THE STRUCTURE OF Mg24 AND Si28 AT HIGH EXCITATION ENERGY

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THE STRUCTURE OF Mg24 AND Si28 AT HIGH EXCITATION ENERGY

D. Bromley, L. Chua, A. Gobbi, P. Maurenzig, P. Parker, M. Sachs, D.

Shapira, R. Stokstad, R. Wieland

To cite this version:

D. Bromley, L. Chua, A. Gobbi, P. Maurenzig, P. Parker, et al.. THE STRUCTURE OF Mg24 AND

Si28 AT HIGH EXCITATION ENERGY. Journal de Physique Colloques, 1971, 32 (C6), pp.C6-5-C6-

16. �10.1051/jphyscol:1971602�. �jpa-00214820�

JOURNAL

DE

Colloque C6, supplkment au no 11-12, Tome 32, Novembre-Dtcembre 1971, page C6-5

THE STRUCTURE OF MgZ4

AND Si2' AT HIGH EXCITATION ENERGY (*)

D. A. BROMLEY, L. CHUA, A. GOBBI, P. R. MAURENZIG (**), P. D. PARKER, M. W. SACHS, D. SHAPIRA, R. G. STOKSTAD, and R. WIELAND

A. W. Wright Nuclear Structure Laboratory, Yale University New Haven, Connecticut, U. S. A.

Rbume. - Les fonctions d'excitations pour lcs rhctions Ol6(C12, a)Mg24 et C'2(016, a)Mg24 a des energies de 18 A 21 MeV dans le centre de masse mettent en evidence I'importance des struc- tures intermediaires du type en quartet dans le Mg24 ct Si28. Des mesures de coincidences triples dans l'etat final a trois corps mettent Cgalement en evidence des configurations en agregats Cl2 -t C12dans Mg24.

Abstract.

Excitation functions for the 016(C12, a)Mg24 and C12(0'6, a)Mg24 reaction for center-of-mass energies from 18 to 21 MeV show evidence for the importance of a-cluster inter- mediate structure in both Mgz4 and Si28. Triple coincidence measurements of the resulting 3-body final state also show evidence for Cl2 + C12 cluster configurations in Mg24.

Introduction. - A great amount of interest and activity has recently been centered around the possible existence of cluster-like configurations in the s-d shell nuclei and on the opportunities for studying this type of structure with heavy-ion induced reactions. Since the discovery of sharp states a t high excitation energy in MgZ4, selectively populated in the 016(C12, u)MgZ4 reaction [I], and the demonstration that these states possessed high angular momentum [2], a substantial amount of experimental investigation has been direc- ted toward elucidating the nature of these states and the reaction mechanism associated with their forma- tion. Paralleling these efforts, recent theoretical developments [3] have been made which would suggest that existence of x-cluster or

quartet

configurations in this mass region. The possibility of heavier clusters contributing to the structure of Mg24, e. g. C12 + C12 quasi-molecular configurations, has been raised by the early experiments of Bromley, Kuehner and Almqvist [4] on the CI2 + C1* reaction and by the recent experiments of Patterson, Winkler and Zaidens [5] which extended the earlier data to lower bombard- ing energies. The positions of the quasimolecular resonances [4] are indicated in figure 1 at -- 20 MeV excitation in MgZ4 and are now known [5] to extend down to -- 17 MeV excitation. Also indicated in figure 1 are the positions of the 0' members of the

M~

size-

FIG. 1. - Energy level diagram for

showing selected levels of interest to the present experiment together with the threshold

energies for ^the available ^decay channels. Predicted positions of quartet configurations [3] are also shown.

lowest quartet configurations predicted by Arirna ct

In part A of this paper we shall investigate the al. [3], where [ x , y, z] denotes the number of clusters

importance of cluster phenomena in both the mecha- in the 1 p, 2 s-1 d and 2 p-1 f shells, respectively.

nism of the 016(C12. u)MgZ4 reaction and in the structures of M~~~ and si2' i t high excitation energy.

(*)

Work supported by U. S. Atomic Energy Commission

Contract AT(30-1)-3223. In part B, evidence is presented for the existence of

( * * )

Permanent address

Universita di Firenze. Istituto di C12 + C12 quasimolecular structure in Mg24, possibly

~,

Fisica, 50125 Firenze, Italy. of a type not seen in previous experiments [4], [5].

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971602

C6-6 D. A. BROMLEY, L. CHUA, A. GOBBI A. The mechanism of the 016(C'2, a)MgZ4 reaction.

--

The initial observation made by Middleton et al. [ l ] was that a few states (e. g. those shown a t - ¹⁶

MeV in Fig. 1) were strongly and selectively populated in the 0'6(C12, cr)MgZ4 reaction (at EClz ⁼ 36 MeV), in a region where a high level density is expected.

These states were of quite narrow width, i. e. less than 40 keV, and exhibited smooth angular distributions [I].

Measurements of or-cz correlations and x-decay branch- ing ratios a t Yale and subsequently a t Pennsylvania [6] added the third main characteristic now known or these states, viz. that they are predominantly states of high angular momentum, with spins typi- cally 2 6. Apart from the characteristics of selective population, narrow width, and high spin, little else was definite regarding either the nature of these states or the nature of the reaction mechanism populating them.

The possible mechanisms for the reaction vary in a continuous manner from that of the statistical com- pound nucleus t o that of the direct transfer of eight or twelve nucleons. Midway between these extremes lies the concept of intermediate structure in which the reaction proceeds through a broad state in the compound system whose lifetime is only somewhat longer than the typical collision time associated with a direct reaction. Governing all of the possible types of mechanisms will be the approximate selection rules imposed by the Coulomb and angular momentum barriers in the entrance and exit channels ; in fact, these considerations by themselves go a long way towards explaining the fact that high spin states are preferentially populated in this particular reaction, where the exit channel cannot carry away the large angular momenta brought in by the heavy ions in the entrance channel.

Certain aspects of the information available on the O ' ~ ( C ' ~ , c r ) ~ g ' ~ reaction and on related reactions support different pictures for the reaction mechanism, and the possibility that the reaction contains contri- butions from several different mechanisms cannot be excluded. The formation of a statistical compound nucleus is suggested by the observation [7], [lo] of rapid changes in cross section with bombarding energy.

The mechanism for the population of the lowlying states in MgZ4 has already been shown by Halbert et al.

to be generally consistent with compound-nucleus formation [I I], [12]. Furthermore, states a t high excitation energy in AlZ7, presumably also of high spin, are selectively populated in the c L 2 ( 0 1 6 , p)AIz7 reaction [13] a t

= 36 and 60 MeV, and it is unlikely that such a reaction would proceed by a mechanism other than compound-nucleus formation.

In support of a direct mechanism for population of these states a t high excitation energies, one can cite the smooth, generally forward peaked angular distribu- tions presented in ref. [I], and the fact that asymme- tries about 900 center-of-mass angle in the angular distributions have been observed [2]. Furthermore,

both the projectile and target nuclei themselves have a propensity for cluster-type structure which would enhance a direct transfer of cr-clusters. The ClZ(N14, d)MgZ4 reaction [I41 also selectively popu- lates a number of states a t high excitation in Mg24, some of which may be identified (at least on the basis of measured energies) with those seen in the C'2(0'6, cr)MgZ4 and 0 1 6 ( ~ ' 2 , a)MgZ4 reactions [I], [2]. This is consistent with the transfer of a C L 2 or three cr-particles occurring in these reactions. On the basis of such a direct-transfer model, one might expect that the NL4(N14, ~ x ) M g ~ ~ reaction would not selectively populate the aforementioned states, and this is indeed observed to be the case [IS].

However, the N14(N14, cr)Mg24 results [IS] may also be interpreted in terms of a compound-nucleus mechanism since the angular momentum matching conditions here are quite different than those of the 0'6(C'2, a)MgZ4 and C'Z(0'6, p)AlZ7 reactions.

Table I lists the angular momentum conditions in the entrance and exit channels for a number of reac- tions for the excitation of a state a t - 17 MeV in the residual nucleus. The channel radius is given by 1 . 4 4 ( ~ : ' ~ + A:'~) fm . For the reactions such as C L 2 ( O L 6 , a)MgZ4, C L Z ( 0 1 6 , P)A127, and C12(NL4, d)MgZ4 the population of states in the residual nucleus with high angular momentum should be greatly favored by the large angular momentum mismatch between the entrance and exit channels, as represented by A(kR).

The observation of the selective population of high spin states by these reactions is in agreement with these angular momentum considerations. In the case of the NL4(NL4, x)MgZ4 reaction the angular momenta in the entrance and exit channels are very nearly matched a t the N14 energies used in [I 51. This condi- tion is much more favorable for the population of low-spin states than in the measurements where A(kR) is large. This can account, therefore, for the eva- poration-like spectrum of 1-particles [I 51 since the low-spin states are broader a n d have a higher density than the high-spin states. Thus the selective or non- selective behavior of all four of these reactions can be understood in terms of angular momentum balance of a compound-nucleus reaction mechanism.

The measurements [I61 a t Brookhaven on the C'~(O'*, H ~ ~ and C L 2 ( O L 8 , ) M ~ ~ c r ) ~ g ' ~ ~ reactions are not as unambiguous in their interpretation. The results presented in figure 2 for the C ' ~ ( O ' ~ , c z ) ~ g ' ~ reaction indicate some selective population of states below - 22 MeV in MgZ6, but these states are not very prominent over the evaporation-like background.

Yet the angular momentum mismatch is only one unit

lower than for the C12(016, 1)MgZ4 reaction a t

17 MeV excitation, and the mismatch increases for

higher excitation energy, where no structure is observed

a t all. It might be argued that the small value of

Ef, for the C12(0'8, H ~ ~ reaction would inhibit ) M ~ ~ ~

its population of the high-spin states near 17 MeV

in MgZ4 ; however, the reaction should still selectively

T H E STRUCTURE OF

A N D SIPS AT HIGH EXCITATION ENERGY

Ecm Ex E:m

Reaction (MeV) (kR)i (MeV) (EL ^{= 17 MeV) (kR), A(kR) Selective}

-

- - - - -

C12 +

^MgZ4 + ^He4 20.6 17.9 37.4 10.4 8.4 9.5 Yes

25.7 20.0 42.5 15.5 10.2 9.8 Yes

c12 +

^{+ P C )} 25.7 20.0 42.5 13.9 4.6 15.4 Yes

N14 + ^N14

^MgZ4 + ^{He4 (b)} 10.1 12.7 37.3 10.3 8.3 4.4 N o

14.0 15.0 41.2 14.2 9.8 5.2 N o

C" + ^N14

^MgZ4 + ^d

22.1 17.6 37.2 8.8 5.3 12.3 Yes

25.4 18.9 40.5 12.1 6.2 12.7 Yes

C12 + ^0''

^MgZ4 + ^{He6 (d)} 28.0 21.8 51.7 6.6 8.3 13.5 N o C" +

^MgZ6 + ^{He4 (")} 28.0 21.8 51.7 24.0 13.0 8.8 See Fig. 2

(") Reference [ 131. (b) Reference [15]. (') Reference [I 41. (d) Reference [ I 61.

L ^I

-. ⁸

3 : .OD aoe Goo 7w seo 9m I.wo

FIG. 2 . - Alpha particlc spectrum observed in the

reaction

The insert shows the region of excitation energy in

from 13 to 23 MeV with the vertical scale

expanded by a factor of 5.

populate the high-spin states near 12 MeV in ~g~~

for which E,',

11.6 MeV and A(kR)

10.8. N o such selective population was observed.

Another possibility for the 0 1 6 ( ~ ' 2 , a ) ~ g ' ~ reaction mechanism, in addition t o the direct a n d compound pictures, is that of intermediate structure in the SiZ8 compound system. The existence of cr- cluster o r quartet structure a t high excitation energy in Size is suggested by the calculations of Arima et al. [3]. This was previously noted in ref. 181 a s a possible explanation for the width of the structure

observed in excitation functions measured [8] in the range Ecm

19.7-21.3 MeV. Recently, Gastebois et al.

have reported [lo] excitation functions measured over the region ECm = 19.3-24.0 MeV and have noted a strong correlation in the cross sections for states in Mg24 a t 15.15 MeV and a t 16.55 MeV excitation.

(The state at 16.55 MeV is actually a n unresolved doublet [I]). Thcy suggest that this may constitute evidence for quartet-type [3] intermediate structure in si2'.

The present experiments have been undertaken in order t o resolve some of the existing ambiguities in the interpretation of the mechanism of the 0'6(C12, cr)MgZ4 reaction. The most straightforward and thorough method for establishing the nature of a reaction mechanism consists of measuring complete angular distributions for each of many closely spaced bombarding energies, a s has been done by Halbert et al. [I I, 121 for the states in Mg24 below 6 MeV.

Such a measurement is a formidable task. Fortunately, a statistical compound nuclear mechanism requires that cross sections be symmetrical about 900 c. m., when averaged over an energy which is large compared to the fluctuation width ( - 250 keV a t

E,.,. -- 20 MeV). Thus, the existence of a direct or intermediate-structure component in the reaction mechanism can be detected by measuring excitation functions a t two symmetric angles over an energy range large compared to the fluctuation width.

We have, therefore, measured excitation functions

in the range E,, - ¹⁸

²¹ MeV for an oxygen

C6-8 D. A. BROMLEY, L. CHUA, A. GOBBI

beam bombarding a natural carbon target and for a carbon beam and silicon monoxide target. In each case, the a particles were detected at O,,, - ^{20, which}

corresponds to center-of-mass angles of - 1770 respectively. The advantages of measuring at - ^{30 and}

very forward angles in the laboratory system are twofold - cross sections are generally larger and a larger detector solid angle (6.2 x sr.) may be used. The disadvantage with such an arrangement, however, is that an absorber is required in front of the detector t o prevent the forward scattered heavy-ions from reaching the detector. The a-particle straggling in this absorber then places a lower limit on the reso- lution which can be attained. This limit for a - ^{13 mg/}

cm2 Ni absorber is - 150 keV. This problem has been greatly reduced by the apparatus shown in figure 3. The absorber system shown here consists typically of 2 mg/cm2 of Havar and - ^{2 mg/cm2}

o,f hydrogen. The straggling expected for this is

- 100 keV, which represents a significant improve- ment over the use of metallic absorbers. In addition the absorber thickness is easily varied to correspond to changes in beam energy.

FIG. 3. -Scale drawing of target-detector gcornetry used for the measurement of excitation functions for the C12(016, a) and OL6(CL2,

reactions. After passing through the target the incident beam is stopped in the tantalum beam stop (2.65 mm in diameter and 1.5 mm thick). The 2 mglcm2 Havar absorber foil and

gas (typically at a pressure of 2 atmospheres) were used to prevent the forward scattered heavy ions from the target

from reaching thc Si(SB) detector.

with a counter telescope had shown that groups due to other particles were sufficiently weak in the region of interest to warrant their neglect

Nevertheless, measurements were occasionally performed with increased absorber-gas pressures to check for peaks due to other particles.

E,, = 2 0 . 4 0 0 M s V

U 500

2 5 0

CHANNEL NUMBER

FIG. 4. -Alpha particle spectra from the Clz(Ol6, a) and 016(C12,

rcactions. Peaks are labelled by their excitation energies in Mg24. T h e peaks labelled

C

in the 016(Cl2, a) spectrum are due to the CIZ(C12, a)Ne?0 reaction on carbon

contaminants.

The results we obtained with this system are present- ed in figure 4 for ECLl = 35.63 and Eo,, = 47.60 MeV which correspond to very nearly thc same center of mass energy. The resolution for a-particles is typi- cally 150 keV FWHM, and was obtained using target thicknesses of - 20 pgm/cm2 and - 35 pgm/cm2 for C12 and SiO, respectively. Carbon deposition on the SiO target during bombardment presented a problem in that the C12(C12, r ) reaction is intense and produces an a-particle spectrum with structure similar to that of the 016(c12, a) reaction. A shroud, cooled with liquid nitrogen and placed around the target, and frequent changing of the target minimized the contami- nant peaks, and short measurements on a carbon target facilitated their identification. No direct particle iden- tification was employed since previous measurements

The various peaks in the spectra in figure 4 are labelled with their corresponding excitation energies in MgZ4 and, for strongly populated states, have uncertainties of ^f 25 keV in the region E,, 5 15 MeV and + 50 keV for the region 2 17 MeV. Weakly populated states have somewhat larger errors. The energy calibration was based on the state at 6.007 keV and on the state at 16.840 MeV [ l ] and incorporated the dE/dx-values given by Northcliffe and Schil- ling [I71 to correct for energy losses in the absorber.

The assumption was made that peaks observed at

(I) The detector thickness was chosen equal to the range

of - ⁴⁰ MeV a-particles eliminating the possibility of high

energy proton or deuteron groups.

T H E STRUCTURE O F Mg24 A N D Si28 AT H I G H EXCITATION ENERGY C6-9

16.84 MeV excitation in both spectra correspond to the same state in MgZ4. Aside from this assumption, the excitation energy values shown in figure 3a and 36 are independent. This assumption is supported by an absolute energy calibration based on the peak cor- responding to proton recoils from the small amount of hydrogen present in both targets, by the fact that well-resolved states, e. g. those at - 14.14 and

- ^15.1 5 MeV, yield the same excitation energy in both spectra, and by the fact that coincidence measure- ments on the x-decay of the 16.84 MeV state, as populated by both beams [ 2 ] , 161, indicate similar branches to the 4' and 2' states of Ne20. Peak posi- tions and areas were determined by simultaneously fitting up to six Gaussian functions on a linear back- ground. Absolute cross sections were obtained by lowering the beam energy below the Coulomb barrier and normalizing to the Rutherford cross section. The individual measurements were normalized to the number of particles scattered at 450 by a film of gold of a few pgm/cm2 thickness which had been evaporated onto the target.

Preliminary excitation functions have been extracted for many of the states appearing in the spectra of figure 4. In fourteen cases it was possible to follow groups which correspond, with reasonable confidence, to the same state in Mg24. 1n other cases, the presence of contaminant peaks or unresolved doublets rendered this difficult. Figurc 5 presents excitation functions measured for low-lying states of Mg24. These excitation functions are very similar to those observed for states below 6 MeV by Halbert et al. [I I], [12], and successfully analyzed in terms o f a statistical compound nuclear mechanism. The cross sections for these states do not exhibit any apparent correlation in their respective dependencies on energy and angle, and, when averaged over energy, the cross sections are nearly symmetric, with maximum deviations from symmetry being approximately a factor of 2. A detailed analysis of the energy-averaged asymmetry and its statistical significance is in progress.

Excitation functions for states at higher excitation in Mg24 are presented in figures 6 and 7. Here again, the fluctuations of - 250 keV width arising from

E.., 8" MQ'. E... 8" .',CM

I

n t o ZI u rn 20 II

C" BEAM 0" BEAM

Ecm, Me"

FIG. 5.

Excitation functions measured a t

z

for the FIG. 6. -- Excitation functions measured at Olilh x

for the Cfz(Ol6, a) and 016(Cl?,

reactions populating states in

and 016(C12, a) reactions populating states in Mg24 betwccn 6.0 and 9.5 MeV in excitation. The uncertainty Mg24 between 13.4 and 15.5 MeV in excitation. The uncertainty

in the absolute cross section is 1: 30 %. in the absolute cross section is 30 %.

C6-10 D. A. BKOMLEY, L. CHUA, A. GOBBI statistical compound-nucleus formation are present.

However, of the cases measured with the C12 beam and plotted here all but one of the cross sections show a distinct correlation with a width of - 1.5 MeV upon which the fluctuations are superimposed. This type of correlation (observed here for seven states) is inconsistent with the statistical model and constitutes direct evidence of the existence of a broad structure in the 016(Ci2, a ) ~ reaction. (Note that these g ~ ~ states were not chosen on the basis of the existence of such a correlation but only on the technical conside- ration of being able to confidently extract peak areas from the observed spectra.)

C' BEAM

0"

E,, MeV

FIG. 7. - Excitation functions measured at

z 2O for the ClyOc6, a) and 016(C12, a) reactions populating states in Mgz4 between 16.3 and 16.84 MeV in excitation. The uncertainty

in the absolute cross section is f 30 %.

There are several other important features to be noted in figures 5-7. Although the states a t 13.44 and 16.28 MeV show roughly similar correlations for both beams (i. e. both angles), the correlations present for the states at 13.86 and 16.84 MeV, populated with the c12 beam, are clearly absent when these

states are populated with

beam ('). Thus, corre- lations of - 1.5 MeV width are observed some of which exhibit approximate symmetry about 900 cm and some of which are clearly asymmetric. Further- more, the state at 15.15 MeV (noted by the Saclay group [lo]) appears to show the broad, correlated structure above E,, -- 20 MeV, but not below this energy. Finally, we note that the correlations, present for many states above 13 MeV in figures 6 and 7 are absent for those states shown in figures 5, i. e. for states below 10 MeV excitation

These features of the excitation functions and the broad structure exhibited by the 0 l 6 ( C l 2 , a)MgZ4 reaction may be understood to a large extent with the a-cluster model of Arima, Ginocchio and Gillet [3].

In this model, the broad structure would correspond to the formation of a-cluster states a t -- 36-39 M ~ V excitation in SiZ8. Such formation is greatly enhanced by the fact that both target and projectile are a- conjugate nuclei. The observed width of - ^{1.5 MeV}

for the broad structure implies, furthermore, that one or more of the a-particles in siZ8 a t this excitation energy is loosely bound. The formation of cluster states in si2* will therefore be enhanced for partial waves corresponding to grazing collisions while the somewhat lower partial waves will favor the forma- tion of the statistical compound nucleus. Thus, the states in MgZ4 which are strongly coupled to the SiZ8 system show a broad correlation with statistical fluc- tuations superimposed thereon. In the following discussion, we shall refer to the broad structure as a n

((

intermediate

structure, reflecting its interpretation in terms of the formation of an intermediate state in the SiZ8 system.

The cluster states relevant to the intermediate structure, if preferentially induced by high partial waves, must have high angular momentum and there- fore are not expected to correspond to the J" = ' 0

((

band head

energies in [3]. For a given configuration the states of interest lie above the band head energy and may correspond to the recoupling of the

particles of a particular structure to higher angular momentum, e. g. rotational cluster states.

( 2 )

The excitation functions labelled r( 16.59

and cr 16.56

were extracted from groups which are known [I], [2], [6] to correspond to a doublet. Both members of the doublet are present at each angle with the 16.59 MeV state populated predo- minately by thc

beam and the 16.56 (16.54 in [I]) MeV state more intensely populated by the Clz beam, at Ecm

20.5 MeV. Our experimental resolution (- 80 keV FWHM excitation in Mg24) is insufficient to unfold the two components and thus the excitation functions must be regarded as the sum of the two components. The correlation of the summed components and the large magnitude of the cross

d a

section (=

- 16 mb/sr at Ec.

21 MeV for the carbon

e.m.

1

beam, howcver, are quite striking.

(3)

There are a great number of states present in the region

of 17-22 MeV excitation. Analysis of this region and other

regions is still in progress and includes a search for states which

may exhibit an energy-averaged asymmetry with respect to

90° c. m.

THE STRUCTURE OF

AND Si'S AT HIGH EXCITATION ENERGY

The absence of intermediate structure in the low- lying states can also be accounted for by the quartet model. The low-lying states in Mg24, if of a quartet nature, would be predominantely of the [320] confi- guration (see Fig. 1). These states have a large overlap with the low-lying states of Si28 [330], which are of the form MgZ4 [320] + a. However, the cluster states populated at - 38 MeV in Si2"of the type [231], [312] and [222]) have little overlap with the low-lying states of Mg24 but can overlap with the higher-lying states of ~g~~ (see Fig. 1).

The interpretation of the presence, for some states, and absence for others of broad structure a t symmetric center-of-mass angles is somewhat ambiguous. We note that the - 1.5 MeV width of the intermediate structure implies a lifetime of - ^{4 x} s for the compound system. This is of the order of the nuclear traversal time for the emitted a-particle, so that asym- metry in the angular distributions for the broad intermediate structure might be expected for some states. This characteristic lifetime is, however, also comparable to the collision time of the

and C12 ions in the entrance channel, which suggests that a direct-reaction mechanism may also explain some of the results for particular states. With regard to the uniqueness of the interpretation in terms of a-cluster intermediate structure, we note that a width of

- 1.5 MeV approaches the widths of the gross struc- ture observed in heavy ion elastic scattering stu- dies [18]. This suggests that the observed structure might be associated with a sharply defined (in energy space) absorbtion of partial waves corresponding to a grazing collision. Such an effect in the entrance channel would naturally imply a structure in the elastic scatter- ing and other channels of width similar to that observ- ed in the Mg24 and a-channel and with a definite phase relationship. Measurements on the elastic and inelastic scattering cross sections are in progress and should provide a n answer to these questions. It is also possible that the above mentioned mechanism is intimately related to that of a broad intermediate structure of a-clusters in the Si28 compound system.

Generally, however, the results presented in figures 4-6 may be understood with the quartet model [3] and may therefore be interpreted as evidence for the exis- tence of a-cluster structure for highly excited states in MgZ4 and in SiZ8 and for the presence of interme- diate structure in the 016(C12, a)MgZ4 reaction. We plan also to extend the excitation functions over a wide range of energy in order to test the preliminary conclusions based on the limited range presented here.

Assuming a n interpretation in terms of the a-cluster model, several speculative comments may be made concerning both the reaction mechanism and this structure. First, the structure observed for the 14.14 state, which has been assigned [19] as the 8' member of the K" = 2' band in MgZ4, would suggest that this band contains, a t high excitation, a cluster-like component in its wave function (most likely [230]).

Second, we note that the absence of intermediate structure for the low-lying states also suggests that the a-cluster states in Si28 are not strongly coupled with the states of the statistical compound nucleus, but remain rather pure in spite of their broad width and high excitation energy. An interesting test of this suggestion would be to measure excitation functions for C12(016, P)A127 reactions. In this case, the inter- mediate structure, present in the entrance channel, should not be coupled to the exit channel a s it can be in the case of C ' ~ ( O ' ~ , a)MgZ4, and one would not expect to see any broad structure in the excitation function.

The lack of structure in the a-particle spectra for the N14(N14, a ) ~ g ' ~ reaction I151 may be explained both on the basis of angular momentum matching and statistical compound nucleus formation and on the basis of the expected absence of inter- mediate structure, since neither projectile nor target is a-conjugate. The C12(018, a)Mg26 reaction [16]

shows some indication (Fig. 2) of a selective popula- tion of states in the region below 22 MeV, but the absence of strongly populated states, such a s are present in the ~ ' ~ ( 0 ' ~ ~ a ) ~ g ' ~ reaction (Fig. 4), is striking. Apparently, the addition of the two neu- trons to

in the entrance channel and to Mg24 in the exit channel greatly reduces the propensity of these nuclei to form a-clusters.

Although the present investigation of the impor- tance of a-cluster phenomena in the structures of MgZ4 and SiZ8 and in the 016(C'2, a)Mg24 reaction mechanism has yielded new information on the nature of the a-cluster states, there remain, however, a number of interesting questions to be answered.

B. The structure of Mg24 at high excitation. - In part A we have investigated the importance of a- cluster phenomena in the structure of high-lying states in MgZ4. The question of the existence of even heavier clusters in Mg24 is the logical consequence of both the experimental results just described and the quartet model. D o quartets themselves couple to configurations which resemble a Be8 or C" nucleus ? The experiments of Bromley et al. [4] and Patterson et al. [5] indicate that C12 + C12 molecular configurations are impor- tant. Michaud and Vogt [20] interpret these results not in terms of C12

molecules

but rather in terms of three a-particles coupled to a C" core. In either case, the measurements of ref. [4] show that the resonances in the C12 + C1' reaction a t and below the Coulomb barrier are of low spin (see Fig. 1). However, in the present experiments it is known that the C12(016,

~ r ) reaction selectively populates high-spin states. ~ g ~ ~ The following experiment was designed specifically to search for heavy-cluster configurations of high spin in Mg24 by direct observation of the decay of Mg24 into heavy cluster components. The various decay modes and their thresholds are shown in figure 1.

The decay of ~ g ' ~ , formed in the C12(016, a)Mg24

C6-12 D. A. RROMLEY, L. CHUA. A. GOBBI reaction, into NeZ0 + a has been studied in a n

earlier experiment [2], [8] in which a position-sensitive detector was used in conjunction with a detector at O0 t o observe the angular correlation of the successively

C 3 0

0

50' 70' 90" 110' 130" 50' 70' 90' llO" 130°

Angle c.m.

(a)

Angle c.m.

(b)

FIG. 8. - Angular correlations [Z], [8] measured for the alpha- particlc decay of states in

to the ground state of Nezo via

the reaction

a ) ~ g 2 4 * ( a ) ~ e i : .

emitted a-particles [2 I]. These experiments enabled the determination of spins, parities, and a-decay branching ratios for a number of states in MgZ4. Figure 8 presents examples of the correlations measured and spins determined in these earlier measurements.

From this work it was clear that a-decay was by far the strongest decay mode 'for the states above

- 11 MeV in MgZ4. In order to detect heavier nuclei in the presence of such a large background of a-particles, a second position sensitive detector was added to the system in order to measure the positions and energies of all three particles present in the final state of the reaction. The resulting over-determination of the properties of the final state is a n indispensable tool in the analysis of the data.

A schematic diagram of the apparatus and data handling system (using an ISM 360144 computer) is given in figure 9. The position sensitive detectors were collimated to -- 7 mm x 50 mm and covered labo- ratory angles from 150 to 7 5 O . The detection system at 00 was the same as was described for the excitation function measurements in part A. A large permanent magnet was installed in the scattering chamber t o prevent electrons from reaching the detectors. The experiment was performed a t

⁼ 58.3 MeV with a - 20 pgm/cm2 carbon target. The energy and position calibrations of the position sensitive detectors were effected by observing the elastic scattering of

from a gold foil a t a variety of bombarding energies with a precisely machined grip placed in front of the detectors. Since the detectors exhibited non-linearities in both position and energy, the calibration of these quantities was done simulta- neously in two dimensions. The seven linear pulses indicated in figure 9 were digitized for each triple coincidence and stored on magnetic tape as well a s in the computer memory. Using the absolute position and energy calibrations for each of the three detectors, the digitized pulses were converted, by software, directly to units of MeV and laboratory angle.

DETECTORS

FIG. 9. - Schematic diagram of the experimental arrangement used for the triple correlation measurements.

The analysis of over two million triple-coincidence

events proceeded in the following order. Each event

was either passed or rejccted by a series of one and

two-dimensional gatcs which, cumulatively, enabled

the determination of the species, excitation energy,

and angular correlation of the reaction products. A

THE STKUCTURE OF

AND Sizs AT HIGH EXCITATION ENERGY C6-13

two-dimensional time gate was first applied to sort the events according to their mutual relationship in time. Figure 10 presents a two-dimensional time spectrum with To, plotted against To,. The three types of random events which can occur in a triple coincidence experiment are clearly indicated. The diagonal line corresponds, for example, to events in which a true coincidence takes place in detectors I and 2 (see Fig. 9) and a n a-particle arrives a t a random time in the O0 detector. The intensity of this line arises from the high kinematic coincidence rate produced by heavy ion elastic and inelastic scattering into detectors 1 and 2. The vertical and horizontal lines arise from events in which a real coincidence occurs between detectors 0 and 1 or 0 and 2, with a random particle in the remaining detector. Triple coincidence events are located at the intersection of these three lines. A rectangular gate 100 ns wide was set around this region, and gates of identical size were placed along each of the three well defined random event lines, and also on the region which corresponds to a random event in all three detectors.

Events passing through these gates were then appro- priately flagged. A proper random subtraction for a triple coincidence experiment requires such a proce- dure, which is greatly facilitated by the use of event-by- event recording.

2-D T I M E SPECTRUM

FIG. 10. - Two-dimensional time spectrum obtained in the triple correlation experiment. Real triple coincidences occur

the region near (To1

400 ns, To2

600 ns). The treatment of the various random coincidcncc contributions is discussed

in the text.

The detection of one of the three particles in the exit channel a t O0 requires that the momenta of the other two particles transverse to the beam direction be equai and opposite. This requirement yields the relation

M,/Mz = Ez sin2 02/El sinZ 8 , .

Since each of the quantities on the right-hand side of this equation is measured directly, a

mass ratio

spectrum, as shown in figure I I, is easily obtained. This constitutes a n effective determination of the individual particle species since the sum of the masses must equal 28 and the absorber renders the O0 detector

sensitive only to light particles. The mass ratio spectrum exhibits symmetry about unity since the position sensitive detectors are symmetric about the beam axis. The background in this spectrum arises mainly from real triple coincidences corresponding to four-body break up. Note the large peaks a t mass- ratio values of 115 and 5 corresponding to

a, + r + ^Ne20

and the peak at unity corresponding to a, + CIZ + cl2.

I MASS RATIO SPECTRUM I

FIG. 1 1 . - Plot of mass-ratio spectrum of the decay products of states in

The peaks at 115 and 511 correspond to decay to Nezo + a ; the peaks at 112 and 211 correspond to decay into

+ ^Ben : and the peak at 111 to fission into CIZ -I- C12.

The peaks a t 112 and 2 imply the observation of a, + Be8 +

in the exit channel. This is consistent with the geometry of the detection system and the typical angular opening of the cone of a-particles (- 50, half-angle) defined by the inflight decay of the

~e~ nucleus. A rough calculation indicates that the detection efficiency for both a-particles from the BeS is well over 50 %.

A one-dimensional gate was then set on each of the peaks in figure 1 1. Events in these gates were subjected to further scrutiny to eliminate the four-body back- ground present in the mass plot. The known energies, positions, and masses of the particles in the 00 detector and in one of the position sensitive detectors were used to calculate the energy and position which the remaining particle must have in the other position- sensitive detector. If the remaining particle was observed to have the correct position and energy (within some preset limits) the event was accepted.

The next step in the analysis was to determine the excitation energies of the now-identified out-going particles. The quantity

+ ^{Q =} EO + El + ^E2

was determined based on the measured energies and

C6-14 D. A. BROMLEY L. CHUA, A. GOBBI positions of the two lightest particles and the calculated

energy of the heavy particle. Figure 12 presents

<(

Q-value

spectra for each of three gates set on

the mass-ratio spectrum. The arrows denote the predicted positions of the peaks based on the absolute energy calibration of the three detectors.

~e'O(4.25)

t ~e'O(1.63)

o

M A S S RATIO G A T E ON

Eo-= 58.3

+

E.+EA+EB MeV

FIG. 12. - Spectra for each of the 3 decay channels, plotted as a function of the total kinetic energy in the 3 body final state.

Peaks are identified corresponding to the residual nuclei in their ground states and in various excited states.

The properties of the three-body final state were thus completely specified ; it remains only to present the sorted events in a form designed to reveal the physical process under investigation. For our purposes, this form is a plot of the triple coincidence yield versus the excitation energy in ~ g ' ~ , this quantity being defined by the energy of the

first

a-particle, a,,, observed a t 00. Figures 13-16 present the triple coincidence yields for four outgoing channels as a function of the energy of the a-particle observed at 00.

These figures display events which have passed through the gates set on the spectra in figure 10 (time), 1 1 (mass ratio) and 12 (Q-value). Real and random events were subjected to identical processing, the random events being subtracted only after all gates were applied. The cut-off a t low a-particle energies, determined by the thickness of the absorber a t 0°, does not affect the shape of the spectrum beyond the

lowest two channels shown. The random to real-plus- random ratio was of the order of or less than a few percent in regions where the spectra contain more than - 20 counts per channel. Finally, tests of internal consistency were made throughout the course of the analysis. No evidence for improper sorting of the events was found. An important external check on the analysis is provided by the requirement that the angular distributions for break up of MgZ4 into C12 + C12 and with C12 + C12 (4.4) be symmetric about 900 c. m. angle in the MgZ4 system. The measured angular distribution exhibited this symmetry.

The sharp groups in figure 13 correspond to events in which the intermediate stage of the

0 1 6

+ C12

a. + a + NeZ0 (4')

reaction proceeded through definite states in MgZ4.

The smoothly varying background underneath these sharp groups can arise from low spin states with large widths or from narrow states, each of which is populated with a small cross section, but which are very dense. Contributions to the background may also arise from the detection of the second a-par- ticle (i. e. from the decay of MgZ4) a t 00 and the first a-particle in one of the position sensitive detectors.

I I I I

30 25 2 0 15

E,,,, P4gZ4iP4ev)

FIG. 13. - Triple-coincidence yield as a function of E,, gated by the peak in figure 12 corresponding to a final state comprised

of

i-

+ NeZo* (4.25).

Another mechanism, which can contribute to the yield in figure 13 but which does not involve the formation of ~ g ' ~ , is the break-up of the C12 nucleus into three cr-particles, one of which attaches to the

016

projectile to form NeZ0 (4.25). Thus, it is possible to demonstrate the formation of a state in MgZ4 only if a distinct peaks is observed in the Ea0 spectrum.

The spectra shown in figures 14-16 each exhibit a

smoothly varying background similar in shape and

in magnitude. Tn these cases, the reaction can proceed

either by a break-up of the

projectile (Fig. 15, 16)

or a break-up of the C" target nucleus (Fig. 14),

all of which processes are expected to yield a smoothly

varying spectrum of a-particles. Indeed, the fact that

the

backgrounds

in figure 15 (ao + C12 + C1'

T H E STRUCTURE O F Mg24 A N D Si

AT HIGH EXCITATION ENERGY C6-15

and in figure 16 ^(or0 + C12 + C1 (4.4)) are comparable argues in favor of a break-up mechanism ; if the reaction proceeded through states in Mg24, the much lower penetrability for the C12 (4.4) channel would preclude the onset of this process until

4 : ,LJ,~;~,,

,

0 10 2 0 3 0 Ea,(MsV)

I

3 0 25 20 15

E.,,.

t4gz4(t4ev)

FIG. 14. - Triple-coincidence yield as a function of Em, gated by the total Be8 +

spectrum in figure 12.

F1c.115.

Triple-coincidence yield as a function of E,, gated by the ground-state peak in the Cl2

i- Cl2 spectrum in figure 12.

r-,

^{, ,}

^{...,... ,}

E a d M e V )

3 0 25 20 15

Eexc.

MgZ4(t4ev)

FIG. 16. - Triple-coincidence yield as a function of E, gated by the peak in figure 12 corresponding to a 3 body final state

comprised of xl + C12 + Cl2* (4.43).

N

25 MeV excitation in Mg24. We have made optical- model calculations of transmission coefficients (Fig. 17) for the break-up of ~g~~ into various clusters, and find that both the shapes and sizes of the gross back- ground in figures 15 and 16 are inconsistent with the formation and decay of states in MgZ4. Analysis of the data in terms of a break-up mechanism is being undertaken to check the above arguments in more detail.

E,,, in M ~ ' ' ( M e V )

FIG. 17. -Transmission coefficients for the various open channels for the decay of Mg24 have been calculated with a n optical model code, and are plotted here, normalized to the C12 + C12 transmission coefficient. For a given excitation energy in Mg24, the orbital angular momentum, L, in the exit channel was determined by the I-value for which T~(ao) x 112. For the particles in the ground state, L

J

18 - 1, and this value is also given in figure 17, labelled as Mg24 (J). This represents an approximate lower limit on the spin of states in Mg24* which can beexcited in theCl2(016, a)Mg24reaction a t Eorh

58 MeV.

In cases where one of the nuclei in the exit channel has non- zero spin, this amount of angular momentum was subtracted from the orbital angular momentum to be carried away. Although these calculations are not very precise, they d o give a n order- of-magnitude guide to the selection rules imposed by the Coulomb

and centrifugal barriers.

Having discussed the general shape of these four spectra, we note now the definite peaks in the or, + C12 + C12 spectrum (Fig. 15) at excitation energies of 22.0 and 30.7 MeV in Mg24. It is unlikely that such sharp structure can arise from the direct break-up of the target or the projectile. Were this not the case, the spectra of figures 14 and 16 should also show such structure. We cite thesepeaks, therefore, as evidence for states a t 22.0 and 30.7 MeV in Mg24 which have C12, C12

molecular

configurations.

The measured widths of these states (4), respectively, are -- 380 keV and 230 keV, which is significantly larger than the width contributed by the resolution of the 00 detection system. These total widths are comparable to the Wigner limit for the reduced width - ^{300 keV.}

Angular distributions for the decay of these states are presently being analyzed and may allow limits to

(4) It is possible, of course, that each of the observed peaks

corresponds t o a group of more narrow, unresolved states. In

this case the measured widths are only upper limits.

C6-16 D. A. BKOMLEY, L. CHUA, A. GOBBI be placed on their spins. The state a t 30.7 MeV

is likely to have a high spin, e. g. in the region 12-18 units, a s the cr-particle leading to the formation of this state can carry away little angular momentum.

Similar arguments would place a lower limit of

- 6-8 on the spin of the 22.0 MeV states. The mea- sured widths of the states in terms of the Wigner limit, however, imply upper limits of - 4-6 and 10-12 for the states a t 22.0 and 30.7 MeV, respectively. These arguments are crude and, of course, quite sensitive to the choice of channel radius. Nevertheless, the above considerations favor the interpretation of the states observed here a s rather pure C12 + C I Z configurations rather than as configurations of three alpha particles outside a C12 core. Were this latter configuration present, the decay of the state by rr emission would be much more strongly favored than C12 emission.

The measurements [4], [5] on the C12(C12, CIZ) and C12(Ct2, cr) reactions, which have located mole- cular resonances a t excitation energies between 17 and 20.3 MeV excitation in MgZ4, preferentially populate states of low spin. This is shown by the measured spins [4] and by penetrability arguments, since the resonances occur a t and below the Coulomb barrier.

Thus the state seen a t 30.7 in the present work by virtue of its inferred high spin, is probably not the same type of configuration as was observed at - 20 MeV excitation [4]. The state a t 22 MeV, depending on whether its spin is - ^{6 or} - 10, may or may not be associated with the resonances observed in reference [4]. The width of this state is - ^{3 times}

larger than the molecular states a t -- 20 MeV.

Although the analysis of these data is still in progress and the results should be regarded as preliminary,

it appears that we have observed the production and decay of C12 + C12 molecular configurations in MgZ4 via the C12(016, a)Mg24(C12)C12 reaction.

The fact that a decay of the state a t 30.7 MeV via the C12 + C I Z (4.43) channel is not observed in the spec- trum of figure 16 is not necessarily evidence against this state being of the type of quasi-bound molecular states which were purposed by Imanishi [22] and by Scheid, Greiner and Lemmer [23]. In these models, the quasi-bound states were coupled to inelastic excitations of one of the component nuclei. Figure 17 indicates a reduction in penetrability by a factor of 10 for the C I Z (4.4) MeV channel, which would place such a decay a t the limit of observation with the present statistical precision. Further refinements will be necessary to see if evidence can be found for the pro- duction and decay of other cluster configurations such as

+ Be8.

Acknowledgements. - It is a pleasure to acknowledge here the technical assistance of Dr E. Fehr, Mr C. Gingell and M r K. Sato.

Footnote added in proof. - Subsequent measure- ments in this laboratory have shown this to be incor- rect. Final state interactions between an alpha par- ticle and a carbon nucleus involving specific states in

having large alpha particle width have been shown to be capable of leading to such structure in these spectra. While we cannot exclude the possibility of direct C12 + C12 breakup the most irecent data suggest that the two peaks in figurc 15 are primarily due to such final state interactions. A more complete publication concerning these later measurements is in preparation.

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