Spin assignments in 33S from the reaction 32S(d,p)33S

I 1.E.I: I

Nuclear Physics 82 (1966) 574--592; (~) North-Holland Publishing Co., Amsterdam

3.A

Not to be reproduced by photoprint or microfilmwithout writtenpermissionfrom the publisher

I

S P I N A S S I G N M E N T S I N aas F R O M T H E R E A C T I O N asS(d, p)aas J. M. O'DELL t, R. W. KRONE and F. W. PROSSER, Jr. Department of Physics, University of Kansas, Lawrence, Kansas t t Received 22 February 1966 Abstract: The gamma rays emitted in the decay of several of the low-lying states of 3aS have been observed in coincidence with the proton groups populating these states in the reaction asS(d, p) aas. Angular correlations obtained between the protons, detected at 0 ° with respect to the incident beam, and the gamma rays were analysed by the method of Litherland and Ferguson to determine the spins and population parameters of the 1.965, 2.313, 2.937 and 3.224 MeV states of asS, as well as the multipole mixing ratios and branching ratios of the gamma-ray transitions. The following results were obtained using a deuteron bombardment energy Ea = 2.541 MeV. The 3.224 MeV state has spin t and decays to the ground state and the first excited state. The 2.937 MeV state has spin ~ and decays with equal intensities to the ground state and the 1.965 MeV state. The 2.313 MeV state has a probable spin t and decays to the ground state and the first excited state. The 1.965 MeV state has spin t and decays only to the ground state. There is some evidence for the presence of a state at 1.35 MeV, which may be the 6+ state predicted at 1.38 MeV. It appears to decay by a two step transition with F-ray energies of 0.51 and 0.84 MeV; this, together with the weakness of the proton group, causes the identification to remain tentative at present. NUCLEAR REACTIONS 3sS(d, PT); E = 2.0-3.0 MeV, measured Ep, Er, py-coin, pT(0). 8aS deduced levels J, ~r. Natural target.

1. InUoducfion The 33S nucleus is one of the m e d i u m - l i g h t nuclei with incomplete i n f o r m a t i o n a b o u t the level parameters. T h e energies o f m a n y levels are well k n o w n but, as recently as 1964, the spectroscopic properties of only a few of these levels h a d been established 1, 2). Recent shell m o d e l calculations o n nuclei with mass n u m b e r .4 = 29 to 40 by G l a u d e m a n s et al. 3) have led to definite predictions o f the spin a n d excitation energy of some o f the positive parity states expected. These are generally in fair agreement with experimental observations. A n o t a b l e exception is the prediction o f a state i n 3aS at 1.38 M e V having spin ~ a n d positive parity. This state c a n n o t be identified with the first excited state at 0.841 MeV a n d differs significantly i n energy f r o m the next k n o w n state at 1.965 MeV. t Present address: Universityof California, Lawrence Radiation Laboratory, Livermore California. tt Work supported in part by the U.S. Atomic Energy Commission. 574

a~S(d, p)SSS REACTION

575

Relatively few processes are available that can be used conveniently to obtain detailed information about the 33S nucleus. The majority of the experimental work has been done using either the 32S(d, p) or the 32S(n, ~)33S reactions. The (d, p) reaction is a powerful tool for determining the orbital angular momentum In of the captured neutron, which in turn allows the determination of the parity and limits on the spin of the excited states. Since the energies of the various proton groups can be obtained with great accuracy and a high degree of resolution, this process is ideally suited to establish not only the existence, but also the energies of the states in the residual nucleus. The neutron capture reaction, on the other hand, is capable of yielding considerable information about the decay properties of the levels in 33S. Several different cascades have been identified, the two most prominent ones passing through the l = 1 negative parity states at 5.71 and 3.22 MeV. The decay properties for these states have been established and their spins and parities determined from conventional angular correlation studies. Unfortunately, this reaction does not show any significant cascades to any of the low-lying positive parity states and has, therefore, not been useful in obtaining spectroscopic information about these states. The present experiments were undertaken to attempt a more detailed study of the properties of the 3.224, 2.937 and 1.965 MeV levels of 33S and to search for the theoretically predicted 1.38 MeV level. This work was done by investigating the gamma-ray spectra in coincidence with the proton groups resulting from the 32S(d, p)33 S reaction and by analysing the proton-gamma angular correlations for various geometrical arrangements 4). An obvious benefit of this method is, of course, that one observes only the gamma radiation resulting from the excitation of a particular level in the nucleus. In spite of this and many other advantages, this procedure has so far been little exploited. The principal reason for failing to make this kind of observation has been the experimental difficulties involved. Deuteron induced reactions are almost always accompanied by a strong background of neutrons, either from competing reactions or from the beam striking parts of the beam tube extension. These neutrons, in turn, create an enormous background of gamma radiation which in part results from the activation of the gamma-ray detector itself. Only by using sophisticated counting equipment has it been possible to observe the relatively weak gamma radiation of interest. Standard techniques in gamma-ray spectroscopy may, of course, be used to obtain the decay schemes and branching ratios of the spectra observed. An analysis of the proton-gamma correlations is, however, simple only for special geometrical arrangements. It was shown by Litherland and Ferguson 5) that it is possible to obtain important structure information, independent of the reaction mechanism involved, if one observes the proton groups with an axially symmetrical counter placed either at 0 ° or 180° with respect to the beam direction. This method was used to determine the spin of some of the excited states of 33S and the multipole mixing parameters of the gamma radiation emitted and to give an estimate of the relative importance of direct interaction and compound nucleus formation to the reaction cross section.

576

J . M . O'DELL et al.

2. Experimental Procedure The experiments were performed using deuterons with energies ranging between 2.0 and 3.0 MeV from the University of Kansas Van de Graaff generator. Beam currents larger than 0.5 #A could not be used because of target deterioration and the deuteron induced neutron flux resulting from the 1 2 C ( d , n ) 1 aN reaction. The beam was defined by a series of collimators consisting of tantalum apertures. This collimating system limited the beam to be 2.5 mm in diam at the target. The build-up of carbon inside the target chamber was further minimized by the use of three liquid nitrogen cold traps, Viton O-rings and glass, rather than plexiglas, windows for all viewing ports. PROTON SPECTRUM 10K

32

3.224

33

S (d,p)S

Ed: 2.541 MeV 8K

8p : 130 °

Z < 6K 'r U ¢v

2.937

~ 4K

2.313

z O

u 2K

1

•

/t

% 0

20

40

60

80

100

120

140

CHANNEL NUMBER Fig. I. Typical spectrum of the proton groups from the deuteron bombardment of a natural sulphur target. T h e asS p r o t o n p e a k s are identified by t h e excitation energies o f t h e levels to w h i c h t h e y correspond. T h e g r o u n d state p r o t o n g r o u p f r o m the a*S(d, p)s6S reaction is indicated.

Targets were prepared by evaporating natural Sb2S a on gold leaf foils supported by tantalum frames. Although no attempt was made to measure the thickness of each target, it is estimated on the basis of sample weighings that a typical target was approximately 100#g/cm z thick. Experience showed that target thickness did not affect noticeably the resolution of the proton groups. All proton spectra were obtained with a 100 mm 2 0 R T E C silicon surface barrier detector which was placed 3.1 cm from the centre of the target. The half angle subtended by the detector was 0.180 rad. The proton detector was mounted on a movable arm inside the target chamber, which could be rotated through 360 °. The deuterons were stopped by a 25 #m thick tantalum foil placed in front of the proton

577

3sS(d, p)SSs REACTION

detector. This tantalum foil limited the resolution of the detector to 130 keV F W H M . Fig. 1 shows a typical proton spectrum taken with the proton detector at 130° and E d = 2.541 MeV. There appears to be no significant broadening of the peak resulting from the proton group leading to the 2.937 MeV level of 3aS. It was assumed, therefore, that any contribution to this group from the 2.970 and 2.869 MeV levels was less than the statistical accuracy of the experiments. The gamma-ray detector was a 7.6 cm x 7.6 cm NaI(T1) crystal, with its front face 9 cm from the centre of the target. The detector was mounted on a horizontal arm pivoted about the vertical axis of a semi-circular table which served as the angular correlation table. The position of the vertical axis of the target chamber was measured to be within _ 2 mm of the vertical axis of the correlation table. The isotropy of the system was checked by observing the angular distribution of the gamma rays from

GAMMA--RAY

IOK

SPECTRUM

SS2(,IS33 E = 2.541 MeV

z 8K Z

- -

x 1,~0-

-

d

"I-

u 6K

~_4K 0

U

2K

,

0.84 i~'

20

40

,

,

,

,

60

80

100

120

CHANNEL

~ °°°°'~'°~'~°°~' .... 140

160

180

NUMBER

Fig. 2. Gamma-ray spectrum from the bombardment of a natural sulphur target using 2.541 MeV deuterons. The most prominent peaks in the spectrum are identified.

the ½+ level of 33S at 0.841 MeV. This angular distribution served as a monitor each time angular distributions of the gamma rays from the other levels were taken. This method of checking the isotropy of the target arrangement indicated that the system was isotropic within the statistical errors, which were approximately + 2 ~o. The pulses originating from the gamma-ray detector were routed into separate quarters of a Technical Measurements Corporation Model 404 multi-channel analyser. In order to record only those gamma rays which were in coincidence with a specific proton group, the inputs of the analyser were gated subject to the following requirements: all proton pulses were examined first by Hamner "jitter-free" single channel pulse-height analysers with their windows set to correspond to the proton energies of interest. The coincidence units then produced the gating pulses whenever

~. hi. O'DELL et al.

578

3.224

2.937 MeV LEVEL

A~eV LEVEL

1400

300

1200

).97

w Z Z 1000

0.84

"lu

_ 200

~. 800

1.97

Z u

600

8 2.38

J

100

400

_•!I ----~~t

2.94

200

I

20

40 CHANNEL

20

60 80 NUMBER

60 80 NUMBER

1.965 MeV LEVEL

Z313 MeV LEVEL 300

300 0.84

Z Z .< -r U u.i a..

40 CHANNEL

200

2OO

1.47

1.97

Z o

o

L) 100

lOO

\ 2.31

--

-- I " ~ " ~ 1 20 40 CHANNEL

I

60 NUMBER

80

20

40 CHANNEL

6O 8O NUMBER

Fig 3. Gamma ray coincidence spectra for the 3.224, 2.937, 2.313 and 1.965 MoV levels in aaS.

8~S(d, p)S3S REACTION

579

a coincidence was obtained between a g a m m a ray and a proton within the required energy range. This method permitted simultaneous observation of four different coincidence spectra. In actual practice it was found that a resolving time 2~ = 20 nsec resulted in a ten to one ratio of true to chance coincidences. This is well within the capability of the H a m n e r coincidence system used. The information accumulated in the multi-channel analyser was recorded on punched paper tape and then transferred to punched cards. An I.B.M. 1620 computer was used for simple data reduction and, in conjunction with the I.B.M. Autoplotter system, to prepare accurate graphs of the gamma-ray spectra. It was originally intended to utilize the (d, pv) process to test the pertinence of direct reaction theories over this range of proton energies and mass number. F o r this reason a large number of p r o t o n - g a m m a correlations were observed with the proton detector at angles other than 0 ° and at deuteron energies corresponding to maxima in the a2S(d, p) reaction 6). An attempt to interpret these correlations in terms of the reaction mechanism involved has been only moderately successful 7). All the data reported in the present paper were taken at a deuteron energy of 2.541 MeV and with the proton detector located at 0 ° with respect to the beam axis. At each angle the number of proton pulses for each group, the number of gammaray pulses, the number of resulting coincidences, the length of time necessary to accumulate the gamma-ray spectrum and the charge integrated on the target chamber were recorded. To check the proper functioning of the system, the gamma-ray pulses were delayed an additional 0.5/~sec at least twice during each correlation run and the same data as above were recorded. The angular distribution of the g a m m a rays emitted by the decay of the 0.841 MeV level was determined as well and used to check isotropy, target deterioration and electronic drift. Since only four of the five spectra of interest could be recorded during any given run a number of the correlation runs were repeated routinely, permitting a check on the consistency of the data. As soon as any angular correlation was completed, the computer was used to calculate resolving times, to normalize the number of true coincidences to a constant number of proton counts for each angle and to compute the rms deviation of the number of true coincidences. Chance spectra obtained by introducing an additional 0.5 psec delay were used to calculate the ratio of chance coincidences in each gamma-ray spectrum to the total number of counts in the chance spectrum. This ratio was used to correct each gamma-ray spectrum for chance coincidences. Fig. 2 shows a typical gamma-ray spectrum obtained without the coincidence requirement. Fig. 3 illustrates how much the various gamma-ray spectra are simplified with the coincidence requirement in force. 3. Results

The analysis of the gamma-ray angular correlations observed in these experiments is most readily accomplished by using the population parameter method described by Litherland and Ferguson 5). These authors have shown that in a nuclear reaction

580

"$. M. O'DELL e t al.

of the form C(hl, h2)B* only a limited number of magnetic substates of B* will be populated, provided that the emergent particle group h 2 is observed along the beam axis. For this case the angular distribution of the gamma rays resulting from the decay of the state B* whose population parameters are P(y) to a state C is given by

W(O) = ~ AkPk(cos 0), with the coefficients Ak expressed in terms of the interfering multipolarities, L and L', of the gamma radiation, the multipole mixing parameter 6 and the solid angle correction Qk. The possible magnetic substates 7 that may be populated are obtained by adding vectorially the spin of the target nucleus to the intrinsic spins of the incident and emergent particles. Since a2S has zero spin one expects, therefore, two values, i.e., P(½) and P(½). This method has recently been exploited by various authors 4, a,9) who have shown that this constitutes a powerful method to obtain spectroscopic information about many low-lying states. The gamma-ray distributions resulting from (d, p) reactions may also be analysed by assuming a direct interaction mechanism. Satchler and Tobocman have shown xo) that, using the plane wave approximation, the angular distribution can again be written in the simple form W(O) = ~ 9kPk(COS O) provided that the protons are observed along the symmetry axis. It may be demonstrated ~) that this result is independent of possible distortion effects in the stripping mechanism assumed, provided the target nucleus has spin zero and subject to the assumptions of ref. lo). The values of the coefficients gk can therefore always be related to the population parameters P(?). The stripping theory, however, invokes the additional requirement that only that substate may be populated which corresponds to the projection quantum number of the captured particle. In the present case the observed value of the population of the ½ substate sets, therefore, the minimum contribution of compound nucleus formation to the reaction cross section. 3.1. T H E 3.224 MeV L E V E L

Of the excited states in 33S that were investigated, the spin and parity of only the 3.224 MeV level is known from previous experiments. Studying the 32S(d, p?) reaction, Chase 11) was able to identify transitions to the ground state and first excited state of 33S. The decay involves, therefore, the only three bound states in the nucleus with well-established assignments of spin and parity. Thus the study of the 3.224 MeV level serves as a good illustration of the method of analysis used. Data were obtained with a deuteron bombarding energy of 2.541 MeV and with the proton detector placed at 0 ° with respect to the beam axis. Spectra were observed with the gamma ray detector placed at 30°, 45 °, 60 °, 90 °, 105°, 135° and 150 ° with respect to the beam axis. The gamma-ray angular correlations observed are shown in fig. 4. The uncertainty of the experimental points, estimated to be + 10 ~, is primarily caused by errors introduced in "unfolding" the gamma-ray spectra. The procedure followed in

a~S(d, p)aaS REACTION

581

fitting the data to the Legendre polynomical expansion here, as in all further cases, was to attempt least squares fits with kin, X successively 0, 2, 4 and 6 and to retain the highest order which resulted in a significant improvement in the goodness-of-fit parameter. For this case, no improvement was found beyond kmax = 2, as expected, and the resulting coefficients were A2 = 0.20+0.05 and A2 = - 0 . 2 4 + 0 . 0 8 for the 3.22 MeV and 2.38 MeV gamma rays, respectively. The fitted value of .40 and the efficiency of the gamma-ray spectrometer were used to obtain the relative intensities

j.i/i

6

5 Io

/J

/~"/'/ ±

iI

"~- T

3.224-~ 0

~

~

o

~J 3-

1

L.J Z w r~

i

0.841"--~0

Z U

0

1.0

ANGULAR

DISTRIBUTIONS

3.224-MeV

LEVEL

I

i

I

i

0.8

0.6

0.4

0.2

I i

I

I

I

I

0.0

0.2

0.4

0.6

0.8

1.0

cos2e Fig. 4. Angular distributions for the three gamma rays arising from the decay of the 3.224 MeV level in s3S.

of the cascades observed. The computed values of 36_+ 3 % and 64 + 3 % for the 3.224 --, 0 and 3.224 ~ 0.841 transitions, respectively, are in good agreement with the earlier results of 40 and 60 ~o reported by Chase. A contour plot of the coefficient A2 was prepared by mapping these coefficients as a function of population parameter P(½) and multipole mixing coefficient 6 (fig. 5). The area of intersection of the contour for the 3.224 ~ 0 transition with that of the 3.224 --* 0.841 has no special significance since the 3.22 MeV and 2.38 MeV gamma rays may have different values of 5. The

582

J.M. O'DELL et aL

only requirement which must be satisfied is that these transitions have the same value of the population parameter P(½). Studying the gamma radiation resulting from neutron capture in 328, Manning and Bartholomew 22) have shown that both the 3.22 MeV ({- -~ {+) and 2.38 MeV (½- -* ½+) gamma rays correspond to pure E1 transitions. This is in agreement with the present results which show that a value of 6 = 0 is allowed for both gamma rays. This, in turn, fixes the value of P(½) to be 0.76_+0.07. Since P(½) = 1 is predicted if the reaction cross section is completely accounted for by a stripping process, one is led to conclude that there is at least a small contribution of compound nucleus formation to the reaction mechanism. 1.0

0.6 PIt/2)

3.224 M e V

0.4

0.0

LEVEL

3"2"*lf2+• 3.224~ 0.841

B

-80

i

-60

-40

-20

0 20 Arctan5

40

60

80

Fig. 5. C o n t o u r plot showing the possible values o f P(½) and the mixing ratio ~ for the gamma rays which de-excite the 3.224 MeV level o f a3S. 3.2. T H E 2.937 M e V L E V E L

This level decays by gamma radiation to the ground state and to the 1.965 MeV state which in turn decays entirely to the ground state of a3S. The present data show that both cascades occur within experimental error with equal intensity. This level has been previously investigated by Endt and Paris la) using the 32S(d,p)aaS reaction. The analysis of the stripping distribution favours an assignment /, = 3, which indicates that this level is probably the f~ single-particle state expected in this energy range of 33S. Because of the close proximity of the 2.970 and 2.869 MeV states, the observed proton and gamma-ray spectra were carefully examined to detect the possible excitation of either of these states. No statistically significant change in shape of either the proton group identified with the 2.937 MeV state or of the gamma-ray spectra associated with it was observed at any of the several deuteron energies and proton counter angles used. Also, no change in the branching ratio was found for these several correlations. While this does not rule out significant populations of the 2.970 and 2.869 MeV states in this experiment (the relative populations may remain constant over the range of conditions employed or their decays may exhibit branching ratios identical to that of the 2.937 MeV state), it makes such populations unlikely. It was concluded, therefore, that, in the absence of unfortunate coincidence, the cross

SsS(d, p)Sa$ REACTION

583

sections for formation of either of these states are at most 5 70 of that for the 2.937 MeV state. G a m m a - r a y spectra were observed at 60 °, 75 °, 90 ° , 120 °, 135 ° and 150 ° . Angular correlations for the 2.937, 1.954 and 0.972 MeV g a m m a rays were obtained from these spectra. Least-squares Legendre polynomial fits resulted in coefficients A2 and A4 summarized in table I. The 2.94 MeV g a m m a ray corresponds to a transition between a level that is suspected to have J~ = 7 - and a level which is known to have J~ = ~+. Since such a transition may proceed by E3 as well as M2 multipolarity, the angular correlation m a y contain terms as high as Pr(cos 0). With five independent angles, a least squares fit to this order is possible in principle. Unfortunately, the combination of the unavailability of angles closer than 30 ° to the symmetry axis and the large uncertainty in the data points led to an erratic behaviour of the least squares fits when kmax = 6 was used. This manifested itself in the sudden increase in the magnitude of the terms, characteristic of exact fits, and often in physically impossible, i.e., negative intensity, solutions. In the case of the 2.94 MeV g a m m a ray, the value of E 3 - M 2 mixing ratio TABLE 1 Coefficients A2 a n d A4 in the e x p a n s i o n W(O)= ~AkP~(cos 0) resulting f r o m t h e a n g u l a r correlations o f g a m m a rays t a k e n at Ex = 2.937 M e V a n d t h e p r o t o n c o u n t e r placed at 0 ° with respect to the deuteron beam Gamma ray (MeV)

A2

A4

2.94 1.97 0.97

0.00+0.12 --0.95 4-0.06 --0.354-0.10

--0.374-0.16 --0.01 4-0.14

Transition 2.937 ~ 0 1.965 ~ 0 2.937 ~ 1.965

calculated on the basis of the fit to order P4(cos 0), to be discussed below, would correspond to an expected experimental value of A 6 ~ 0.2. While the standard deviation of such an A 6 term would be larger than this, the best values of both A2 and A , and their associated errors would be altered slightly by its presence. Rather than attempt an arbitrary adjustment of these values, it was decided to test for a region of overlap in the contour plots and, if such was found, to recognize the range of parameters indicated by this overlap as a lower limit to this range on the basis o f the present data. The analysis of the gamma-ray correlations was made by assuming that the spin of the 2.937 MeV level was either { or -~ and that the spin of 1.965 MeV level was ~, ~ or ~-. 7 Contour maps for the 2.937 --, 0 and 2.937 ~ 1.965 transitions were computed for all possible combinations of spins of these levels. The possible mixing ratios for the 0.97 MeV g a m m a ray consistent with these contours were then used to compute contour maps for the 1.965 ~ 0 transition of the 2.937 ~ 1.965 ~ 0 cascade. Contour maps were also computed for the correlation of the 1.97 MeV g a m m a ray observed in coincidence with the protons from the 1.965 MeV level. Consistent results

584

J.M. O'DELL e t al.

were obtained only when it was assumed that the 2.937 MeV level has J = ~-, 7 the 1.965 MeV level has J = ~, and the 0.97 MeV g a m m a ray has 3 ~ 0. Fig. 6 shows the contour m a p computed for the 1.965--, 0 transition in the 2.937 ~ 1.965 ~ 0 cascade with J = ~ for the 2.937 MeV level, J = ~ for the 1.965 MeV level, and t5 = 0 for the 0.97 MeV g a m m a ray. The contour maps for the 2.937 -~ 0 and 2.937 ~ 1.965 transitions ( J = 7 for the 2.937 MeV level and J = for the 1.965 MeV level) are shown in fig. 7. These plots show that P(½), for the 2.937 MeV level, is restricted to a value 0.69 + 0.06. It is also seen that with this limit on P(½), the (L = 3)/(L = 2) mixing ratio for the 2.94 MeV g a m m a ray is either 0.48+0.09 or 1.64+0.45 and that the E2/M1 mixing ratio of the 1.97 MeV g a m m a ray is 0.79 + 0.26. The mixing ratio for the 0.97 MeV g a m m a ray has two permissible values; of these only 6 = 0 is consistent with the allowed value of P(½) for the 2.937 ~ 1.965 -~ 0 cascade. This value of P(½) limits the contribution of the stripping mechanism to the reaction cross section to be less than 0.69+0.06. 1.0

0.8

0.6

p(l~)

0.4

0.2 0.0

-80

-60

-40

-20

0 20 Arctand"

40

60

80

Fig. 6. Contour plot showing the possible values of P(½) and the mixing ratio (5 for the 1.97 MeV gamma ray arising from the decay of the 2.937 MeV level of 3sS.

If, as reported, l. = 3 for the 2.937 MeV level and l, = 2 for the 1.965 MeV level, the present experiments show that the 2.937 MeV level has J " = 7 - and the 1.965 MeV level has J " = ~+. One is forced to conclude, therefore, that the 2.94 MeV g a m m a ray contains a mixture of E3 and M2 radiation, which competes on an equal basis with the pure E1 transition to the {+ level at 1.965 MeV. Using the Weissk o p f estimates for single particle transition probabilities, one expects the E 1 transition to be favoured over the M2 transition by a factor of 104. The Weisskopf estimates also predict a ratio of 0.002 for E3/M2 radiation probabilities, or a mixing ratio 6 = 0.045, which is smaller by a factor of 10 than the lower value of 6 found by the above analysis. It is evident that the observed branching ratio for the two transitions requires a major reduction of the dipole matrix element and probably collective enhancement of the electric octupole transition probability. Using the computation of Glaudemans the wave function for the 2.937 MeV level can reasonably be constructed by coupling an f~ orbital to the ground state orbitals of the 32S nucleus.

asS(d, p)aSS REACTION

585

As the leading terms, one then obtains for the 2.937 MeV state and for the ground state of 338 ~k~-{ - 0.5(2s) 4 f~ + 0.4(2s) 2 (d~) 2 f~}, ~b~+{ -- 0.6(2s) 4 d ~ - 0.2(2s) 2 (d~) 3~}. If one computes the transition amplitudes between these levels, one finds that the observed mixing ratio (0.48 +0.09 or 1.64+0.45) for the E3/M2 radiation is still significantly larger than can be accounted for 14). This conclusion is not likely to be effected by an increase in the assigned error to account for the P6(cos 0) term which should be present in the angular correlation; however, transition strengths, in Weisskopf units, of 10 -5, 10 -1 and 10 for the El, M2 and E3 radiations, respectively, are consistent with the data and not inconsistent with typical strengths in this region is, 16). 1.0 0.8 P(I121 0.6

0,4

0.2 0.0 -80

-60

-40

-20

0 20 Arctand"

40

60

80

Fig. 7. Contour plot of the possible values of P(½) and the mixing ratio ~ for the 2.94 and 0.97 MeV gamma rays which de-excite the 2.937 MeV level of 3aS.

In order to estimate the relative strength of the ground state transition and the cascade through the 1.965 MeV state, it is instructive to contemplate the possible origins of this level. The above analysis indicates that this state has spin ) and positive parity which suggests that it may be the second excited state theoretically predicted to have an energy of 1.38 MeV. The wave function for this level is, according to Glaudemans, @~+{ - 0.7(2s) 3~(d~)22- 0.1 (2s)l~r (d~)~}. The present experiments have provided, however, some evidence which suggests that a state in a 3S may indeed exist at 1.35 MeV. Should this be positively confirmed, it would be tempting to interpret the 1.965 MeV state as a d~ hole state which is to be expected at approximately this energy range. Such a state would correspond, for instance, to the well known hole state in alp at 2.24 MeV. A fair approximation for such a hole state is the wave function of the ground state of 335 with a particle

586

J . M . O'DELL e t al.

promoted from a d~ orbital into a d½ orbital, i.e., ~k~. { - 0.6(2s)'(d~) 2 (d~)- 1 _ 0.2(2s)2 (di)a(di)- 1 } . A comparison of this wave function with the wave function for the 2.937 MeV level shows that a transition between these states requires more than one nucleon to change its orbital. A gross change in the particle orbitals is thus involved, which prevents their connection by a single particle operator, and, as a consequence, one should expect that this transition is highly forbidden. The same argument is applicable for the {~+ state predicted by Glaudemans at 1.38 MeV. 3.3. T H E 2.313 M e V L E V E L

This level is observed to decay to the ground state and the 0.841 MeV state of 33S. Previous measurements have shown that the state has In = 2, which fixes its parity as positive. Although the present experiments have established the decay scheme and the relative intensities of the gamma rays, it was not possible to arrive at a completely satisfactory assignment for the spin of the state. Proton-gamma angular correlations were obtained at a deuteron energy of 2.541 MeV and the proton counter set at 130 °, 100 °, 70 °, 40 ° and 0 °. Additional angular 1.0

0.8

0.6

P(1/2) 0.4

0.2

0.0

-80

-60

-40

-20

-80

-60

-40

-20

0

20

40

60

80

0

20

40

60

80

1.0

0.8

0.6 " PO/2) O.4

0.2

0.0 Arctanar

Fig. 8. Contour plots of possible values of P(½) and the mixing ratios of the gamma rays which deexcite the 2.313 M e V level of aaS. These contours were plotted assuming the spin of the 2.313 M e V level to be ~.

azS(d, p)SaS REACTION

587

correlations were measured with the proton detector placed at 100 ° for incident deuteron energies of 2.172, 2.260 and 2.671 MeV. The eight sets of correlations were analysed by fitting the data to the expansion W(O) = ~ Ar` cos m(~k-fir,). 1O) An inspection of the results shows that, for half the cases investigated, a best fit requires a term in cos 4(~k-f14). Because of the restriction m < 2J one is led immediately to a unique assignment J~ = ~+ for this level. A more detailed analysis of the data casts, however, considerable doubt on this conclusion. One would expect, for instance, that the 1.47 MeV gamma ray by which this state decays to the ½+, first excited state, is predominantly E2 in character. This TABLE 2 Coefficients A2 a n d A4 in the e x p a n s i o n W(0) = Y~A~P~(cos 0) resulting f r o m the a n g u l a r correlations o f g a m m a rays t a k e n at E x = 2.313 M e V a n d the p r o t o n c o u n t e r placed at 0 ° with respect to the deuteron beam Gamma Ray(MeV)

A2

2.31 2.31 1.47 1.47

A4

--0.40±0.10 --0.27i0.09 0.25-*-0.14 0.41 :k0.09

Transition

--0.44±0.16

2.313 2.313 2.313 2.313

--0.27:k0.14

O.8 ~ ~ e 2

313.-MeV

0.6

~ ~ ~ ~

Assignment

0 0 0.841 0.841

{+ {+ {+ {+

~ ~ ~ ~

{+ {+ ½+ ½+

Lev

3/2.-.~312• 2.313"-~'0

PO/21

3,,2--,~/2@ 2.313--,0.841

0.4 0.2 0.0

-80

-60

-40

-20

0 20 A r c t a n o~

40

60

80

Fig. 9. C o n t o u r plots o f possible values o f P(½) a n d the mixing ratios o f the g a m m a rays w h i c h deexcite the 2.313-MeV level o f 3sS. T h e s e c o n t o u r s were plotted a s s u m i n g the spin o f the 2.313 M e V level to be ].

may be ascertained in the usual fashion by observing the gamma-ray angular correlations with the proton counter set at 0 ° and fitting the results to an expansion of Legendre polynomials (table 2). Fig. 8 shows the contour maps obtained if one assumes the assignment J" = ~+, i.e., an expansion including terms with coefficients A 2 and A4. It is seen that consistent results can only be obtained if one permits an M3/E2 mixing ratio equal to at least 0.35 which is by three orders of magnitude larger than expected. If one assumes, however, that the 2.313 MeV state has spin ½+, the angular

588

J.M. O'DELL et aL

correlation data must be fitted to an expansion containing terms not higher than A2. Such as assignment would allow the state to decay by either M1 or E2 radiation to either the ground state or first excited state. The contour maps prepared for this case, shown in fig. 9, give acceptable values for the M1/E2 mixtures required. One is therefore left with the unhappy choice of accepting either the inordinately large M3/E2 mixing required by a J = ~ assignment or of arguing that the cos 4(~k-fll ) term in the observed correlations is due to unfortunate statistics. The recent investigation by Schiffer and others 17) have not only verified the assignment In = 2 for this state, but also shown that the stripping pattern of the protons is typical of one expected for a ½+ state. On the basis of the present information it would appear, therefore, that the ½+ assignment is preferred. Should this assignment indeed be correct, the 2.313 MeV level can be identified with the level predicted by Glaudemans with an excitation of 2.77 MeV. The wave function describing this level shows a considerable amount of configuration mixing which would account for the almost isotropic stripping patterns observed both at this laboratory 6) with deuteron energies between 2.0 and 3.0 MeV, and by Holt and Marsham is) with a deuteron energy of 8.18 MeV. 3.4. T H E 1.965 MeV L E V E L

In agreement with all previous investigations this state is found to decay entirely to the ground state. Table 3 summarizes the results from two different correlation runs. TABLE 3 Coefficients A S and A~ in the expansion 14/(0) = ~AkPk(cos/9) resulting f r o m the angular correlations o f g a m m a rays taken at E x = 1.965 MeV and the p r o t o n counter placed at 0 ° with respect to the deuteron beam G a m m a ray (MeV) 1.97 1.97

AS --0.68 4-0.08 --0.54!0.07

At --0.18-4-0.15 --0.02-4-0.13

The contour maps, shown in fig. 10, were prepared using weighted averages of the coefficients A2 and A 4 and assuming the J = ~ assignment resulting from the measurements made in the study of the 2.937 MeV state. Inspection shows that a fit is readily made, consistent with the value of ~ required from the 2.937 ~ 1.965 ~ 0 cascade. The relatively small value of P(½) = 0.42___0.12 required by the value of iS, as indicated by the vertical dashed lines, shows that the contribution of the stripping mechanism to the reaction cross section for this level is small. This state is assigned a probable positive parity on the basis of the probable In = 2 assignment of previous work and a spin of ~ from the present work. 3.5. T H E S E A R C H F O R T H E 1.38 MeV L E V E L

Fig. 11 shows a logarithmic presentation of a typical proton spectrum taken at

sSS(d, p)SSS REACTION

589

1.0

0.8

0.6 p(1,~) 0.4

0.2 o.o

-80

-60

-40

-20

0 20 Arctangt"

40

60

80

Fig. 10. Contour plot of the possible values of P(½) and the mixing ratio 6 of the 1.97 MeV g a m m a ray which de-excites the 1.965 MeV level of 8sS. The vertical dashed lines shown are limits on ~ obtained from the analysis of the 1.97/VfeV g a m m a ray observed in the decay o f the 2.937 MeV level.

3.224 2.937

1.965 100

½ x

z z < .-ru

i

i

5 S

32

(d,p)S

33

Ed=2.541 , eV ep= 1 0 0 °

0

[ 20

t 40

I 60

I 80

I 100

J 120 CHANNEL

I 140

F 160

I 180

200

NUMBER

Fig. 11. Proton spectrum from bombardment of a natural sulphur target with 2.541 MeV deuterons. The counts per channel are plotted on a log scale to emphasize the weak protons groups. The proton peaks are identified by the excitation energies of the levels in asS to which they correspond.

590

~. M. O'DELL e t al.

E d = 2.541 MeV. It is evident that there is some structure between the proton groups corresponding to the levels at 0.841 and 1.965 MeV in a3S. The weak proton group appearing at 1.66 MeV in the 33 S spectrum has previously been identified by Wilson 6) as the ground state group from the 34S(d, p)aSS reaction on the basis of an approximate kinematical analysis. The second peak which would correspond to a 1.34 MeV level in 33S, although found over a wide range of bombarding energies and many angles of observations, is, unfortunately, not well enough resolved to make a kinematical analysis meaningful. Since such a level must decay either to the ground state or by a two step cascade through the 0.841 MeV state, it seemed practical to investigate this structure by attempting a detailed study of p r o t o n - g a m m a coincidences. Fig. 12 shows a spectrum of the g a m m a rays in coincidence with protons

100

Z 80 7" "r"

u

uJ 60

0.~

g40

J

U

0.84

20 ~

..o

° o

I

20

I

o

%o

J

40

CHANNEL

I

o

Oo
o O ~ o ~ ~oooo°

r

60

ol

I

::O/o I

80

NUMBER

Fig. 12. Spectrum of g a m m a rays observed in coincidence with p r o t o n s whose energy correspond to a level in s3S between 1.8 and 1.0 MeV.

which would leave 3 3 S with an energy of 1.38 MeV. Since no structure is observed above 1 MeV a one step transition to the ground state is evidently ruled out. The two peaks seen in the spectrum are readily identified as a 0.84 MeV g a m m a ray resulting from coincidences with the tail of the 0.84 MeV proton group, and a 0.51 MeV g a m m a ray expected from the chance background of the large annihilation radiation. One is tempted, however, to argue that a significant part of this radiation may be due to a two-step transition from a 1.34 MeV state in 33S. This hypothesis was tested with considerable care 7,19) by observing the intensities of the two g a m m a rays as the energy of the proton group was varied in small steps to cover the excitation energy range in 33 S between 1.0 and 1.8 MeV. The results, although not conclusive,

8zS(d, p)3aS REACTION

591

give a strong inference that a state at 1.34 MeV does exist and that it decays predominantly by a two step cascade. An attempt is presently being made to observe this state using the 35C1(d, ~t) reaction to verify the conclusions of this experiment. Until corroborating evidence is found the existence must be considered as questionable. 4. Conclusions Table 4 and fig. 13 summarize the results obtained. Shown are the various gammaray transitions observed, the branching ratios and the spins and parities of the lowlying levels in 33S investigated. On the basis of the present experiments the spin of only the 2.313 MeV level remains in doubt; the existence of a state at 1.34 MeV, 3/23.224 L=l 2.970 7/2- -- 3 2.937 T 2 2.869 5o~5 50~5 (3/2)+_ 2.313

I

1.965 36±3 (i.35) . . . .

[ 39±3

64±3 -[---

512 +

t

98*2 61±3

------I-----

f

I I

i

0.841

112+

3/2+ 5 33 Fig. 13. Energylevel diagram of 8aS. predicted by Glaudemans, needs additional verification. The appearance of enhanced E3 transition rates, of which the decay of the 2.937 MeV state appears to be an example, in this region of nuclides and their evident connection with collective modes of excitation makes their measurement of considerable importance. With this in mind, a repetition of the present experiment, with an annular particle detector to allow unobstructed gamma ray detection at 0 ° and to remove the necessity of a beam foil, is underway in the hope of obtaining a more precise value for the E3-M2 mixing ratio of this transition.

592

J. M. O'DELL e t al. TABLE 4 Results of the angular correlation measurements in the s2S(d, py)3sS reaction

State in asS (MeV)

J~

P(½)

3.224

3-

0.764-0.07

2.937

~-

0.69-t-0.06

2.313

1.965

(3) +

0.124-0.12

(~+)

0.164-0.13

3+

0.424-0.12

Transitions observed

Relative intensity

Competing multipoles

3.224 ~ 0 3.224 ~ 0.841 2.937 ~ 0

364-3 64!3 504-5

M2/E1 M2/EI E3/M2

2.937 1.965 2.313 2.313 2.313 2.313 1.965

504-5 984-2 394-3 61 4-3 394-3 61 ± 3 984-2

M2/E1 E2/MI E2/M1 E2/MI E2/M1 M3/E2 E2/M1

~ 1.965 --~ 0 ---~0 ~ 0.841 -+ 0 --~ 0.841 ~ 0

P(~) is the population of the subtstates m = 4-½, with P ( ½ ) + P ( t )

Mixing ratio 0 ~) 0 ~) 0.484-0.09 1.644-0.45 0.084-0.09 0.794-0.26 0 a) 0 a) 1.3 4-0.6 --0.45 4-0.09 0.79-60.26

= 1.

a) The value 0 is chosen arbitrarily on physical grounds from the many possibilities compatible with the observed angular correlations.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19)

P. M. Endt and C. van der Leun, Nuclear Physics 34 (1962) 185 P. M. Endt and C. van der Leun, Nuclear Physics 53 (1964) 540 P. W. M. Glaudemans, G. W. Wiechers and P. J. Brussaard, Nuclear Physics 56 (1964) 548 J. A. Becker, L. F. Chase, Jr., D. B. Fossan and R. E. McDonald, Bull. Am. Phys. Soc. 10 (1965) 713 A. E. Litherland and A. J. Perguson, Can. J. Phys. 39 (1961) 788 F. L. Wilson, AEC Technical Report C00-1120-33 (1964) J. M. O'Dell, AEC Technical Report C00-1120-39 (1965) A. R. Poletti and E. K. Warburton, Phys. Rev. 137 (1965) B595 E. K. Warburton e t al., Phys. Rev. 138 (1965) BI04 G. R. Satchler and W. Tobocman, Phys. Rev. 118 (1960) 1566 L. F. Chase, Thesis, Stanford University (1958) G. Manning and G. A. Bartholomew, Phys. Rev. 115 (1959) 401 P. M. Endt and. C. H. Paris, Phys. Rev. 110 (1958) 89 P. Goldha/nmer, private communication N. B. Gove, Topical Conference on Bases for Nuclear Spin-Parity Assignments, Gatlinberg, Tennessee, (1965) 3 C. van der Leun, private communication J. P. Schiffer, L. L. Lee, Jr., A. Marenov and C. Mayerb6ricke, Bull. Am. Phys. Soc. 10 (1965)510 J. R. Holt and T. N. Marsham, Proc. Phys. Soc. 66A (1953) 467 J. M. O'Dell and F. W. Prosser, Jr., Bull. Am. Phys. Soc. 9 (1964) 667