Elastic and inelastic deuteron scattering on 12C in the energy range from 60 to 90 MeV

I 2.E:2.L [ I

Nuclear Physics A253 (1975) 263--273; ~ ) North-Holland Publishing Co., Amsterdam N o t to

be reproduced by photoprint or microfilm without written permission from the publishe~

ELASTIC AND INELASTIC DEUTERON SCATTERING ON 12C IN THE ENERGY RANGE FROM 60 TO 90 MeV O. ASPELUND, G. H R ~ H U S S , A. KISS, K. T. K N O P F L E , C. MAYER-BORICKE, M. R O G G E , U. SCHWINN, Z. SERES and P. T U R E K

Institut fiir Kernphysik, Kernfarschungsanlage ?iilich, D-5170 Jiilich, IV. Germany Received 7 August 1975 Abstract: Elastic and inelastic scattering of deuterons on ~2C has been investigated in the incident energy range between 60 and 90 MeV. Angular distributions between 10 ° and 80 ° (lab) have been measured for states up to approximately 15 MeV; at still higher excitation energies some prominent groups of levels show up in the spectra, including a very broad structure peaked at 27 MeV. The elastic and inelastic scattering angular distributions were analyzed in the framework of standard optical model and coupled-channel analysis, respectively. The quadrupole deformation parameter was found to be ~2 = --0.48q-0.02, independent o f incident energy. The angular distributions for the second 0 + and first 3 - state were analysed using a rotationvibration coupling scheme.

E

N U C L E A R REACTIONS x2C(d, d), (d, d'), E = 60.6, 77.3 and 90.0 MeV; measured ~r(Ed,, 0). Deduced optical potentials, x2C levels deduced quadrupole deformation and coupling parameters.

1. Introduction

There is only very little information available on the elastic and inelastic deuteron scattering on 12C in the energy range above 60 MeV. The data of the Orsay group ~) taken at about 80 MeV incident energy provide the elastic angular distribution in the angular range from 10° to 45 ° (0c.m.) and in addition some information on the inelastic scattering to the first 2 + and 3- states. In order to provide optical model parameters for deuteron induced reactions on 12C in the energy range of the Jfilich Isochronous Cyclotron JULIC, it was desirable to investigate elastic deuteron scattering in the higher energy range up to 90 MeV in more detail. Moreover, it was interesting to study 12C levels by inelastic scattering up to higher excitation energy in order to test collective properties of such states. Indeed, it is one of the essential properties of the 12C nucleus that it shows typical features of a collective nature 2). The structure of the excited ~2C states has been discussed in the last years in a number of theoretical and experimental investigations ~-~8) from different points of view, however, without arriving at a fully consistent picture. In order to be able to check the consistency of the parametrization of experimental results it was desirable to provide experimental data for different energies in the range between 60 and 90 MeV. Therefore, the present work reports on 12C(d, d') 263

264

O. ASPELUND et al.

investigations at three incident energies. States of ~2C up to 23 MeV excitation energy have been identified. The analysis is done in terms of the optical model and in the framework of coupled-channel calculations.

2. Experimental techniques Angular distributions of deuteron groups corresponding to elastic and inelastic scattering on 12C have been measured from I0 ° to approximately 80° (lab system) generally in 1° steps at incident energies of 60.6, 77.3 and 90 MeV. The experimental work has been performed at JULIC using the unanalyzed extracted deuteron beam 19). Beam monitoring was accomplished in the usual way by means of a Faraday cup located 4 m behind the scattering chamber and by a monitor detector. The intensities typically ranged from about 5 nA for the smaller scattering angles to about 500 nA for the larger angles. The beam spot was focused to better than 2 mm diameter. The target was a 3.21 mg/cm2 self-supporting foil of natural carbon. The zero point of the absolute angular scale was uncertain within about 0.I degree. This was established by means of appropriate left-right symmetry experiments. After passing a 19 #m mylar window, the scattered deuterons were detected outside the 20 cm diameter scattering chamber 2o) by means of detector telescopes. The detector telescopes were operating in the usual AE-E mode using Si surfacebarrier counters as A E detectors, and Ge(Li) diodes of the side-entry 2t) type, produced in the detector laboratory of this institute, as E-detectors. A typical A E counter thickness was 400 gin; the Ge(Li) diodes had standard lengths of 25 ram. The energy resolution in the particle spectra was about 250 keV corresponding to the 0.3 % energy spread in the unanalysed beam. This was sul~cient to allow a fairly detailed study of the deuteron spectra up to high excitation energies of 12C.

3. Experimental results Fig. 1 shows a lzC(d, d') spectrum measured at 77.3 MeV incident energy. The evaluation of the measured spectra was performed by an automatic data acquisition program described elsewhere 22). For energy calibration the elastic peak and the peak corresponding to the 3- state at Ez = 9.638 MeV have been used. After calibration, a "kinematics" computer program was used to identify the lzC states especially those at higher excitation energies. Only those deuteron groups were selected, which were seen systematically in the spectra and showed correct kinematic behaviour as a function of scattering angle. Essentially, six excited levels were observed up to 15 MeV excitation energy (fig. 1): the ground state and the states at 4.44, 7.65, 9.64, 12.71, and 14.08 MeV. The corresponding spin-parity values are: 0 +, 2 +, 0 +, 3-, 1+ and (4+), respectively za). In a number of spectra there were indications, though with poor statistics,

12C(d, d)

265

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for the systematic occurrence of additional weak deuteron groups at the 12C excitation energies of 10.8_+0.2 MeV and 11.8_+0.2 MeV. In order to exhaust all experimental information, systematic excitations above 15 MeV have also been searched for. The only criterion was the correct kinematic behaviour of these deuteron groups as a function of scattering angle. Fig. 1 shows a spectrum to demonstrate the existence of deuteron groups corresponding to higher excitation energies. Such groups have been found at the excitation energies 18.3_+0.3 MeV, 20.6_+0.3 MeV and a broad peak at 21.9_+0.3 MeV. The structure of the d-spectra above 15 MeV excitation energy is quite similar to that of the ~-particle spectra at E= = 147 MeV [ref. 2+)]. On the other hand, it is worthwhile to mention that the prominent peak at E, = 19.5 MeV found in proton scattering at 45 and 155 MeV [ref. 25)], was neither seen in this work nor in the ~-spectra. In the giant quadrupole resonance region a very broad peak is seen of several MeV half-width. The maximum of this peak is located at about 27 MeV. This is in agreement with earlier E2 giant resonance results z6) obtained from 12C(p, p') experiments; it also coincides well with the theoretical expectation for the giant

266

O. ASPELUND etal.

E2 isoscalar resonance predicted at about 27.5 MeV according to the relation E ~, 63 A - ~ MeV. The main uncertainties in the evaluation of the cross sections were those due to target thickness, detector efficiency, beam current integration and solid angles. The error in the absolute cross section is estimated to be about 15 % overall. The measured angular distributions of the elastic and several inelastic deuteron groups are depicted in figs. 2, 3 and 4. Due to background and poor statistics, the angular distributions of the other inelastic groups are rather uncertain and have therefore not been included in figs. 2-4. They tend to show little structure.

4. Analysis of the data The experimental differential cross sections have been analyzed in the framework of the phenomenological rotation-vibration collective model. The aim was to look i

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for the relevance and consistency of the model in describing the scattering data for different incident energies. The method of coupled channels has been used because of the large deformation of z2C. The analysis was divided into two parts. First an optical model analysis was performed for the elastic data. The results of this analysis were used as starting parameters for the coupled-channel calculations described in the second part. 4.1. O P T I C A L M O D E L A N A L Y S I S

The optical model analysis presented is a standard one ~' 27) and was performed by means of the Raynal computer program MAGALI 2s). The Coulomb potential

268

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Vc(r) used is that of an uniformly charged sphere, and the Coulomb radius was fixed to rc = 1.3 fro. Both volume and surface absorption were considered in separate calculations. Mixed absorption was not investigated. For comparison with other investigations t' 27), two sets of calculations have been performed using the radius parameters rv = 1.05 fm and 1.25 fm for the real potential. In agreement with earlier investigations 1,27), the explicit inclusion of spin-orbit terms did not result in significantly better fits, showing that spin-orbit interaction does not play a major role for such a light nucleus as 12C. The 1.05 fm real radius parameter case presented dimculties in the sense, that the real potential depth showed the unphysical trend to increase with increasing energy. Surface absorption gave reasonable energy dependences 27) with the larger real radius parameter (rv = 1.25 fro). Volume absorption did not give sufficiently consistent results. The best fit potential parameters are tabulated in table 1. They are remarkably consistent with those obtained at 52 MeV [ref. 27)]. The quality of the fits is equal

269

12C(d, d) TABLE 1 Optical model parameters for elastic d-scattering on 12C for 60.6, 77.3 and 90 MeV Ee

V

av

W,

rw

aw

(MeV)

(MeV)

(fin)

(MoV)

(fro)

(fm)

60.6 77.3 90.0

67.30 65.99 65.33

0.64 0.64 0.67

13.34 14.98 18.04

1.24 1.18 1.12

0.60 0.65 0.70

rv = 1.25 fm and rc -~ 1.30 fm. The form of the optical model potential is

U(r)

d Vc(r, rc)-- Vf(r, rv, a t ) ~14W, ~trf(r, rw,

aw),

where

f(r, rt, at) ~ (1 +exp[(r--rtAt)/at])-1.

to that shown in figs. 2-4 for the elastic data calculated with the coupled-channel program. 4.2. C O U P L E D - C H A N N E L ANALYSIS

The results of previous experiments concerning inelastic scattering can essentially be described in terms of a collective model assnming a deformed tzC ground state [refs. 8-11)] and expecting the second 8-10, 18) and the third 11, 14. 17) member of the ground-state rotational band to be the 4.44 MeV 2 + and the 14.08 MeV (4 +) states, respectively. The structure of the 0 + state at 7.65 MeV is not well understood 12-1s). In coupled-channel analyses this level was tentatively discussed in terms of a ~-vibration 17, as). The 3- state at 9.64 MeV showed strong octupole-vibrational properties in inelastic scattering 1, 3, 9). The following presentation of the coupled-chaunel (CC) analysis 29) is divided into two parts, the first concerning the ground-state band separately and the second part taking additionally into account the first excited 0 + and 3- states. Considering the negligible effect of spin-orbit interactions in the standard optical model calculations and also in this CC analysis, the spin of the deuteron was not explicitly taken into account. According to the above results of the optical model analysis, the radius of the real part of the potential was fixed throughout the analysis to r v = 1.25 fm. In the calculations the following parameters were varied: the depth of the real potential V, the depth of the surface absorption potential Wi, the radius of the imaginary potential rw, the diffuseness parameters a v , aw and the coupling constants for the bands. The calculations were performed by means of the Tamura coupled-channel code JUPITOR-1 in its Karlsruhe version 3o).

O. A S P E L U N D et al.

270

4.2.1. Ground-state band. In the calculations, the experimental angular distributions for the 0 + ground state and the first excited 2 + level at 4.44 MeV were fitted assuming a static quadrupole deformation of tZC and coupling the 0 + ground state, the 2 + 4.44 MeV and the (4 +) 14.08 MeV levels. Input parameters for the CC analyses were those of table I with f12 = +0.45. The experimental angular distributions for the ground state and the 4.44 MeV state have been well reproduced by the calculations. Tables 2a and b give the optimum parameter sets for negative and positive f12 values, respectively. The fits for either sign of P2 are of the same quality as those shown in figs. 2, 3 and 4 so that TABLE 2 The o p t i m u m parameter sets from CC calculations

Ed (MeV)

V

av

W,

r.

a.

(MeV)

(fro)

(MeV)

(fro)

(fm)

(a) 60.6 77.3 90.0

66.5 66.1 64.6

0.64 0.63 0.64

P2

go +

g3-

--0.49 --0.47 --0.47

0.26 0.26 0.28

0.20 0.20 0.19

0.43 0.42 0.42

0.26 0.26 0.26

0.26 0.26 0.24

Oblatedeformation of 12C 12.8 14.0 16.0

1.16 1.17 I.II

0.65 0.65 0.70

(b) Prolate deformation of 12C 60.6 77.3 90.0

66.6 66.8 65.9

0.63 0.63 0.63

12.1 13.9 15.8

1.17 1.14 1.07

0.67 0.67 0.74

Included are the 0 +, 2 +, 4 + states o f the ground-state band and the first excited 0 + and 3 - states o f 12C. For both oblate and prolate deformations rv = 1.25 fm and rc = 1.30 fro.

a determination of the sign of the deformation was not possible. Within experimental errors, the deformation P2 was found to be independent of the incident energy with /t2 = -0.48 +0.02 and 1/2 --0.42+0.02. The potential parameters of table 2 are only slightly different from those of the optical model (table 1). Using the parameters of table 2, the 4 + angular distribution was calculated. The agreement between this calculated and experimental angular distributions for the 14.08 MeV state, assumed to be the 4 + state, is not as good as that for the two lower members of the ground-state rotational band; however, it tends still to be significant, especially with respect to the absolute cross sections. Fig. 3 shows the calculated curve for Ed = 77.3 MeV. The type of agreement with the experiment is typical also for the other two cases. For comparison, we also tried to describe the angular distributions for the first 0 + and 2 + states assuming the 12C to be a spherical vibrational nucleus. Since the calculations are similar, fits of the same quality as in the rotational case could be obtained, but the coupling parameter was found to be unusually large (0.65).

x2C(d, d)

271

4.2.2. States outside the ground-state band. In this section the interpretation of the angular distributions for the first excited 0 + and 3- states is discussed. For the purposes of the CC calculations the 7.65 MeV 0 + and the 9.64 MeV 3- states were coupled to the ground-state rotational band in terms of a rotation-vibration scheme, assuming that they are of fl-vibrational 17, la) and octupole-vibrational [refs. a, 9, 1o)] character, respectively. The best theoretical curves for the 7.65 MeV 0 + and the 9.64 MeV, 3- state are shown in figs. 2, 3 and 4 when using a 0+-2+-4+-0+-3 - coupling scheme with parameters as shown in table 2a (negative f12). As far as some additional calculations indicated, the parameters obtained from the pure g.s. band CC calculations do not change significantly by including the additional coupling of the 3- and 0 + states. Since the structure of the 7.65 MeV state is not well understood so far 12-1s), it was not unexpected that the theoretical fits to the angular distributions (figs. 2--4) are not so good as for the other states below 10 MeV excitation energy. For 77.3 and 90 MeV incident energy the fits to the angular distributions for the octupole vibration state at 9.64 MeV are better for negative f12 (table 2a) than for positive f12 (table 2b), suggesting an oblate 12C shape (see figs. 2--4). The coupling parameter for the 3- state was again independent of the bombarding energy (table 2),

5. Conclusions

In the large range of incident deuteron energies from 60-90 MeV, the experimental angular distributions for the 0 + ground state and the 2 + first excited state of 12C could be consistently described in the framework of rotational excitations and channel coupling. There is some indication that the 14.08 MeV (4 +) level is the third member of the ground-state rotational band. Using a rotation-vibration coupling scheme, the angular distributions of the 3(9.64 MeV) octupole-vibrational state could be best described if a negative t2 value for the rotational excitations was employed. The structure of the 7.65 MeV 0 + level is certainly more complicated than that assumed in our analysis. In table 3 the value of the deformation parameter found in the present study (f12 = -0.48 +0.02) is compared with results derived from other experimental investigations including inelastic scattering, T-transition probability and electron scattering measurements. The present t2 value is in good agreement with that found at 80 MeV incident deuteron energy t). In agreement with the discussion in ref. 1o) table 3 shows that the t2 values, resulting from light composite particle scattering, cluster around a value which is about 25 ~ smaller than the average t2 value from p-scattering. As far as the sign of the deformation is concerned our result, indicating a negative deformation, is in agreement with the general conjecture about the oblate shape of 12C

272

O. ASPELUND et aL

TAnLE 3 Deformation parameters /~2 and ~s and corresponding deformation lengths ~2 and ~s of x2C from different experiments Method

(n, n') (p, p') polarized protons (p, p') (p, p') (p, p') (p, p')

(d, d') (d, d') (d, d') (SHe, SHe') (% ~') (% u') (% ,,') (e, e') B(EL)

Incident energy (MeV)

Method of analysis

14.7 30.4

CC CC

40 46 155 1000

52 60.6 77.3 90.0 80.0 100 104 139 166 183 25O

DWBA CC DWBA multiple collision theory and deformed harmonic osc. wave function DWBA CC

~ ")

~2 = ~2Rv ")

~s ")

(fm)

-0.60 --0.66

--1.71 b) -1.61 b)

~s = ~sRv ")

Ref.

(fro)

0.33

0.94 b)

is)

9)

0.60 0.6 c) 0.67 -0.70 ~)

1.62 b) 1.61 ©) 1.38 b)

0.44 0.41 c) 0.57

1.18 b) 1.12 c) 1.17 b)

sl) 17) sz) 33)

0.57

1.63 b)

0.37

1.06 b)

--1.37

0.20-4-0.02

0.57

s) present results

1.35 b) 1.25 --1.07-4-0.05

0.35-4-0.06 0.30

1.0 b) 0.75

1) s4) s)

0.24 0.18

0.68 0.55 b)

xo) SS) 11)

--0.48-4-0.02

DWBA DWBA Anstern-Blair theory DWBA DWBA Nilsson model

0.474-0.05 0.51

0.46 0.30 --0.5

deduced B(EL)

0.60

1.27 0.92 b)

7)

*) Values as published unless noted otherwise (whenever a sign of the quadrupole deformation was published it was always negative and is quoted in this tame). b) Obtained from ~L (multiplying by the published Re). ©) Averaged value of published results. d) ~2 calculated from the published R./Rffi -~ 1.4.

[refs. 2, 4, 5, s, 9, xl, 33)]. T h e d e f o r m a t i o n length 6 L, e x t r a c t e d f r o m inelastic h a d r o n scattering tends to b e c o m e s o m e w h a t smaller at higher incident energies.

W e gratefully a c k n o w l e d g e useful discussions w i t h Prof. T. T a m u r a . W e t h a n k the m e m b e r s o f the staff o f the c y c l o t r o n a n d the d e t e c t o r l a b o r a t o r y f o r their h e l p a n d excellent c o o p e r a t i o n d u r i n g the course o f the experiments.

x2C(d, d)

273

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