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Spin assignments for states in 20Ne via the 12C(16O, 20Ne∗)8Be transfer reaction
Nuclear Physics A568 (19941271-286 Noah-Holl~d
NUCLEAR PHYSICS A
Spin assignments for states in 20Ne via the 12C(160, 20Ne*)8Be transfer reaction W.D.M. Rae, S.C. Allcock i, J. Zhang a Department of Physics, University of Oxford, Nuclear Physics Laboratory, Keble Road, Oxford, OXI 3RH, UK
Received 3 August 1993
Abstract The cr-transfer reaction 12C(‘60, Z”Ne*)8Be has been studied at Eub = 150 MeV. The t60cu anguiar correlations from the decay of MNe* have been measured and analysed with a strong absorption model to make spin assignments for many high-spin states at high excitation in ZONe.
Key words: NUCLEAR REACTIONS r2C(t60, 20Nel, E = 150 MeV; measured cr@,, cp,). “Ne levels deduced J, rr. Strong absorption model analyses.
1. Introduction 20Ne is one of the most thoroughly studied nuclei from both an experimental and a theoretical viewpoint. Its structure of two neutrons and two protonts outside a closed 160 core makes it particularly suitable to be studied with cluster models, and indeed it was one of the first nuclei to be treated in this way by Buck et al. [l]. The relatively small number of nucleons, together with the wealth of accumulated spectroscopic data extending up to an excitation energy of around 30 MeV [2,3], has led to the widespread use of the lower-lying energy levels as a testing ground for a variety of nuclear models. In common with other sd-shell nuclei, 20Ne is well suited to the study of behaviour at high spin and large deformation [4]. Rxperimentally 20Ne has been investigated using a wide variety of reactions, although only a few studies have reached excitation energies above 20 MeV. There have been several applications of angular-correlation techniques to extract spins in a similar manner to the present work. Most recently Hindi et al. [S] and Young et al. 161used the reaction 12C(‘2C, ar)20Ne*(a)‘60 to identify over 20 levels between
’ Present address: AT&T Istel Ltd., Redditch, UK 2 Permanent address: Shanghai Institute of Nuclear Research, China. 0375-9474/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved SSDI 0375-9474(931E0450-M
272
WD.M. Rae et al. / Spin assignments (I)
excitation energies of 12.1 and 23.4 MeV by means of double &a,) or triple + 160 1) angular correlations. Sanders et al. [7] utilized the ease (a,a#o* g.?.. with which ‘Be may be detected at very forward angles to obtain a-8Be angular correlations for scattering angles near 0” for the inverse of the reaction used here, namely i60(i2C, 8Be)20Ne*(a)‘60, in the excitation-energy region 7.1-22.9 MeV. The 160(6Li, d)20Ne *(a)i60 reaction has also been extensively investigated by means of da angular correlations, by both Fou et al. [8] and the Russian group led by Artemov. The latter group has made a systematic study at successively higher bombarding energies [9-121, covering the region E, = 19-50 MeV. Many spin assignments have also been made via resonances in elastic and inelastic scattering of a-particles by 160. This technique has a very long history, having first been used in 1940 by Ferguson and Walker [13]. Over the years the increase in available beam energies has enabled a comprehensive picture to be built up (see for instance ref. [14] and references therein) although detailed excitation functions only exist for bombarding energies below about 32 MeV, corresponding to an excitation energy of about 30 MeV. The studies at highest energy which are most relevant to the present work are the following: Mehta, Hunt and Davis covered the excitation region 12.7 Q E, G 20.0 MeV [15], and Hausser et al. the range 16-18.5 MeV [16]. Takeda et al. measured excitation functions for energies in the range E, = 20-24.5 MeV [17], while Bergman and Hobbie covered the very wide range in excitation energy from 19.9 to 28.7 MeV [18]. All of these studies used phase-shift analyses of the angular distributions to assign spins to the observed resonances. More recently Billen comprehensively investigated the energy region 14.6 GE, G 20.4 MeV [19]; his data were subsequently re-analyzed with an improved fitting program by Riedhauser
mu. Our experiment was originally driven to search for high spin (J > 8A) states, in particular the possible lo+ states in “Ne, predicted by many models [4,21-231. A small part of the data which concentrate on analysis of lO+ strength has previously been published [24]. In this paper we present the analysis of the rest of the data. 2. Experimental
details and data analysis
The experimental technique and method of data analysis have been generally described previously [25-271 and the particular details of this experiment are to be found in ref. [24]. Fig. 1 shows the Q3 (the three-body Q-value) spectrum, with an overall resolution of about 1 MeV, the ground-state Qgpp peak and the peak corresponding to the 2+ state of ‘Be are clearly separated, but the excited states of 160 around 6-7 MeV are not resolved. In the excitation-energy spectra (Fig. 2) the resolution is better than 200 keV at forward angles and low excitation energy, increasing to _ 350 keV at the highest excitation energy and most backward angles. In addition to the states known
W.D.M. Rae et al. / Spin assignments (I)
273
Q3 14000 II,,,=-7.37
12000 -
12cPO, ZONe') ‘Be 1 decays
MeV
/ 150 MeV
10000-
%e 2.94 (2+) BOO06000-
1 MeV -
-
160*(6-7 MeV)+ %e 2.94 (2+)
4000 -
SrJftuare cut 2000 0. 0
-I 50
100
150 4,
200
250
I 300
(channels)
Fig. 1. Q3 spectrum for the reaction 12C(160, 160a)‘Be at E(160) = 150 MeV. The peaks labelled by %* MeV may contain contributions from the states 0’ (6.05 MeV), 3- (6.13 MeV),2+ (6.92MeV), l- (7.12 MeV) which are not individually resolved.
previously, which were used to give an energy calibration, the 9- at 22.87 MeV is very strongly excited, and there are peaks at about 23.6, 24.2 and 25.4 MeV, and a bump about 2.5 MeV wide centred on 27.5 MeV, in agreement with the work of Katori et al. [29]. The ‘Be2+ spectrum shows that the low-lying states are excited relatively more strongly, especially the 5- at 10.26 MeV. The spectrum for decays to 160* shows peaks which could be the 7- (16.65) and 9- (21.06) decaying to the 2+ (6.92 MeV) state in 160 and the 8+ (17.30) decaying to the 3- (6.13 MeV) state in 160. There is also a large structure which is in the correct place for the decay of the 27.5 MeV resonance to the O+ or 3- level in 160 but it is contaminated by breakthrough from the group of states at 20-23 MeV decaying to the ground state of 160. The mutual excitation spectrum shows similar structure at the low end. In order to check that the structures in the spectra do not arise from any other of the three possible two-body final-state interactions, the relative kinetic energies for the other two possible pairs of particles, E,,,(a-‘Be) and E,,(8Be-‘60) were calculated to look for states in 12C and “Mg, resp ectively. No structure at all was evident in E,Ja-‘Be), and in E,,(8Be-160), only some broad structures which moved with the detector angles. Two-dimensional plots of each as a function of Erel(~-160) (similar to the modified Dalitz plots in ref. [28]) revealed no sharp states in either 12C or “Mg which might be misidentified as states in 20Ne. The broad structures seen in E,,(8Be-‘60) are in agreement with the work summarized in ref. [30], carried out to investigate whether the broad peaks seen in
WD.M. Rae et al. / Spin assignments (I)
274
J
I
%
I
3 s+uno,
I
axmp!m!oI
i
5 J
f
I
D s+uno, a>“ap!,“!o)
I
1
3
P s+unoa
amapy!oJ
I
s
WBM. Rae et al. / Spin a~si~ments 0)
275
inclusive a-particle spectra from izC(i60, cr) at forward angles [31] were caused by direct population of “*C + r*C molecular resonance states in 24Mg. The positions of the peaks were found to vary with bombarding energy, indicating that states in 24Mg were not in fact res~nsible. The sequential process of cu-pickup to “Ne* resonances followed by a-decay to 160_ was shown to be able to explain most of the observed structure in the single*-particle spectra. The positions of the peaks seen in this experiment at the most forward angles (peaks about 3-4 MeV wide centred on E, = 29, 35, 44, 48, 53 and 59 MeV for $,(lab) = 3”-27”) agree quite and 51-56 well with those at 6, = 7” in ref. [31] (E, = 27-29,31-35,38-42,43-48 MeV).
3. Angular correlations of q, decay In view of the ambiguity concerning the decays to excited states, only the angufar correlations for LYEdecay have been studied. We produced two-dimensional differential cross sections as a function of 0 * and #. Here 8” and J/ are defined as the angles, in the centre of mass with respect to the beam, of 20Ne*-8Be and the a-‘“0 relative velocities, respectively, We fitted our data with a strong absorption model as has been described in refs. [25,321. We display our fits as projections onto the ffro axis. The projection procedure, which is essentially an averaging procedure along the ridges in the e*# space, has been described elsewhere 1271. 3.1. Discrete states The double differential cross section as a function of 8* and JI for the decays of the well-known discrete states is shown with SAM fits in Fig. 3 as projections onto the J10 axis (e* = 0). It was found that the correct angle for the projection could usually be determined to the nearest degree by requiring the main ridge to be centred in e. = O”, while the bin size in tie was chosen to give a reasonable compromise between the number of points and good statistics. Reasonably good fits to all the states were obtained, and the spin assigrmrents are quite unambiguous. All the first are for single spins, with the exception of the 9- at 22.87 MeV. The angular correlations for this state are quite different from those of the nearby 9- at 21.06 MeV, and require the coherent addition of another spin to remove the main ridge near 0” and produce the observed rise at backward angles. The only additional spin which gives a good fit is 8+, in quite a large proportion - about 65% of the 9- amplitude - although even then the minima are still too deep, implying the presence of an underlying background of other spins. Support for SC strength at this excitation comes from 160t6Li, d) [9] and 160((u, ac,) [17,181. It should be noted in passing that there are two different reasons for the apparent weakening of the main ridge which is usually prominent at lfio= 0” in the
216
WD.M. Rae et al. / Spin assignments (I)
Fig. 3. Double differential cross sections for states in 2oNe populated in the reaction 1*c(160, ‘60,.S.a)8Be,S. at E(‘6O) = 150 MeV. Preferred strong absorption model fits are shown as solid lines.
one-dimensional projections of the data (as for instance in the 21.06 MeV 9projection): either a coherent mixture of two or more spins, or the position of the ridges relative to the data area in e*@ space. The latter is the case for all the lower excitation states in Fig. 3. The former applies to the 22.87 MeV data. In addition to the above levels, the high-energy shoulder visible on the 15.34 MeV 7- peak was analysed separately. In the forward-angle spectra this is resolved as a small peak at about 16.1 MeV. The parameters from the fit to the 15.34 MeV 7- give rather a poor fit here, as the spacing of the ridges in the fit is slightly too wide (Fig. 4a). An 8+ fit (Fig. 4b) gives a spacing which is too narrow, but a coherent mixture of the two with about 63% 7- and 37% 8+ by cross section reduces the x2 by over 30% and gives the correct spacing (Fig. 4~). This excitation energy lies in the gap between the high-resolution 160((u, a,) data of Caskey (E, = 12-15.5 MeV, 1331) and Billen (E, = 16.4-21.05 MeV, [191>.However, the 8+ member of the K” = 0; band is quite close, at 15.87 MeV, and has previously been seen in several a-transfer reactions such as 160(13C, 9Be), 160c7Li, t> and i60(i1B 9 7Li> 1341;this is probably what we see. 3.2. Excitation energy slices In the preliminary sort it was found that the resonance at E, = 27.5 MeV could be fitted quite reasonably as a whole assuming a spin of lo+, and on the basis of the number of ridges in the two-dimensional angular correlations the lO+ strength
KDM
Rae et al. / Spin assignments (Z)
277
Fig. 4. The same as Fig. 3, but for the 16.1 MeV state. Three fits are shown, assuming contributing spins of (a) 7-, (b) 8+ and (c) 7- +8+.
seemed to extend downward to lower excitation. Any high-spin, high-energy states stand up in our spectra at backward detector angles; above E, = 19 MeV the energy spectra from these backward angles are markedly enhanced. The fits already given cover the region E, Q 19 MeV, so it was necessary to analyse the upper end of the spectrum in slices of excitation energy in order to search for lO+ strength. The E, gates were chosen to be of roughly equal width (400-600 keV), wider at the top end of the spectrum in order to obtain reasonable statistics. The 24 slices are shown in Fig. 5, each labelled by a letter from a to x. Each slice contains between 800 and 8000 events. For each slice the triple differential cross section d3a/do* dw, dE, (mb * sr -’ MeV-‘) was produced, and a projection over the full data area was made in the same way as for the discrete states. 3.2.1. Fitting procedure The strong absorption model (SAM) has been used to fit the experimental double differential cross sections as described by Rae et al. [25,32] and as used in ref. [27]. For a given set of SAM parameters the quantity to minimize was the sum of the residuals
x;=c (d*w,
- d2uew,)2
278
KD.M.
Rae et al. / Spin assignments (I)
36
Fig. 5. Enlarged version of the upper end of the spectrum of z”Ne from the reaction 1*C(‘60, ‘60,.S.~)8Be,S. given previously in Fig. 2a, showing the slices of excitation energy into which the spectrum was divided for analysis.
with the sum being taken over the whole two-dimensional defined an additional quantity
0*$ data area. We
x; = C ((d2~s&-(d2%,,))*, where the data and theory are first averaged along the ridges before ~12 is calculated. The cross section for a sum of two spins was calculated assuming coherent addition of two different spin components with the amplitudes (Y,/3 and the phase difference 4. The parameters CX,/3 and r$ were all allowed to vary to minimize ,Y:,~.The choice of C$= 90” results in an incoherent sum of the two spins which would be appropriate for non-overlapping resonances. If two resonances overlap and are both excited, their amplitudes are added coherently as explained above. If, on the other hand, they are narrow and non-overlapping but separated by less than the experimental resolution, their contributions must be added incoherently by cross section. Incoherent addition may therefore be viewed as a special case of coherent addition where the amplitudes add with a relative phase of 90”. Thus the fitting procedure includes both possible ways that two spins may add. As an illustration Fig. 6 shows the cross section for the 22.87 MeV 9- state in 20Ne which was found to require a significant component of 8+ strength. Three calculations using the coherent addition procedure with equal amplitudes of 9and 8+ strength and relative phases of o”, 90”, 180” are shown in (a)-(c) respec-
279
Fig. 6. Double differential crass section for the 22.87 MeV 9- state in 20Ne, with strong absorption model calculations showing the effect of adding equal amplitudes of 9- and 8’ strength in different ways. Part (a)-(c) show the results of coherent addition with various relative phases and part (d) the result of incoherent addition.
tively, together with the result of the incoherent addition of equal amplitudes of 9- and 8’ in (d). The expression for the cross section takes the form
With r# = 180” as the rdative values of cr and /3 are changed from fy = 1, 8 = 0 to iy = 0, /3 = 1 the spacing of the ridges changes smoothly from that of spin J1 to that of spin J2. With zero relative phase, the spacing changes in the same way but now the main ridge is attenuated and the ridges at large & are enhanced. In the example of Fig. 6, the ridges in the theoretical prediction are more widely spaced than those in the data because the ratio of 8+ to 9- strength is too high. With a relative phase of 90” the minima are filled in at large t&,, but the main ridge is stiIl prominent.
280
W.D.M. Rae et al. / Spin ~si~~nts
f’r)
3.2.2. Results for each slice
Table 1 summarizes the spins and corresponding amplitudes obtained from the SAM fits for each slice, using the x,” minimization technique. Where more than one ~mbination of spins produces a similar ~22,all are Iisted under “alternatives”, with the dominant spin given first in each case. Also shown are selected states in *‘Ne seen to a,-decay in other reactions, principally 160c6Li, d) and 160(a!, two> which would be expected to excite the same states as the present reaction. The quoted ~22 is the reduced ~22 for the fit to the whole two-dimensional data area, obtained simply by dividing the value of ~22by the number of points (N 450-~), since the number of free parameters is relatively small. The accuracy of the amplitudes (Yand p is estimated to be of the order of & 15% from the spread in values obtained using the different fitting procedures. Except in background regions, the dominant spin was always clear and always agreed upon by the two set of fits. The fact that two different fitting procedures (x,’ and xt> produced the same results for at least the dominant spin is a strong argument for the correctness of these conclusions. However, in most cases where the addition of a small amount of a second spin was required to improve the fits, it was not possible to find one clearly preferred candidate. This probably reflects the data that we are trying to fit angular correlations with a sum of only two amplitudes where often three or more may actually be contributing (this is obvious from Billen’s a-scattering data). Thus the fit obtained with a single spin will usually have minima which are too deep, or backward-angle ridges which are too small, and so the addition of a small amount of almost any other spin improves the fit. In general, the second spin deduced is therefore not very credible, although there are exceptions such as slice h where the second spin is quite strong (about half the dominant amplitude in this case) and consequently may be believed. Conversely, in the background regions where the statistics are rather poor and the structure not very well-defined, several spins are probably contributing and it is impossible to differentiate between them. None of the fits required two amplitudes to be added completely incoherently, suggesting that in each case the resonances overlap. This probably reflects the intrinsic width of the states at high excitation (see the known widths given in Table 1). Fits with a coherent sum of three or four spins were also tried. They did in general give significantly better fits to the data, but there were now too many free parameters: a good fit could be obtained with almost any combination of spins, so no meaningful info~ation could be extracted. The effects of using different SAM parameters were also investigated. It was found that the spins deduced were not affected by changing the values of these parameters. The angular-correlation data are shown in Fig. 7. It is obvious that even background slices (slices covering regions with no peaks) yield angular correlations which are structured and with an angular dependence characteristic of large angular momenta, but which change with excitation energy. This conclusion was
281
U?D.M. Rae et al. / Spin assignments (I) Table 1 SAM fits to q-decays previous work
of 20Ne by regions of excitation energy, with selected levels of “Ne
Previous work
This work EX
J”
xi
amplitudes (&15%0)
17.96-19.01 (a)
(7-I
0.8
0.12(7-j 0.10 (6+)
( f 0.05 MeV)
19.01-19.62 (b)
19.62-20.29 (c)
20.29-20.82 (d)
(dominant)
7-
7-
9-
1.5
0.39 (7-1 0.26 (6+)
1.8
0.32 (7-j 0.24 (6+)
1.7
0.44 (9-j 0.25 (7-I
9-
3.4
0.66 (9-I
21.31-21.86 (0
8+
2.1
0.53 (8+)
21.86-22.49 (g)
8+
2.9
0.41 (8+)
22.49-22.94 (h)
9-
3.2
0.69 (9-j 0.28 (8+)
(8+)
alternatives Jy + JT (xi)
J”
E, (MeV
ref.
f keV)
20.82-21.31 (e)
22.94-23.38 (i)
from
2.2
0.41 (S+) 0.23 (9-j
7-+ 4++ 7-+ 6++
7-+
7-+
9-+ 9-+
4+ 58+ 5-
(0.8) (0.8) (0.9) (0.9)
18.002 + 18.022 + 18.080 f 18.122 + 18.283 f 18.427 + 18.491+ 18.617+ 18.7 + 18.742 It 18.957 f 19.048 + 5- (1.6) 19.161+ 19.295 + 19.4 + 19.41 f 19.533 f 4+ (2.0) 19.727 f 19.842 + 19.9 + 19.988 f 20.15 20.165 f 20.341+ 8+ (1.8) 20.341 f lO+ (1.9) 20.416 + 20.464 *
10++8+ (2.2) lo++ 9- (2.5)
15 5 24 4 10 19 17 18 100 24 23 15 14 24 100 200 23 23 38 100 31
754+ 76+ 758+ 7141 6+ 196 8+ (87) 5236 6+ 426 7320 a 7280 6+ 249 6+ 328 8+ 353 6+ 320 ’ 7128 4+ 250 7281 6+ 133 7133 7212 6+ 280 5-
[161 DO1 Lm LN PO1 m-u DO1 DO1
20.478 + 20.683 + 20.704 f
11 b 250 6 78 11 = _ 120
(8+) 98’ (10’)
[91 DOI [201 DO1 DO1 DOI 191 1151 1201 1201 DO1 [91 m D81 1201 1201 r201 DO1 DO1 151 DOI [5]
20.772 20.977 21.08 21.29 21.3 21.70 21.8 21.82 22.3 22.30 22.43 22.87 23.2 23.3 23.49 22.87 23.2 23.3
32 33 30 d
77978+ 78+ 78+ 7798+ 8+ 8+ 98+ 8+
[201 [71 1171 [91 1181 [91 1171 [91 1181 1171 171 [91 [I81 1171 171 191 1181
+ f +
37 13 13 31 28
f 100 f 100 f 100
f 40 e + 100
f 31 e zt 100
286 312 100 300 240 a 250 240 a 400 240 a 400 600 225 500 550 225 500
DO1
282
W.D.M. Rae et al. / Spin assignments
(I)
Table 1 (continued) This work E* ( f 0.05 MeV) 23.38-23.85 (j)
Previous work .J” (dominant) 8+ (9-)
~22 amplitudes (* 15%) 2.3 0.33(8+)
23.85-24.48 (k)
9- (8+)
2.1
24.48-24.93 (1)
8+ (lo+)
1.5
24.93-25.36 (m) lO+
1.8
25.36-25.80 (n)
1.7
25.80-26.35 (0)
26.35-26.90 (p)
26.90-27.41 (q)
(lo+) (lo+)
10+
lO+
0.20 (9-j 0.35 (9-j 0.31(8+) 0.24 (S+) 0.23 (lo+) 0.35 (lo+) 0.24 (9-j 0.35 (lo+) 0.18 (9-j
1.1 0.23 (lo+) 0.09 (9-)
1.8 0.36 (lo+) 0.14 (11-)
2.0 0.41 (lo+) 0.01 (11-j
27.41-27.92 (r)
lO+
1.8 0.38 (lo+)
27.92-28.45 (s)
lO+
1.5 0.36 (lo+)
28.45-28.95 (t)
lO+
28.95-30.05 (u)
lO+
30.05-31.03 (v)
10+
1.1 0.27 (lo+) 1.4 0.23 (lo+) 0.10 (9-) 0.8 0.19 (lo+) 0.11(9_) 1.0 0.16 (lo+) 0.12 (9-) 1.0 0.12 (lo+) 0.11(9-)
31.03-32.77 (w) lO+ 32.77-35.13 (x)
lO+ (9-)
alternatives JT +Jc (~22)
E,
r
(MeV f keV)
‘JII. &eV)
lO+ (2.4)
ref.
550
8+
23.6 f 100 24.1 24.15
300 400
9- (8+) 8+ 8+
1171 [91 [I81 [171
25.0
600
8+
W31
8++ lO+ (2.4) 23.49 9-+
J”
8++ 9- (1.6) 10++ 9- (2.0)
8++ 9- (1.6) lo++ 8+ (2.0) 8++ 9- (1.1)
25.67 + 25.7
lo++ 8+ (1.2) lo++ 11- (1.2) 10+ (1.3) 9-+ 8+ (2.0) 27.0 lo++ 8+ (2.2) 27.1 lo++ 9- (2.2) 27.2 27.2 lo++ 8+ (2.2) 27.0 lo++ 9- (2.2) 27.1 lO+ (2.4) 27.2 27.2 28.0 g 28.1 28.2 28.3 lo++ lo++ lo++ lo++ 10++
ll- (1.6) 29.4 h 8+ (1.7) 11- (0.9) 8+ (1.0) 11- (1.1)
10++ 11- (1.1) (33.4)
50
f
=500 400
I31
H81
N 2800 700
98+
98+ 8+ 10+ 11lo+
I351 [291 [lOI 1181 [351 [361 DOI I351 1181
10+
[ill
10+
IllI
- 2800 700 1600
700
WI [lOI k31
lo++ 8+ (1.2)
a On the assumption (following ref. [20]) that the widths quoted in ref. [9] are in the laboratory frame. b K” = (02). Tentative spin assignment in ref. [5]; a coherent admixture of (lo-15)% 7- or 6+ improved the fit. ’ Branching ratio to 160a,S, reported as 6 14%. Spin assignment tentative because decay channel unclear; 9- component seemed to be indicated. d Krr= l-. Also seen in 160(‘Li, t) [37], r60(r1B, ‘Li) and 160(13C, 9Be) [34], 160(~, aa) [18] and *W*c, cu) [51. e K” = O-. Also seen in 160(‘Li, t) [37], 160(“B, 7Li) [34], 160(a, (Y,) 1181and ‘*C(12C, (Y)[5]. f Reported in 160(‘Li, t) at E(‘Li) = 60 MeV. s Resonance first observed (and spin assigned) in backward-angle elastic a-scattering, but also seen in ‘70(3He, (us) [38] and r9F(p, (~a) [39]. h Ref. [ll] reports a broad structure corresponding to E,C2’Ne) = 29-36 MeV in the deuteron spectrum from ‘60(6Li, d) at an incident energy E(6Li) = 57.8 MeV. The da angular correlations remain the same across this region, suggesting a series of broad, overlapping lO+ resonances. This is confirmed at higher incident energy in ref. [12].
W.D.M. Rae et al. / Spin assignments
(I)
Fig. 7. Triple differential cross sections for the excitation energy slices in z”Ne, from the reaction 1*C(160, ‘60,,,a)8Bes,,, at E(160) = 150 MeV. The preferred strong absorption model fits are shown as solid lines.
also reached by Young et al. in their double and triple angular-correlation measurements of i2C(i2C, cy>161, in disagreement with the conventional assumption that the background is a superposition of broad low-spin states giving rise to an isotropic angular correlation. An incoherent isotropic background term was tried in the fits, to take into account this as well as contributions from processes other than sequential decay. In the cases where a single-spin fit could be improved by the admixture of a small proportion of almost any other spin, an isotropic background did improve the fit; this was generally the case where the peak in question was superimposed on a background in the spectrum, for instance the lO+ resonance and the 8+ state at 21.6 MeV. The amplitudes for the L = 7, 8, 9 and 10 components of the best fit to each slice are shown as a function of excitation energy in Fig. 8, together with a measure of the overall triple differential cross section for each slice. The lO+ amplitude is not definite around E, - 25 MeV (the region covered by slices 1 to 0) where equally good fits could be obtained assuming a dominant spin of 8+. The shift towards higher angular momenta as the excitation increases is quite evident. The peaks in the 7- and 8+ amplitudes correspond well with previously known states. The wide bump in the 7- amplitude covering E, = 18.0-20.3 MeV agrees
284
W.D.M. Rae et al. / Spin assignments (I)
1.61
16
b
.
20
24
26
32
36
,?&(20Ne)(MeV) Fig. 8. Results of the fits to excitation energy slices in 20Ne. The solid lines show the amplitude of each angular momentum component required to fit the data. The points give an approximate measure of the total triple differential cross section d3u/dO* da, d.E, at the centre of each slice,in arbitrary units. Errors (not shown) are estimated to be of the order of + 15% for the amplitude, while statistical errors in the cross section are smaller than the size of the points.
with the group of three 7- levels reported at 18.7, 19.4 and 19.9 MeV by Artemov et al. in 160(6Li, d) [9], and the peak in the 8+ strength at E, = 21.3-23.0 MeV agrees with their group of 8+ levels at 21.3, 21.8, 22.3 and 23.2 MeV. The wide range (up to at least 25 MeV) over which L = 8 continues to dominate is also in agreement with the global optical-model analysis of 160(a, a) elastic scattering by Michel et al. [14] and the OCM study of Ohkubo et al. [40]. Both of these suggest that the wide bump observed at some angles in the experimental excitation function at around E, = 21.5 MeV is caused by an L = 8 shape resonance. In contrast with the usual assignment they interpret this as being the 8+ member of the K” = 0: band. The 9- strength shows clearly the two well-known states at 21.06 and 22.87 MeV, and the next peak confirms a tentative assignment of Artemov et al. at 23.6 MeV [9]. The fourth peak, of width nearly 1 MeV and centred on E, = 25.4 MeV, is in a region where no 9- strength has previously been reported, but it is well correlated both with a broad peak in the cross section at 25.4 MeV and with broad levels at about 25.7 MeV reported in 160((r, cy) [183 and i60c7Li, t) 131. The lO+ amplitude shows a resonance of width about 2.5 MeV centred on an excitation energy of approximately 27.5 MeV. There is also evidence that the lO+
KD.M. Rae et al. / Spin assignments (I)
285
strength extends up into the continuum as far as the limit of statistics at E, - 35 MeV. Both these conclusions are in agreement with the work of Artemov et al. [ll], except that no evidence could be found for their 9- state at 27.1 MeV, the lO+ resonance also agrees reasonably well with the conclusions of Bergman and Hobbie [18]. Artemov et al. found that the angular correlations for the entire range E, = 29-36 MeV were similar and could all be fitted with 1P,, I 2. Here we can see that the angular correlations for slices u, v, w and x (E, = 28.95-35.13 MeV) are indeed all similar, although the structure washes out as the excitation and slice width increase. However, they are not well described by a pure lO+ fit, but require the coherent addition of 9- strength to obtain the correct spacing. The lO+ strength at E, - 28 MeV also agrees well with all the calculations listed earlier, in particular those of Ragnarsson et al. [4] for their strongly deformed lO+ state. A lO+ component is also needed to obtain the best fit to the data at about 24.7 MeV (possibly extending to about 25.2 MeV) but although this assignment ties in well with the lower lO+ state of Ragnarsson et al., it must be regarded as more tentative. The possible lO+ strength found at E, = 23.2 MeV in slice i is even more tentative. No further suggestions of lo+ strength were found below this excitation energy.
4. Conclusion We have presented r2C(i60, 20Ne*)8Be transfer reaction data for discrete states with emphasis on the region of excitation of 20Ne from 18-35 MeV. The strong absorption model has been used to analyse the angular correlations. Spin assignments are made for a number of excited states and are compared in detail with other related experimental work and theoretical predictions on 20Ne. In particular we confirm a broad resonance at E, = 27.5 MeV with J” = lo+ which we reported earlier [24]. The lO+ strength appears to extend up to 35 MeV. However, we found no conclusive evidence for a lO+ state at lower excitation energy and below 23 MeV no evidence at all for lO+ strength could be found.
The authors thank P.R. Keeling, A.E. Smith, B.R. Fulton, D.W. Banes and S. Marsh for help during the experiment, and Dr. A.C. Merchant, in particular, for carefully reading the manuscript.
[l] B. Buck, C.B. Dover and J.P. Vary, Phys. Rev. Cl1 (1975) 1803 [2] F. Ajzenberg-Selove, Nucl. Phys. A475 (1987) 1
286 [3] F. Ajzenberg-Selove,
W.D.M. Rae et al. / Spin assignments (I)
Nucl. Phys. A392 (1983) 1 I. Ragnarsson, S. Aberg and R.K. Sheline, Phys. Ser. 24 (1981) 215 M.M. Hindi, J.H. Thomas, D.C. Radford and P.D. Parker, Phys. Rev. C27 (1983) 2902 KC. Young, Jr., R.W. Zurmiihle, J.M. Lind and D.P. Balamuth, Nucl. Phys. A330 (1979) 452 S.J. Sanders, L.M. Martz and P.D. Parker, Phys. Rev. C20 (1979) 1743 C.-M. Fou, D.P. Balamuth, R.W. Zurmiihle and K.C. Young, Jr., Phys. Rev. C20 (1979) 1754 K.P. Artemov, V.Z. Goldberg, I.P. Petrov, I.N. Serikov, V.P. Rudakov, V.A. Timofeev, R. Wolski and J. Szmider, Sov. J. Nucl. Phys. 22 (1976) 125 [lo] K.P. Artemov, V.Z. Goldberg, I.P. Petrov, V.P. Rudakov, I.N. Serikov and V.A. Tiiofeev, Sov. J. Nucl. Phys. 23 (1976) 257 [ll] K.P. Artemov. V.Z. Goldberg, I.P. Petrov, V.P. Rudakov, I.N. Serikov, V.A. Timofeev, R. Wolsky and J. Schmider, Sov. J. Nucl. Phys. 26 (1977) 4 [12] K.P. Artemov, V.Z. Goldberg, I.P. Petrov, V.P. Rudakov, I.N. Serikov and V.A. Timofeev, Sov. J. Nucl. Phys. 36 (1982) 779 [13] A.J. Ferguson and L.R. Walker, Phys. Rev. 58 (1940) 666 [14] F. Michel, J. Albinski, P. Belery, Th. Delbar, Gh. Grkgoire, B. Tasiaux and G. Reidemeister, Phys. Rev. C28 (1983) 1904 [15] M.K. Mehta, W.E. Hunt and R.H. Davis, Phys. Rev. 160 (1967) 791 [16] 0. Hlusser, T.K. Alexander, D.L. Disdier, A.J. Ferguson, A.B. McDonald and I.S. Towner, Nucl. Phys. A216 (1973) 617 [17] M. Takeda, S. Kato and T. Yamazaki, J. Phys. Sot. Japan 30 (1971) 56 [18] C. Bergman and R.K. Hobbie, Phys. Rev. C3 (1971) 1729 [19] J.H. Billen, Phys. Rev. C20 (1979) 1648 [20] S.R. Riedhauser, Phys. Rev. C29 (1984) 1961 [21] Y. Fujiwara et al., Suppl. Prog. Theor. Phys. 68 (1980) 29 [22] M. LeMere, Y.C. Tang and D.R. Thompson, Phys. Rev. Cl4 (1976) 23 [23] A.V. Bystrenko, Sov. J. Nucl. Phys. 40 (1984) 247 [24] SC. Allcock, W.D.M. Rae, P.R. Keeling, A.E. Smith, B.R. Fulton and D.W. Banes, Phys. Lett. B201 (1988) 201 [25] W.D.M. Rae and R.K. Bhowmik, Nucl. Phys. A420 (1984) 320 [26] A.E. Smith, S.C. Allcock and W.D.M. Rae, Nucl. Phys. A441 (1985) 701 [27] W.D.M. Rae, S.C. Allcock, S. Marsh and B.R. Fulton, Phys. Lett. B156 (1985) 167 [28] S. Shimoura, A. Sakaguchi, T. Shimoda, T. Fukuda, K. Ogura, K. Katori and H. Ogata, Nucl. Phys. A452 (1986) 123 [29] T. Shimoda, S. Shimoura, T. Fukuda, M. Tanaka, H. Ogata, I. Miura, E. Takada, M.-K. Tanaka, K. Takimoto and K. Katori, J. of Phys. G9 (1983) L199 [30] T. Murakami, E. Ungricht, N. Takahashi, Y.-W. Lui, Y. Mihara, R.E. Neese, E. Takada, D.M. Tanner, R.E. Tribble and K. Nagatani, Phys. Rev. C29 (1984) 847 [31] K. Nagatani, T. Shimoda, D. Tanner, R. Tribble and T. Yamaya, Phys. Rev. Lett. 43 (1979) 1480 [32] S. Marsh and W.D.M. Rae, Phys. Lett. B153 (1985) 21 1331 G. Caskey, Phys. Rev. C31 (1985) 717 [34] H.S. Bradlow, W.D.M. Rae, P.S. Fisher, N.S. Godwin, G. Proudfoot and D. Sinclair, Nucl. Phys. A314 (1979) 171 [35] R. Ceuleneer and F. Michel, Phys. Lett. B43 (1973) 365 [36] A.A. Cowley and G. Heymann, Nucl. Phys. Al46 (1970) 465 [37] M.E. Cobern, D.J. Pisano and P.D. Parker, Phys. Rev. Cl4 (1976) 491 [38] A.A. Cowley and G. Heymann, Phys. Lett. B30 (1969) 618 [39] A. Stabler, W. Buck, G. Staudt and H. Oeschler, Nucl. Phys. A275 (1977) 269 [40] S. Ohkubo, Y. Kond6 and S. Nagata, Prog. Theor. Phys. 57 (1977) 82 [4] [5] [6] [7] [8] [9]
NUCLEAR PHYSICS A
Spin assignments for states in 20Ne via the 12C(160, 20Ne*)8Be transfer reaction W.D.M. Rae, S.C. Allcock i, J. Zhang a Department of Physics, University of Oxford, Nuclear Physics Laboratory, Keble Road, Oxford, OXI 3RH, UK
Received 3 August 1993
Abstract The cr-transfer reaction 12C(‘60, Z”Ne*)8Be has been studied at Eub = 150 MeV. The t60cu anguiar correlations from the decay of MNe* have been measured and analysed with a strong absorption model to make spin assignments for many high-spin states at high excitation in ZONe.
Key words: NUCLEAR REACTIONS r2C(t60, 20Nel, E = 150 MeV; measured cr@,, cp,). “Ne levels deduced J, rr. Strong absorption model analyses.
1. Introduction 20Ne is one of the most thoroughly studied nuclei from both an experimental and a theoretical viewpoint. Its structure of two neutrons and two protonts outside a closed 160 core makes it particularly suitable to be studied with cluster models, and indeed it was one of the first nuclei to be treated in this way by Buck et al. [l]. The relatively small number of nucleons, together with the wealth of accumulated spectroscopic data extending up to an excitation energy of around 30 MeV [2,3], has led to the widespread use of the lower-lying energy levels as a testing ground for a variety of nuclear models. In common with other sd-shell nuclei, 20Ne is well suited to the study of behaviour at high spin and large deformation [4]. Rxperimentally 20Ne has been investigated using a wide variety of reactions, although only a few studies have reached excitation energies above 20 MeV. There have been several applications of angular-correlation techniques to extract spins in a similar manner to the present work. Most recently Hindi et al. [S] and Young et al. 161used the reaction 12C(‘2C, ar)20Ne*(a)‘60 to identify over 20 levels between
’ Present address: AT&T Istel Ltd., Redditch, UK 2 Permanent address: Shanghai Institute of Nuclear Research, China. 0375-9474/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved SSDI 0375-9474(931E0450-M
272
WD.M. Rae et al. / Spin assignments (I)
excitation energies of 12.1 and 23.4 MeV by means of double &a,) or triple + 160 1) angular correlations. Sanders et al. [7] utilized the ease (a,a#o* g.?.. with which ‘Be may be detected at very forward angles to obtain a-8Be angular correlations for scattering angles near 0” for the inverse of the reaction used here, namely i60(i2C, 8Be)20Ne*(a)‘60, in the excitation-energy region 7.1-22.9 MeV. The 160(6Li, d)20Ne *(a)i60 reaction has also been extensively investigated by means of da angular correlations, by both Fou et al. [8] and the Russian group led by Artemov. The latter group has made a systematic study at successively higher bombarding energies [9-121, covering the region E, = 19-50 MeV. Many spin assignments have also been made via resonances in elastic and inelastic scattering of a-particles by 160. This technique has a very long history, having first been used in 1940 by Ferguson and Walker [13]. Over the years the increase in available beam energies has enabled a comprehensive picture to be built up (see for instance ref. [14] and references therein) although detailed excitation functions only exist for bombarding energies below about 32 MeV, corresponding to an excitation energy of about 30 MeV. The studies at highest energy which are most relevant to the present work are the following: Mehta, Hunt and Davis covered the excitation region 12.7 Q E, G 20.0 MeV [15], and Hausser et al. the range 16-18.5 MeV [16]. Takeda et al. measured excitation functions for energies in the range E, = 20-24.5 MeV [17], while Bergman and Hobbie covered the very wide range in excitation energy from 19.9 to 28.7 MeV [18]. All of these studies used phase-shift analyses of the angular distributions to assign spins to the observed resonances. More recently Billen comprehensively investigated the energy region 14.6 GE, G 20.4 MeV [19]; his data were subsequently re-analyzed with an improved fitting program by Riedhauser
mu. Our experiment was originally driven to search for high spin (J > 8A) states, in particular the possible lo+ states in “Ne, predicted by many models [4,21-231. A small part of the data which concentrate on analysis of lO+ strength has previously been published [24]. In this paper we present the analysis of the rest of the data. 2. Experimental
details and data analysis
The experimental technique and method of data analysis have been generally described previously [25-271 and the particular details of this experiment are to be found in ref. [24]. Fig. 1 shows the Q3 (the three-body Q-value) spectrum, with an overall resolution of about 1 MeV, the ground-state Qgpp peak and the peak corresponding to the 2+ state of ‘Be are clearly separated, but the excited states of 160 around 6-7 MeV are not resolved. In the excitation-energy spectra (Fig. 2) the resolution is better than 200 keV at forward angles and low excitation energy, increasing to _ 350 keV at the highest excitation energy and most backward angles. In addition to the states known
W.D.M. Rae et al. / Spin assignments (I)
273
Q3 14000 II,,,=-7.37
12000 -
12cPO, ZONe') ‘Be 1 decays
MeV
/ 150 MeV
10000-
%e 2.94 (2+) BOO06000-
1 MeV -
-
160*(6-7 MeV)+ %e 2.94 (2+)
4000 -
SrJftuare cut 2000 0. 0
-I 50
100
150 4,
200
250
I 300
(channels)
Fig. 1. Q3 spectrum for the reaction 12C(160, 160a)‘Be at E(160) = 150 MeV. The peaks labelled by %* MeV may contain contributions from the states 0’ (6.05 MeV), 3- (6.13 MeV),2+ (6.92MeV), l- (7.12 MeV) which are not individually resolved.
previously, which were used to give an energy calibration, the 9- at 22.87 MeV is very strongly excited, and there are peaks at about 23.6, 24.2 and 25.4 MeV, and a bump about 2.5 MeV wide centred on 27.5 MeV, in agreement with the work of Katori et al. [29]. The ‘Be2+ spectrum shows that the low-lying states are excited relatively more strongly, especially the 5- at 10.26 MeV. The spectrum for decays to 160* shows peaks which could be the 7- (16.65) and 9- (21.06) decaying to the 2+ (6.92 MeV) state in 160 and the 8+ (17.30) decaying to the 3- (6.13 MeV) state in 160. There is also a large structure which is in the correct place for the decay of the 27.5 MeV resonance to the O+ or 3- level in 160 but it is contaminated by breakthrough from the group of states at 20-23 MeV decaying to the ground state of 160. The mutual excitation spectrum shows similar structure at the low end. In order to check that the structures in the spectra do not arise from any other of the three possible two-body final-state interactions, the relative kinetic energies for the other two possible pairs of particles, E,,,(a-‘Be) and E,,(8Be-‘60) were calculated to look for states in 12C and “Mg, resp ectively. No structure at all was evident in E,Ja-‘Be), and in E,,(8Be-160), only some broad structures which moved with the detector angles. Two-dimensional plots of each as a function of Erel(~-160) (similar to the modified Dalitz plots in ref. [28]) revealed no sharp states in either 12C or “Mg which might be misidentified as states in 20Ne. The broad structures seen in E,,(8Be-‘60) are in agreement with the work summarized in ref. [30], carried out to investigate whether the broad peaks seen in
WD.M. Rae et al. / Spin assignments (I)
274
J
I
%
I
3 s+uno,
I
axmp!m!oI
i
5 J
f
I
D s+uno, a>“ap!,“!o)
I
1
3
P s+unoa
amapy!oJ
I
s
WBM. Rae et al. / Spin a~si~ments 0)
275
inclusive a-particle spectra from izC(i60, cr) at forward angles [31] were caused by direct population of “*C + r*C molecular resonance states in 24Mg. The positions of the peaks were found to vary with bombarding energy, indicating that states in 24Mg were not in fact res~nsible. The sequential process of cu-pickup to “Ne* resonances followed by a-decay to 160_ was shown to be able to explain most of the observed structure in the single*-particle spectra. The positions of the peaks seen in this experiment at the most forward angles (peaks about 3-4 MeV wide centred on E, = 29, 35, 44, 48, 53 and 59 MeV for $,(lab) = 3”-27”) agree quite and 51-56 well with those at 6, = 7” in ref. [31] (E, = 27-29,31-35,38-42,43-48 MeV).
3. Angular correlations of q, decay In view of the ambiguity concerning the decays to excited states, only the angufar correlations for LYEdecay have been studied. We produced two-dimensional differential cross sections as a function of 0 * and #. Here 8” and J/ are defined as the angles, in the centre of mass with respect to the beam, of 20Ne*-8Be and the a-‘“0 relative velocities, respectively, We fitted our data with a strong absorption model as has been described in refs. [25,321. We display our fits as projections onto the ffro axis. The projection procedure, which is essentially an averaging procedure along the ridges in the e*# space, has been described elsewhere 1271. 3.1. Discrete states The double differential cross section as a function of 8* and JI for the decays of the well-known discrete states is shown with SAM fits in Fig. 3 as projections onto the J10 axis (e* = 0). It was found that the correct angle for the projection could usually be determined to the nearest degree by requiring the main ridge to be centred in e. = O”, while the bin size in tie was chosen to give a reasonable compromise between the number of points and good statistics. Reasonably good fits to all the states were obtained, and the spin assigrmrents are quite unambiguous. All the first are for single spins, with the exception of the 9- at 22.87 MeV. The angular correlations for this state are quite different from those of the nearby 9- at 21.06 MeV, and require the coherent addition of another spin to remove the main ridge near 0” and produce the observed rise at backward angles. The only additional spin which gives a good fit is 8+, in quite a large proportion - about 65% of the 9- amplitude - although even then the minima are still too deep, implying the presence of an underlying background of other spins. Support for SC strength at this excitation comes from 160t6Li, d) [9] and 160((u, ac,) [17,181. It should be noted in passing that there are two different reasons for the apparent weakening of the main ridge which is usually prominent at lfio= 0” in the
216
WD.M. Rae et al. / Spin assignments (I)
Fig. 3. Double differential cross sections for states in 2oNe populated in the reaction 1*c(160, ‘60,.S.a)8Be,S. at E(‘6O) = 150 MeV. Preferred strong absorption model fits are shown as solid lines.
one-dimensional projections of the data (as for instance in the 21.06 MeV 9projection): either a coherent mixture of two or more spins, or the position of the ridges relative to the data area in e*@ space. The latter is the case for all the lower excitation states in Fig. 3. The former applies to the 22.87 MeV data. In addition to the above levels, the high-energy shoulder visible on the 15.34 MeV 7- peak was analysed separately. In the forward-angle spectra this is resolved as a small peak at about 16.1 MeV. The parameters from the fit to the 15.34 MeV 7- give rather a poor fit here, as the spacing of the ridges in the fit is slightly too wide (Fig. 4a). An 8+ fit (Fig. 4b) gives a spacing which is too narrow, but a coherent mixture of the two with about 63% 7- and 37% 8+ by cross section reduces the x2 by over 30% and gives the correct spacing (Fig. 4~). This excitation energy lies in the gap between the high-resolution 160((u, a,) data of Caskey (E, = 12-15.5 MeV, 1331) and Billen (E, = 16.4-21.05 MeV, [191>.However, the 8+ member of the K” = 0; band is quite close, at 15.87 MeV, and has previously been seen in several a-transfer reactions such as 160(13C, 9Be), 160c7Li, t> and i60(i1B 9 7Li> 1341;this is probably what we see. 3.2. Excitation energy slices In the preliminary sort it was found that the resonance at E, = 27.5 MeV could be fitted quite reasonably as a whole assuming a spin of lo+, and on the basis of the number of ridges in the two-dimensional angular correlations the lO+ strength
KDM
Rae et al. / Spin assignments (Z)
277
Fig. 4. The same as Fig. 3, but for the 16.1 MeV state. Three fits are shown, assuming contributing spins of (a) 7-, (b) 8+ and (c) 7- +8+.
seemed to extend downward to lower excitation. Any high-spin, high-energy states stand up in our spectra at backward detector angles; above E, = 19 MeV the energy spectra from these backward angles are markedly enhanced. The fits already given cover the region E, Q 19 MeV, so it was necessary to analyse the upper end of the spectrum in slices of excitation energy in order to search for lO+ strength. The E, gates were chosen to be of roughly equal width (400-600 keV), wider at the top end of the spectrum in order to obtain reasonable statistics. The 24 slices are shown in Fig. 5, each labelled by a letter from a to x. Each slice contains between 800 and 8000 events. For each slice the triple differential cross section d3a/do* dw, dE, (mb * sr -’ MeV-‘) was produced, and a projection over the full data area was made in the same way as for the discrete states. 3.2.1. Fitting procedure The strong absorption model (SAM) has been used to fit the experimental double differential cross sections as described by Rae et al. [25,32] and as used in ref. [27]. For a given set of SAM parameters the quantity to minimize was the sum of the residuals
x;=c (d*w,
- d2uew,)2
278
KD.M.
Rae et al. / Spin assignments (I)
36
Fig. 5. Enlarged version of the upper end of the spectrum of z”Ne from the reaction 1*C(‘60, ‘60,.S.~)8Be,S. given previously in Fig. 2a, showing the slices of excitation energy into which the spectrum was divided for analysis.
with the sum being taken over the whole two-dimensional defined an additional quantity
0*$ data area. We
x; = C ((d2~s&-(d2%,,))*, where the data and theory are first averaged along the ridges before ~12 is calculated. The cross section for a sum of two spins was calculated assuming coherent addition of two different spin components with the amplitudes (Y,/3 and the phase difference 4. The parameters CX,/3 and r$ were all allowed to vary to minimize ,Y:,~.The choice of C$= 90” results in an incoherent sum of the two spins which would be appropriate for non-overlapping resonances. If two resonances overlap and are both excited, their amplitudes are added coherently as explained above. If, on the other hand, they are narrow and non-overlapping but separated by less than the experimental resolution, their contributions must be added incoherently by cross section. Incoherent addition may therefore be viewed as a special case of coherent addition where the amplitudes add with a relative phase of 90”. Thus the fitting procedure includes both possible ways that two spins may add. As an illustration Fig. 6 shows the cross section for the 22.87 MeV 9- state in 20Ne which was found to require a significant component of 8+ strength. Three calculations using the coherent addition procedure with equal amplitudes of 9and 8+ strength and relative phases of o”, 90”, 180” are shown in (a)-(c) respec-
279
Fig. 6. Double differential crass section for the 22.87 MeV 9- state in 20Ne, with strong absorption model calculations showing the effect of adding equal amplitudes of 9- and 8’ strength in different ways. Part (a)-(c) show the results of coherent addition with various relative phases and part (d) the result of incoherent addition.
tively, together with the result of the incoherent addition of equal amplitudes of 9- and 8’ in (d). The expression for the cross section takes the form
With r# = 180” as the rdative values of cr and /3 are changed from fy = 1, 8 = 0 to iy = 0, /3 = 1 the spacing of the ridges changes smoothly from that of spin J1 to that of spin J2. With zero relative phase, the spacing changes in the same way but now the main ridge is attenuated and the ridges at large & are enhanced. In the example of Fig. 6, the ridges in the theoretical prediction are more widely spaced than those in the data because the ratio of 8+ to 9- strength is too high. With a relative phase of 90” the minima are filled in at large t&,, but the main ridge is stiIl prominent.
280
W.D.M. Rae et al. / Spin ~si~~nts
f’r)
3.2.2. Results for each slice
Table 1 summarizes the spins and corresponding amplitudes obtained from the SAM fits for each slice, using the x,” minimization technique. Where more than one ~mbination of spins produces a similar ~22,all are Iisted under “alternatives”, with the dominant spin given first in each case. Also shown are selected states in *‘Ne seen to a,-decay in other reactions, principally 160c6Li, d) and 160(a!, two> which would be expected to excite the same states as the present reaction. The quoted ~22 is the reduced ~22 for the fit to the whole two-dimensional data area, obtained simply by dividing the value of ~22by the number of points (N 450-~), since the number of free parameters is relatively small. The accuracy of the amplitudes (Yand p is estimated to be of the order of & 15% from the spread in values obtained using the different fitting procedures. Except in background regions, the dominant spin was always clear and always agreed upon by the two set of fits. The fact that two different fitting procedures (x,’ and xt> produced the same results for at least the dominant spin is a strong argument for the correctness of these conclusions. However, in most cases where the addition of a small amount of a second spin was required to improve the fits, it was not possible to find one clearly preferred candidate. This probably reflects the data that we are trying to fit angular correlations with a sum of only two amplitudes where often three or more may actually be contributing (this is obvious from Billen’s a-scattering data). Thus the fit obtained with a single spin will usually have minima which are too deep, or backward-angle ridges which are too small, and so the addition of a small amount of almost any other spin improves the fit. In general, the second spin deduced is therefore not very credible, although there are exceptions such as slice h where the second spin is quite strong (about half the dominant amplitude in this case) and consequently may be believed. Conversely, in the background regions where the statistics are rather poor and the structure not very well-defined, several spins are probably contributing and it is impossible to differentiate between them. None of the fits required two amplitudes to be added completely incoherently, suggesting that in each case the resonances overlap. This probably reflects the intrinsic width of the states at high excitation (see the known widths given in Table 1). Fits with a coherent sum of three or four spins were also tried. They did in general give significantly better fits to the data, but there were now too many free parameters: a good fit could be obtained with almost any combination of spins, so no meaningful info~ation could be extracted. The effects of using different SAM parameters were also investigated. It was found that the spins deduced were not affected by changing the values of these parameters. The angular-correlation data are shown in Fig. 7. It is obvious that even background slices (slices covering regions with no peaks) yield angular correlations which are structured and with an angular dependence characteristic of large angular momenta, but which change with excitation energy. This conclusion was
281
U?D.M. Rae et al. / Spin assignments (I) Table 1 SAM fits to q-decays previous work
of 20Ne by regions of excitation energy, with selected levels of “Ne
Previous work
This work EX
J”
xi
amplitudes (&15%0)
17.96-19.01 (a)
(7-I
0.8
0.12(7-j 0.10 (6+)
( f 0.05 MeV)
19.01-19.62 (b)
19.62-20.29 (c)
20.29-20.82 (d)
(dominant)
7-
7-
9-
1.5
0.39 (7-1 0.26 (6+)
1.8
0.32 (7-j 0.24 (6+)
1.7
0.44 (9-j 0.25 (7-I
9-
3.4
0.66 (9-I
21.31-21.86 (0
8+
2.1
0.53 (8+)
21.86-22.49 (g)
8+
2.9
0.41 (8+)
22.49-22.94 (h)
9-
3.2
0.69 (9-j 0.28 (8+)
(8+)
alternatives Jy + JT (xi)
J”
E, (MeV
ref.
f keV)
20.82-21.31 (e)
22.94-23.38 (i)
from
2.2
0.41 (S+) 0.23 (9-j
7-+ 4++ 7-+ 6++
7-+
7-+
9-+ 9-+
4+ 58+ 5-
(0.8) (0.8) (0.9) (0.9)
18.002 + 18.022 + 18.080 f 18.122 + 18.283 f 18.427 + 18.491+ 18.617+ 18.7 + 18.742 It 18.957 f 19.048 + 5- (1.6) 19.161+ 19.295 + 19.4 + 19.41 f 19.533 f 4+ (2.0) 19.727 f 19.842 + 19.9 + 19.988 f 20.15 20.165 f 20.341+ 8+ (1.8) 20.341 f lO+ (1.9) 20.416 + 20.464 *
10++8+ (2.2) lo++ 9- (2.5)
15 5 24 4 10 19 17 18 100 24 23 15 14 24 100 200 23 23 38 100 31
754+ 76+ 758+ 7141 6+ 196 8+ (87) 5236 6+ 426 7320 a 7280 6+ 249 6+ 328 8+ 353 6+ 320 ’ 7128 4+ 250 7281 6+ 133 7133 7212 6+ 280 5-
[161 DO1 Lm LN PO1 m-u DO1 DO1
20.478 + 20.683 + 20.704 f
11 b 250 6 78 11 = _ 120
(8+) 98’ (10’)
[91 DOI [201 DO1 DO1 DOI 191 1151 1201 1201 DO1 [91 m D81 1201 1201 r201 DO1 DO1 151 DOI [5]
20.772 20.977 21.08 21.29 21.3 21.70 21.8 21.82 22.3 22.30 22.43 22.87 23.2 23.3 23.49 22.87 23.2 23.3
32 33 30 d
77978+ 78+ 78+ 7798+ 8+ 8+ 98+ 8+
[201 [71 1171 [91 1181 [91 1171 [91 1181 1171 171 [91 [I81 1171 171 191 1181
+ f +
37 13 13 31 28
f 100 f 100 f 100
f 40 e + 100
f 31 e zt 100
286 312 100 300 240 a 250 240 a 400 240 a 400 600 225 500 550 225 500
DO1
282
W.D.M. Rae et al. / Spin assignments
(I)
Table 1 (continued) This work E* ( f 0.05 MeV) 23.38-23.85 (j)
Previous work .J” (dominant) 8+ (9-)
~22 amplitudes (* 15%) 2.3 0.33(8+)
23.85-24.48 (k)
9- (8+)
2.1
24.48-24.93 (1)
8+ (lo+)
1.5
24.93-25.36 (m) lO+
1.8
25.36-25.80 (n)
1.7
25.80-26.35 (0)
26.35-26.90 (p)
26.90-27.41 (q)
(lo+) (lo+)
10+
lO+
0.20 (9-j 0.35 (9-j 0.31(8+) 0.24 (S+) 0.23 (lo+) 0.35 (lo+) 0.24 (9-j 0.35 (lo+) 0.18 (9-j
1.1 0.23 (lo+) 0.09 (9-)
1.8 0.36 (lo+) 0.14 (11-)
2.0 0.41 (lo+) 0.01 (11-j
27.41-27.92 (r)
lO+
1.8 0.38 (lo+)
27.92-28.45 (s)
lO+
1.5 0.36 (lo+)
28.45-28.95 (t)
lO+
28.95-30.05 (u)
lO+
30.05-31.03 (v)
10+
1.1 0.27 (lo+) 1.4 0.23 (lo+) 0.10 (9-) 0.8 0.19 (lo+) 0.11(9_) 1.0 0.16 (lo+) 0.12 (9-) 1.0 0.12 (lo+) 0.11(9-)
31.03-32.77 (w) lO+ 32.77-35.13 (x)
lO+ (9-)
alternatives JT +Jc (~22)
E,
r
(MeV f keV)
‘JII. &eV)
lO+ (2.4)
ref.
550
8+
23.6 f 100 24.1 24.15
300 400
9- (8+) 8+ 8+
1171 [91 [I81 [171
25.0
600
8+
W31
8++ lO+ (2.4) 23.49 9-+
J”
8++ 9- (1.6) 10++ 9- (2.0)
8++ 9- (1.6) lo++ 8+ (2.0) 8++ 9- (1.1)
25.67 + 25.7
lo++ 8+ (1.2) lo++ 11- (1.2) 10+ (1.3) 9-+ 8+ (2.0) 27.0 lo++ 8+ (2.2) 27.1 lo++ 9- (2.2) 27.2 27.2 lo++ 8+ (2.2) 27.0 lo++ 9- (2.2) 27.1 lO+ (2.4) 27.2 27.2 28.0 g 28.1 28.2 28.3 lo++ lo++ lo++ lo++ 10++
ll- (1.6) 29.4 h 8+ (1.7) 11- (0.9) 8+ (1.0) 11- (1.1)
10++ 11- (1.1) (33.4)
50
f
=500 400
I31
H81
N 2800 700
98+
98+ 8+ 10+ 11lo+
I351 [291 [lOI 1181 [351 [361 DOI I351 1181
10+
[ill
10+
IllI
- 2800 700 1600
700
WI [lOI k31
lo++ 8+ (1.2)
a On the assumption (following ref. [20]) that the widths quoted in ref. [9] are in the laboratory frame. b K” = (02). Tentative spin assignment in ref. [5]; a coherent admixture of (lo-15)% 7- or 6+ improved the fit. ’ Branching ratio to 160a,S, reported as 6 14%. Spin assignment tentative because decay channel unclear; 9- component seemed to be indicated. d Krr= l-. Also seen in 160(‘Li, t) [37], r60(r1B, ‘Li) and 160(13C, 9Be) [34], 160(~, aa) [18] and *W*c, cu) [51. e K” = O-. Also seen in 160(‘Li, t) [37], 160(“B, 7Li) [34], 160(a, (Y,) 1181and ‘*C(12C, (Y)[5]. f Reported in 160(‘Li, t) at E(‘Li) = 60 MeV. s Resonance first observed (and spin assigned) in backward-angle elastic a-scattering, but also seen in ‘70(3He, (us) [38] and r9F(p, (~a) [39]. h Ref. [ll] reports a broad structure corresponding to E,C2’Ne) = 29-36 MeV in the deuteron spectrum from ‘60(6Li, d) at an incident energy E(6Li) = 57.8 MeV. The da angular correlations remain the same across this region, suggesting a series of broad, overlapping lO+ resonances. This is confirmed at higher incident energy in ref. [12].
W.D.M. Rae et al. / Spin assignments
(I)
Fig. 7. Triple differential cross sections for the excitation energy slices in z”Ne, from the reaction 1*C(160, ‘60,,,a)8Bes,,, at E(160) = 150 MeV. The preferred strong absorption model fits are shown as solid lines.
also reached by Young et al. in their double and triple angular-correlation measurements of i2C(i2C, cy>161, in disagreement with the conventional assumption that the background is a superposition of broad low-spin states giving rise to an isotropic angular correlation. An incoherent isotropic background term was tried in the fits, to take into account this as well as contributions from processes other than sequential decay. In the cases where a single-spin fit could be improved by the admixture of a small proportion of almost any other spin, an isotropic background did improve the fit; this was generally the case where the peak in question was superimposed on a background in the spectrum, for instance the lO+ resonance and the 8+ state at 21.6 MeV. The amplitudes for the L = 7, 8, 9 and 10 components of the best fit to each slice are shown as a function of excitation energy in Fig. 8, together with a measure of the overall triple differential cross section for each slice. The lO+ amplitude is not definite around E, - 25 MeV (the region covered by slices 1 to 0) where equally good fits could be obtained assuming a dominant spin of 8+. The shift towards higher angular momenta as the excitation increases is quite evident. The peaks in the 7- and 8+ amplitudes correspond well with previously known states. The wide bump in the 7- amplitude covering E, = 18.0-20.3 MeV agrees
284
W.D.M. Rae et al. / Spin assignments (I)
1.61
16
b
.
20
24
26
32
36
,?&(20Ne)(MeV) Fig. 8. Results of the fits to excitation energy slices in 20Ne. The solid lines show the amplitude of each angular momentum component required to fit the data. The points give an approximate measure of the total triple differential cross section d3u/dO* da, d.E, at the centre of each slice,in arbitrary units. Errors (not shown) are estimated to be of the order of + 15% for the amplitude, while statistical errors in the cross section are smaller than the size of the points.
with the group of three 7- levels reported at 18.7, 19.4 and 19.9 MeV by Artemov et al. in 160(6Li, d) [9], and the peak in the 8+ strength at E, = 21.3-23.0 MeV agrees with their group of 8+ levels at 21.3, 21.8, 22.3 and 23.2 MeV. The wide range (up to at least 25 MeV) over which L = 8 continues to dominate is also in agreement with the global optical-model analysis of 160(a, a) elastic scattering by Michel et al. [14] and the OCM study of Ohkubo et al. [40]. Both of these suggest that the wide bump observed at some angles in the experimental excitation function at around E, = 21.5 MeV is caused by an L = 8 shape resonance. In contrast with the usual assignment they interpret this as being the 8+ member of the K” = 0: band. The 9- strength shows clearly the two well-known states at 21.06 and 22.87 MeV, and the next peak confirms a tentative assignment of Artemov et al. at 23.6 MeV [9]. The fourth peak, of width nearly 1 MeV and centred on E, = 25.4 MeV, is in a region where no 9- strength has previously been reported, but it is well correlated both with a broad peak in the cross section at 25.4 MeV and with broad levels at about 25.7 MeV reported in 160((r, cy) [183 and i60c7Li, t) 131. The lO+ amplitude shows a resonance of width about 2.5 MeV centred on an excitation energy of approximately 27.5 MeV. There is also evidence that the lO+
KD.M. Rae et al. / Spin assignments (I)
285
strength extends up into the continuum as far as the limit of statistics at E, - 35 MeV. Both these conclusions are in agreement with the work of Artemov et al. [ll], except that no evidence could be found for their 9- state at 27.1 MeV, the lO+ resonance also agrees reasonably well with the conclusions of Bergman and Hobbie [18]. Artemov et al. found that the angular correlations for the entire range E, = 29-36 MeV were similar and could all be fitted with 1P,, I 2. Here we can see that the angular correlations for slices u, v, w and x (E, = 28.95-35.13 MeV) are indeed all similar, although the structure washes out as the excitation and slice width increase. However, they are not well described by a pure lO+ fit, but require the coherent addition of 9- strength to obtain the correct spacing. The lO+ strength at E, - 28 MeV also agrees well with all the calculations listed earlier, in particular those of Ragnarsson et al. [4] for their strongly deformed lO+ state. A lO+ component is also needed to obtain the best fit to the data at about 24.7 MeV (possibly extending to about 25.2 MeV) but although this assignment ties in well with the lower lO+ state of Ragnarsson et al., it must be regarded as more tentative. The possible lO+ strength found at E, = 23.2 MeV in slice i is even more tentative. No further suggestions of lo+ strength were found below this excitation energy.
4. Conclusion We have presented r2C(i60, 20Ne*)8Be transfer reaction data for discrete states with emphasis on the region of excitation of 20Ne from 18-35 MeV. The strong absorption model has been used to analyse the angular correlations. Spin assignments are made for a number of excited states and are compared in detail with other related experimental work and theoretical predictions on 20Ne. In particular we confirm a broad resonance at E, = 27.5 MeV with J” = lo+ which we reported earlier [24]. The lO+ strength appears to extend up to 35 MeV. However, we found no conclusive evidence for a lO+ state at lower excitation energy and below 23 MeV no evidence at all for lO+ strength could be found.
The authors thank P.R. Keeling, A.E. Smith, B.R. Fulton, D.W. Banes and S. Marsh for help during the experiment, and Dr. A.C. Merchant, in particular, for carefully reading the manuscript.
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