26Mg states observed via 22Ne + α

NUCLEAR PHYSICS A

Nuclear Physics A571 (1994) 265-275

Norm-IIoIland

26Mgstates observed via 22Ne + cx CA. Ravis I7 R. Abegg ’

Received 24 August 1993

We report differential cross-section measurements at i 5 angles for the reaction 22Ne(cu,cue) 22Ne for 3.8 $ E, 6 I1 MeV in steps d I5 keV and infer 92 resonances and 21 possible resonances, in many cases identifying or limiting the spin and parity. In addition, we measured inelastic scattering data from I& = 6.1 MeV (ai) and Ea = 9.9 MeV (a~) to Em = 11.0 MeV.

1. Intruductiou

As a consequence

of the extensive study of 24Mg states through *‘Ne $ a scattering [ 1,2], a considerable body of data on 22Ne + a scattering has also been accumulated. Previous work [3]resulted in excitation functions for the elastic and inelastic (to the first two excited states of 22Ne) scattering for 13.4s E, (MeV) < 20.8, and concluded, even at these high excitation energies from about 22 to 28 MeV, that the data could not he explained

by a purely statistical

inte~retation.

At lower energies [ 41 two resonances

at E, = 3.245 and 3.418 MeV were assigned spin and parity 3-. A modem compilation [ 51 omits these two resonances and hence incorrectly implies that there are no reported natural parity states above about 12.5 MeV in excitation energy. The present data, at up to 14 sirn~~eo~ angles, cover the region from E, = 3.8 MeV (cre), E, = 6.1 MeV ((~11, and E, = 9.9MeV ((~2)to E, = 11.0 MeV. Levels in 26Mgfor 13.8 G En (MeV) d 19.9 are deduced and, in many cases, J” assignments are made (or limited) based on the elastic scattering data. I Permanent University of 2 Permanent University of

address: TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, Canada V6T 2A3; and Manitoba, Department of Physics, Winnipeg, Manitoba, Canada R3T 2N2. address: TRIUMF, 4004 Wesbrook Ma& Vancouver, IX, Canada V6T 2A3; and AIberta, Department of Physics, Edmonton, Alberta, Canada T6G 2N5.

0375-94?4/94/$07.00 @ 1994 - Elsevier Science B.V. AI1 rights reserved SSDI0375-9474(93)E0522-A

CA. Davis, R. Abegg / 2aMg

266

2. Experimental procedure Details of the experiment may be found in ref. [ 1 ] and further details regarding equipment and error analysis in ref. [6]. The natural abundances of the three stable neon isotopes are 20Ne : “Ne : “Ne

= 90.48Oh : 0.27Oh : 9.25W. The first figure in ref. [ 1 ] is

a spectrum of alphas scattered at a relatively forward angle from the natural neon target (buffered by a flow of 4He at the beam entrance channel) and showing a clear separation between the “Ne(cr, (~0) and the much larger 2oNe (a, (~0) ground state peaks. Over the excitation range the energy steps were 10 or 15 keV. The error in energy amounted

to about 10 keV and the systematic

error in cross section to 2-3% [ 1,2].

3. Results Figs. 1 and 2 show the N 6800 elastic scattering differential cross sections as a function of (Yenergy for 11 of the 15 angles. The level density and compaction of the data may prevent the reader from following even qualitatively how we inferred the “Mg levels and parameters shown in Table 1. Hence, in Figs. 3 and 4, we have enlarged a 500 keV

E,

(MeV)

E, (MeV)

Fig. 1. Excitation functions of 22Ne(a, a~)~~Ne differential cross sections. See Figs. 3 and 4 for an enlarged plot of the region 6.5 < Ea Q 7.0 MeV.

C.A. Davis, R. Abegg / 26Mg

261

22Ne(a.a,)22Ne

8

c,,;138.0”

I

I-4

142.4”

155.2”

4

5

6

7

8

9

IO

II

E, (MeV)

Fig. 2. Same as for Fig. 1, but for back angles.

region (Em = 6.5 to 7.0 MeV) to such a size that the reader may follow the specific arguments used in sect. 5 to limit or specify JR of resonances in this energy interval. Similar arguments were used to infer the other levels of Table 1. Fig. 5 shows five excitation functions of the N 3 100 (cy,cr1) inelastic scattering differential cross sections for the first “Ne excited state (2+, 1.275 MeV). Fig. 6 shows some of the N 600 (a, (~2) inelastic scattering differential second “Ne excited state (4+, 3.351 MeV)*.

cross sections, at four angles, for the

4. Analysis At any given energy data were available at only 8 to 14 angles. For a full S-matrix analysis, lmax + 1 complex matrix elements are required, where &,, is the largest orbital angular momentum contributing to the scattering amplitude. In our case, resonances with spin as high as 7 may be present in the data, and an even higher lmaxmight be necessary to establish reasonable fits to the data, for which we obviously have an insufficient number of angles. The resonant parameters are then derived from the energy dependence of the various S-matrix elements. At each energy, however, there are many independent solutions. For an isolated resonance the correct solution, involving a proper variation * The interested reader may contact the authors for a copy of the data.

C.A. Davis, R. Abegg / 26hJg

268

TABLE 1 Resonances

in 2aMg deduced from the present work

Ln.

J”

WV) 3.883 (3.944) (3.985) (4.055) 4.145 4.215 4.275 (4.340) (4.40) 4.440 4.415 4.545 4.550 4.621 4.660 4.80 4.860 4.951 4.967 5.070 5.102 5.170 5.25 5.278 5.385 5.490 5.540 5.630 5.650 5.740 a (5.850) 5.880 5.93 5.977 (6.080) 6.16 6.230 6.300 6.39 6.442 6.57 6.57 6.60 6.615 6.665 6.715 6.750 6.784

13.896 13.948 13.983 14.042 14.118 14.177 14.228 14.283 14.33 14.368 14.397 14.456 14.461 14.521 14.554 14.67 14.723 14.800 14.813 14.900 14.928 14.985 15.053 15.076 15.167 15.256 15.298 15.374 15.391 15.467 15.560 15.586 15.63 15.668 15.755 15.82 15.882 15.941 16.02 16.061 16.17 16.17 16.19 16.207 16.250 16.292 16.321 16.350

d 13 Q 13 < 13 < 13 21 21 Q 13 25 N 100 38 Q 13 50 17 Q 13 60 25 20 Q 13 34 25 Q 13 17 34 Q 13 17 17 21 17 17 d 13 < 13 13 15 17 25 75 30 20 50 17 17 Q 13 d 13 Q 13 13 G 13 Q 13 d 13

w+,2+1

03+,2+1 to+,1-J

;d4d) (not 3) (3-J (5-J (even) (l-,3-) (even) y5-4) (3-1 3even 64 even 32+ (6+) K)+,4+1 even o+, (l-,3-),4+ (4+,6+) (even ) (5- 1 even even (0+,4+) even (0+),2+ even (not 2+) 6+ odd (3-) even 6+ (5-J (odd) even 2+ 6+ 2+ (1-I

CA. Davis,

269

R.Abegg / 26h4g

TABLE 1 -continued

EX WW

r,.m

(MeV) (6.82) 6.84 a 6.89 6.92 7.120 7.155 7.210 7.225 7,275 7.340 7.390 7.480 7.565 7.66 (7.82) 7.91 7.99 8.115 8.15 8.270 8.360 8.365 (8.410) 8.440 8.480 8.575 8.630 8.655 8.700 8.710 8.755 (8.86) 8.90 (8.91) 9.06 9.12 (9.130) (9.230) 9.26 9.32 9.415 9.46 9.49 9.62 (9.635) 9.70 9.77 (9.776) 9.845

16.38 16.40 16.44 16.47 16.634 16.664 16.711 16.723 16.776 16.820 16.863 16.939 17.011 17.09 17.23 17.30 17.37 17.476 17.51 17.607 17.683 17.687 17.725 17.751 17.785 17.865 17.912 17.933 17.971 17.979 18.017 18.11 18.14 18.15 18.28 18.33 18.334 18.419 18.44 18.50 18.575 18.61 18.64 18.75 18.762 18.82 18.88 18.881 18.939

d 13 25 13 13 c 13 17 38 13 13 13 21 21 21 21 25 25 35 17 42 21 10 100 <8 8 21 8 30 8 25 ~8 8 85 30

&

J”

WV)

~8 25 35 ~8 ~8 60 30 17 <8 30 30 8 25 17 ~8 42

even even (O+, 4+, 6+ ) 4+ (3-7 7-) (O+, l-,2+,4+) even (not 4) (o+,l-,3-,4+,7-) (5- 1 even (not 4) 5even (0+,6+) even (6+

1

(7- 1 even (1-) even even even even (not 3, 8) (0+,2+,4+,6+) (not 3, 5, 8) (8+) (7-) (4+ ) (l-,3-) (o+, l-,3-,4+) even even even (odd)

(5_) (even) odd even (not 2) (6+) (not 4, 8) (not 2) (3-,4+)

270

C.A. Davis, R. Abegg / z6hfg TABLE 1-continued

-&I

EX

r c.m.

(MeV)

(MeV)

WV)

(9.87)

18.96 19.05 19.07 19.155 19.206 19.265 19.303 19.35 19.392 19.474 19.616 19.75 19.789 19.806 19.848 19.895

25 13 60 21 13 17 8 N 85 21 ~8 35 38 13 17 ~8 25

(9.98) N 10.00

10.100 10.160 10.230 10.276 N 10.33 10.380 (10.477) 10.645 10.80 (10.850) 10.870 (10.920) 10.975

J”

(6+) 4+ (not 3, 8) 6+, (7- 1 (4+) (5-) 6+ (O+,l-,5-,6+) ~6 (O+,l-,2+,5-,6+)

(not 3, 7)

a Probable doublet.

in an Argand diagram for the resonant I, can be followed as a function of energy. For many overlapping resonances this can no longer be done. In our previous analysis of 24Mg states from 20Ne(a, cro)“Ne [ 1 ] we had adopted the simplification on the above technique of dividing the reaction into resonant and non-resonant amplitudes [ 7,8]and parametrizing the non-resonant amplitudes and phases as linear functions in energy. This was successful in fitting some of the data (up to 16angles per energy, with ten times the statistics on average) in the 24Mg case, otherwise the procedure outlined below was used. In the present data set, no resonance parameters could be extracted from fitting the data. For the case of elastic scattering, with a spin structure of O+ + O+ 4 O+ + O+, and with a qualitative examination of the behavior of the excitation function at angles near where the various PL(cos 0 ) have zeros or maxima, one is able to assign or restrict the L (and hence JR) of the corresponding compound nuclear state in 26Mg. One may also estimate r and the resonant energy, but these parameters may be affected by nearby resonances and other background amplitudes changing the phase of the Breit-Wigner resonant shape and concealing the behavior of one resonance in the structure of the others. Thus, the resonant energy may also be uncertain by an amount dependent on r, and r itself may also be difficult to extract with precision. However, this analysis is unambiguous only for a relatively isolated resonance. For resonances of different spin but approximately the same width and resonant energy it is not possible to make definite assignments. In the present case the level density is so great and the statistics so poor that only a small fraction of the supposed resonances are given definite J” assignments. Table 1 summarizes the results. Less certain resonances and spin assignments (or

271

C.A. Davis, R. Abegg / 26Mg 150 120 90 60 30

32 24 16 8 0 6.5

6.6

6.7

6.6

6.9

6.6

6.7

6.8

6.9

7.0

Em (Me'Q

Fig. 3. Excitation functions of **Ne(a, crs f”Ne differential cross sections over the energy region 6.5 d Eel $ 7.0 MeV (enlarged from Figs. 1 and 2). Lines are a guide to the eye to assist the reader in locating suggested resonances (indicated by the arrows) and follow the arguments of sect. 5.

restrictions)

are indicated

in parentheses.

5. Energy levels from Eo! = 6.5 to 7.0 MeV This section is included to give an example of some of the arguments necessary to assign or restrict assignment of the spin and parity of the levels observed in this work. The reader should compare the arguments to the data presented in Figs. 3 and 4. A very prominent level is seen around En = 6.570 MeV at 90” and 167.7” of about 20 keV width in the lab. (&,. N 17 keV). It is weak at 74.5” (Pd(76.2’) = 0) and very weak at 100S” and 105.5” (&(103.8”) = 0). It is present at 115.1” and 124.5”, but becomes very narrow (Z&,. 6 13 keV) at 129.1” (& ( 131.4’) = 0), indicating the presence of a second level at the same energy. A broader structure again at 138.0” is virtuallygoneat 155.2” (Ps(155.0”) = 0,&(158.8”) = O).Thenarrowstructureisseen at 163.6” broadening again at 167.7’. Thus, there is a doublet at Eb, = 6.570 MeV, the most prominent member being a 6+, and a weaker narrower resonance being a possible

272

C.A. Davis, R. Abegg / “Mg

80 60 40 20 0 6.5

6.6

6.7

6.8

6.9

6.6

6.7

6.8

6.9

7.0

E. 0-W

Fig. 4. Same as for Fig. 3, but for back angles.

5-. A level at E, = 6.615 that is seen weakly at 90.3”, but more definitely at 85.1”, and is, thus, probably even or of high odd spin, is quite narrow. It is a noticeable dip at 74.5’ (P4(70.10) = 0, Pa(76.2”) = 0); just barely perceptible at 100.5’ (Ps( 100.6”) = 0); very strong, though perhaps at somewhat lower energy, at 105.5” (Pa (103.8”) = 0); and present also at 115.1” (Pd( 109.9”) = 0, PT( 113.9“) = 0). It is present also, at 124.4” and 129.1” (Ps(121.7”) = 0, P2(125.3”) = 0, &(131.4“) = 0), but gone at 138.0” (P,(137.9O) = 0, PS( 143. lo ) = 0). And again present at back angles, though perhaps again at somewhat lower energies, 155.2” (P~(l55.0”) = 0), 163.6” (Pr(161.6”) = 0) and 167.7”. We conclude that this may be a doublet, one even, and the other probably odd at a slightly lower energy (E, N 6.60 MeV). A narrow resonance at E, = 6.665 MeV is seen as a sharp rise at 85.1” and 90.3” and is, therefore, of even spin. It is seen at 74.5” (near zeroes of P4 and Pa) and as a rise of the same sign at 100.5” and 105.5” (near zeroes of P4, PS and Pa). It is very weak or unobservable at 124.5” and 129.1’ (and clearly weakening at adjacent angles), close to a zero of Pz at 125.3”. It is present again at back angles, though much less noticeable at 167.7”, where the cross section is generally - 40 mb/sr. This is consistent with a spin

CA . . Davis , R . Abegg / z6Mg

213

E, (MeV) 15.0 I 40

t

I

16.0 I

I

17.0 I

I 8

,,,,=70.4’-

18.0 I

I

I

69.7”

155.9”-

155.6”

164.0”-

163.8”

40-

E, (MeV)

Fig. 5. Differential cross sections for 22Ne(a, ai )22Ne*.

and parity assignment of 2+. There is a narrow resonance at E, = 6.715 MeV at 85.1” and 90.3” and thus of even spin. It is not present at 74.5” (Pa(76.2’) = 0), weakly seen at 100.5” and not observable at 105.5” (Pa(103.8”) = 0). It is strong at 115.1” and 124.5” but gone at 129.1” (Pe(131.4’) = 0). It is observable at 138.0” and very strong at 167.7’, but much weaker at 155.2” and 163.6“ (Pe(158.8”) = 0). This is quite clearly a 6+ state. At E, = 6.750 MeV there is a narrow resonance observed at 85.1” and 90.3” and thus of even spin. It is also observed strongly at 74.5” (near zeroes of Pa and Pa) and is noticeable at 100.5” (near zeroes of P6 and Ps). It vanishes at 124.5” (P2( 125.3”) = 0) and is weak at adjacent angles. It is very strong at 138.0” and 155.2” (straddling a zero of Ps) and is still noticeable at 163.6” and 167.7”, thus consistent with a low spin. This state is clearly a J” = 2+. At E, = 6.784 MeV there is a narrow resonance most strongly observed at 155.2” (Ps (155.0”) = 0) that is gone at 90.3”, and therefore odd, and either not observed or

CA. Davis, R. Abegg / 26Mg

274

10.0

11.0

10.0

II.0

E, (MeV) Fig. 6. Differential

cross sedions

for 22Ne (a, a2 )22Ne*.

very weak from 74.5” to 100.5”, thus probably of low spin. It is definitely present at 124.5” and 138.0” (near zeroes of Ps and P7 and close to Pj( 143.1”) = 0), but becomes washed out at back angles, which is consistent with a low spin. This resonance is probably a 1 -, though a 3- cannot be completely ruled out. At E, = 6.84 MeV we see a resonance at 129.1’ (near PZ and P6 zeroes) with Km. = 25 keV. It is also observed at 90.3” and 85.1’, and is thus of even spin, and is observed at 75.4” (near P4 and Pa zeroes). This might be enough to restrict the J” to O+ or 8+, but the odd shape at some angles indicates that this may be a doublet complicated even further by a possible narrow resonance some 20 keV lower in (x energy, as observed, for example, at back angles. At E, = 6.92 MeV we see a strong resonance at back angles (IL,,. = 13 keV) with a weaker and narrower resonance just below it at E, = 6.89 MeV. This pair is clearly seen at 90.3” and 85.1” and are, therefore, of even spin. Observation at 163.6” rules out P8; and a reasonably strong presence at 124.5” rules out Pz. The higher of the two is present but weaker at 142.4” (Pa (142.8’) = 0), consistent with a zero at the 149.4” zero of Pd. Both resonances are weak also at 115.1” (P4(109.9”) = 0) and 74.5’ (P4(70.1’) = 0). The 6.92 MeV state is noticeable at 129.1’ and 155.2” near P6 zeroes. The higher of the two is definitely a 4+, the lower is even and possibly either O+, 4+ or 6+.

C.A. Davis . R . Abegg / 26Mg

275

6. Conclusions

Over the 26Mg excitation

energy region of 13.83 6 Ex (MeV)

< 19.9 1 we have identi-

tied 12 natural parity states and suggest their spins and parities based on a comparison of the data with the locations of the zeroes of the Legendre polynomials. For 80 additional levels we list the resonant energies and infer limits or restrictions for the spin-parity assignments. An additional 2 1 more doubtful resonances in Table 1 have E, in parenthesis. For two of these, restrictions for J” were possible because excursions occurred at angles consistent with such assignments. The most recent compilation of levels [5] in “Mg lists 147 levels above the E, = 7.84 MeV, 2+ state, only four of which fall within the excitation energy region studied here. Three of these are identified as 6- unnatural parity states, and the one at Ex = 13.958 f 0.010 MeV is listed as (O-6)-. The latter is well matched in energy with our possible 13.948 MeV state, but otherwise there is no information to confirm this. Quite clearly, there are great difficulties in absolutely identifying many of these resonances and many other resonances have probably been missed. We hope the reader will accept the identifications as a guide to the structure of 26Mg and not as a complete explanation of the natural parity levels which is not accessible from the data. The authors greatly appreciate the advice and comments of Hugh T. Richards. We also thank James Billen, Dan Steck, Steve Riedhauser and Lawrence Ames for their assistance with data collection. This work was supported in part by the United States Department of Energy.

References [ 1] R. Abegg and C.A. Davis, Phys. Rev. C43 (1991) 2523 [2] [3] [4] [5] [ 61

C.A. Davis, Phys. Rev. C45 (1992) 2693 C.A. Davis, Phys. Rev. C24 (1981) 1773 E. Goldberg, W. Haeberli, A.I. Galonsky and R.A. Douglas, Phys. Rev. 93 (1954) 799 P.M. Endt, Nucl. Phys. A521 (1990) 1 C.A. Davis, Ph.D. thesis, University of Wisconsin ( 198 1). Available through University Microfilms, Inc., Ann Arbor, Michigan [7] 0. Hiiusser, T.K. Alexander, D.L. Disdier, A.J. Ferguson, A.B. McDonald and IS. Towner, Nucl. Phys. A216 (1973) 617 [8] J.H. Billen, Phys. Rev. C20 (1979) 1648