molecular resonances and spin alignment in 12c+16o inelastic scattering

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Volume 125, number 1 PHYSICS LETTERS 19 May 1983 MOLECULAR RESONANCES AND SPIN ALIGNMENT IN 12C + 160 INELASTIC SCATTERING T. TAZAWA Technical College, Yamaguchi University, Tokiwadai, Ube 755, Japan and J.Y. PARK 1 and Y. ABE Research Institute for Fundamental Physics, Kyoto University, Kyoto 606, Japan Received 16 December 1982 Recent data on spin alignment of the 3- state (6.13 MeV) of 160 are analysed from molecular viewpoints in the coupled channel approach. The dominance of the aligned configuration on resonances around 20 and 22 MeV is well explained in the framework of the band crossing model. Resonance phenomena in heavy ion reactions have been observed well above the Coulomb barrier in vari- ous combinations of lighter heavy ions [ 1]. Studies of fusion excitation functions, combined with the calcu- lated numbers of open channels, suggests a systematic existence of surface transparency in interaction be- tween heavy ions [2], providing a favorable condition for the observation of resonances. Measurements have been extended to favorable systems, for example those including 14C and resulted in unveiling hitherto unknown resonances [3,1 ]. Most successful models for the resonance phenomena are those based on the molecular viewpoint [4], which explain gross and in- termediate structures typically observed in the 12C + 12C, 12C + 160 and 160 + 160 systems. The band crossing model (BCM) emphasizes the importance of aligned configurations [5]. Quasi-rotational bands with the aligned configurations cross with the elastic molecular rotational band, in spite of the additional excitation energy AE, as schematically shown in fig. 1. Thus, the aligned configurations are expected to couple strongly to the elastic channel and to be observ- ed as prominent resonances. Tanimura and one of the present authors (T.T.) [6]*also have shown that the doublet-like resonances observed in the 12C + 160 system have dominant aligned configurations as pre- dicted by the BCM, although their structures are due I Permanent address: Department of Physics, North Carolina, State University, Raleigh, NC 27650, USA. / / / ~ j~'./Strong Coupling Region J J(J+l ) scale cross Fig. ]. Schematic diagram of crossing of the elastic and an aligned inelastic molecular band. Existence of non-aligned molecular bands should be also noticed. to the competition of the resonances among the ine- lastic channels. These theoretical spin predictions in the above models are, however, contradictory to the recent angular correlation measurements [7]. They also suggested that the non-aligned quasi-rotational band next to the aligned one also plays an important role, and the spins of higher members of the doublets are two units smaller than those of lower members [8]. For the single 2 + excitation of the 12C + 12C scat- tering Tanimura and Mosel [9] compared recently predictions of several models with spin alignment 30 0 031-9163/83/0000 0000/$ 03.00 (9 1983 North-Holland

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Volume 125, number 1 PHYSICS LETTERS 19 May 1983

MOLECULAR RESONANCES AND SPIN ALIGNMENT IN 12C + 160 INELASTIC SCATTERING

T. TAZAWA Technical College, Yamaguchi University, Tokiwadai, Ube 755, Japan

and

J.Y. PARK 1 and Y. ABE Research Institute for Fundamental Physics, Kyoto University, Kyoto 606, Japan

Received 16 December 1982

Recent data on spin alignment of the 3- state (6.13 MeV) of 160 are analysed from molecular viewpoints in the coupled channel approach. The dominance of the aligned configuration on resonances around 20 and 22 MeV is well explained in the framework of the band crossing model.

Resonance phenomena in heavy ion reactions have been observed well above the Coulomb barrier in vari- ous combinations of lighter heavy ions [ 1]. Studies of fusion excitation functions, combined with the calcu- lated numbers of open channels, suggests a systematic existence of surface transparency in interaction be- tween heavy ions [2], providing a favorable condition for the observation of resonances. Measurements have been extended to favorable systems, for example those including 14C and resulted in unveiling hitherto unknown resonances [3,1 ]. Most successful models for the resonance phenomena are those based on the molecular viewpoint [4], which explain gross and in- termediate structures typically observed in the 12C + 12C, 12C + 160 and 160 + 160 systems. The band crossing model (BCM) emphasizes the importance of aligned configurations [5]. Quasi-rotational bands with the aligned configurations cross with the elastic molecular rotational band, in spite of the additional excitation energy AE, as schematically shown in fig. 1. Thus, the aligned configurations are expected to couple strongly to the elastic channel and to be observ- ed as prominent resonances. Tanimura and one of the present authors (T.T.) [6]*also have shown that the doublet-like resonances observed in the 12C + 160 system have dominant aligned configurations as pre- dicted by the BCM, although their structures are due

I Permanent address: Department of Physics, North Carolina, State University, Raleigh, NC 27650, USA.

/ / / ~ j ~ ' . / S t r o n g Coupling Region

E° J J(J+l ) scale cross

Fig. ] . Schematic diagram of crossing of the elastic and an aligned inelastic molecular band. Existence of non-aligned molecular bands should be also noticed.

to the competition of the resonances among the ine- lastic channels. These theoretical spin predictions in the above models are, however, contradictory to the recent angular correlation measurements [7]. They also suggested that the non-aligned quasi-rotational band next to the aligned one also plays an important role, and the spins of higher members of the doublets are two units smaller than those of lower members [8].

For the single 2 + excitation o f the 12 C + 12 C scat- tering Tanimura and Mosel [9] compared recently predictions of several models with spin alignment

30 0 031-9163/83/0000 0000/$ 03.00 (9 1983 North-Holland

Volume 125, number 1 PHYSICS LETTERS 19 May 1983

data [10] of Munich group which differ somewhat with the measurement of Yale group [ 11 ]. They con- cluded that although the four models, namely the dif- fraction model [12], the DWBA model [13], the strong-coupling model [ 14] and the band crossing model [5], all reproduce the measured gross structure of the integrated cross sections [15] fairly well, they are not very successful in reproducing the measured spin alignments. Our band crossing calculation for the spin alignment in the inelastic scattering of the 12C + 12C system leading to the first 2 + excited state using the latest parameters for the imaginary potential [ 16], which provide a satisfactory account for the fusion cross section, can give a better agreement with the measured alignment [ 10].

Recently the spin alignment of the outgoing 160(3 , 6.13 MeV) has been measured at the center- of-mass energy from 19 to 23 MeV [17]. The data show the enhancements correlating with two doublet- like resonances around 20 and 22 MeV. The spin align- ment or the magnetic substate population is one of the crucial physical quantities, as is recognized intui- tively from fig. 2. I f the aligned configuration of in- trinsic spin I and orbital angular momentum I domi- nates in resonance states over those of the other angu- lar momentum couplings as predicted by the BCM, the intrinsic spin should be perpendicular to the scat- tering plane and the magnetic substate population,

dac'c [ / ~ dac'c P(m) = - ~ c ' [ m [ ~ ~ m '

on the resonance is expected to be very large for Iml = I and very small otherwise in the coordinate system in which the quantization axis is perpendicular to the scattering plane as shown in fig. 2. The spin alignment,

Y ~/ ~ , e Ikf

ik i f,. ~ 1 " ~ /i~ .__OE.c., - - - x

Fig. 2. Intuitive picture for spin alignment of resonances with aligned configuration and the coordinate system.

A= ~P(m)- ~ P(m), Im I=I Im I<I

is expected to be close to unity (in general, - 1 . 0 ~<A <~ 1.0), in contrast to the statistical value 0.0 for the case o f U = 3 . Hence the experimental data above indicate that two doublet like resonances have an aligned configuration as a dominant one as predicted by the BCM. Above intuitive picture is readily verified by a qualitative argument of the quantum mechanical expression as follows.

Supposing that a resonating partial wave dominates in the scattering amplitude, the inelastic scattering cross section to the magnetic substate n7 is given by

d°c'-----c'l ~ ] 2 a ~ ( I m l m l l J r n + m l )iJ-I (1) d ~ c ' t m gc l m l

I

j m / ( a c ' ) * ]2 X exp (io l + ioj)S ,oJYl YJ, m +m/(ac) ,

where S-matrix elements with the total angular mo- mentum J are denoted as Sac,,c with channel c (ii). Other symbols are obvious. Assuming further that a single sub-channel S-matrix is large and other compo- nents are negligible, i.e.,

SiJl,OJ ~ 6I,IR , (2)

then eq. (1) simplifies as

d o c ' c / d ~ c ' I m

[ 12 ~ (Ira lRmllJm + mr) YtRmt(ac,) Y~j,m+m¢ac) m l (3)

Here it should be noted that if an aligned configura- tion dominates predominantly in a resonance as sug- gested in the BCM, then l R -- J - I but if a non-aligned one dominates as in ref. [8], then l R = J - I + 2. Taking into account that 0 = 0 ' = 7r/2,

YlRml(rr/2 , ~)

~-- - - ~ ( 2 l + 1) 1/2 [(/R + 1/2) 2 -- m2]-l/4exp(iml4)),

which indicates that I mll = l R contribute dominantly. As is well known, the Clebsch-Gordan coefficients including only one small angular momentum can be approximated by a matrix element of finite rotation,

( _ ) I - I R +J d I (Ira lR ml[J m + ml) -- , j - t R ,m~) ,

where, cosfl = rnl/[lR(l R + 1)] 1/2 ~- -+1. By utilizing

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Volume 125, number 1 PHYSICS LETTERS 19 May 1983

the above approximat ion, the expression (3) is reduc-

ed to

doc'c/d~2c' Im ~ (dI_lR ,m (fl)) 2

X 12 . [ ~m YlRml(rr/2' ~)) YffJ'm+ml(rr/2' O) (4)

and finally

d°c'c/d~2c'lm ~ ~m,J_lR or 8m,_(J_lR) , (5)

since d/m,,m(+l) = ~m,m' or (-)I+m6m,_m,. Thus, the substate popula t ions , P(m = -+ iJ - I R [), are expected to be enhanced on resonances. Consequent ly , the al ignment A is enhanced or reduced depending on

which conf igurat ion dominates in a resonance state, an aligned or non-al igned one.

In order to analyse the above data on the spin al ignment quant i ta t ively, we have to treat the dynam- ical couplings between the elastic and excited molecular rotat ional bands under scattering boundary

1.0

<[

0.5

0.0

E v

4.0;

i i i i

Kyushu Data

12 C + 160 ~} 160 3 ~ ~ /

3.0

2.0

lO o / ° Calculated O" 3_

0 i i I i . . . . . I , , i

15.0 17. 5 20.0 22.5 25.0 27. 5

EC. M .( MeV )

Fig. 3. Calculated excitation functions of spin alignment and inelastic cross section to the 160(3-, 6.13 MeV) state are compared with the experiments. Spin alignment is averaged over the particle angle q~ from 95 ° to 145 °. Experimental data on the bottom are not inelastic cross sections but inclusive ones of the y-ray with E~, = 6.13 MeV.

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Volume 125, number 1 PHYSICS LETTERS 19 May 1983

Table 1 The real part of the optical potential is a sum of the gaussian (short range core) and the Saxon-Woods (long range attraction). All the parameters are very similar to those of ref. [5]). Geometrical parameters of the imaginary part are chosen to be the same as those of the long range part of the real one. Changes are made of the strength of the imaginary part so as to give absolute values of the elastic and the fusion excitation functions comparable to experimental ones. Couplings are also made to be a little stronger and hence the depths of the real part are made to be shallower than those in ref. [5]).

Core part Attractive part Imaginary part Coupling

VG g Vt V2 = V3 = V4 Ro a W 0 R Q_. J ~2 3"3 (MeV) (fm -2) ( M e V ) (MeV) (fm) (fm) (MeV) (fm) ( M e V ) (N.D.) (N.D.) (N.D.)

100.0 0.156 -21.0 -19.0 6.01 0.4 -0.3 XEc.m. 6.01 -8.0 0.5 -0.2 0.15

condition, i.e., to solve the coupled channel equation. In the present calculation phenomenological potentials as well as coupling interactions are introduced as in ref. [5], so as to describe the molecular bands. The parameters adopted are listed in table 1. We include excitations of the 2 + state (4.44 MeV) of 12C, the 3 - state (6.13 MeV) of 160 as well as their mutual exci- tation. (The total number of the sub-channels is 20.) Calculated excitation functions of the spin alignment of the outgoing 1 6 0 ( 3 - , 6.13 MeV) and the angle- integrated inelastic cross section are compared with the experimental data in fig. 3. It is readily seen that the experimentally observed enhancement at resonance energies are well reproduced, although the absolute values of the alignment are always slightly larger than the experimental ones. Another characteristic aspect of the calculated results is that the enhancements cor- relate with resonances in the integrated cross section in accord with the above intuitive and qualitative arguments, although resonance energies and relative strengths in the inelastic cross sections and the spin alignment vary depending on the coupling parameters /32 and 3'3. In conclusion, two doublet-like resonances observed at 20 and 22 MeV in the 12C + 160 system have a dominant aligned configuration with the in- trinsic spin of the excited 160 and the orbital angular momentum being coupled to give a maximum total spin, as predicted by the BCM.

In the present preliminary results, spins of the res- onance peaks are 13 , 14 +, 14 +, 15- (overlapping doublet) , 16 + (overlapping doublet) respectively from low to higher energies. Recent experimental spin assing- ments [7] of 12 + for the 20.5 MeV resonance and 13 - for the 22.6 MeV resonance differ from those predicted by the BCM, namely 14 + and 15 respectively. Theo-

retical predictions of the resonance spins, however, are not so definite, as is readily seen by the fact that one of the 13 - resonances with dominant aligned con- figurations comes close to the 14 + resonance as a re- sult of coupling interactions. The elastic and aligned molecular rotational bands obtained in a bound state approximation cross with each other at spins 12 -14 , where four molecular bands (one is elastic and the other three are aligned) mix with each others and the resultant states share the elastic and inelastic aligned configurations. The states with the same spin spread over about 3 MeV or more. They have overlaps in energy with those having the neighboring spins and even the next neighbors (spin difference is 2). Details will be published elsewhere. However, it should also be noted that many contradictory spin assignments [7,18,19] have been reported for the states at 20.5 and 22.6 MeV and, as pointed out in ref. [17], spin assignments for these states are rather ambiguous when compared with those at 19.7 and 22.0 MeV.

In the present calculation we have employed the J-dependent imaginary potential according to ref. [20], which reduces contributions of lower total angular momenta to the cross sections. One can use another parametrization, for example, a short-ranged potential which is recently shown to be successful in explaining the excitation functions of fusion cross sections systematically [ 16]. In this potential non- aligned rotational bands could also show up them- selves as resonances in inelastic cross sections. How- ever, as discussed above, no enhancements in spin alignments may be expected. Careful studies are re- quired for a consistent understanding of the spin align- ment and angular correlation data, which will provide us more precise information about nuclear structures of resonances and reaction mechanisms.

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Volume 125, number 1 PHYSICS LETTERS 19 May 1983

We are grateful to Dr. N. Ka to for sending us their

data prior to the publ icat ion. One of the authors

(Y.A.) would like to acknowledge Dr. Y. K o n d o and

Dr. T. Matsuse for their encouraging discussions at

the early stage o f the work and Dr. S. Okabe for pro-

viding us his coupled channel code. T. Tazawa expresses

his thanks to Professor M. Nogami, Professor B.

Imanishi and Dr. O. Tanimura for con t inued encour-

agement . One o f us ( J . Y 2 . ) is grateful to Pfofessor:

W. Greiner and Professor W. Scheid for their encour-

agements and supports and to Professor Z. Maki for

the kind hospi ta l i ty ex tended to him at the Research

Inst i tute for Fundamenta l Physics, K y o t o University.

Referen ces

[ 1 ] K. Eberhard, ed., Proc. of the Symp. on Resonances in Heavy ion reactions (Bad-Honnef, 1981)Lecture Notes in Physics, Vol. 156 (Springer, Berlin, 1982); Proc. Intern. Conf. on Resonant behavior of heavy ion systems, ed. G. Vourvopoulos (Aegean Sea, Greece, 1980).

[2] F. Haas and Y. Abe, Phys. Rev. Lett. 46 (1981) 1667. [3] D. Konnerth et al., Phys. Rev. Lett. 45 (1980) 1154. [4] B. Imanishi, Nucl. Phys. A215 (1969) 33;

W. Scheid, W. Greiner and R. Lemmer, Phys. Lett. 25 (1970) 176; J.Y. Park, W. Greiner and W. Scheid, Phys. Rev. C16 (1977) 2276; O. Tanimura and T. Tazawa, Phys. Rep. 61 (1980) No. 4; Y. Abe, Y. Kond~ and T. Matsuse, Prog. Theor. Phys. Suppl. 68 (1980) Ch. IV.

[5] T. Matsuse, Y. Abe and Y. Kond~, Prog. Theor. Phys. 59 (1978) 1904.

[6] O. Tanimura and T. Tazawa, Phys. Lett. 83B (1979) 22. [7] C.M. Jachcinski et al., Phys. Lett. 87B (1979) 354;

J.R. Beene et al., Phys. Rev. C21 (1980) 167. [8] T. Tazawa and O. Tanimura, Phys. Rev. Lett. 46 (1981)

408. [9] O. Tanimura and U. Mosel, Phys. Lett. l14B (1982) 7.

[ 10] W. Trombik, in: Proc. Symp. on Resonances in heavy ions reactions, ed. K.A. Eberhard (Bad-Honnef, 1981) Lecture Notes in Physics, Vol. 156 (Springer, Berlin, 1982).

[ 11 ] K.A. Erb, in: Proc. Intern. Conf. on Resonant behavior of heavy ion systems (Aegean Sea, Greece, 1980).

[12] R.L. Phillips, K.A. Erb, D.A. Bromley and J. Weneser, Phys. Rev. Lett. 42 (1979) 566.

[13] L.E. Cannell, R.W. Zurmuehle and D.P. Balamuth, Phys. Rev. Lett. 43 (1979) 837.

[14] O. Tanimura and U. Mosel, Phys. Lett. 105B (1981) 334.

[15] T.M. Cormier et al., Phys. Rev. Lett. 40 (1978) 924. [16] K. Hatogai, M. Ohta and S. Okai, Prog. Theor. Phys., to

be published. [17] N. Kato et al., Phys. Lett. 120B (1983) 314. [18] P. Charles et al., Phys. Lett. 62B (1976) 289. [19] D. Shapira et al., Phys. Lett. 71B (1977) 293. [20] R.A. Chatwin et al., Phys. Rev. C1 (1970) 795.

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