A comprehensive study of the 34S + α system

N U C L E A R PHYSICS A

ELSEVIER Nuclear Physics A 604 (1996) 286-304

A comprehensive study of the 345 -+- system Zs. Ftiltip a, G. L6vai a, E. Somorjai a, A.Z. Kiss a, j. Cseh a,

P. Tikkanen b, j. Keinonen b a Institute of Nuclear Research of the Hungarian Academy of Sciences, Debrecen, Pf. 51, H-4001 Hungary

b Accelerator Laboratory, University of Helsinki, Hameentie 100, SF-00550 Helsinki, Finland

Received 6 February 1996

Abstract

The 34S + a system has been studied both experimentally and theoretically. Excitation functions of the 34S(o~, y)38Ar reaction have been measured over the alpha bombarding energy range E~ = 3.4-4.4 MeV. The low background provided by the 100% enriched (implanted) target allowed one to observe 10 new resonances, some of them attributed previously to the 32S contamination of the target. Decay schemes, spin-parity values, reduced electromagnetic transition probabifities and resonance strengths have been determined. A semimicroscopic algebraic 34S + a cluster model has been used to describe the new resonances together with the low-lying states of the 38Ar nucleus. This analysis indicates that the J-~ = 1- resonances may not be good candidates for the first state of a K ~ = 0 - band predicted to start in the Ex "~ 10-11 MeV region.

PACS: 21.60.Fw; 21.60.Gx; 23.20.Lw; 25.20.Lv; 27.30.+t Keywords: 345(ot, 'y)38Ar; Ect = 3.4-4.4 MeV; 3BAr levels deduced; Implanted target; Semimicroscopic algebraic cluster model; Dynamic symmetry

1. Introduction

a-clustering is known to be important for a number of nuclei around the A --~ 36-44

mass region. The most prominent examples are the 4°Ca and 44Ti nuclei, the energy

spectra of which contain states with well-developed 36At + O~ and 4°Ca + a character,

respectively (see Refs. [ 1,2] and references therein). These states can be assigned to

K ~ = 0 + and 0 - bands, which are sometimes interpreted as inversion doublets [ 3 ]. Such

structures have already been identified in the spectra of some Na-type light nuclei, such

as 160 ~-- 12C + a and 2°Ne ~- t60 + a. Recent calculations based on a local potential

model suggested the existence of a similar situation for the 3BAr nucleus as well [4].

The K ~r = 0 + c~-cluster band is known to be builLon the first excited fir = 0 + state at

0375-9474/96/$15.00 Copyright © 1996 Elsevier Science B.V. All fights reserved PH S0375-9474(96)001 73-X

Zs. Fiilrp et al./Nuclear Physics A 604 (1996) 286-304 287

Ex = 3.377 MeV in this case, while its negative-parity partner is predicted to start above

Ex = I0 MeV [4]. The first member of this band is expected to appear as a j~r = 1- resonance in various a-transfer reactions, and, in particular it should show up in the 34S(a,'y)38Ar reaction at E,~ _~ 3-4 MeV.

Although several experimental investigations [5-7] have been carried out on the 34S(a, ~')38Ar reaction using the well-known benefits of the a-capture reactions, still no

comprehensive data are available. Not only information concerning the known resonances

is missing but the existence of certain resonances is questionable. One of the limitations

of the earlier investigations using exclusively NaI detectors is that up to 7 or 8 MeV gamma-ray energy the neutron background caused by the 13C(a, n)160 reaction did not

permit to investigate gamma transitions to any excited states. Another problem is the lack of the overlapping energy interval in the earlier investigations between E , = 3.5-

3.6 MeV [6,7]. The measurements in this bombarding energy region made by Phillips [ 8] utilized only NaI gamma detectors. Recently a measurement was carried out aiming

at the (a , 7) cross sections between E~ = 2.7-9.4 MeV, but the setup allowed to investigate solely the 1 --~ 0 transition for 38Ar nucleus, i.e. no primary transition could

be detected [9]. In addition to the above-mentioned problems the effect of target contamination can

not be neglected in the case of the previous measurements. Excitation functions have

been thoroughly investigated by Chevallier et al. [7] in the alpha bombarding energy range of 3.6-4.8 MeV. Due to the presence of 32S contaminant nuclei, three reso-

nances are supposed to be caused by ( a , y ) reactions on 32S. On the contrary, the

latest compilation for the sd-shell nuclei [ 10] attributes two resonances (E,~ = 3.989 and 4.024 MeV) to 345(a,'y) though these resonances are in the 32S(a,y) reaction

according to Ref. [5]. The motivation of the present investigation is to search for other than r ~ 0 transi-

tions with the benefits of special arrangements for clean vacuum and implanted (100%

enriched) targets, which have been proved to be very successful also in our earlier inves- tigations [ 11,12]. We also wanted to make a link between the energy intervals of earlier

reliable measurements. The aim of the present study is to scan the E~ = 3.4-4.4 MeV

energy range using implanted ( 100% enriched) targets with special attention paid to the resonances in question, to search for new resonances and to determine several properties

of known resonances with better accuracy. The theoretical interpretation of the resonances seen in the 34S(a,y)38Ar reaction

and their decay schemes call for the description of the 38Ar ~34 S -'}- a system at lower

excitation energies as well. In this analysis we use the Semimicroscopic Algebraic

Cluster Model (SACM) developed recently [ 13]. This model has proved successful in the description of various cluster systems in the lower half of the sd shell [ 14,15], and the example of the 38Ar nucleus offers an opportunity to test it near the closure of the sd shell as well.

288 Zs. FiilOp et al./Nuclear Physics A 604 (1996) 286-304

2. Experimental arrangements

The measurements were performed with 6 to 9 / zA 4He+ beams from the 5MV Van

de Graaff generator of ATOMKI (Debrecen) collimated into a spot of 5 mm in diameter. The target was perpendicular relative to the beam. The target holder contained practically

no iron for eliminating background from the (n, n 'y ) reaction and provided direct water cooling for the target backing. The deposition of contaminants during bombardment was

minimized by an LN2 cooling trap which had a large surface compared to the volume

of the target chamber and was close to the target. Indium sealings were also used to

achieve a carbon-free vacuum. A negative bias of 300 V in front of the target and a

closed-circuit water cooling was applied in the case of yield curve measurements to

provide accurate target current data.

In both the excitation curve and branching ratio measurements implanted targets were used. They were prepared by implanting a 20/ . tg/cm 2 dose of 10-50 keV 345 ions into

0.4 mm thick Ta backing in the isotope separator of the University of Helsinki. Highly enriched (97.1%) 345 material (obtained from V / O Techsnabexport, Moscow, Russia)

was used for implantation. Special care was taken to avoid the blistering effect often responsible for target deterioration at helium bombardment when tantalum backing is

used [ 16]. The stability of the target was checked by two different methods according to the

type of measurement. Regular remeasurements of the strong well-known resonance at

E~ = 3158 keV provided the target checking at excitation function measurements, while

continuous monitoring of the counting rate of the strongest peak from the reaction was

done at branching ratio measurements. With the exception of one measurement done with a Ge(Li) detector a 10 cm x

10 cm (diameter) NaI(T1) detector placed at an angle of 55 ° relative to the beam

direction was used for excitation curve measurements. The target-detector distance was 4 cm. The branching ratio measurements were performed with a HARSHAW 105 cm 3

Ge(Li) detector with a typical resolution of 3 keV at 1.3 MeV placed at a distance of 3 cm from the target and 55 ° relative to the beam direction. The detector was surrounded

by a 5 cm thick lead shield for decreasing the laboratory background, and a 3 mm thick lead cover in front of it served to eliminate the high-intensity low-energy radiation from

the Ta backing. The long-term stability of the spectrometer system was checked by position measurements of the laboratory background peaks. The Ge(Li) detector was

used in some cases also for the detailed investigation of the excitation function. For the energy calibration of the accelerator the E~ = 2792.4 4- 1.1 and 3199.5 4-

1.1 keV resonances of the 23Na(ot, y)27A1 reaction [17] were used on an Na2WO4 evaporated target. The efficiency calibration of the Ge(Li) detector was performed using a 226Ra source [ 18 ] and specially selected resonance transitions in (p, 9') reactions [ 19] for the low- and high-energy region, respectively.

Z~. FiilOp et al./Nuclear Physics A 604 (1996) 286-304 289

I I

%'0 a) 4.267 1500 -

4 . 1 6 7 3 .777

1000 I 4.079

, , ~, . ._~ y10 >..

3 . 980 . I I I I ,804 4.019 l

3866 I

I I I b) 4264

I

,.,+ ,.o++ i tlt

. - .

I 14.289 I

1 5 0 0 4 .167

I

1000

500

Y0

2000

1000

Y1

4.164 [ ~ 1 | ~ . . -

..,.r~! '~.i 1000 ............::.'..::::.':

2000

03.75 I I , I '8 4.00 4.25 3.75 4.00 4.25 4.5 E(~(MeV)

Fig. 1. The excitation function of the 34S(ot, y)38Ar reaction in the alpha bombarding energy range Ea = 3.75-4.4 MeV for T0 and 7* transitions. Left: the present results using implanted targets. Right: taken from Ref. [7].

3. Experimental results

The excitation functions have been determined by the NaI detector using 9.5-11.5 MeV

and 7.5-9.5 MeV gamma energy windows relevant to the primary transition to the ground

state (3'0) and the transition to the first excited state (Yl), respectively. The bombarding

energy step varied between 2 and 10 keV, depending on the structure of the excitation

function. We applied a correction for the energy shift caused by the implantation depth.

The measurements were repeated with implanted targets having different thicknesses.

The target thickness, which includes the energy resolution of the accelerator, has been measured on the E , = 3158 keV strong, narrow resonance.

The above-mentioned 70 and "~1 excitation functions taken on an implanted target are shown in Fig. 1 (left) compared to an earlier measurement [7] on an enriched

Ag2S target (right). As is well demonstrated in Fig. 1, the background was considerably reduced in our measurement (notice also the different scales). The reduction is especially

remarkable in the case of Yl. The resonances denoted by (a), (b) and (c) were supposed [7] to be present due to the 32S(ce,7) reaction. Our measurements proved that resonances (a) and (b) belong to the 34S(~,30 reaction. Furthermore, as will be shown later, the branching ratios of their decay have also been determined using a

Ge(Li) detector. It can also be seen in Fig. 1 that resonance (c) is not present in the excitation curve measured by us. Since we used implanted targets and the background was considerably reduced we may accept the statement of Ref. [7] that this resonance

290 Zs. Fiilfp et aL /Nuclear Physics A 604 (1996) 286-304

1600

1200"

(..) :1.

0 0

.-° 8 0 0 - ~ -

Z

4002

0 ,, , 3.Z

3.563

3.407

3. 8 3.497

I I I I I l l l l l l l l l l l l l l l l l l l l l l l l l l l l l

3.3 3.4 3.5

3.673 *

A 3.603 3.6'8 8 !', ! r I

~ o ' ' '~' ' f I I t t

Z i t i i I I

• I I

o 3.64 ' 3.g6 ' 3.g8 ' 350

E,~(MeV)

3"777,

2 3.804 ~ [ ,"L 3.866

K,h¢,,~ r, i k v,,r II. ",,7 ~ L L = . ~ " , , - - , ~ "

i i i i i i i i i i 1 | 111111111 i i i i i i i i i i | 11 i i i i i i i i i i i i

3.6 3.7 3.8 3.9 4.0 - E(~(MeV)

Fig. 2. The excitation function of the 34S(a,y)38Ar reaction in the alpha bombarding energy range

Ea = 3.4-3.9 MeV measured on 15 keV thick implanted targets. The dashed line denotes Yl, while the solid line denotes 70 transitions. The new resonances are marked by asterisks.

belongs to the 32S target nucleus.

Fig. 2 shows the measured excitation function in the E~ = 3.4-3.9 MeV bombarding

energy region using 15 keV thick implanted targets. Seven new resonances appear in

this region, three of which are present only in the ~q excitation function.

In Fig. 3 the excitation function in the 3.77-4.24 MeV alpha energy region are shown measured on targets with a thickness of 7 keV. Five new resonances appear in this

region, three in the 9'1 excitation function only. Two of them are also present in Fig. 2. The strengths and alpha bombarding energies of the resonances have been determined

by a relative method with a reference point of E,~ = 3777 keV resonance for the strength

and E,~ = (3497 ± 5) and (37775:5) keV for the resonance energies [10]. For the

excitation energy determinations the Q = 7207.4 -t- 0.8 keV [ 10] value has been used.

The strengths, excitation and alpha bombarding energies as well as the determined

spin-parity values of the new resonances are shown in Fig. 4, where resonance decay

branchings are also given for all measured resonances. Let us make some comment regarding some of the investigated resonance states.

(a) E~ = 3563, 3603, 3777, 3886 keV. New branchings have been measured for these known resonances giving more accurate decay information owing to the reduced

Z~. Fiil6p et al . /Nuclear Physics A 604 (1996) 286-304 291

Fig. 3. 7 keV

800"

600"

( J

g - ~ - ... 4 0 0 -

Z

200 2

3.804 ,',., e i

200- !

(D J

21so- '., ,;..,,,,

/ "\ 50 -'/

0 3.78 3j79 3;80 3.71 3.182 3.83

E o((MeV)

I I ! I |

I | I !

--"-, | 3.886 " [4.019 ,,I

II i l l I l l I

• 1 l l . ! 1 [ , ; ,, , ;1,, | ! i l l

| i t I I | II I I

• I 0J | ~e , ,11 v i V

I i i i i i l l l i l l l l i i i i i l l 1 1 1 1 1 i i i ] I i i i i i i i i i i i I I I I I T I I I I I I I I I

3.7 3.8 3.9 4.0 4.1 4.2 1..3

Eo~(MeV) The same as Fig. 2, but in the alpha bombarding energy range Ea = 3.77-4.24 MeV and measured on thick implanted targets.

f4.]67

II Ii

f % 0 I I 0 , I I I

I I i I Io i i I I i I I i

I I i

, I I i

background. (b) E~ = 3673, 3688, 3698 keV. Since the members of this new triplet are rather

close to each other, 15 keV thick targets have been used for the lowest energy member for the branching ratio measurement while for the others 7 keV thick targets were used in order to reduce the effect of the neighbouring resonances.

(c) E~ = 3804 keV. This is a new triplet; however, it can hardly be separated even by using 7 keV thick targets (see Fig. 3, enlarged section). We measured excitation functions for this triplet also with a Ge(Li) detector (see Fig. 5) and found that the members cannot be clearly separated since their decays and branching ratios are similar. Based on the Ge(Li) excitation curve measurements we supposed the effect of the first member to be negligible and determined the strength and branching ratios using measurements on the strongest member of the triplet.

(d) E,~ = 3886 keV. This resonance seems to be a doublet (Fig. 3); however, the measured gamma spectra proved that only the first member is a resonance belong- ing to the 3 4 S ( ~ , ' 7 ) reaction. The origin of the second peak is unknown.

(e) E~ = 3673, 3980 keV. The decay modes of these new resonances give the possibility of a spin-parity determination based on measurements only at two

292 Zs. FfilSp et al./Nuclear Physics A 604 (1996)286-304

Ea(MeV) Ex(MeV)

4.019 10.803 - - 14

3.980 10.768 Lu

3.932 10.726 I

3.886 + 10,684 - - 91

3.866 10.666 - ~

3.804 10.611

_+0.005

5.73

5.55 5.51 5.16 5.08 4.88 4.57 3.94 3.81 2.17 0

j~

30 1, I u'} I 4 10 7

• 5 3 2 7 I J 10 10

51 23 18 8 -

7 5 17 3 5

s (o~.y) [eW

(1-.2 +) 1.7 _+ 0.6

2 + 2.1 -+ 0.7

1.3 -+ 0.4

1- 0.7- + 0.2

-- (2+,3-,4 +) 1.5 _+ 0.5

-- 1.3_+0.5

(1.2) + 3- 2 +

2-(1-,3-) 3- 2 + 2* 3- 2+ (a) 0 +

E=(MeV) Ex (MeV)

3.777 + 10.586

3.732 10.547

3.698 10.516

3.688 10.507

3.6?3 10.494

3.603 + 10.431

3.563 + 10.395

3.548 10.382

- - o o :~ I ': I " I

' 9 42 49 I I I

- 31 5 3 7 9

- - 31 6 9 I

- - 56 30 1/,

- - 9 2 5 2 1

- - ? 9 8 8 - 5

I 80 2 0

J~' S (o~,',/) [eV ]

1- 2.6 +0.9

0.25 -+0.08

0.06 +0.03

0.02 _+0.01

1- 0.05 +0.03

I - 8 +-4

1- 2.8 _+0.9

0.004-+0.002

+0.005

5.59 2+ 5.16 2 + 4.71 0 + 4.57 2 + 4.48 4 - 3.94 2 + 3.81 3- 3.38 O+ 2.17 2+ 0 O+

(b)

Fig. 4. Part of the 3BAr level scheme in the 10.3-10.8 MeV excitation energy region. The previously known resonances are denoted by crosses. The relative error of the branchings are 20% (50% when the branching is smaller than 5%).

Zs. Fiil6p et al./Nuclear Physics A 604 (1996) 286-304 293

500-

400"

300"

>" 200-. 4--,,,0

100-

r--1 \

3.785 3.795 3.805 3.815 3.825 3.835 Ea(MeV)

Fig. 5. The excitation function of the 34S(ot, 7)38Ar reaction in the alpha bombarding energy range Ea = 3.795-3.825 MeV measured with a Ge(Li) gamma detector.

angles, i.e. 55 ° and 90 ° [20]. The values are J~ = 1- and 2 + for the E , = 3673 and 3980 keV resonances, respectively.

Of those resonances that have not been discussed separately, only strengths and

branching ratios were determined because of their weakness or close distances to other resonances.

4. Semimicroscopic 348 + ¢]f cluster model of the 3SAr nucleus

4.1. General aspects

In the Semimicroscopic Algebraic Cluster Model (SACM) the internal structure of the

clusters are treated in terms of the Wigner-Elliott SU(3) shell model [21,22], while their relative motion is described by the vibron model with a U(4) group structure [23]. The

model space is constructed microscopically, but the interactions are phenomenological ones, expressed in terms of group generators [ 13].

Cluster systems in which one of the clusters is a closed-shell nucleus and the other

an even-even nucleus with Tz = ( N - Z ) / 2 , can be described in terms of the restricted U ~ ( 4 ) ® Uc(3) ® UR(3) model of the semimicroscopic algebraic approach [ 13]. Here

294 Zs. Fiil6p et al./Nuclear Physics A 604 (1996) 286-304

the restriction means that the interactions do not have isospin dependence and that all the states have the same T = T z value. Technically the situation here is similar to that for the 14C + a cluster model of the 180 nucleus [ 14]. Like in that example, the relevant group chain which supplies quantum numbers to label the model states is

UcSr(4) ® Uc(3) ® UR(4) D u S ( 2 ) Q U ~ ( 2 ) ® U c ( 3 ) ®UR(3)

[ rC , ¢C , ,,'c fC l , [ n Cl , c c n2 ,n3 l [N, 0 ,0 ,0 ] , Sc, Tc, [n~,0,0l J l , / 2 . / 3 '

u ( 3 )

[ nl , n2, n3 ],

@ ucS (2) ® uT(2) D 0 (3 ) ® suS (2) @SUcr (2) D SU(2) ® suT(2)

x , L , J },

(1)

where the groups with subscript C characterize the structure of the 34S core in terms of the SU(3) shell model, the ones with subscript R refer to the relative motion of the 34S and 4He clusters, while those without subscript arise from the SU(3) coupling of the two sectors. S and T stand for spin and isospin, respectively.

In our approach we assume that the 18 nucleons occupying the sd shell represent the [4, 4,4, 4, 2] permutational symmetry in the ground state of the 34S nucleus, and the distribution of the 2 x 18 = 36 oscillator quanta assigned to these nucleons correspond to the c c c [n I , n 2 , n 3 ] = [ 16, 14, 6] Uc (3) representation. According to this, the orbital part of the 348 wave function carries the (Ac,/zc ) = (2, 8) labels, and contains two states with Lc = 2, 4, 6, 8, and one with Lc = 0, 3, 5, 7, 9, 10. Due to the antisymmetry of the wave functions the permutational symmetry also determines the relevant irreducible representations of the UcSr(4) spin-isospin group [22,24]. The only allowed spin- isospin configuration for this system is Tc = 1, Tcz = 1 and Sc = 0. This implies that the angular momentum of the 348 states belonging to these quantum numbers is determined exclusively by the orbital part of the wave function. According to this, we assign the J~ (Ex) = 0 + (0.0 MeV), 2 + (2.218) and 4 + (4.689) 345 states to (,~c, IXc ) Xc = (2, 8) O,

and the 2 + (3.304), 3 + (4.877) and 4 + (6.251 ) ones to ( Ac, txc ) Xc = (2, 8) 2. The relative motion of the 34S and the 4He clusters is characterized by n~, the

number of oscillator quanta in the relative motion. Its lowest allowed value in this case is nm~nin = 8, as the four nucleons assigned to the 4He nucleus can occupy states of the sd shell without major shell excitations (Wildermuth condition). We have chosen N, the maximal number of n~, to be 10. As described in Ref. [ 13], this choice fixes the size of the model space, but does not influence the calculated values of observables significantly, n~r also determines the parity of the model states as 7r = ( - 1 )n=. Keeping only the essential quantum numbers the model states can be labeled as

I (2, 8), n~r; (a , l z ) x f f M ) . (2)

The ( h, /z) irreducible representations are determined by the (2, 8) ® (n~r, 0) SU (3) outer product. Some of the resulting (A,/x) irreps correspond to 3BAr Pauli-forbidden

Zs. FiilOp et al./Nuclear Physics A 604 (1996) 286-304

Table 1 Allowed SU(3) representations of the model space of the 34S + a system for n~ = 8, 9 and 10

295

n~r (A,/x)

8 9

10

(0,4), (2,0) (3,6), (2,5), (1,4), (0,3), (4,4), (3,3), (2,2), (1,1), (5,2), (4,1), (3,0) (6,8), (5,7), (4,6), (3,5), (2,4), (1,3), (0,2), (7,6), (6,5), (5,4), (4,3), (3,2), (2,1), (8,4), (7,3), (6,2), (5,1), (4,0)

states, or to spurious excitations of the centre-of-mass motion, and they have to be excluded [ 13]. The allowed (A,/z) SU(3) multiplets are displayed in Table l.

Following the usual algebraic treatment [ 13,14] the wave functions and the operators are factorized into core and relative motion components, which facilitates the calculations

to a considerable extent. The situation is simplified further if we restrict the calculations to the SU(3) dy-

namical symmetry limit, i.e. if we approximate the Hamiltonian by terms diagonal in the basis (1). In this case the model states (2) can be brought into one-to-one corre-

spondence with experimentally observed states. This choice also introduces well-defined selection rules for electromagnetic transitions arising from the tensorial character of the

transition operators [ 13 ]. The energy spectrum obtained from the semimicroscopic algebraic cluster model in

the SU(3) dynamical symmetry limit is characterized by rotational bands, which are labeled by quantum numbers n~, (A,/z) and X. This pattern was found to be a realistic approximation in previous applications of the model to cluster systems belonging to the lower half of the sd shell [ 14,15]. It was also found that bands with a large eigenvalue

of the C2(SU(3)) Casimir operator are situated lower in energy. The members of the rotational bands are connected by relatively strong E2 transitions,

due to the structure of the T (E2) transition operator [ 13]

Tn(E2) = QR()(2 ) ,,.-~(2) , - '~Rm + qc ~Rm ' ( 3 )

composed of generators of the SUR(3) and SUc (3) groups. The intensity of interband transitions with AA = A/z = zk 1 scales with the difference of the parameters qR and qc.

Similar selection rules apply to the magnetic dipole transition operators generated by

[13]

Tm(M1 ) ~ r ( l ) (1) = egR ~t~Rm -~- gC Lcm

=gRJ(m 1~ + (gc ~ ~,(l~ - - S R ) ~ C m " ( 4 )

Here j(1) is diagonal in the basis (1), therefore there is only one parameter to fit M1 transition data.

The electric dipole transition operator [ 13 ]

Yn(, El ) = dRD(.? ) (5)

296 Zs. F(ilOp et al./Nuclear Physics A 604 (1996) 286-304

operates exclusively on the relative motion component of the wave function, and connects states with An~ = ~: 1; ZlA = + 1, /tAt = 0 and zlA = 0, zlAt = T 1.

4.2. Detai led analysis

The ground state and the first excited state of the 38Ar nucleus with J~ = 2 + at

Ex = 2.167 MeV can be assigned to the model band labeled by n,r(A, At)X = 8(0,4)0. The third (j~r = 4 +) member of this band is expected to be at somewhat higher

energy (Ex -~ 5-6 MeV), and it should decay to the first 2 + state. The two remaining

states of the (A, At) = (2 ,0) SU(3) multiplet (see Table 1) with J~ = 0 + and 2 + are also expected to be somewhat higher in energy, and with (in principle) forbidden

electromagnetic transitions to the first two states.

We assign the rest of the positive-parity energy spectrum to model states with n~r = 10,

i.e. to the major shell with 2hzo excitation. This section of the model space contains an

abundance of SU(3) multiplets (bands), some of which contain states up to J = 14. The

J~ = 0 +, 2 +, 4 +, 6 + and 8 + states at Ex = 3.377, 3.937, 5.350, 7.288 and 8.569 MeV are

thought to be members of a K ~ = 0 + band, due to the rotational arrangement of these states, and also due to the enhanced E2 transitions between its members with J~ = 2 +,

4 + and 6 + [25,4]. (There was, however, some controversy about the interpretation of the level at Ex = 7.288 MeV [26].) In terms of the semimicroscopic algebraic cluster

model these states can be assigned to a model band with n,r = 10, and X = 0. We expect

the (A, At)X = (6, 8)0 band to lie at lowest energy, therefore we assign the five states mentioned above to this SU(3) multiplet.

Due to the strict selection rules described in the previous section, this choice pre-

dicts forbidden E2 (and M1) transitions from this band to the ground-state band with

n,~ (A, At)X = 8 (0, 4)0. This also applies to other positive-parity bands in this region, as

the selection rules of the model predict transitions to the ground-state band only from bands with low values of A and At. According to the structure of the phenomenological

Hamiltonian, these states are expected to be somewhat higher in energy. This approxima- tion seems realistic for the ground state, as E2 (and M1) transitions to it are generally

weak. However, there are some relatively strong E2 transitions to the first excited state, which indicates that the selection rules following from the SU(3) dynamical symmetry

approximation are too restrictive in some cases. Negative-parity states can be assigned to lhto major shell excitations (n~r = 9). In

particular, the lowest-lying such states can be interpreted as experimental correspondents

of the n~r(A, At)X = 9 (3 ,6 )3 model band. The last member of this band has J = 9, and can be assigned to the J~ = 9 - state at Ex = 10.174 MeV. Other low-lying negative- parity states are expected to belong to the (A, At)X = (3,6)1, (2,5)2, (2,5)0, (4,4)4, etc. SU(3) quantum numbers. Most of the E2 and M1 electromagnetic transitions between these bands are allowed in terms of the model, the most intensive ones being those that change only X, and those that modify ,~ and At with only 1 unit. We can use this information to arrange the experimental states into model bands. An important consequence of the SU(3) dynamical symmetry approximation is that most of the E1

Z~. FiilOp et aL /Nuclear Physics A 604 (1996) 286-304 297

transitions are forbidden from these bands to the ground-state band. This again seems

to be a realistic approximation. We have used these results to generate a model energy spectrum with the simple

energy formula

E=e+yRnrr+SRC2(nrr ,O) +8'C2(A,1.*) +O(- -1 )n '~x2+f l t J (J+ 1). (6)

This expression can be considered to be a harmonic oscillator spectrum distorted by

various interaction terms. The strength of the harmonic term was fixed by choosing

yR = hzo = 11.5 MeV, a value characteristic for nuclei with A = 34. C2(,~,/z) = ,~2 +/zz + 2t/, + 3a + 3/z is the eigenvalue of the Casimir operator for the ( a , / , ) SU(3) representation. The 2 '2 term describes the splitting of bands with different X within an

SU(3) multiplet. We have introduced the parity-dependent factor ( - 1 ) "~ to account for

the observation that bands with higher values of X tend to be higher and lower in energy

for positive- and negative-parity states, respectively. The primes in 8' and /3' indicate that these parameters were fitted separately for

the five states belonging to the lowest (n,~ = 8) shell. As can be seen from the data

(see Fig. 7), these states follow a rotational pattern distinctly different from that of

the states belonging to higher shells. In the fitting procedure we first considered those

states that either had definite spin-parity J'~, or had uncertain J'~, but were involved

in electromagnetic transitions with numerical data for B(E2), B(M1) or B(E1). This, altogether, included 22 positive-parity, and 20 negative-parity states. We then applied a

weighted least-square fit procedure to determine the parameters in Eq. (6). We have

used the weights proportional to (Ex ÷ C ) - t with C = 1 MeV. Furthermore, in case

of states with indefinite value of J~ we divided it further with the number of possible jrr assignments. This correction helped to suppress uncertainties arising from the less

well-known levels. The resulting model spectrum is displayed in Fig. 6, while the

corresponding experimental states are shown in Fig. 7. The parameters (in MeV) of

Eq. (6) obtained from the fitting procedure are • = -48.953, 8R = -0.4369, 88 =

-0 .1632 89 = 810 = -0.0290, 0 = 0.1425, /38 = 0.3365, /39 = /310 = 0.0651. (See Tables 2 and 3 for band assignments.)

As can be seen from Figs. 6 and 7, the distribution of experimental and model states up to Ex ~ 9 MeV is similar for energy levels with natural J~ assignment, while a large number of non-natural-parity levels are missing from the experimental spectrum.

These states are less well-known experimentally, and may be accounted for by the large

number of levels with unknown J~ assignment [ 10]. Figs. 6 and 7 indicate that the structure of some bands deviates from the approximate

rotational (Ex -~ J ( J + 1)) pattern. This shows that the SU(3) dynamical symmetry approximation of the model Hamiltonian may be too simple in this case, and more realistic interactions may be needed. This band assignment, however, may be justified if we take into account electromagnetic transition data between their states as well.

A relatively large amount of numerical information is available for the E2, M1 and E1 transition strengths of the 3SAr nucleus [26,27]. However, the multipolarity of the transitions is uncertain in many cases. This is partly due to the uncertain J~ assignment

298 Zs. Fiil6p et al./Nuclear Physics A 604 (1996) 286-304

Ex (MeV)

- - 1 0 + ~ 9 +

- - 9 +

- - 9 + ~ 8 +

--8+__8 + - - 9 " - - 8 *

- - 8 + __7 + --7- '---7- --7+.... 7 +

- - 6 + - - 8 L 6 : _ _ 6 ~ 5 - 8 - - - 7 + ~ 6 +

--7+.__6+.__6 + - - - 6 - __ 6 + _ 6 + _ 5+

__4+ __7--5:__ 5_ --8" ~3- __5:--4- ~4+ --5--5++

- L 1_._7 ~__ 4___ 2 _---6+--- 5 + +.~ 3+._ 5"---- 4 " 4+ __6"----4_---;

__2 + ~ 3 - - _ _ 3 ~ 0 - - -4+ ' - -4 :__ 2+ - - 3+..__ 3 * - - 5 - - - - 2 7 . -2 - __6" 2_ - - 3 + --2+..--2 +

--I- __4+__ ~ 2 + __3 + __1 + --4- --5- 2 -- O+ __ 1 +

- - 3 - __2 + 4 - - - 4 - __0 +

- - 0 +

1 2 +

_ 1 0 +

8(2.0)0 9(3,6)1 9(2,5)0 9(4,4)2 10(6,8)0 10(8,4)0 10(?,6)0 10(5,7)1 8(0,4)0 9(3,6)3 9(2,5)2 9(4,4)4 9(4,4)0 10(6,8)2 10(8,4)2 10(?,6)2

Fig. 6. T = 1 energy levels of the 3BAr nucleus, as described by the Semimicroscopic Algebraic Cluster Model. The model bands are labelled by quantum numbers n~r(A,/x)X and parity.

of the energy levels. Also, there are only few transitions where the mixing ratios are

known, and the B(E2) and B(M1) data displayed in [26] represent upper limits for these quantities in most cases.

We have fitted the two parameters of the T (E2) transition operator (3) by using a

least-square fit procedure, in which we considered transitions with known 8(E2/M1) mixing ratios [26]. In order to suppress uncertainties as much as possible, we used the inverse of the relative error of B(E2) as weight in each case, i.e. we relied more heavily

on more precisely known transitions. The numerical value of the resulting parameters in Eq. (3) are qR =2.098 and qc = 1.119.

The results are summarized in Table 2. As expected, there is a number of E2 transitions

that are forbidden in the model, due to the assumption of SU(3) dynamical symmetry. Most of them are transitions between major shells with 2ha~ and 0hco excitations (i.e. those with n~ = 10 and 8), but there are also some within the 2hco major shell. Most of these transitions are, however, relatively weak. The most significant exceptions are some transitions from 2hzo states to the first excited state, indicating that more realistic interaction terms (mixing states between major shells) may be needed. In-band transitions between positive-parity states are, however, reproduced reasonably well.

Selection rules are less restrictive for E2 transitions between negative-parity model

Zs. Fiil6p et al./Nuclear Physics A 604 (1996) 286-304 299

Table 2 Reduced E2 transition probabilities (in W.u.) between 3BAr states. Experimental B(E2) values were taken from Ref. [26], except when stated otherwise. Uncertain J~" assignments are denoted by parentheses

Experimental data Theory

JF(Ex i) f f (Ex f) B(E2)Exp B(E2)Th n~-(A,/z)K i ~ f

2+(2.167) 0+(0.0) 3.2 4- 0.2 a,b 3.7 8(0,4)0 8(0,4)0 (4+)(6.485) 2+(2.167) 0.6 4- 0.5 3.4 8(0,4)0 5-(4 .586) 3-(3.810) 0.19 4- 0.02 a,b 3.8 9(3,6)3 9(3,6)3 9-(10.174) 7-(8.972) 3.3 4- 1.1 a,b 8.8 9(2,5)2 (2 - ) (5 .084) 3-(3.810) 36 -4- 15 11.4 9(3,6) 1 9(3,6)3 3-(5.513) 3-(3.810) 3.0 4- 1.4 3.9 9(3,6)3 (4 - ) (6 .042) 3-(3.810) 14 4- 3 1.2 9(3,6)3

4-(4 .480) 45 4- 9 7.4 9(3,6)3 5-(4.586) 21 4- 5 10.6 9(3,6)3

5-(5.658) 3-(3.810) 2.9 4- 0.7 b 0.09 9(3,6)3 5-- (4.586) 16+_~9 b 6.0 9(3,6)3

(2--)(6.496) 3--(3.810) 19 4- 7 2.6 9(2,5)2 9(3,6)3 4-- (4.480) 40 -4- 15 4.2 9(3,6)3 3 - (4.877) 170 4- 70 23.4 9(2,5)2

3-(4 .877) 3-(3.810) 0.8 +~.88 b 1.6 9(3,6)3 4--(6.211) 4--(4.480) 58 4- 19 1.2 9(3,6)3

5-- (4.586) 6 ± 2 0.03 9(3,6)3 5--(7.070) 5--(4.586) 3.3 ~ 1.1 a 0.7 9(3,6)3 (3--)(6.622) 3--(3.810) 2.3 :k: 0.8 0.014 9(2,5)0 9(3,6)3 (4- ) (6 .674) 4--(4.480) 8 4- 3 0.000 9(4,4)4 9(3,6)3 4--(6.601) 3--(3.810) 0.32 4- 0.12 0.17 9(4,4)2 9(3,6)3

0 2 ~+°88 b 0.15 9(3,6)3 4--(4.480) . v 0.28 5-(4.586) 4.3 ~ 1.0 0.2 9(3,6)3 3--(4.877) 68 4- 13 0.6 9(2,5)2

(2--)(7.538) 4--(4.480) 4.1 4- 2.3 0,1 9(4,4)0 9(3,6)3 0+(3.377) 2+(2.167) 1.4 4- 0.1 a 0 10(6,8)0 8(0,4)0 2+(3.937) 0+(0.0) 2.3 :zl: 0.4 0 8(0,4)0

2+(2.167) 7.5 :k: 1.5 0 8(0,4)0 4+(5.350) 2+(2.167) 1.0 ~ 0.3 0 8(0,4)0

2+(3.937) 31 ~z 9 b 47,4 10(6,8)0 6+(7.288) 4+(5.350) 80 4- 40 b 52,2 10(6,8)0 2+(5.595) 0+(0.0) 0.06 :]: 0.02 0 10(6,8)2 8(0,4)0

0+(3.377) 4.3 :t: 1.5 22,0 10(6,8)0 2+(3.937) 40 4- 14 36.4 10(6,8)0

2+(4.565) 2+(2.167) 22 Jz 7 0 10(8,4)0 8(0,4)0 4+(6.276) 2+(2.167) 0.37 ~ 0.16 0 8(0,4)0

2+(3.937) 1.4 ~ 0.7 0 10(6,8)0 2+(5.157) 0+(0.0) 0.08 4- 0.03 0 10(8,4)2 8(0,4)0

2+(2.167) 7 ~z 2 0 8(0,4)0 (3+)(6.053) 2+(3.937) 4.9 ~ 1.1 0 10(6,8)0

2+(4.565) 21 ~ 4 1.3 10(8,4)0 (1)+(5.552) 0+(0.0) 0.15 4- 0.08 0 10(7,6)0 8(0,4)0

2+(2.167) 3.9 & 1.8 0 8(0,4)0 (2+)(6.214) 0+(0.0) 0.8 :]: 0.4 0 10(7,6)2 8(0,4)0

2+(2.167) 5 4- 2 0 8(0,4)0 (4+)(7.682) 2+(2.167) 0.42 4- 0.23 0 10(5,7)1 8(0,4)0

From Ref. I27]. b Used to fit model parameters.

300 Zs. Fillip et al./Nuclear Physics A 604 (1996)286-304

Table 3 Reduced M1 transition probabilities (in W.u.) between 3BAr states. Experimental B(MI ) values were taken from Ref. [26], except when stated otherwise. Uncertain j~r assignments are denoted by parentheses

Experimental data Theory

JT(Ex i) JCf(Ex f ) B(MI)Exp B(M1)Th n~r(A,/x)x i ~ f

4- (4 .480) 3-(3.810) 0.057 4- 0.016 a 0.072 9(3,6)3 9(3,6)3 5-(4 .586) 4-(4.480) 0.11 4- 0.01 a 0.I1 9(3,6)3 ( 2 - ) (5.084) 3 - (3.810) 0.017 4- 0.007 0.004 9(3,6) 1 9(3,6)3 3-(5 .513) 3-(3.810) 0.0026 4- 0.0012 0.0030 9(3,6)3

4-(4 .480) 0.039 4- 0.012 0.006 9(3,6)3 3 - (4.877) 0.10 4- 0.02 0.03 9(2,5)2

(4 - ) (6 .042) 3-(3.810) 0.020 -4- 0.004 0.001 9(3,6)3 4-(4 .480) 0.032 4- 0.006 0.010 9(3,6)3 5-(4.586) 0.013 4- 0.003 0.009 9(3,6)3

5-(5.658) 4-(4 .480) 0.041 4- 0.009 0.003 9(3,6)3 5-(4.586) 0.55 4- 0.11 b 0.012 9(3,6)3

(2- ) (6 .496) 3-(3.810) 0.040 4- 0.014 0.210 9(2,5)2 9(3,6)3 3-(4.877) 0.13 4- 0.05 0.09 9(2,5)2

3-(4.877) 3-(3.810) 0.30 4- 0.07 b 0.03 9(3,6)3 4-(6 .211) 4-(4 .480) 0.052 4- 0.017 0.035 9(3,6)3

5-(4.586) 0.0048 4- 0.0016 0.156 9(3,6)3 5 - (7.070) 5 - (4.586) 0.022 -t- 0.006 a 0.029 9(3,6)3 (3 - ) (6 .622) 3--(3.810) 0.0053 -4- 0.0019 0.0001 9(2,5)0 9(3,6)3 (4--)(6.674) 4-(4.480) 0.011 4- 0.004 0.001 9(4,4)4 9(3,6)3

5-(4.586) 0.17 4- 0.04 0.001 9(3,6)3 (2- ) (5 .858) 3-(3.810) 0.15 4- 0.03 0.002 9(4,4)2 9(3,6)3

3-(4.877) 0.20 4- 0.06 0.02 9(2,5)2 4-(6 .601) 3-(3.810) 0.0007 4- 0.0003 0.009 9(3,6)3

4-(4 .480) 0.15 4- 0.02 b 0.005 9(3,6)3 5-(4.586) 0.0052 -t- 0.0012 0.0003 9(3,6)3 3-(4.877) 0.060 4- 0.012 0.0001 9(2,5)2

( 0 - ) (6.682) 1 - (5.734) 0.50 4- 0.13 0.024 9(4,4)0 9(3,6) 1 2+(3.937) 2+(2.167) 0.0072 4- 0.0015 0 10(6,8)0 8(0,4)0 6+(7.288) 6+(6.408) 0.06 4- 0.03 0 10(8,4)0 2+(5.595) 2+(3.937) 0.032 4- 0.011 0.004 10(6,8)2 10(6,8)0

2+(4.565) 0.08 4- 0.03 0 10(8,4)0 2+(4.565) 2+(2.167) 0.037 -t- 0.011 0 10(8,4)0 8(0,4)0

2+(3.937) 0.043 4- 0.014 0 10(6,8)0 4+(6.276) 4+(5.350) 0.11 4- 0.05 0 10(6,8)0 2+(5.157) 2+(2.167) 0.018 4- 0.006 0 10(8,4)2 8(0,4)0

2+(3.937) 0.12 4- 0.04 0 10(6,8)0 (3+)(6.053) 2+(3.937) 0.0065 4- 0.0014 0 10(6,8)0

2+(4.565) 0.014 4- 0.003 0.002 10(8,4)0 4+(5.350) 0.51 4- 0.09 0 10(6,8)0

(1+)(5.552) 0+(0.0) 0.0014 4- 0.0007 0 10(7,6)0 8(0,4)0 2+(2.167) 0.013 4- 0.006 0 8(0,4)0 2+(3.937) 0.18 4- 0.08 0.001 10(6,8)0 2+(4.565) 0.5 -I- 0.2 0.01 10(8,4)0

7+(8.077) 6+(6.408) 0.65 4- 0.16 a 0.004 10(8,4)0 (2+)(6.214) 2+(2.167) 0.022 4- 0.011 0 10(7,6)2 8(0,4)0 (2+)(7.101) 2+(2.167) 0.010 q- 0.004 0 10(5,7)1 8(0,4)0

a From Ref. [27]. b Determined from known 8(E2/M1) mixing ratio.

Zs. FiilOp et aL /Nuclear Physics A 604 (1996) 286-304 301

E x

(MeV) --9-

--(4+._~) 2+ --0 ÷

_ _ 5 -

- - 3 -

- - 7 -

_ _ 8 +

- - 7 +

- - ( 2 - ) --(4+) __6 +

-- 5- --(Z +) (4-) --4--- (0=) 6+

1.2 ./ ~3",, ~ 4 3 + + __ (2+ ) -i=(4-) 4- - - - 5 - - - ( 2 - ) _ _ 2 +

3- --4 + __2 +

- - (2" ) 3- __0 + - - 2 +

- - 2 +

- - 0 "

- - 2 +

-- - - 0 ÷

Fig. 7. Experimental states of the 3BAr nucleus arranged into bands predicted by the model. J~ values in parentheses indicate ambiguous spin-parities.

states, which we assign to lhto excitations. Comparing the experimental B(E2) values

with the theoretical ones we find that the former ones usually exceed the latter ones (as

expected), but their trends are reasonably correlated. The parameter related to the core part of the E2 transition operator in Eq. (3) can

also be used to calculate E2 transitions between 34S states assigned to the (Ac , t zc ) =

(2 ,8) S U c ( 3 ) multiplet. There are three such transitions [27] in our approach with pure E2 character: B(E2;2+(2.13) ~ 0 + ( 0 . 0 ) ) = 5.7 ± 0.3 W.u., B(E2;4+(4.69) --~

2+(2.13)) = 8.7 ± 1.0 W.u., B(E2;2+(3.30) ~ 0+(0.0)) = 0.72 ± 0.05 W.u. and one where M1 transitions are also possible: B(E2; 2+(3.30) --~ 2+(2.13)) = 4.1 ± 1.0 W.u.

The corresponding theoretical values, 11.7 W.u, 15.3 W.u, 0.59 W.u. and 1.1 W.u. are

in reasonable agreement with the experimental data indicating that the qc value defined

from E2 transitions of the 3BAr nucleus is consistent with the 3 4 8 data as well. Since jCl) = L(l) + L(c 1) is diagonal in the basis ( 1 ), the strength of magnetic dipole

transitions depends only on one parameter, i.e. on the difference of gc and gR in Eq. (4). We have determined this single parameter from a least-square fit procedure, using all the available B(M1) data [26,27] with the inverse of the relative error as weight. The

numerical value of the fitted IgR -- gcl parameter is 0.2375, which we have used to determine the B(M1)Th values displayed in Table 3.

It is remarkable that our results for the M1 transitions within the (A,/z) X -- (3, 6)3 and (2,5)2 bands are very close to the experimental data. Transitions that change X by

302 Zs. Fiil6p et al./Nuclear Physics A 604 (1996) 286-304

the 2 units in our approach also compare favourably with experiment: such transitions

for the SU(3) multiplets ( ,L/z) = (3,6), (6,8) and (8,4) are generally weak, and

B(MI)Exp usually exceeds B ( M 1 ) ~ by a factor of 3 to 8. Similarly to the E2 transitions, the calculated transition probabilities are more realistic

for negative-parity states, in the sense that there are many forbidden transitions between

positive-parity states. Electric dipole transitions for the 3BAr nucleus are generally weak: the strongest one

(connecting the lowest J~" = 3 - and 2 + states) has B(E1) = (2.34-0.8) × 10 -3 W.u. and only two others exceed 10 -3 W.u. Fifteen others fall between 10 -4 and 10 -3 W.u. and

there are 5 more that are even weaker [26,27]. Most of these transitions are forbidden

in the SU(3) dynamical symmetry approximation of the SACM, because they would

require a significant change of ~ and /z, while the electric dipole transition operator

(5) is able to account for only a limited change of these quantum numbers. A slight

breaking of the SU(3) dynamical symmetry would lift these strict selection rules.

4.3. Interpretation of the 34S(o[, y)3SAr resonances above Ex > 10 MeV

Combining the structure calculations of Subsection 4.2 with the new experimental

data presented in Section 3 a more complete analysis of the (a , y) resonances can be

given. The new (and re-analyzed) data include J~ values, decay schemes and, in some

cases, even reduced electromagnetic transition probabilities. Even if the multipolarities

of the electromagnetic transitions are not known in many cases, the structure of the resonances can be estimated from the branching ratios to 15 low-lying states with a

relatively well-understood structure. The SU(3) dynamical approximation would imply strict selection rules for these electromagnetic transitions. We, of course, do not expect

these selection rules to be fulfilled completely in reality, nevertheless the decay patterns of the resonances can give a hint about their composition. In particular, we can analyze the structure of the j,r = 1- resonances, which can be candidates for the first member

of the K ~ = 0 - band predicted in Ref. [4]. The five j~r = 1- resonances prefer decaying to the ground, or first excited state with

a branch of at least 90% (see Fig. 4). The B(E1) values for the transition from the Ex = 10.395, 10.431, 10.494, 10.586 and 10.684 MeV states to the ground state are 0.86,

2.81, 0.01, 0.83 and 0.22 x 10 -3 W.u., respectively. (Transitions to the first excited state are generally an order of magnitude weaker.) These transitions are considerably weak

in comparison with electric dipole transitions in other light nuclei; nevertheless, three of them are still among the largest observed B(E1) values for the 38Ar nucleus [26,27].

There are few J~ = 1- model states in the SACM which in the SU(3) dynamical symmetry approximation decay to the first two 38Ar states labeled by n~(A,/x) =

8(0 ,4) . These are the ones with n~(A,/x) = 9(1 ,4) and 9(0,3). We can assume that the j~r = 1- resonances contain dominantly admixtures of these states, j,r = 1- states are also expected in this region from the n~ = 11 (i.e. 3hw) shell. These include, for example, the n~r(A,/~)X = 11 ( 11,6)0 band, which would have similar characteristics as the K ~ = 0 - a-cluster band predicted in Ref. [4] as the "inversion doublet" of the

Zs. Fiil6p et al./Nuclear Physics A 604 (1996) 286-304 303

known K "r = 0 + band. Electric dipole transitions to the ground state from this band (or

from one with a dominant component of this type), however, are highly forbidden in the

SACM due to the largely different quantum numbers of the initial and final states. These

arguments seem to indicate that the J'~ = I - resonances which prefer decaying to the

ground state contain dominantly n~- = 9 model states and may not be good candidates

for the first member of the K '~ = 0 - cluster band of Ref. [4].

The remaining resonances can be classified into two groups according to their electro-

magnetic decay patterns. The first group contains states which (similarly to the J~" = 1-

resonances) decay dominantly to the lowest two states. The new J~ = 2 + resonance at

Ex = 10.768 MeV belongs to this group, indicating that in terms of the SACM it might

contain dominantly n~, = 10 states with low values of a and /z, i.e. (A,/z) = (0,2) ,

(1,3) or (2,4). The new resonances at Ex = 10.382, 10.507 and 10.611 MeV without J'~

assignments are also members of this group, which indicates that they may be mainly

n,r = 9 or 10 (i.e. lho) or 2ho)) states. The other group is formed by states that have

non-negligible branching ratios to states labeled by relatively large ,~ and # values.

We expect these states to have sizeable contributions from the n~. = 11 and 12 (i.e. 3

and 4hw) shells as well. This applies to the two new resonances with ambiguous J'~

assignment (Ex = 10.666 MeV, J'~ = ( 2 + , 3 - , 4 + ) ; Ex = 10.803 MeV, J ~ = ( 1 - , 2 + ) )

and the other ones with unknown spin-parity (Ex = 10.516, 10.547 and 10.726 MeV).

5. Summary

The 345 -1- O~ system has been studied both experimentally and theoretically. Ten

new resonances have been found in addition to the five known ones in the E~ =

3.5-4.1 MeV bombarding energy region. The basic properties (resonance energies,

strengths, branchings and spin-parity values) of those resonances have been determined.

More accurate branching ratios of the previously known resonances have also been

measured. The unambiguities regarding the possible 32S target impurities at the earlier

measurements have been clarified.

More efforts are needed for the investigation of the 4.1-4.2 MeV alpha bombarding

energy region as well as of the resonances which are close to each other. It demands an

excitation curve to be measured with a high-efficiency Germanium detector.

The new resonances have been analysed in terms of a semimicroscopic algebraic

345 + O~ cluster model, which has also been used to describe the low-lying part of

the 3BAr spectrum. In the latter region approximately 40 experimental states have been

assigned to 17 model bands and a large number of E2 and M1 transitions have been calculated. Although the general performance of the model was worse in this case than

for nuclei in the lower half of the sd shell, it gave insight into the structure of a number

of low-lying 3BAr states. We used this information to analyse the electromagnetic decay

properties of the 345 -[- a' resonances and we found that the J'~ = 1- resonances might

not be interpreted as the head of a K '~ = 0 - band predicted to start in this region.

304 Zs. FEiliJp et al . /Nuclear Physics A 604 (1996) 286-304

Acknowledgements

G.L. and J.C. thank Prof. E Iachel lo for s t imulat ing discussions on the theoret ical

aspects o f this subject. This work was part ly supported by the O T K A (Gran t Nos.

T016638 and T14321 ) and by the U S - H u n g a r i a n Science and Technology Joint Fund

(Gran t No. 3 4 5 / 9 3 ) .

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