fulltext

Spin assignments for quasi-molecular resonances from

angular correlation techniques

(

 )

A. H. WUOSMAA

Physics Division, Argonne National Laboratory - Argonne IL. 60439 USA (ricevuto il 23 Luglio 1997; approvato il 15 Ottobre 1997)

Summary. — Particle angular correlation techniques have been used to

deter-mine the spins of three resonances observed in the inelastic scattering reaction 12_C(12_C,12_C[3,

])12C, betweenEc

:m:=25 MeV and 35 MeV. The results are compared

with previous suggested spin assignments in this energy region, and with the predic-tions of the Band Crossing Model.

PACS 25.70.Ef – Resonances.

PACS 25.70.Pq – Multifragment emission and correlation. PACS 01.30.Cc – Conference proceedings.

1. – Introduction

The study of resonances in the scattering of12C+12C attracted a great deal of atten-tion some years ago, with the associaatten-tion of peaks in the excitaatten-tion funcatten-tions for scatter-ing and transfer reactions in this system with quasi-molecular structures in the composite nucleus24Mg [1, 2]. Resonances in this system have been linked to extended, deformed cluster configurations in24Mg at high excitation energy [3], but reaction models are often able to reproduce at least the qualitative features of the data (e.g., [4]). Progress in the understanding of the nature of resonances in this and other systems has, however, often been hampered by the lack of precise experimental information. In many cases, reso-nances in the12C+12C system appear in inelastic reaction channels where the channel spin is non-zero. The usual method of measuring inclusive scattering angular distribu-tions thus becomes insensitive to the resonance spin due to the complicadistribu-tions arising from the spin of the excited scattered heavy ion. As a result, few rigorous spin assignments have been available for resonances in inelastic scattering channels with non-zero chan-nel spin. Some progress was made by resorting to particle-gamma-ray angular correla-tion measurements [5-7], however definitive measurements are complicated and, without a 4



-gamma-detector apparatus, the results are often model dependent and difficult to interpret.

( 

)Paper presented at the 174. WE-Heraeus-Seminar “New Ideas on Clustering in Nuclear and

Atomic Physics”, Rauischholzhausen (Germany), 9-13 June 1997.

20.0 25.0 30.0 35.0 40.0 EC.M. (MeV) 1.0 2.0 3.0 4.0 5.0 σ (15 o < θLAB < 25 o ) (mb)

Fig. 1. – Excitation function for the12C(12C,12C[3,

])12C reaction from Fulton et al.

An excellent example of this situation is found in the inelastic scattering of12C+12C at centre-of-mass energies between 20 and 40 MeV. Cormier et al. [8] and Fulton et al. [9] observed pronounced resonance-like features in the excitation functions for the single and mutual 2+, and 0+2 and 3,

final states, respectively. Cormier suggested spins for resonances in the 2+excitations of 14+, 16+, and 18+ for resonances near 25, 30 and 36 MeV, respectively, although later gamma-ray correlation experiments [7] indicated that these spins may be too low by two units of angular momentum. For the 3,

case, no such data have been available, as the 3,

state in12C is unbound with respect to alpha decay to the ground state of8Be, which in turn decays into two alpha particles. An analogous particle angular correlation measurement is in principle possible, but until recently, the technical requirements of such an experiment could not be met with available detectors. The excitation curve for the 3,

+g.s. channel from [9] appears in fig. 1.

2. – Experiment

To study particle-particle angular correlations in the12C+12C(3,

) channel, we have employed arrays of four, and six, 32-element double-sided silicon strip detectors (DSSDs) to detect the alpha particles from the decay of the 3,

(9.64 MeV) level in12C populated in inelastic12C+12C scattering. Data have been obtained at several energies between

E

c

:

m

:

=23 to 37 MeV [10]. The manner in which we isolate the 3,

+g.s. inelastic scat-tering channel, and identify the first alpha particle in the sequential decay 12C(3,

)!



+8Beg

:

s

:

(2



), is illustrated in fig. 2. Shown in fig. 2a) is an excitation energy spectrum

from alpha-particle pairs, assuming that they arise from the decay of8Be. For events in which the relative energies of two of the three detected alpha particles are consistent with a8Be in its ground state, we then calculate the corresponding excitation energy for the decaying12C (fig. 2b). For groups of three alpha particles whose relative energies are consistent with a12C in its 3,

state, the kinematic correlation between the reconstructed kinetic energy and scattering angle of the decaying12C then determines the inelastic scattering

Q

-value (fig. 2c). The 3,

+g.s. excitation appears at

Q

=,9

:

64MeV.

The acceptance of the detector array has been studied using a Monte Carlo simulation, which contains the geometry of the experimental setup, as well as all of the kinematic information for the sequential reaction. All particle angular distributions are assumed to

-35.0 -25.0 -15.0 -5.0 Q Value (MeV) 0 2000 4000 6000 8000 Counts/80 keV 7.0 8.0 9.0 10.0 11.0 12.0 Ex(12C) (MeV) 0 1000 2000 3000 Counts/10 keV 0.0 1.0 2.0 3.0 4.0 Ex (8Be) (MeV) 0 10000 20000 Counts/10 keV 3-+g.s. 3-+2+ 3-+0+ 3-+3 -3- (9.64 MeV) 0+(7.65 MeV) _(b) (c)

Fig. 2. – a) Relative energy forparticle pairs. b) Relative energy for 3particles. c)Q-value

spectrum for 3,

events.

be isotropic in their respective centre-of-mass frames. The extracted angular correlation data are corrected for detection efficiency as determined from this simulation.

3. – Results

Following Satchler [11], under the simplifying assumptions that only a single, resonant, partial wave is present in the entrance channel, and only a single

l

value is present in the exit channel, the theoretical expression for the angular correlation

W

(

; ;

)reduces to

W

(

; ;

)=   P

m

h

l

3,

mm

j

J

0i

Y

l

m

(

;

0)

Y

,

m

l

(

;

) 

2. Here,



is the12C centre-of-mass

scattering angle, and and



are the angles of emission of the alpha particle from the decaying12C, measured with respect to the beam in the12C centre-of-mass frame. In our experiment, we average the correlation function over the region of



subtended by the detector array,



25o,40o.

A matrix of the angular correlation data obtained at an energy of 33.5 MeV, near the peak of a resonance in the 3,

+g.s. channel, appears in fig. 3. Here, the abscissa cor-responds to the decay angle of the alpha particle emission angle , and the ordinate to the12C scattering angle



. In a simple picture, the slopes of the parallel ridges in the angular correlation matrix are approximately equal to the ratio of the12C spin (in this case 3) to the orbital angular momentum

l

[12]. A projection of the correlation matrix along these ridges onto the



axis should then follow the behaviour expected at = 0o,

0 180 90 0 θ (deg) ψ (deg)

Fig. 3. – Angular correlation matrix for the 3,

+g.s. excitation atEc

:m:=33.5 MeV. The ordinate is

the12C scattering angle, and the abscissa the alpha-particle emission angle .

W

(



proj)j

P

l

(cos



)j2, where

l

is the orbital angular momentum quantum number.

Figure 4a)-e) shows projections of the angular correlation matrices obtained at en-ergies across the resonance near

E

_c

:

_m

:

=33 MeV. At the energy nearest the excitation-function peak,

E

_c

:

_m

:

=33.5 MeV, the

l

value most consistent with the data is

l

=15. The

0.0 30.0 60.0 90.0 θproj (deg) 10 100 10 100 1000 100 1000 W( θproj ) (arb. units) 100 100 (a) (b) (c) (d) (e) 29.5 MeV 31.0 MeV 33.5 MeV 34.5 MeV 37.5 MeV L=11 L=11 L=15 L=15 L=13

Fig. 4. – Projected angular correlations for several energies across a resonance observed in the 12_C+12_C(3,

) excitation. The data obtained near the resonance peak (Ec

:m:=33.5 MeV) are

30.0 60.0 90.0 θC.M. (deg) 0 1000 2000 3000 0 1000 2000 0 2000 4000 W( θC , ψα =0 o ,180 o ) (arb. units) 0 2000 4000 0 1000 2000 27.0 MeV 29.0 MeV 30.9 MeV 33.1 MeV (b) (c) (d) (e) Fig. 5. –12C+12C(3,

) inelastic scattering angular distributions for alpha emission angles 0o

and 180o. The dashed and solid curves represent squared Legendre polynomials of order 13 and 15, respectively.

kinematics of the reaction favors the assumption of an aligned configuration, where the

12_{C spin and the orbital angular momentum are parallel, an assumption supported by the}

alpha-particle angular dependence of the correlation matrix. Under this assumption, we can assign a spin value of

J



=18+to the resonance near 33 MeV.

Model-independent information about the

l

value may be obtained by studying data at specific alpha-particle emission angles. As can be seen by examination of the simple single-

l

correlation function given above, at alpha-particle angles of either =0oor 180o,

only the

m

=0 substates can contribute to the cross-section. There, the angular distribu-tion as a funcdistribu-tion of



is simply proportional to a squared Legendre polynomial of order

l

. Figure 5 shows such angular distributions at five energies between

E

c

:

m

:

=23 and 33 MeV. At the lowest energy, the angular distribution is irregular, does not suggest any preferred

l

value. At the peaks of the two lower resonances (figs. 5b, c), however, the angular dis-tributions become oscillatory, with a phase which closely matches a squared Legendre polynomial of order 13. With the assumption of an aligned configuration, this value cor-responds to a spin assignment of

J



=16+for the resonances near

E

_c

:

_m

:

=27 and 29 MeV. At

E

_c

:

_m

:

=30.9 MeV, away from any resonance, the angular correlation is again unstruc-tured (fig. 5d). At the peak of the next resonance (fig. 5e), however, the angular correlation again becomes oscillatory, with a phase closely matching that of a Legendre polynomial of order 15, corresponding to a resonance spin of

J



=18+.

those of Cormier et al. for resonances in the single and mutual 2+ excitations, as well as the predictions of calculations from the Band Crossing Model [4]. Cormier suggested dominant entrance-channel angular momenta near 14 at centre-of-mass energies near 27 MeV, and near 16 for

E

c

:

m

:

33 MeV. Band crossing model calculations supported these

suggestions for the3 ,

+g.s. excitation, although the potential for this calculation was ad-justed to match the dominant

l

values observed in elastic scattering. From the current work, we note that these spins are too low by two units of angular momentum. This result is consistent with the work of Sugiyama et al., who reached the same conclusions for the single 2+excitation from studies of particle-gamma-ray angular correlations [7]. It is also interesting to note that the experimental rotational spacing between the centroid of the spin 16 strength and the spin 18 resonance, of

h

2_/(2

I)=82 keV, is nearly identical to what

is expected for either a simple picture of two touching12C spheres, or from a superde-formed triaxial cluster configuration predicted by the cranked alpha-cluster model [3]. This observation further supports the suggestion that these resonances possess a quasi-molecular nature.

4. – Conclusion

The present results clearly demonstrate that particle angular correlation techniques can provide new information about the old question of quasi-molecular resonance be-haviour. Spin assignments for resonances observed in the 3,

+g.s. inelastic scatter-ing channel in the12C+12C system have been obtained for three resonances between

E

c

:

m

:

=25 and 35 MeV. The spacing between the two 16+resonances, and one 18+ reso-nance, is consistent with the conclusion that these are indeed quasimolecular states. The experimental techniques which made these measurements possible, which utilize arrays of highly segmented silicon detectors, provide many new opportunities for studying com-plex phenomena in heavy-ion scattering, and will likely lead to many new and interesting results in the future.

  

I wish to thank D. J. HOFMANfor substantial assistance in the analysis of the data presented here, and for many useful discussions. This work was supported by the U. S. Department of Energy, Nuclear Physics Division under contract W-31-109-Eng-38.

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[5] CANNELLL. E. et al., Phys. Rev. Lett., 43 (1979) 837. [6] JACHINSKIC. M. et al., Phys. Lett. B, 87 (1979) 354. [7] SUGIYAMAY. et al., Ph. Lett. B, 159 (1985) 90. [8] CORMIERT. et al., Phys. Rev. Lett., 40 (1978) 924. [9] FULTONB. R. et al., Phys. Rev. C, 21 (1980) 198. [10] WUOSMAAA. H. et al., Phys. Rev. C, 54 (1996) 2463.

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