A1 are well known and the measured stripping angular distributions indicate /-values for the ground and 0.84 MeV states consistent with J~ = 52.-=and ½+. The / = 4 to the 2.21 MeV level will, of course, not be measurable. This is all in accord with observation and in view of these unambiguous stripping patterns among levels with known spins and parities we may conclude with reasonable certainly that the /values of the 2.97, 3.68, 5.75 and 6.78 MeV levels are 2, 0, 0 and 0, respectively. Thus the spins of the 2.97 and 3.68 MeV states, J~ = ~- and J = ½+, agree with the tentative assignments by van der Leun et al. 12). These levels lack equivalents in 2SMg/25A1 and it will be shown below how this can be understood in terms of the different available configurations. By comparison with the neighbouring nuclei 25Mg and 29Si one may expect a J~ = ~-- level at 3.9 and a J~ = ~z- level at 4.5 MeV. Spins of J~ --- ~- for the 3.95 and J~ = ~- for the 4.40 MeV levels are reconcilable with the measured angular distributions. 4.2. THE S-VALUES The spectroscopic values from the stripping reaction will now be discussed from the point of view of the rotational model, the weak coupling collective model and the centre-of-gravity model. 4.2.1 Rotational model. The ground state, i.e. orbit 5 is predicted to have S = 0.33 independently of the core deformation agreeing with the experimental value. It seems 13), however, that the ground-state wave functions of 26Mg and 27A1 must be adjusted in order to account for the observed 27Al(d, no) and 26Mg(d, to) reduced widths. The l d , component of those ground states is only about 0.6 and 0.8 respectively giving an S-value for the l = 2 component in 26Mg(d, n) of 0.16, close to the lower experimental limit. In this model the S-values for the 2.21 and 3.00 MeV levels are zero, i.e. the observed yield to the third excited state would be due to compound nucleus formation. The observed spin, energy sequence and v-ray decay of the first, second and fourth excited states has suggested that those states belong to Nilsson orbit 9. This hypothesis is not quite confirmed for the J~ = g)+ and ~ ~ levels, but consistent with the J~ = ½+ level. With a deformation slightly less than that of mass 25 (q ~ 2) one has for the 0.84 MeV level: Sth = 0.72, Scxp = 1.0; for the 1.01 MeV level Sth = 0.10, Sexp = 0.3 and for the 2.73 MeV level Sth = 0.02, Sexp = 0.15. In mass 25 the next higher Nilsson orbit is number 11. If this orbit likewise gives rise to the 2.97 and 3.68 MeV levels, in 27A1, the deformation must be r/ > 5 to generate the inverted level order and then it also yields the reasonable S = 0.15 for the 2.97 MeV level. However, the predicted S for the 3.68 MeV level is an order of magnitude too large and the large deformation is unrealistic.

2~Ma'(d, n)~'Al REACTION

319

4.2.2. Weak couplino collectit'e model. The relevance of this model has been discussed in an accompanying paper 14). Wave functions for the aluminuim nucleus ~0Nmvt./s are being constructed from the coupling of the single-particle shell model states (q~ts) in the orbits Ida-l; d~-j2o._ 2s~ and d~_o. ldl, to the core states ZNk~ in this expansion

The stripping reaction populates states based on the unexcited core wave function goooThe absolute spectroscopic factor to the ground state is simply S .... = CoZoo~S .... ( l d 0 where S,.m.(ld÷) is the spectroscopic factor for the transfer of the ld I orbital in the shell model. In terms of the cfp expansion of the shell model states we have 13) S .... ( l d , ) = 11 ((d~)ll,~zl}(dl)l°; 0) 2 = .~ and S .... (g.s.) = 0.25 which is within the experimental limits. The ratio of S-factors for the two J = ~ levels (the ground-state and the 2.73 MeV level) is governed by the ratio, CZooo ~/Coo2 ,I" = 3.2. Since the experimental value is S ( J = s~)/S(J = {*) = 2 + 1, the prediction is supported by this model. This particular intensity ratio is also given by the inelastic scattering experiments '). Using the notation of Crawley and Garvey one has (1 - A 2) A -z = 3.0+0.3. The single particle shell model S-value for the 2s½ transfer is unity for each isospin state. From ref. ~2) we have S(E~ = 0.84 MeV) = 0.5, just within the experimental error. The weak coupling model predicts roughly equal spectroscopic factors to the two lowest J = a levels which is in accord with observation. 4.2.3 "Centre-of-gravity" model. This model suggested by nucleon scattering experiments ~' a) predicts zero or small spectroscopic factors to all (but the two Y = s) levels. Clearly this model is rejected. 5. Summary Below 3 MeV excitation the result of the present experiment does not show a marked preference for either the strong or the weak coupling model. Both models fail to yield the small empirical yield to the 3.68 MeV level, however, and it seems unlikely that a reasonable adjustment of the parameters will bring closer agreement.

320

a. LAWERGREN

The tentative spectroscopic factors o f the tentative J~ = ~ - and 3 - levels at 3.95 a n d 4.40 are too small for the prediction of S-values for Nilsson orbit 14. Macfarlane a n d F r e n c h 13) have suggested that the odd parity levels in 25A1 arise from the weak c o u p l i n g of 2p a n d If orbits to the Mg-core. I f this also is the case for 27A1, the oddparity states must be spread over other higher lying levels in order to satisfy the sum rules for spectroscopic factors of those orbits. Indeed a strong l = 1 transition has been observed 15) leading to a level at 8.2 MeV. The l = 0 t r a n s i t i o n to the 5.75 MeV level is similar to those measured in neighbouring nuclei, although this particular t r a n s i t i o n is weaker. The a u t h o r is much indebted to Drs. B. Macefield a n d D. Wilmore for the use of their D W B A a n d optical model search programmes and to A. T. G. Ferguson, G. C. M o r r i s o n a n d F. S. Levin for valuable comments.

References 1) H. Niewodniczanski et al., Nuclear Physics 55 (1964) 386; J. Kokame, K. Fukunaga and H. Nakamura, Phys. Lett. 14 (1965) 234; G. M. Crawley and G. T. Garvey, Phys. Lett. 19 (1965) 228; G. C. Bonazzola, E. Chiavassa and T. Bressani, Phys. Rev. 140 (1965) B835 2) A. de-Shalit, Phys. Rev. 122 (1961) 1530 3) V. K. Thankappan, Phys. Rev. 141 (1966) 957 4) A. T. G. Ferguson, Contemp. Phys. 5 (1964) 269 5) B. Lawergren, Phys. Lett. 13 (1964) 61 6) L. L. Lee, Jr. et al., Phys. Rev. 136 (1964) B971 7) 1. Slaus and W. P. Alford, Phys. Rev. 114 (1959) 1054 8) G. C. Morrison, A. T. G. Ferguson and J. E. Evans, Proc. Rutherford Int. Conf. (1961) p. 575 9) R. B. Glover, Phys. Lett. 16 (1965) 147 and private communication 10) J. B. French and M. H. Macfarlane, Nuclear Physics 26 (1961) 168 11) B. Lawergren, A. T. G. Ferguson and G. C. Morrison, Nuclear Physics, to be submitted 12) C. Van der Leun, P. M. Endt, J. C. Kluyver and L. E. Vrenken, Physica 22 (1956) 1223 13) M. H. Macfarlane and J. B. French, Revs. Mod. Phys. 32 (1960) 567 14) B. Lawergren, Nuclear Physics, to be submitted 15) B. Trumpy and A. Graue, Physica 22 (1956) 1155(A)