Energy levels in 23Na

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Nuclear Physics A99 (1967) 465--472; (~) North-Holland Publishing Co., Amsterdam

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Not to be reproduced by photoprint or microfilm without written permission from the publisher

ENERGY LEVELS IN 23Na J. D U B O I S f

California Institute of Technology, Pasadena, California f~: Received 17 April 1967

Abstract: The energy levels in 2aNa have been investigated by means of the reaction ZSMg(d,a)2aNa. Deuterons with energy of 10.0 MeV were accelerated with the ONR-CIT tandem accelerator and the reaction products were analysed with a double-focussingmagnetic spectrometer at 20°, 30° and 60°. The level density agrees with that for 2aMg. No evidence for levels at 2.405 and 2.870 MeV in 2aNa was found. E

NUCLEAR REACTIONS eSMg(d,c023Na, E = 10 MeV. ~aNa deduced levels. Enriched target.

1. Introduction Low-lying levels in 23Na have been studied extensively 1) up to 5 MeV excitation energy. From the measurement of inelastically scattered protons on /3Na using a broad-range magnetic spectrograph, Buechner and Sperduto 2) found proton groups corresponding to levels at 0.440, 2.078, 2.393, 2.641, 2.705, 2.983, 3.678, 3.850, 3.915, 4.431 and 4.778 MeV with relative errors ranging from 3 to 10 keV. The first two levels were also observed by Endt et al. 3) some years earlier from magnetic analysis of the alpha particles from the 25Mg(d, c~)23Na reaction. Hansen et al. 4) have, in a low resolution study of the same reaction, been able to establish that the total cross sections (averaged over bombarding energy) for the (d, ~) reaction to definite states in 23Na are approximately proportional to ( 2 I + 1). From magnetic analysis of alpha particles from the 24Mg(3He, cz)ZaMg reaction, Dubois and Earwaker s) recently have established many new levels in 23Mg between 5 and 7 MeV excitation energy. Since only a few levels were known in the corresponding energy interval in the mirror nucleus 23Na ' the present investigation was started to look for the missing levels in 23Na" Below 5 MeV, good agreement between corresponding levels in 23Na and 23Mg was obtained. Lancman et al. 6) suggested, however, from a recent study of the decay of 23Ne two new excited states in 23Na at 2.405 and 2.870 MeV. If they are right, it is disturbing that no corresponding states in 23Mg could be detected. Perhaps the structure of these two levels is not predominantly of hole character and accordingly the levels should not be strongly populated in a (3He, a) pickup reaction. However, the t On leave f r o m Chalmers University of Technology, G6teborg, Sweden.

** Work supported in part by the Office of Naval Research [Nonr-220(47)]. 465

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assignments of the two new levels in 23Na are based on very weak g a m m a branches and it is therefore also the purpose of the present work to try to find more firm evidence for their existence. The 2 SMg(d ' c023Na reaction was chosen for this investigation since it has a high Q-value which facilitates the measurements of higher levels and since it favours the population of high-spin states, as was pointed out above. This reaction might then populate the two controversial levels fairly strongly as they are supposed 6) to have spin -~-.The first T = az level in 2aNa should be above 7 MeV so there should be no isospin selection rules inhibiting the low-lying levels (T = l ) in 2aNa by the (d, ~) reaction.

2. Experimental procedure and results A 10 MeV deuteron beam with an intensity of 0.3 pA was obtained from the O N R CIT tandem accelerator. To prepare the targets, metallic magnesium enriched in z 5Mg to 93 % was evaporated under vacuum from a small tantalum oven onto thin carbon foils. A target thickness of about 100 pg/cm 2 was used. The alpha particles produced in the reaction were analysed in a 61 cm, double-focussing magnetic spectrometer. The particles were detected in an array of 16 solid-state counters placed in the focal plane of the spectrometer. In front of the counters, 1.5 m m slits were placed. In order to cover the entire m o m e n t u m space of interest, runs with slightly different magnet field were performed. The magnetic field was measured with an N M R device. The frequencies for the different alpha groups were determined and the corresponding energies calculated using the spectrometer constant 7) determined from 212po alpha particles. A slight energy dependence of the spectrometer constant was taken into account. Corrections for the target thickness were also included. Basically, three different runs were performed at 20 °, 30 ° and 60 ° to the beam direction and with an exposure of 150 pC. Many runs covering just a part of the alpha spectrum were also performed when improved resolution or statistics were needed. In fig. 1, the run at 20 ° is shown. The alpha groups identified as being due to the 25Mg(d ' ~.)a3No reaction are labelled by the numerical order of excitation of the corresponding levels in 23Na. Impurity groups were observed from the laC(d, ~)l°B, 13C(d, ~)11B, 160(d, ~)14N and 24Mg(d, 0022Na reactions. They could be identified from their energy variation with angle. These groups are labelled by the symbol of the residual nucleus with a subscript to indicate the appropriate excited states. The Qvalues for the above-mentioned reactions calculated from the observed alpha groups all agreed within the experimental errors ( + 2 0 keV) with those which can be calculated from the known masses 8). As an additional check on the contaminations, an alpha spectrum was measured at 30 ° under identical conditions using natural magnesium instead of enriched 25Mg as target. Though the close-lying triplet slightly below 2 MeV in 22Na was not completely resolved, good agreement was obtained with high resolution work on the

eaNa ENERGY

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2 4 M g ( d , ~ ) 2 2 N a reaction by Hinds et al. 9) in the region o f interest in the present investigation, i.e. up to 3.6 MeV excitation energy in 2ZNa. The assignments o f the 23Na alpha groups as they are presented in fig. 1 have been made from all runs. Thus, impurity groups disturbed some of the 23Na groups at 20 ° but these latter could be observed more favourably at other angles. Some o f the 23Na groups turned out to be close-lying doublets or triplets. For instance, the triplet group t

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14, 15 and 16 suggested in fig. 1 was also seen at 60 ° while at 30 ° only two members of the triplet could be identified, t h o u g h the width of the group was such that it very well could account for all three members. The doublet 30 and 31 is not very conclusive in fig. 1 but in all runs it was in fact suggested to be a doublet in spite of a slight influence f r o m group 29. The same is true for the 36, 37, and 41, 42 doublets and they are also shown in fig. 2 in a run which was measured with slightly thinner targets and better statistics. The g r o u p 39 looks in fig. 2 as a doublet but there was no strong support for this idea in the other runs.

470

J. DUBOIS

The excitation energies o f the levels in 2 3Na o b t a i n e d in the present investigation are given in table 1 a n d are based on the average values f r o m the different runs. The errors q u o t e d are the uncertainties o f the excitation energies relative to the g r o u n d state. U p to 4.8 MeV, the excitation energies o f the levels are in very g o o d agreement with the d a t a o b t a i n e d f r o m inelastic p r o t o n scattering 2). W h e n this investigation was completed, the a u t h o r was i n f o r m e d t h a t the 25Mg (d, ~)23Na r e a c t i o n also was studied by H a y a n d K e a n 10) a n d where their results overlap with those in the present investigation, there is evidently very g o o d agreement. TABLE 1

Energy levels of 2~Na from the 2~Mg(d, 0~)2~Nareaction Group number

0 1

2 3 4 5 6 7 8

9 10 11 12 13 14

Excitation energy (keV)

Group number

Excitation energy (keV)

Group number

Excitation energy (keV)

0 438- 6 2079- 8 2393- 8 2640 10 2705- 8 2988 8 3681--10 3851 12 3915 12 4433 -12 4772 12 5380 15 5535 12 5741~20

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

5759±20 5779±20 5930±15 5965±15 6046112 6114±12 6194±15 6236±15 6311±20 6347±15 6583±12 6621±15 6738~15 6825~15 6870~15

30 31 32 33 34 35 36 37 38 39 40 41 42 43

6913120 6944~20 7077~15 71315_15 7188i15 7272-k15 7394~20 7409~20 7448±15 7481:k20 7565±20 7686±15 7713±25 7746~15

3. Conclusions and discussion

N o evidence was f o u n d for the existence o f levels at 2.405 and 2.870 M e V in 23Na" I f the latter level really exists, it is p o p u l a t e d in the 2SMg(d ' ~)23Na r e a c t i o n with less t h a n 0.1%o o f the intensities o f the transitions to the g r o u n d state or the closelying level at 2.705 MeV. It is difficult to p u t an u p p e r limit for the relative t r a n s i t i o n s t r e n g t h to a possible level at 2.405 M e V since it w o u l d be very close to the 2.393 M e V level. However, there were no i n d i c a t i o n s in any spectra t h a t the 2.393 M e V level is a doublet. I n fig. 3, the levels in 23Na a b o v e 4 M e V o b t a i n e d in the present investigation are s h o w n in a level scheme together with the levels in 23Mg in the c o r r e s p o n d i n g energy region 5). Below 4 M e V excitation energy the largest energy difference between corr e s p o n d i n g levels in these two m i r r o r nuclei was 130 keV [ref. s)]. F r o m fig. 2 it seems that for energies below 5.7 MeV, the c o r r e s p o n d i n g levels in 23Mg are shifted

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J. DUBOIS

in energy by a b o u t 100 keV. A b o v e 5.7 M e V energy the level density seems to be too high to select j u s t f r o m energy c o n s i d e r a t i o n s the c o r r e s p o n d i n g levels in the two nuclei. The n u m b e r o f levels established in the two nuclei up to 6.8 M e V are, however, the same in the two nuclei. I n o r d e r to c o m p a r e further the level densities between 23Na a n d Z3Mg, we follow the m e t h o d o f statistical analysis first suggested by Ericson ~ ) . In fig. 4 are p l o t t e d against the excitation energy E, the quantities log N(E) for b o t h nuclei, where N(E) is th~ n u m b e r o f excited levels with energy less or equal to E. The nuclear t e m p e r a t u r e ~ is defined by 1

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The two curves are a l m o s t parallel a n d give b o t h ~ = 2.1 MeV. There are also m a g n e t i c s p e c t r o g r a p h d a t a available for levels in 25Mg up to a b o u t the same excitation energy (i.e. 7 M e V ) a n d they also give ~ = 2.1 M e V [ref. 12)]. The a u t h o r wishes to express his a p p r e c i a t i o n o f having the o p p o r t u n i t y o f w o r k i n g in the s t i m u l a t i n g milieu created by the staff o f the Kellogg R a d i a t i o n L a b o r a t o r y , and he t h a n k s Mr. R. M o o r e for his assistence in p e r f o r m i n g the c o m p u t e r calculations involved in this work.

References

1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)

P. M. Endt and C. van der Eeun, Nuclear Physics 34 (1962) 21 W. W. Buechner and A. Sperduto, Phys. Rev. 106 (1957) 1008 P. M. Endt, J. W. Hafner and D. M. Van Patter, Phys. Rev. 86 (1952) 518 O. Hansen, E. Koltay, N. Lund and B. S. Madsen, Nuclear Physics 51 (1964) 307 J. Dubois and L. G. Earwaker, to be published H. Lancman, A. Jasin'ski, J. Kownacki and J. Ludziejewski, Nuclear Physics 69 (1965) 384 J. H. McNally, Ph.D. thesis, California Institute of Technology (1966) F. Everling, L. A. Koening, J. H. E. Mattauch and A. H. Wapstra, Nuclear data tables, Part 1 (National Academy of Sciences, 1961) S. Hinds, H. Marchant and R. Middleton, Nuclear Physics 51 (1964) 427 H. J. Hay and D. C. Kean, private communication T. Ericson, Nuclear Physics 11 (1959) 481 N. MacDonald and A. C. Douglas, Nuclear Physics 24 (1961) 614