Investigation of the decay properties of high-spin two-nucleon states via the28Si(α, dγ) 30P reaction at Eα = 50MeV

1M1 2B "

Nuclear Physiev A329 (1979) 93-108 ; © North-Solland Publlahinp

Co., Amsterdam

Not to be reproduoed by photoprint or microfilm without written permission from the publisher

INVESTIGATION OF THE DECAY PROPERTIES OF HIGH-SPIN TWO-NUCLEON STATES VIA THE "Si(a, dy)3°P REACTION AT Fi, - 50 MeV J. C. VERMEULEN, C. R. BINGHAM t, D. DUKHUIZEN, R. J. DE MELIER and L. W. PUT. Kernfysich Versnelkr Instituut, Ryksunioersiteit Groningen, Groningen, the Netherlands Received 17 April 1979 Abstract : The 28Si(a, dy)"P. reaction was studied at E, - 50 MeV. Outgoing deuterons were detected at 0,b = 15P and d-y angular correlations were measured . For the strongest transition in the (a, d) reaction leading to the F., = 7.20 MeV ; J` = (5, 6, 7) + state the correlations were analysed in the framework of both PWBA and DWBA . Differences between the two approximations were in general found to be too small to distinguish between them except for one case where the DWBA analysis tends to be more exclusive. From the analysis a J` = 5 + value was - found for the E, = 4.34 MeV state which decays with an almost pure E2 transition of 15 f 3 W.u . to the $ - 1 .97 MW level. The decay scheme . and possible J` values of the E, - 7198 f 7 and 6467 t 4 keV states are discussed.

E

NUCLEAR REACTIONS 2sSi(a, dy), E = 50 MeV; measured dy(B) at Bâ n = 15°. 3°P deduced levels, J, x. AE-E surface barrier telescope and Ge(Li) detectors, natural target . PWBA and DWBA analysis.

1. Introdot:don Studies of ((z, d) reactions on sd shell target nuclei at E..,--- 50 MeV have demonstrated that this reaction selectively populates proton-neutron states coupled to maximum spin "). In the lower part of the sd shell (d~s states are found to tie the dominant transfers t-3) and similarly (f ).2, transfers are expected to be the strongest transitions in the upper part of the shell '). The selectivity for the dominant transfers is due to the large negative reaction Q-value which kinematically favors transitions to high-spin states, a good overlap of the relative s-motion of the proton-neutron pair with the relative s-motion in the projectile and the large spectroscopic factors involved in the transitions. Additional support) for the Jar = 7+ assignments for these states in the A = 30-42 nuclei has been the linear dependence of the binding energy ofthe "(f.,)"! states on their mass number A . TheJ` = 7+ assignments in these nuclei are merely based on the arguments mentioned above except for "Sc and 34C1, where the J'° value is well established 6, 20~ In the case of the 2"Si(a, d)3°P and 32S(a, d)34C1 reactions a DWBA analysis has t On leave from the University of Tennessee, Knoxville, Tennessee, USA.

93

94

J. C . VERMEULEN et al .

been carried out 4-'). It was found that the deuteron angular distributions for the strongest transitions (to the E_ = 7.20 and 5.32 MeV states in 3°P and 3401, respectively) are best fit by an L = 6 DWBA curve. In 3°P with a (f.,)2 microscopic form factor description the P = 7 + possibility is the only one that correctly relates the observed strength relative to the lower states. Altogether the Jx = 7 + assignments for the states in question are very plausible but still somewhat model dependent. The aim of the present particle-y-coincidence experiment is (i) to try to get a modelindependent. Jx assignment for the strongly populated states and in particular the state at Ei = 7.20 MeV in 3°P by means of the "Si(a, dy)3°P reaction, (ii) to establish the decay mode of these states and (iii) to check the PWBA assumption that due to the momentum matching these high-spin states are fully aligned by comparing the y-angular correlations with those calculated in a DWBA framework. A different motivation of this study is to investigate the feasibility of the particle-y technique with Ge (Li) counters for states at high excitation and large negative Q-value for which high bombarding energies are required. This technique is standard at lower energy beams at (Tandem) Van der Graaffs where the particle detector usually is placed at either 0° or 180° (see e.g. in ref. e)). Due to the different beam properties this type of experiment has not been extensively used with cyclotron beams of about 50 MeV. The high cross section for the (a, d) reaction (1-2 mb/sr) allows the use of Ge(Li) detectors. In a nucleus like 3°P with high level density a good y-ray energy resolution is required to identify the transitions in the decay. At the same time this high resolution technique in principle enables the measurement of e.g. Doppler shifts. In the present experiment the y-ray decay of the E_ = 7.20 and 6.47 MeV states has been investigated with Ge(Li) detectors in coincidence with deuterons detected at Blab = 15°. The y-yield has been measured at six angles between 30° and 174° with respect to the direction of the recoiling 3°P nucleus. 2. Experimental technique The experiments were carried out using non-analysed cc-particle beams with currents up to 100 nA from the KVI cyclotron. A schematic view of the detection system is given in fig. 1. The target consisted of a 220 pg/cm2 layer of natural silicon on a 10-20 ug/cm2 carbon backing. The angle between the beam and the target was 45° in order to increase the path length for the recoiling nuclei in the target material. The beam was focussed on the target, located at the "centre" of a half-moon shaped scattering chamber (R = 22 cm) and afterwards refocussed with a quadrupole lens into a shielded Faraday cup at a distance of 7 m from the target . At the height of the reaction plane the scattering chamber wall was of 3 mm aluminium in order to keep y-ray absorption low. The scattering chamber contains a target ladder and a rotatable detector holder . This rotation axis coincides with the axis of the turntable for the y-ray detectors. A AE-E counter telescope was used to detect the reaction products. The telescope

Fig . 1 . Schematic view of the experimental setup including the half-moon shaped scattering chamber, the target, the particle detector telescope, and the two rotatable y-ray detectors.

consisted of two silicon barrier detectors with thicknesses of 1 and 5 mm, respectively. In front of the telescope, at a distance of 6.25 cm from the target, a circular collimator with a diameter of 5 mm was placed, thus subtending a solid angle of 5 msr. During the experiments the particle telescope was positioned at 15° with respect to the beam direction, being the best permissible angle with respect to the ratio of (a, d) count rate versus total count rate and total yield. Hardware particle identification yielded a complete separation of proteeps, deuterons and tritons. For the detection of the y-rays two 110 cm' Ge(Li) detectors were employed which were placed at the flat side and at the cylindrical side of the chamber at distances of 12.8 and 23.6 cm from the target, respectively. Both Ge(Li) detectors were shielded with lead from y-rays entering from other directions than the target. Detector efficiencies and energy calibrations in this setup were measured by placing ZZNa and 60Co sources at the target position and with a S6Co source placed close to the detectors. Gamma-ray yields coincident with charged particles were measured at 0 = 106°, 70°, 61°, 46° and 0 = 180°, and at 0 = 74° and 158° with 0 = 0° with respect to the beam direction (see fig. 1). This experiment comprised one week of "effective" beam time . Datawere stored event by event on magnetic tape bymeans of a PDP-15 computer. Each event consisted of a particle identification signal, a particle energy signal, two y-ray energy signals and the output from the time-to-amplitude converters (TACK digitized with the TENNELEC-PACE system . The TAC was started by signals from the AE detector and stopped by a suitably delayed y timing signal. The time spectrum consisted of a main peak corresponding to the true plus random coincidences and a number of satellite peaks due to random coincidences only, enabling to correct the data for accidental events. In. the off-line analysis, software gates were set in the mass, the particle energy and the time spectrum, in order to generate the coincident y-ray spectra. The correction for accidental coincidences was performed by subtracting from this spectrum a spectrum generated with an identical gate setting except for the time gate which was set on a satellite peak.

%

J. C . VERMEULEN et ai .

3. Experimental results Fig. 2 presents a deuteron energy spectrum in coincidence with y-rays with 0.6 < E7 < 4 MeV. The energy resolution of about 200 keV is mainly due to the 1500

c

ae

28

Si(a,dy)30 P coincidence deuteron spectrum Ea =50MeV,9d =15°,er =76 ° , ¢r -180° R

1000

0 u

500 h

300

400 500 600 700 CHANNEL NUMBER Fig . 2 . Energy spectrum of deuterons coincident with gamma rays with 0 .6 < E, < 4 MeV. 28

Si(a .dy) 30P E  -50MeV

coincidence 6,,-15 -

gamma

Fig . 3 . Energy spectra of y-rays coincident with deuterons exciting the E, = 7 .20 and 6 .47 MeV states in 3°p.

2esua, d7)30p

97

kinematicbroadening and the energy spread in the non-analysed beam. The spectrum is dominated by the transition to the 7.20 MeV state and shows further the excitation of the 6.47, 4.92, 4.23 and 1.97 MeV states . A detailed analysis of the separate . d)30p experiment will be presented in a forthcoming paper and is partly 26Si(a, described in ref.'). A coincidence -y-ray spectrum for the decay of the E_ = 7 .20 MeV state, corrected . for accidental coincidences as discussed in sect. 2, is given in the upper part of fig. 3. The indicated cascade order is based on the fact that the E_ = 4.34 MeV state is known to decay to the E_ = 1.97 MeV state and is supported by the decrease of the average velocities of the recoiling 30p nuclei deduced from the observed Doppler shifts. Due to the thin carbon backing the recoiling nuclei partly decay outside the target resulting in a broadening of the y-ray lines. For this reason no attempts have been made to extract lifetimes from the Doppler shifts . From the known excitation energy of the 4343 keV level 6 1 and the energy of the primary transition of 2855 f 6 keV, theexcitation energy of the 7.20 MeV state could be determined as 7198 f 7 keV. The deduced decay scheme for this state is shown in fig. 4; the hranchme ratios are the observed intensities normalized to the primary transition . Angular correlations of the 1 .26,1 .97, 2.37 and 2.86 MeV transitions are presented in figs. 6 and 7 together with the results of the calculations which will be discussed in sect. 5. During the data reduction it was found that electronic cut ofis for one of the detectors introduced an uncertainty in the efficiency for the 0.71 MeV y-ray. This transition has therefore been excluded -from the analysis.

12

14

4921

td')

4343

>

6~ 4-

4230 10 2530 1973

709

a

66

YY ~b~

3~

~% 3s

3+

~£ -90 i,

Fig. 4 . Deduced decay scAenies for the F.~ = 7 .20 and 6 .47 MeV states in 30P . Observed -1-ray energies and intensities normalized to the primary transitions are indicated .

98

J . C . VERMEULEN et al.

For the E_ = 6.47 MeV state the statistics per angle was not sufficient to establish the angular correlation. In the lower part of fig. 3 a coincident y-ray spectrum at 07 = 1580, O.t = 00 is shown in which the transitions consistently found in the other spectra areindicated. With the known excitation energy of the4230 keV level and the measured transition energy of 2237±3 keV the excitation energy of the Ex = 6.47 MeV level is 6467 t 4 keV. From a procedure in which the spectra were squeezed to 100 channel spectra and subsequently summed a more complete decay scheme for this state could be extracted. The lines in the summed spectrum are consistent with the following decay : predominantly (75 %) to the P = 4 - state at 4.23 MeV and the remaining 25 % to the E_ = 4.92 MeV; J* = 5 - [ref.')] and the E_ = 4.34 MeV; P = 5 + states. Allowing only small contributions from higher than quadrupole radiation the possible J-values for the E_ = 6.47 MeV state are restricted to 3, 4, 5 and 6. A decay scheme based on this information is given in fig. 4 (see also sect. 6). No discrete y-ray lines were observed in the coincident spectrum for the decay of the third strongly excited state at 7.37 MeV [ref.')]. 4. Analysis of the angular- correlation Irrespective of the reaction mechanism involved in the population ofthe state with spin J, the particle-y angular correlation function for each y-ray transition observed in the decay of this state can be written as W(ey, 0 y)

_ 2:

(4.1) ftrRK(Yob.)UK(YuoobJCKQ(ey' O y ) . x.Q poo Here the Ra and Ua coefficients, given in ref. 9h are only dependent on the characteristics of the observed y-ray transition and of the unobserved transition preceding the observed transition, respectively . For the primary transition in the cascade Ux = 1 . Further the p.Q coefficients are the so-called statistical tensors which are related to the statistical matrix (see eq. (7) of ref. s)) describing the population of the magnetic substates of the initial state, they depend on the reaction mechanism and on op. .eC,,a, the angle at which the particle is detected. The CaQ's are the renormalized spherical harmonics given by CaQ(0y~ ~Y)

=

4a YjQr 2K+1 (0r,

(4.2)

The factors fi correct the angular correlation for the finite size ofthe y-ray and particle detectors and can be calculated for coaxial Ge(Li) detectors according to the procedure-given by Krane lo)_ The sum over Q ranges from -K to K, where K is even and restricted to 0 5 K 5 min (2L', 2J,), L' being the higher multipolarity of the yradiation. For Op .,,.,.. = 0° or 1800 all pz,. will vanish unless Q ^ 0 and the pao can be completely specified by the occupation of the magnetic substates of the decaying

zaSka, dy) 3 °P

99

state. In this case the angular correlation is cylindrical symmetric around the beam axis. In the plane wave Born approximation (PWBA) the transferred angular momentum, L, is perpendicular to the direction of the recoil momentum, k, irrespective of the angle 0P.r,,c.,., and is equally distributed around it. The recoil direction thus will be axis of cylindrical symmetry 11) and hence the pa, in a coordinate system with the z-axis along the recoil direction will be zero for Q :0 0. The method of analysis in the new coordinate system is the same as for the case OP .,,,,,, = 0 or 180°. In this frame the only magnetic substates that can be populated via an S = 1 transfer reaction like (a, d) are those with m = 0, f 1. Often the magnetic substate population is represented by a Gaussian distribution with p(m) = C exp (-am'), where C is the . normalization constant. $y adopting this type of a distribution one deviates from the strict PWBA method and already approaches the more realistic DWBA case (see e.g. fig. 5). The recoil axis will, however, still be symmetry axis and therefore z-axis in this method . In the distorted wave Born approximation (DWBA~ which is known to give a better description of the particle angular distributions, the distortion of the waves of the ingoing and outgoing particles also destroys the orientation of L with respect to k. In this case L is no longer always perpendicular to k or equally distributed around it 12). These effects tend to break the symmetry of the y-ray distribution and are reflected in the fact that the p,,Q are no longer vanishing for Q :0 0. Under certain conditions 13 ) the recoil axis will also be symmetry axis in DWBA. Since these conditions are not fulfilled in the present case the DWBA results should differ from those obtained in the PWBA analysis. However, the differences are expected to be small at small forward angles because the two approximations should yield identical results at 0,.n,,, e = 0° and 180°. For the Er = 1 .26, 1 .97, 2.37 and 2.86 MeV transitions in the decay of the E_ = 7.20 MeV state the two methods have been compared. hi our PWBA analysis the magnetic substate population of the E_ = 7.20 MeV state was described by the emperical population parameter p(m) = exp (-am'). The parameter a was determined in an iterative way, making use of the information that the 1.97 -. 0.71 transition is a known pure E2 transition . The a-value turned out to have a small effect on TABLE 1 Optical model parameters') used in PWBA calculations on the

a d bound state f7 , 1 particles

V

rs

a

Ws

180.0 85 .0

1 .20 1 .20

0 .61 0 .71

26 .9

1 .26

0 .65

') All depths in MeV, all lengths in fm .

"Ska, d) 3 °P reaction

4Wp

r,'

-a,

V. .o .

r.A .

a. .o.

PN1.OC

85 .0

1 .50 1 .25

0 .515 0 .75

24.0

1 .20

0 .75

0.20 0.54

100

J . C. VERMEULEN et al.

the quality ofthe fit to the data and not on the determination of J -values and mixing ratios. The pa, were calculated for the best value of a = 0 .5 as outlined in ref. I'). In the DWBA case the pa, were obtained from the reaction amplitudes calculated with DWUCK-IV (ref. 14))for the Ex = 7.20state assuming a (f.,)2 transfer and opticalmodel parameters as listed in table 1. For this purpose the program ANGCOR has been written. The procedure is similar to the one described by Rybicki et al. a). The ß's obtained with the program DWUCK-IV t have been used to calculate the transition matrix element as used in eq. (2) of ref. 8). For the analysis of the angular correlations for the second and third transition in the cascade the proper Ux coefficients given by Rose and Brink 9) were inserted in eq. (4.1). For these cases the best 6-values found for the preceding transition(s) were used. Relative values of the most significant elements of tke statistical matrix (see eq. (7) of ref. % referred to the recoil axis, as obtained from the DWBA calculation are shown in fig. 5. The values of the diagonal elements agree very well with the PWBA values calculated for a = 0 .5. This means that the high degree of alignment is retained in DWBA and it supports the use oftr = 0.5 in our PWBA calculations . For increasing values of m the off-diagonal elements get relatively more important and they tend to be asymmetrically distributed ; for m = 2 the distribution is shifted towards negative M' values with the maximum occurring at m' = 1. This reflects the fact that the recoil axis is not longer symmetry axis . For both methods y-ray angular correlations were calculated as a function of the mixing-ratio parameter 6 and the J` values for the initial and final states. Values of 6, P, and Jf were regarded as possible solutions when the corresponding normalized X2 values were within the 0.1 % limit. The uncertainty quoted for the values of 6 have been deduced from the intersection of the X2 versus arctan8 curve with (Q1o + 1)/N, where Q2 is the unnormalized X2 value and N the number of degrees of freedom. The results of these calculations are presented in the next section. Since neither PWBA and DWBA are rigorous theories of substate population the use of the X2 test to reject spins and mixing ratios could, strictly speaking, introduce a model dependency in the results. But as the obtained values of min are close to 1 (figs. 6 and 7) this does not have to be a serious limitation in judging the results. S. Results of the angular correlation analysis 5.1 THE DECAY OF THE E. - 7 .20 MeV STATE

The decay ofthis state through the cascade shown in fig. 4 has been analysed both in the modified PWBA and DWBA. As mentioned in sect . 3 the E,, = 0.71 MeV t It should be noted that in DWUCK-IV the ß's apparently are calculated for 0 - 180° for the outgoing particle and not for 0 = 0° as one would expect. The phase of these ß's was changed to correspond with the actual situation in this experiment, ¢d = 0° (see also fig . 1) .

101 18 Si(a, d7)30p

transition has been omitted from the analysis. The formalism and the calculation of the pxq have been discussed in sect. 4. Since the two-nucleon transfer angular distribution for the E_ = 7.20 MeV state is only fit by an L = 6transfer only P _ (5, 6, 7) + have been consdrred.The lifetime of the E_ =. 4.34 MeV level, Tm = 130±50 is (ref. '% allows only small contributions from higher than quadrupole radiation for the decay to the known e) P = 3+ state at E_ = 1 .97 MeV.This combined with the unnatural parity ofthe 4.34 MeV state' s) restricts its J` values to 3+, 4- and 5 + . The decay ofthe E_ = 1.97 MeV level to the ground state and to the E_ = 0 .71 MeV level, both with P = 1 + is well known from the Z9Si(p, y)30P reaction and the mixing ratios b = 0.02±0.03 and -0.01 ±0.02, respectively, as given in ref.') have been used for comparison an internal check on the total procedure. The fits to the data and the corresponding X' distributions for the PWBA and DWBA are given in figs. 6 and 7, respectively. 5.1.1. The PWBA analysis. The E_ = 1.97 UAv statp The angular correlation analysis for the ground state . ansition gives as possible 6-values b = 0.27±0.30 and b = 1.9±1.2. The first one :s in good agreement with the value given in ref. e~ the second one can be rejected on basis ofthis comparison . The same holds for the transition to the E_ = 0.71 MeV level with possible 6-values; 6 = 0.07±0.11 and 6 = 3.2±ó :é. _ The E, = 4.34 MeVstate. For the Jx = 3+ possibility the analysis gives solutions for b = -1 .9±° :ó and 6 = 0.22±0.16. From the lifetime it follows that the total width F = 5.1 ±2.0 meV. The M1 strengths corresponding to these 6-values are 4.0±2.6 and 17±7 mW.u., respectively . Since the recommended upper limit (RUL) for an isospin retarded M1 transition is 30 mW.u. both possibilities can be accepted, although the second possibility would correspond to one of the strongest known retarded M1 strengths ") . A recent analysis of the 3'S(d, a)3 °P reaction 'e) at E d = 2.5 - 5.2 MeV allows forthis state Jx = 1 +, 2+, 4 +, 5+ ,1 -, 3 -,4--and 5 - but excludes the J` = 3 + possibility. For the J` = 4- possibility one 6-value is found : b = -0.27±0.07 corresponding to an M2 strength of 32±15 W.u. Since this value exceeds the RUL of 0.1 W.u. this possibility is rejected From the 6-values resulting from the analysis for the J11 = 5+ possibility only the value of S = 0.02±0.09 should be considered . The other 6-values would correspond to a minimal M3 strength of 2 x 10' W.u. The small value of 6-indicates that the 4.34 MeV state decays with an almost pure E2 y-ray with a strength of 15 ± 3 W.U. The E_ = 7.20 MeV state. As mentioned before the P values to be considered are 5+ , 6+ and 7 +. The lifetime ofthis state is known to fall in the range 3 P< Tm < 10ns ; the lower limit follows from the('He, py) work of Smulders et al.' s), the upper one is based upon the absence of a tail in the time spectrum measured in this experiment. For the J= = 3 + solution for the E_ = 4.34 MeV state only the P = 5 + value was

102

J . C. VERMEULEN et al.

3°P,

28

d nSi(a,dy)

E x =720MeV . B=15°

z - axis along recoil direction

o Cr 1 .0

I

DWBA

É

a

E

0.5

-4

-2

0

2

4 =4

-2

0

2

4 t4

PWBA (c "0.5)

-2

0

2

4

Fig . 5 . Relative values of statistical matrix elements referred to the recoil axis . Results are shown for DWBA and PWBA . Values for negative m are related to the presented results by Ip_ ., _ ..I = {p,, e1 .

as o Lo 0 0.5 0.5 1 .4

m 3

1 .2

1 .0

ae

0.6

.4 0

l:,

I

~V . 1

~1,i,

L97

o

/0

1 .97

EV-L26YW T 71 I~

I~

coste 0.5

1.0 . o

0.5

Lo 0

1

Ti

WV E L9

100

1 .0 o

1

l

434

a'

ET72 .J YW

.

(51

.20 7

ET6YoV

e

720 T E "2»BY@V 11r)

Un

.. axunr

a1x

_

~ ~ %{

~~,

aix _

l..ti

ms

_

s _

7'u

-90

0

.90 -90

0

.90 -90 0 .90 -90 arctan a (deg.)

0

*90 -90

0

.90

Fig. 6. Deuteron-y ray angular correlations observed in the decay of the F,, = 7.20 MeV state in 3oP as function of the angle B relative to the recoil axis . Experimental points at 01, = 0° and 180° are indicated by triangles and circles, respectively . The curves through the data points represent PWBA calculations at the physically most likely values of the mixing ratio 6 . The normalized X' values and the 0.1 % Confidence limit are shown in the lower part of the figure . considered for the E_ = 7 .20 MeV level . For this combination two 8-valves were found : 8 = 0.11 f 0.05 and S = 4 .5 f 1 .8 . The latter value corresponds to an almost pure M3 transition and will therefore be excluded . The P = 3+ possibility for the 4 .34 MeV state can thus not be rejected on basis of the angular correlation for the 7 .20 -+ 4.34 transition .

saSi(a, dy)"P 28

Si(a,dy) 3O P

I -90 I

I

I

I

0

I

I

EQ=50MeV

I

I

" 90

arctan 8 (deg.)

100

N X

7.20

5"

4.34

3'

I Ey296MeV

10

I

180

103

ed015*

l'

120

I

60

I 0

N `60

I

8y(deg.)

120 PIkBA

_ _

1 .4

DWBA

1 .2 1 .0 0.8

_m

0.6 3 0.4 f " 180--ht -90

0.

#90

arctan S (deg.)

180

120

60

0

8y (deg.)

0.2

" 0-

r 60

120

160

Fig. 7 . Deuteron-y ray angular correlation for the decay of the E, - 7 .20 MeV state in 30P as function of the angle 0., relative to the beam axis . The curves through the data points represent DWBA (solid . curves) and PWBA (dash-dot curves) calculations . See also caption of fig. 6 .

The other solution for the E_ = 4.34 MeV state (J'° = 5 +) allows all three J` values for the E_ = 7.20 MeV level. The following possibilities were found : (i) For Jx = 5+ two solutions with b = -1.4±0 .3 and 6 = 0.41±0.11. (ii) For Jx = 6+ one solution with 6 = -022±0.05. (iii) Two solutions for Jx = 7+ : 6 = 0.11 ±0.06 and 6 = 6.3 ±2.2. The latter corresponds to an almost pure M3 transition and will therefore be rejected .

104

J . C. VERMEULEN et ai.

5.1 .2. Vie DWBA analysis .

The calculatiogs were carried out with the px, corresponding to an (fj)i=6 transfer. In general the optimal 6-values extracted are in agreement with the ones obtained in the PWBA. The most interesting difference between the two approximations is the shift in the angular distribution pattern by about five degrees. This shift in seems to be independent ofthe J-values in the transition . fhe changes tjie 6-values might be related to this. shift. Furthermore the amplitude of the angular correlation pattern seems in general to be larger in the DWBA . For the transition of the Ei = 7.20 MeV state to the 4.34 MeV state no new information as far as exclusion of J` or b values is obtained, except for the case in which it is assumed that J~(4.34) = 3 + . In that case the X' distribution only barely gets within the 0.1 % confidence level and from the comparison with the other possibilities this P = 3 + value for the 4.34 MeV level becomes very unlikely . Since DWBA has been proven to be a better description ofthe reaction mechanism of particle transfer reactions than PWBA the analysis of particle-y angular correlations should preferably be carried out in DWBA. This preference, however, is not clearly borne out by the comparison of the two approximations in the present work . Much better statistics would be required to make a clear distinction (see fig. 7). Based on the preference for DWBA we are tempted to exclude the J` = 3 + value for the E_ = 4.34 MeV state from the analysis of the present data, thus leaving J1 = 5+ as only possible Jx value for this state. Support for this statement is found in recent work of Spijkervet 18), which allows several P values except Jx = 3+ (see subsect. 5.1.1). 6. Discoenion Although the present experiment has not given a unique confirmation of the J` = 7+ assignment for the states populated via the strongest transitions in the (a, d) reaction on target nuclei in the upper part of the sd shell, P = 7+ remains the most plausible one in view of the arguments mentioned in sect. 1 . The decay of this state differs from that to be expected in a simple shell model with an (f.,)2 configuration. Since the E_ = 1.97 MeV ; J9 = 3 + state is well described 9) in terms of sd configurations and the electromagnetic operators are single-particle operators it was expected that the E_ = 7.20 MeV state would decay through a (dj~s level, for which the Jx = 5 - , E_ = 4.92 MeV state would be a good candidate. The transition in case of J1 = 7+ would than be of M2 character and because 3°P 'is a self-conjugated nucleus this transition would be retarded . If this transition had the strength of the RUL of 0.1 W.u. its lifetime would be of the order of 1 ns. On the other hand the wave function of the E_ = 4.34 MeV state, to which the E_ ;-- 7.20 MeV level decays, is certainly not predominantly of two-particle character as follows from the weak excitation in the (a, d) reaction and because it requires at least two d,} holes in order to make a P = 5+ state with (sd) shell particles only .

3es 4a,

dy)30 p

105

The small cross section for this state in the 2aSi(a, d)3°P reaction could be due to at least 2p2h components in the "Si ground state, small (f )`s components in the wave function ofthe E_ = 4.34 MeV state and/or two-step processes. The strong excitation of this state in the 32S(d, a)3°P reaction') indicates a strong hole character for this state and favours the first argument for explaining the small (a, d) cross section. The hole character is consistent with the decay of the E_ = 4.34 MeV state with a 15 t3 W.u. strong E2 transition. Shell-model wave functions calculated with the FPSDI interaction 19} predict an E2 strength of 5 W.u. The fact that the decay of the E_ = 7.20 MeV level proceeds through a quite complicated state with a large (d t) -2 components suggests a comparison with the decay of the J; = 7+ state in 3401 that was studied by Baumann et al. 2°) by means of the 2'Al(12C, any)34Cl reaction. In 3401 the isospin retarded M2 transition to the 5 - state is expected to compete more favourably with the 7+ -" 5+ transition because the excitation energies of the P = 7+ and J` = 5- states have decreased whereas that of the JR = 5+ state with strong (dd-2 components should be increased. Baumann et al., however, did not observe the.7+ -+ 5- transition. In 3401 the E_ = 5.32 MeV; Jx = 7+ state decays to the E_ = 4.82 MeV; P = 5+ state which is probably of (f~pt) character 2') and to the E_ = 4.74 MeV ; J = 6 state. In contrast to the E_ = 4.34 MeV, J` = 5+ state in 3°P this J` = 5+ state is strongly excited in the 32S(a, d)34C1 reaction 4. '), supporting the two particle character; the J = 6 state is only excited with moderate strength . In 3°P the E_ = 6.47 MeV state isstrongly seen in the 28Si(a, d)3o.P reaction'). From the fact that the decay of E_ = 7.20 MeV state in 3°P does not proceed through the 6.47 MeV state, we may conclude that the 6.47 MeV state in 3°P is not

-24

Fig. 8 . Q-value systematics for (a, d) reactions exciting (assumed) J` - 6 - and 7 * stata (see also ref. `)) .

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the counterpart of the EI = 4.82 MeV; P = 5+ state in 3401 with probable fop * character 2°). The hole state at 4.34 MeV in 3°P is also not likely to have this character either, but the E_ = 7.37 MeV state is a probable candidate since it is also strongly excited in the 28Si(a, d)3°P reaction 4" ') and has, based on the (a, d) angular distributions 7,h Jx = 5+. The decay ofthe E_ = 6.47 MeV state in 3°P resembles that of the J = 6; Ex = 4.74 MeV state in 3401 ; it also branches mainly to 4- and 5 - states . In 3401 the decay of the 4.74 MeV to the 0.15 MeV ; Jx = 3 + level will favour a x = - assignment because an E3 transition is more likely than an isospin retarded M3. This assignment is also supported by the fact that the (a, d) Q-value for the transition to this state is in nice agreementwith the linear relation between the ¢values for(a, d) reactions strongly exciting (assumed) J* = 6 - states in some sd shell nuclei 4) (see fig. 8} These states are believed to be of (d; If,) character. The validity of the Q-value argument has been suggested by DelVecchio et al. 4) for possible ( 7+ , T-0 states (see also fig. 8) and by Jahn et al. s1) for (fi)2 + T=1 and (fed )s - ,T=1 states. The strong excitation of the E_ = 6.47 MeV state in the 28Si(a, d)3 P reaction can be explained if considerable (d t) -2 admixtures are assumed in the 28Si ground state wave function . These (d-,)-2 components are expected to decrease in amplitude for 3401 which is in agreement with the weaker excitation of the E_ = 4.74 MeV state in 3401 . In 3401 the decay of the 5.32 MeV, J` = 7+ state to the J" = 5 + and 6" states occurs with comparable energies 491 and 572 keV, respectively . Since in 3°P the decay of the 7.20 to the J` = 5 + is energetically so much favoured (2.85 compared to 0.73 MeV) no transition to the E_ = 6.47 MeV is expected to be observed in this experiment . Although the E_ = 7.37 MeV; J` = 5 + state is strongly excited in the 28Si(a, d)3°p reaction no y-ray decay of this state has been observed. If the decay would proceed analogously to that of the Ex = 4.82 MeV state in 34C1, one would expect transitions to the E_ = 4.23 MeV ; J` = 4- state with Ey = 3.14 MeV and to the E,, = 1.97 MeV; Jx = 3 + state with Eq = 5.40 MeV. The latter transition would have the largest strength, but its y-energy is outside our detection range. Another possibility is that the 7.37 MeV state decays by proton emission, but this seems to be less likely because of the incompatibilities of the wave functions. 7. Conclusions

As mentioned in the introduction the aim of the experiment was four-fold. In this section a comparison will be made between the results and the original goals. In the attempt to get a model-independent P assignment for the strongest populated states in (a, d) reactions on target nuclei in the upper part of the sd shell the 28 Si(a, dy) 3°P reaction was studied. From the particle-y angular correlation data no distinction between a P = 5+, 6+ or 7+ assignment could be made for the E_ = 7.20 MeV state.

11%j( a'

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107

Excitation energies of this state and of another fairly strongly populated state in were determined as 7198 t 7 and 6467 t4 keV, respectively. The decay of these states were found to proceed via only a few transitions, which in the case of the E_ = 7.20 MeV level are of almost pure E2 character. For the E_ = 4.34 MeV state, populated in the decay of the E_ = 7.20 MeV level, a J` = 5+ assignment was obtained. The decay of this state with an E2 transition of 15 W.u. indicates its strong collective character, which is supported by the strong excitation of this state in the 32S(d, a) 3°P reaction indicating the presence of large components of at least 2h nature in the 4.34 MeV wave function. Comparison ofthe decay properties of states in 3oP and "Cl combined with the systematics of Q-values for J= = 6- states in sd shell nuclei leads to the suggestions that in 3 °P the E_ = 6.47 MeV state has Jx = 6 - and has a d- 1(sd)Zf., character. For the E_ = 7.37 MeV state the comparison leads to a predominant (f~pds+ configuration in the wave function . Both the PWBA and DWBA analyses yield a magnetic substate population of the E_ = 7.20 MeV state predominated by m = 0 and m = t 1. The symmetry axis in the DWBA treatment is rotated over about 5° with respect to the recoil direction. Further it seems that in general the amplitude of the DWBA angular correlation at 6âb = 15° is larger than for PWBA. In most cases this has only slight effects on the values of 6 and X' except for the 5+ -" 3* possibility for the 7.20 -+ 4.34 transition where the PWBA gives XZ values well within the 0.1 % confidence level whereas the DWBA calculation almost excludes this possibility. The result ofthe DWBA calculation is supported by the recent result of Spijkervet ' s), who excludes P = 3 + for this state, such that in combination with this work JR = 5+ remains as the only possibility. Altogether the DWBA effects have only small influence on the analysis of the angular correlation and therefore the analysis remains to a high extent modelindependent. An experimental confirmation of, the DWBA effects would require much better statistics than obtained in this work or perhaps an experiment at a much larger angle for the outgoing deuteron . Such an experiment would, however, be hampered by a considerable reduced count rate (see sect. 2), The DWBA effects have also been studied and demonstrated in other reactions like inelastic scattering (see e.g. ref. s2)) and single nucleon transfer reactions (see e.g. ref. 23)) . The decay study of the E_ = 7.20 and 6.47 MeV states have demonstrated that the application of particle-y coincidence techniques at cyclotrons is feasible for strongly excited states, provided that the beam quality is such 'that not too much background is produced during beam transport in the vicinity of the scattering chamber. The refocussing of the beam after passage of the,target was of some help in this respect. For angular correlation measurements using Ge(Li) detectors cross sections of at least 1 mb/sr seem to be required in order to collect enough statistics in a reasonable time. Sop

We would like to acknowledge the help and support of the technicâl and administrative staff of the KVI during the several stages of this experiment. We are indebted

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to Drs. D. O. Boerma, P. J. M. Smulders and A. L. Spijkervet for making their results available before publication. This work has been perforated as part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) with financial support of the Nederlandse Stichting voor Zuiver Wetenschappelijk Onderzoek (ZWO). References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23)

E. Rivet, P. H. Pehl, J. Cerny and B. G. Harvey, Phys. Rev. 141 (1966) 1021 C. C. Lu, M. S. Zisnoan and B. G. Harvey, Phys. Rev. 186 (1969) 1086 A. van der Woude and R. J. de Meijer, Nucl . Phys . A258 (1976) 199 R. M . Del Vecchio, R. T. Kouzes and R. Sherr, Nucl. Phys . A265 (1976) 220 H. Nann, W. S. Chien, A. Saha and B. H. Wildenthal, Phys . Rev. C15 (1977) 1959 P. M. Endt and C. van der Leun, Nucl. Phys . A310 (1978) 1 and refs . therein J. C. Vermeulen et al ., to be published: R. J. de Mejer, J. C. Vermeulen, L. W. Put and J. Akkerman, KVI Annual Report (1977) 21 (unpublished) and refs . therein F. Rybicki, T. Tamura and G. R. Satchler, Nucl . Phys . A146 (1970) 659 . H. J. Rose and D. M. Brink, Rev. Mod. Phys. 39 (1967) 306 K. S. Krane, Nucl . Instr. 98 (1972) 105 A. R. Poletti and E. K. Warburton, Phys . Rev. 137 (1965) B595 G. R. Satchler and W. Tobocman, Phys . Rev. 118 (1960) 1566 ; R. Huby, M. Y. Refai and G. R. Satchler, Nucl . Phys . 9 (1958/1959) 94 G. R. Satchler, Nucl . Phys . 18 (1960) 110 P. D. Kunz, University of Colorado (unpublished) D. O. Boerma et al., Nucl . Phys. A255 (1975) 275 P. M. Smulders and D. O. Boerma, private communication P. M. Endt and C. van der Leun, Nucl . Phys. A235 (1974) 28 A. L. Spillcervet, Thesis, Groningen, (1978) (unpublished) B. H. Wildenthal, J. B. McGrory, E. C. Halbert and H. D. Graber, Phys. Rev. C4 (1971) 1708 P. Baumann et al ., Phys . Rev. CIS (1978) 247 R. Jahn et al., Phys. Rev. C18 (1978) 9 W. W. Eidson, J. G. Cramer, D. E. Blatchley and R. D. Bent, Nucl. Phys. 55 (1964) 613 R. N. Boyd, H. Clement and G. D. Gunn, Nucl . Phys. A283 (1977) 434