Angular correlation studies of the 326, 405 and 630 keV Al27(p,γ) resonances

Nuclear Physics 29 (1962) 7 0 - - 8 8 ; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

A N G U L A R CORRELATION S T U D I E S OF THE 326, 405 AND 630 keV Aim(p, ),) R E S O N A N C E S JOHN

I. V A L E R I O t a n d E D W A R D

B. N E L S O N

Department o/Physics and Astronomy, State University o/ Iowa, Iowa City, Iowa it R e c e i v e d 31 M a y 1961 T h e A117(p, y ) $ i ss reaction a t t h e 326, 405 a n d 630 k e V r e s o n a n c e s h a s b e e n i n v e s t i g a t e d . T h e g a m m a r a y s p e c t r a were s t u d i e d w i t h large N a I scintillators a n d a t h r e e c r y s t a l scintillation pair s p e c t r o m e t e r , while d e c a y s c h e m e s a n d r e l a t i v e i n t e n s i t i e s were d e t e r m i n e d b y coincidence t e c h n i q u e s . A n g u l a r c o r r e l a t i o n studies, (13, ~,) a n d (13, y, ~), h a v e e s t a b l i s h e d t h e s p i n a n d p a r i t y of t h e first t w o excited s t a t e s in Si iS, 1.78 a n d 4.62 MeV, as 2 + a n d 4 +, respectively, a n d of t h e p r o t o n c a p t u r e s t a t e s : 11.90 MeV, 4 - ; 11.98 MeV, 4 - ; a n d 12.20 MeV, 3-. A w e a k c a s c a d e b r a n c h , o b s e r v e d a t t h e 405 k e V resonance, proceeds t h r o u g h t h e 8.59 a n d 1.78 M e V levels. Correlation s t u d i e s on t h i s cascade a r e in a g r e e m e n t w i t h a s p i n a n d p a r i t y a s s i g n m c n t of 3 + for t h e 8.59 M e V level.

Abstract:

1. Introduction Numerous sharp resonances are observed 1-4) in the A127(p, y) Si~s reaction for proton bombarding energies below 2 MeV. Rutherglen a al. 5) investigated five resonances between 400 and 700 keV. With the aid of an AW(p, ~)Mga yield curve previously obtained 6), these workers were able to assign spins and parities to various capture states in Si2s by measuring angular distributions of the more prominent gamma rays emitted from these levels. In the range Ep ---- 0.65 MeV to Ep = 2.2 MeV, Gore et al. 7) measured seventeen angular distributions of capture v-rays emitted in transitions to the first excited state with the result that the first excited state of Si ~ was either 2 + or 3 +. In the present work, a more complete investigation s) of the de-excitation gamma rays following proton capture in A1z7 was performed with the principal aim of determining the spin of the second excited state (4.62 MeV level) of Si~s. Gamma ray spectra were taken at the Ep = 226, 294, 326, 405 and 630 keV resonances. Decay schemes and intensities at the 326, 405 and 630 keV resonances formed the basis for (p, 7) (P, X, 7), (P, X, X, 7), (P, 7, r) and (p, 7, X, 7) double and triple correlations at these resonances (X signifies an unobserved gamma radiation). Resonances at Ep = 226 and 294 keV were too weak to warrant correlation measurements. These correlation measurements fixed (1) the spins of the first and second excited states; (2) the spins and parities of the capture states and (3) the mixing parameters of the gamma radiations. * N o w a t C o n v a i r Division, General D y n a m i c s Corporation, S a n Diego, California. *t W o r k s u p p o r t e d in p a r t b y t h e U. S. A t o m i c E n e r g y C o m m i s s i o n . 70

ANGULAR

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71

Shortly after the completion of this investigation there appeared various papers germane to our work. Okano 3) studied y-ray spectra of the four resonances below 410 keV. Spectral decomposition and 0 ° to 90 ° anisotropy measurements at these led to the assignment of spins to various levels. E n d t and Heyligers 10) investigated gamma ray spectra from twelve A12~(p, 7)Si ~8 resonances in the energy range Ep : 500 to Ep : 800 keV. Branching ratios were obtained in the decay of resonance levels with the aid of both singles and coincidence spectra. To keep duplication to a minimum only a portion of our results will be presented. This portion is chiefly the spectra and correlation measurements at the 405 and 630 keV resonances.

2. Experimental Technique A 500 keV Cockcroft-Walton accelerator was used to investigate the 405 keV Al~(p, F)Si 2s resonance. Proton beams of approximately 70/~A were analyzed by a 90 ° deflecting magnet and impinged on the target in a 0.32 cm circular spot. Thin evaporated aluminium targets were found to deteriorate under prolonged bombardment b y these currents, therefore, thick targets were employed for the investigation of this resonance. Gamma ray spectra and correlations were measured just above and below resonance and the contributions due to lower resonances and constant background wePe~subtracted out. This subtraction was safely performed since these contributions were less than 20 % of the total intensity of that observed on resonance. Seven /,A H2 + beams (14 /iA of protons) from a 4 MeV Van de Graaff accelerator were used in the investigation of the 630 keV resonance. After analysis by a 22 ° magnetic deflection the beam was focussed to a 0.15 cm 2 target spot. Aluminium targets of approximately 8 keV thickness were found to be stable under prolonged bombardment. Integrated off-resonant gamma yield above 2.62 MeV was found to be ~ of the resonant yield at this discriminator setting. Two large 12.7 cm × 15.2 cm NaI (T1) scintillation crystals were employed to detect the gamma rays. These crystals provided energy resolution (full width at half maximum) of 7.5 and 8.5 % respectively, for the 2.62 MeV ~,-ray of ThC". Single gamma-ray spectra were taken with a detector at 55 ° to the beam direction and a co-planar reaction monitor detector fixed at 270 °. The output of the first detector (whose orientation was variable from 0 ° to 90 °) was analyzed b y a RCL 9.56-channel pulse-height analyzer. Reaction monitoring was effected through the fixed counter both by counting the number of pulses due to y-rays above 2.6 MeV and those within a suitable window defined b y a single-channel analyzer. All double and triple correlation data were normalized to the number of counts in the chosen window. In most cases five angles from 0° to 90 °, equally spaced in cos ~ 0, were observed in the

72

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correlations. Triple correlations were performed in two independent geometries (to be denoted A and B in the future). In geometry A, the distribution of the first emitted y-ray is measured with respect to the beam direction while the second radiation is observed at 270 ° with respect to the beam and in the plane defined b y the beam and the first emitted y-ray. Roles of the two y-rays are reversed in geometry B. In each case counts from the moveable counter were displayed iu the RCL 256-channel analyzer and all data were taken from the differential spectrum obtained. This allowed correlations of all coincident radiation to be performed at the same time. Similarly, display of the singles spectrum as a function of angle allowed all angnlar distribution to be obtained at one time. A switching arrangement provided viewing of the portion of the spectrum observed b y the fixed detector in the multi-channel analyzer. Adjustment of both the position and width of the window formed b y the single-channel analyzer could be set to ~ of a channel. Repeated checks of the window setting throughout the experimental runs did not reveal any significant gain shifts in the electronic instrumentation.

3. Spectra and Decay Schemes In the analysis of the gamma ray spectra a knowledge of the nuclear levels in Sim is important. Since NaI ('1"1) scintillation detectors only allow a precision of approximately q- I °/o in the energy determination of an isolated spectral line, nuclear excitation energies (Ex) from the results of others who have employed magnetic analysis to reactions which have charged particles as products were used. No attempt has been made to determine directly energies of spectral lines with more accuracy than was necessary for assignment. All energies quoted for y-rays will be those obtained with the aid of known nuclear level excitations. The levels in Si ~8 which are observed in these studies and used in the analysis are shown in fig. 1 with proton bombarding energies, cal~ture state excitations and modes of decay. Excitation energies above 11.80 MeV are taken from E n d t and Braams 11) while levels of lower excitation are those reported b y Hinds and Middleton 1~) on the A1~r (He 8, d)Si ~8 reaction with the observed proton orbital momenta of capture found through angular distributions of the deuteron. Gamma ray spectra observed at the 630 and 405 keV A12~(p, ~)Si ~ resonances are shown in figs. 2 and 3. Coincidence spectra at the 630 keV resonance confirms the 10.42-1.78 MeY cascade to be the main mode of decay. Gating with pulses formed from y-ray., in regions 2, 3 and 4 (fig. 2) easily establishes a 7.56-2.84-1.78 MeV csscade The remaining components of the spectrum at this resonance were not investig. ated. A more detailed decay scheme analysis was performed at the 405 k e y resort

o

4.62

--

4.97 - -

6.8 6.8~}" -6.28 --

--

--

11,90

326 keY

4-

S i 28

11.98

4-

k

I

1

I

405 keV

630 kW 12.20

3-

2+

4+

5+

Fig. 1. Selected e n e r g y levels of Si aS. T h e p r o m i n e n t g a m m a r a y s observed a t t h e 3 resonances are i n d i c a t e d b y vertical lines. P r o t o n orbital m o m e n t a of c a p t u r e reported b y H i n d s a n d Middleton in t h e reaction AI Iv (He a, d)Si u are listed a t t h e left. T h e d o t t e d lines indicate weak, d o u b t f u l g a m m a r a y transitions.

0

7.93

7.3

8.59

0

9.38

9,70

0

5

Ex • (MeV)

Ep,

2000

I 1

I 2

1

7.58

I I I I I I I I 5 4 5 6 7 8 9 1 0 GAMMA RAY ENERGY ( M ~

g4

AI=T (p,~')Si == 6 3 0 keV resononce e = 55 ° G A T E WINDOW

II

IP-

Fig. 2. S p e c t r u m of g a m m a r a d i a t i o n p r o d u c e d a t t h e 630 k e V resonance of AlST(p, y), m e a s u r e d in a 12.7 c m × 15.2 c m NaI(Tl) detector. T h e g a t e window positions indicate p o r t i o n s of t h e s p e c t r u m used in g a t i n g coincidence spectra.

(/) I-Z :::) 0 (.) . IOOC

(1.

n,"

.-I I=.1 Z Z

2.84

H

0 p~

O t~

74

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ance b y gating with regions of the spectrum shown in fig. 3. Some results of these coincidence gate spectra will be presented. Gate 1: The spectrum in coincidence with gate 1 (9.4-10.4 MeV) establNhes the presence of a weak 10.2 MeV gamma ray in cascade with the 1.78 MeV de-excitation gamma ray of the first excited state. Gates 4 and 10: Results from gate 4 (7.1-8.0 MeV) and gate 10 (2.7-3.0 MeV) point to a 7.36-2.84-1.78 MeV triple cascade with the second excited state fed 8000

I

i ~--

I

I

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I

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1.78 2.84

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6000 J I.t.i z z I o

,.=, 400C CL.

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or) I-Z

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ENERGY

7

o,o

8

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(MeV)

Fig. 3. Spectrum of gamma radiation from 405 keV resonance, Al=~(p, y) measured in 12.7cm x 15.2 cm NaI (TI) detector. Spectral regions 1-11 were used in gating coincidence spectra.

b y the 7.36 MeV capture gamma ray. The 3.4 MeV 7-ray of the single spectrum does not appear in this coincidence spectrum. Gates 5 and 9: A gate with region 5 (6.2-7.0 MeV) shows an enhancement of the 3.4 MeV peak. The 3.4 MeV peak is evidence for a coincident 6.8 MeV line. This is confirmed b y gating on region 9 (3.1-3.6 MeV), for then, enhanced 6.8 and 6.3 MeV peaks appear which are not seen in the ungated spectrum. These results confirm the existence of a weak 3.4-6.8-1.8 MeV cascade. Gate 7: Gating on region 7 (total capture peak of 5.10 MeV line) demonstrates coincidence with another gamma ray of approximately the same energy and with the 1.78 MeV gamma ray. Hence, the 5.10--5.10-1.78 MeV triple cascade is demonstrated.

ANGULAR CORRELATION STUDIES

75

Because of the complexity of the 405 keV resonance spectrum, a decision was made to observe the spectrum with a three crystal pair spectrometer. This device produces a single peak for each spectral line and has a resolution of about 4.5 % for 6 MeV radiation. The spectrum taken at 0 ° for this resonance, after subtraction of background radiation, is displayed in fig. 4. A combination of low reaction yield and low detection efficiency for the spectrometer meant 400

1

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PAIR SPECTRUM 405

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GAMMA RAY ENERGY (MeV) Fig. 4. Three crystal scintillation pair s p e c t r o m e t e r s p e c t r u m of radiation from 405 k e V resonance, A12~(p, y).

that long runs had to be taken. Fortunately, overall gain shifts of the systems could be kept to less than ± 1 % over a period of 4 h. A graphical procedure was used in the analysis of the spectrum. Gamma ray line shapes needed for the decomposition of the spectrum were interpolations from monochromatic gamma ray lines of 7.62, 4.43, 6.14 and 11.68 MeV. A summary of the gamma ray lines found is presented in table 1. Included in the table is their assignment energy (ET), proposed transition, relative intensity

J. I. VALERIO AND E. B. NELSON

76

TABLE 1 Pair s p e c t r o m e t e r analysis: 405 keV resonance

~

(MeV) 10.20 9.38 7.92 7.36 6.81 6,147 5.60 5.10

Proposed transition

11.98 9.38 9.70 11.98 8.59 7.93 7.38

-~ -~ -~ -~ -~ -~ -~,

11.98

-~|

/ 6.880 %

5.10 4.60

3.39 2,84 2.60? 2.28?

1.78

1.78 0 1.78 4.62 1.78 1.78 1.78 6.889

6.88o~ 6.8891 11,98 11.98 4.62 11.98 11.98 1.78

-~ -~ -~ -~ -~ -~ -~

1.78 7.38 8.59 1.78 9.38 9.70 0

Relative intensity ± 2 0 % ffi) 3.0 1.1 ].5 52 7.6 5.1 3.7

Experimentally determined energy

Remarks

10.24 4-0.09 9.46 4-0.10 7.96 ± 0 . 0 9 7.360 6.84 ± 0 . 0 9 6.14 + 0 . 0 4 5.64 ± 0 . 1 0

Calibration line

11

5.11 ±O.O6 }

11

5,11 ! 0 . 0 6

5.4 10 63 11 17 100

4.49 ± 0 . 1 3 3.40 ± 0 . 0 4 2,840

F*'(p, at, ~,)01'

Coincident lines

2.58 ~:0.05 2.24 ± 0 . 0 4 1.7754-0.004

Calibration line ThC"

C*'(p, y)

~) As all t r a n s i t i o n s a p p e a r to feed to the 1.78 MeV level (none directly to the ground state we assign a relative i n t e n s i t y of 100 to the 1.78 MeV g a m m a ray.

and energy determination found b y spectral analysis. Errors in the relative intensity have been conservatively assigned a uniform value of ± 20 %. The error is meant to cover subtraction processes, possible angular distribution effects (spectrum was taken at 0 °) and inaccuracies of an approximate quantitative theory for the efficiency of the spectrometer. It is evident from the pair spectrum (fig. 4) that lines at 1.78, 2.84, 3.4, 5.1, 6.8, 7.4 and 10.2 MeV are present in the spectrum as the coincident decay analysis has shown. A three crystal pair spectrometer spectrum taken at the 326 keV resonance (not shown here) also exhibits a 6.8 MeV 7-ray with its coincident partner positioned at an energy of 3.31 MeV and not at 3.4 MeV as in the 405 keV spectrum. This implies that the low energy line is the first component of a triple cascade through the excited state at 8.59 MeV to the 1.78 MeV level. The 4.6, 5.6 MeV gamma rays are consistent with a weak cascade through the levels at 11.98 ~ 7.38 -~ 1.78 ~ 0. The remaining low intensity lines m a y be due to improper subtraction of the underlying resonances and background, although this effect was minimized b y a study of the radiation above and below resonance for a constant time at a constant beam. Some of the weak lines appear to fit the known levels, however, this conjecture could not be verified b y coincidence studies because of their low intensity.

ANGULAR CORRELATION STUDIES

77

4. S p i n s and Parities Results presented in the previous section have shown the capture state 'of the 630 keV resonance to decay mainly by a twofold cascade through the first excited state, while the 405 keV resonance decays mainly by a three-fold cascade through the second and first excited states. Becau,;e of the low yield of the reactions and the complexity of the spectrum, it is not possible with present techniques to perform experiments which determine the spins and parities of more than a few levels. The technique of angular correlations is applied to these dominant modes of decay to obtain a consistent set of spins for the first and second excited states and proton capture states in Si 2s. Difficulties are increased slightly by the fact that the reaction m a y proceed with channel spin mixing. It is known that the ground state spin and parity of A1z~ is {+ and the proton {+. The channel spin parameter t is to be defined as t=

no. of states formed by channel spin 3 no. of states formed by channel spin 2"

Experimental data from each of the measured double and triple correlations were fitted to a linear combination of Po, P2, P4 Legendre polynomials by the method of least squares as outlined by Rose 18). Since all of the double correlations fits were of the form

W(O) = I+A2P~(O), (i.e., no significant Ai coefficient), the reactions do not proceed by s-wave protons and most probably proceed by p-wave proton capture. Choice of higher /-wave protons would lead to further possibilities, but at such low proton energies the effect of the potential barrier should make higher orbital captures improbable. Some theoretical correlation functions were computed upon the assumption of d-wave protons but were ruled out as the analysis progressed because of poor agreement with experimental results. For both double and triple correlations (in the geometry chosen here) the theoretically computed functions can be written in the form

W(O) =

1+

~ a..£pn(o),

(1)

a 0

where 0 is the angle the moveable counter forms with the beam direction. Because of the finite angular resolution of real detectors the observed coefficients to the Legendre polynomial are attenuated with relation to the theoretically computed ones. Rose's la) attenuation factors {)r for cylindrically symmetric counters have been used in this work. Numerical integrations necessary for their computation were performed on an IBM 650 computer. The Q,. were 0.91 for double correlations. For triple correlations Qs varied from 0.82 to 0.93 and

78

J. I. VALERIO AND E. B. NELSON

Q4 varied from 0.50 to 0.77 depending upon the solid angle used at each experiment. It should be noted that the requirements of the Rose calculation are not completely fulfilled in this experiment. These are that the radiation is uniiorm over the face of the crystal and that all pulses due to the y-ray are counted down to zero pulse-height. Here only the high energy portion of the y-ray line (total capture peak) is counted with the result that point counter correlation functions are overcorrected for geometry. These geometric correction factors can be applied either to the theoretical function or the experimental distribution in the case of double correlations. It is more complicated with triple correlations. The correction factors applied to the coefficients of the Legendre polynomials (ar/ao) in this case depend intricately upon quantum numbers and mixing ratios of the transitions. This means that geometric corrections must be incorporated into the theoretical correlation function itself. The inverse process of correction of the observed correlation to obtain the theoretical one cannot be done with triple correlations. All computed correlation functions stated below will be expressions corrected for the finite angular resolution of the detector. 4.1. T H E

10 M e V - 1 . 7 8 M e V C A S C A D E

Angular distributions of the 10.4 and 1.78 MeV y-rays were performed at the 630 keV ( E x = 12.20 keV) and on the 10.2 MeV y-ray at the 405 keV (E x : 11.98 MeV) resonance to obtain the capture state and first excited state spins of Si 2s. The 12.20 MeV excitation level is known to emit x-particles e) to the ground state of Mg~a and has a y-ray distribution which is not isotropic. Consequently, the capture state spin and parity is either 1- or 3 - , assuming p-wave protons. Rubin's 14) work on the AW(d, n)Si ~8 reaction at the 1.78 MeV level requires this level to be either 2+ or 3 +. These facts greatly limit the number of correlation functions to be calculated. 4.1.1. The 630 keV resonance At the 630 keV resonance the measured double correlations (p, y) for the 10.4 and 1.78 MeV radiations are 1--

(0.0572+0.0052)Pz and 1 + (0.0837±0.0060)P~,

respectively. For both of these distributions approximately 40 000 counts were accumulated at each angle in the regions labelled one and four of fig. 2. Counts due to tails of higher energy y-rays were subtracted in region four. Table 2 is a summary of the predictions from possible distributions for the allowed spins a n d parities of the states with pure multipole transitions assumed. At the 630 keV resonance the 3- --~ 2+ --~ 0 + spin sequence is probably the correct one because the values of the channel spin parameter overlap for the two

ANGULAR CORRELATION STUDIES

79

distributions. This argument is not completely rigorous because other 7-ray cascades are known to feed the 1.78 MeV level. But since it is fed mainly by the 10.4 MeV radiation the argument does bear considerable weight. As a further TABLE 9. D o u b l e c o r r e l a t i o n s a t 630 k e V r e s o n a n c e

Spin s e q u e n c e

1---+2 +---~0+ 1--.3+-+0 + 3--+2+--+0 + 3--+3+-+0 +

10.4 MeV A~ = Qsat/ao; Qs = 0.905 A zexp = -- 0.057 :~ 0.005 No: No: Yes: Yes:

A, As If If

= --0.009 = 0.0!3 0.46 < t < 0.53 1.12 < t < 1.13

1.78 MeV A8 = O, aslao;

Q, =

0.905

As exp ~ 0.084=[=0.006

Yes: I f 0.46 < t < 0.53 Yes: I f 0.53 < t < 0.56

C o m p a r m o n b e t w e e n e x p e r i m e n t a l l y o b s e r v e d (At) *xp coefficient a n d predictocl coefficient A t for t h e 10.4-1.78 MeV cascade. The r a t i o aria o is t h e p o i n t c o u n t e r c o r r e l a t i o n coefficient, A t t h e f i n i t e c o u n t e r c o r r e l a t i o n coefficient, a n d t t h e c h a n n e l s p i n p a r a m e t e r . The term "No" indicates disagreement between experiment and theory, while the term "Yes" i n d i c a t e s a g r e e m e n t w i t h t h e e x p e r i m e n t , p r o v i d e d t h e c h a n n e l s p i n Ima'ameter i s i n t h e range stated.

confirmation of this spin sequence, a triple correlation was performed on these two radiations in the geometries A and B described previously. The measured results are Geometry A: 1-- (0.017+0.022)P,, Geometry B: 1+(0.164+0.021)P~. For geometry A this corresponds to 0.36 < t < 0.51 for the channel spin parameter in the calculated (3- -+ 2 + -+ 0 +) correlation function and 0.40 < t < 0.51 for geometry B. These values agree well with those found in the distribution measurements. Fig. 5 is a plot of the least squares fit to the data and the angular correlation coefficients as a function of the channel spin parameter t. A/)4 term appears in the predicted correlation for geometry B. If t h e / ) 4 term is included in the least squares fit, the error in A4exp is larger than the value of the term itself and therefore has little statistical significance. Also the error in A 2exp would increase slightly permitting a slightly larger range for the channel spin parameter t. For the range of t found for geometry B, --0.050 < A, exp < - - 0 . 0 4 6 should have been observed. 4.1.2. The 405 keV resonance The measured angular distribution for the 10.2 radiation at the 405 keV resonance is 1 + (0.206+0.067)P 2 . Total counts of approximately 1000 were extracted at each angle from region one of fig. 3. A summary of the predicted correlations compared to the ex-

80

J.I.

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VALRRIO AND 1~, B. NELSON

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GEC44ETRY &

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GEOMETRY Ill.?ll MIV

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Z. I 0

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TAN "~ i:

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(b) Fig. 5. (a), CO): R e l a t i v e coincidence r a t e b e t w e e n 10.4 of a n g l e for triple correlation m e a s u r e m e n t s , (p, 7, 7'), a t errors a r e indicated. (a'), Co'): Correlation coefficients, s p i n p a r a m e t e r t for t h e 630

M e V a n d 1.78 M e V r a d i a t i o n a s f u n c t i o n t h e 630 k e V r e s o n a n c e . T h e g e o m e t r y a n d A t a n d A , , as a f u n c t i o n of t h e c ~ n n e l keV resonance.

T~SLE 8 D o u b l e correlations a t 405 k e V r e s o n a n c e Spin s e q u e n c e 1-- ---~ 2 ÷ I - -+3 +

2-..-).2 + 2--+3 ÷ 3--+2 + 3--+3+

4- -+2 + 4---).3 +

A t = Qsas/ae: Qs = 0.905 As e=p = 0.206-4-0.067 No: No: No: Yes: Yes:

A a = --0.009 At= 0.013 --0.317 < A s < 0.090 If 0 < t < 0.50 If 3 < t < 0.80

Yes: If 2.17 < t < 7.37 Yes: A s = 0.254 No: A s = - - 0 . 1 7 7

C o m p a r i s o n b e t w e e n e x p e r i m e n t a l l y o b s e r v e d (As) exp coefficient ~.nd p r e d i c t e d coefficient A t for t h e 10.2 M e V 7 - r a y . T h e ratio a=/a o is t h e p o i n t c o u n t e r correlation coefficient, A a t h e finite c o u n t e r correlation coefficient, a n d t t h e c h a n n e l s p i n p a r a m e t e r .

ANGULAR CORRELATION STUDIES

Sl

perimental result is presented in table 3. With the spin of the first excited state established b y the s t u d y of the 630 keV resonance to be two, spin sequences 3- -+ 2 + and 4- -~ 2+ are the only two possibilities remaining for the 405 keV resonance capture y-ray. 4.2. THE

7.4-2.84-1.78 MeV CASCADE

This cascade is the dominant mode of decay at the 405 keV resonance and is also present at the 630 keV resonance. Since the primary y-ray feeds the 4.62 MeV level, it is through this cascade that the spin of the second excited state will be determined. Hinds and Middleton have shown the 4.62 MeV level TABLE 4 Double !

J ;,

Spin sequence

correlations

at 405 keV resonance

7.36 MeV

2.84 MeV

1.78 M e V

A t : Qz az/ao;

-4s = Q.z a.-,/ao;

.'It ~: Q~ a2/ao;

Qz = 0 . 9 1 0

Qs :

Atexp = 0 . 2 8 6 ~ 0 . 0 1 2

A t exp -- O . 2 3 6 : 0 . 0 0 9

3 - --~ 1 + --~ 2 ÷ --~ 0 +

Yes: 0.022 < t < 0.056

No: 6t -~ i m a g .

3- ~

If t =

2 + ~ 2+ ~ 0+

Yes ? : oo, a t = 0 . 3

Yes: 8 . 3 0 < t <: 1 2 . 9

3 - --~ 3 + -4- 2+ - + 0 +

o.91o

Q~ = 0 . 9 0 5

Yes: --4.84 < ¢5t < - - 4 . 3 1 --7.6 < ~ < --0.72 Yes: - - 0 . 0 8 8 < t~t < --3.27 < c5z <

--0.053 --2.91

.~2 exp

:--

0.219::-0.008

No: 0.069 < A t < 0.099 < A s <

0.072 --0.0913

No: --0.107 < At < --0.090 0.019 < A t < 0.022

No: 3 - --~ 4 + - ~ 2 + --~ 0 +

--0.091

<

3 - --~ 5 + - ~ 2 + --~ 0 +

--0.158

<

At

<

0.114

No: A t <

4-

-+ 1 + -~ 2 + -+ 0 +

No: At = 0.447

4-

-~ 2 + -~ 2 + -~ 0 +

A t =

0.256

as

0.281

0.130

Yes?: =

No: ~ t is i m a g .

No: 4 - --~ 3 + - ~ 2 + - + 0 +

A t =

--0.178

4 - - ~ 4 + --~ 2 + - + 0 +

A t =

0.250

A t =

0.217

at

0.275

as =

0.239

Yes?:

4- ~

~

Yes?:

Yes: A t =

0.216

No: A~ = - - 0 . 0 9 1

5 + --¢- 2 + ~ 0 +

ComImudson between eximrimentally observed Aa up coefficient and predicted A s coefficients: 7 . 3 6 - 2 . 8 4 - 1 . 7 8 M e V c a s c a d e , a l ] , ~ i s t h e p o i n t c o u n t e r c o r r e l a t i o n c o e f f i c i e n t , .4 i t h e f i n i t e c o u n t e r c o r r e l a t i o n c o e f f i c i e n t , t t h e c h a n n e l s p i n p a r a m e t e r , a n d ~t t h e M I - E 2 m u l t i p o l e m i x i n g p a x a m e t e r for

the

2.84

MeV

g~mm~

ray.

82

j. L V~SmO

ASD B. B. ~ELSON

is of even parity, since the proton orbital momentum of capture in Alto(Hes, d) Sizs is two, and that possible spins range from 0 to 5. 4.2.1. T h e d05 keV resonance Double correlations were performed on each of the components of the cascade at the 405 keV resonance to assist in choosing between the remaining possibilities, 3- and 4-, for the capture state. Data were taken from regions 4, 10 and 11 of fig. 3 with total counts at each angle of approximately 7000, 13 000 and 25 000, respectively. Tails due to higher energy radiation have been subtracted i n each region. Counts for the 7.36 MeV F-ray distribution were limited to the total capture peak so t h a t contributions due to the underlying 6.8 MeV line could be minimized. The measured distributions are: 1 + ( 0 . 2 8 6 i 0 . 0 1 2 ) P 2 for the 7.37 MeV gamma ray, 1+(0.236±0.009)P~ for the 2.84 MeV gamma ray, 1+(0.219±0.008)P 2 for the 1.78 MeV gamma ray. A summary of the analysis is presented in table 4, where the parameter 8z is the M l - E 2 multipole mixing parameter for the 2.84 MeV gamma ray in those cases where the spin of the second excited state is assumed to be 1,-2 or 3. Considerations of 0+ for the second excited state are not shown as both 2.84 and 1.78 MeV F-distributions are anisotropic. Blocks marked "Yes?" are in each case within the errors stated for the observed distribution, provided the uncorrected coefficient (aJ%) of P2 is used. As was stated previously the geometrical factor (Q2) tends to over-correct this coefficient. It is especially true in the case of the 7.36 MeV line since such a small fraction of the counts due to the F-ray are used in the distribution. From the table, it appears that the most probable spin sequence is

with the second excited state fixed at 4 +. A triple correlation between the 7.36 and 2.84 MeV radiation was performed at this resonance to confirm this spin sequence. %Vindow positions 10 and 3 of fig. 3 were used for geometries A and B, respectively, with coincidence counts totalling about 2600 and 1400 recorded at each angle. The measured correlations Geometry A: l+(0.070+0.019)Pz, Geometry B : 1 + ( 0 . 0 7 1 - 4 - 0 . 0 2 6 ) P 2, compared with the predicted correlations, Geometry A: 1+0.074 P2, Geometry B: 1+0.053 P~+0.031 P4, show agreement with experimental error except for the absence of the P4

ANGULAR

CORRELATION

83

STUDIES

term in the experimental result for geometry B. Errors of the A2exp coefficient would become larger if a/94 term is included in the least squares fit to the data and the error associated with A 4 ~ would be much larger than its value. The least square fit to the experimental data is given in fig. 6. Notice that the fit for both the distribution and correlation is obtained without the use of adjustable channel spin or multipole mixing parameters for this particular spin sequence. I

i

I

J

"'

0 Z bd

I

I Gi~OMETR¥

W

/

1.10

A

t--

-

i

'

I

'

2.84 14eV

1.1¢ ~

I

GIEOttETRY

B

8E~M llel 736 M~

_a 0 Z

f,

W

toc J

•

I 0

t

I

I

I/~

Pl~

I

~

l.OC

' i

I

c o s t e~

(o)

/t I

0

~

i

I + .071P 2

I

t

1/2

GOS=

I I

Ot

(b)

Fig. 6. Relative coincidence r a t e for the 7.36 MeV a n d 2.84 MeV cascade radiation as a function of angle for triple correlation m e a s u r e m e n t at the 405 k e y resonance.

The angular correlation of the first and third members of the cascade, with the intermediate radiation unobserved was obtained in geometry B. Approximately 2000 counts were extracted at each angle from the 1.78 MeV total capture peak with the result Geometry B: 1+(0.033±0.028)Pz for the A12~(p, 7.36, X, 1.78)SP 8 correlation. Assuming a spin sequence of 4- --* 4 + -+ 2 + --> 0 + with pure multipole transitions, the predicted correlation is 1+0.074 P~--0.015 P4. The coefficient of the P4 term found b y the least square fit to the experimental data was much smaller than its associated error and is therefore not stated. The predicted (p, 7.36, X, 1.78) A s correlation coefficient is just outside the standard deviation of the measured value. We observe that the solid angle correction factors (Qr) increase the theoretical P~ coefficient (ar/ao) from

84

1. V A L I ~ R I O

J.

AND

]~. 13. N E L S O N

0.055 to 0.074. As was mentioned previously, the geometrical factors tend to over-correct since data are taken only from the high energy region of the spectral line. The results of this triple correlation agree with the assumed spin sequences. 4.2.2. The 630 keV resonance A triple correlation with the first two members of this cascade has also been performed at the 630 keV resonance. In each of the two geometries, approxiately 1200 counts were recorded at each angle. The measured results are Geometry A: lq-(0.087d:0.031)P~, Geometry B: IA- (0.164-4-0.029)P 2. |

'

I

,

w T.Sm ~

'

I aI~M[TIW A

I

'

3---.-P •

244ulv

I

'

4+~

I

'

I

,

I 80

I

2+

~

8

O.i ~x~wtw(~rAc VaLm[

d

~1.00

,

I

i/2. COS 2 el

i

i

I

o

l

|

I

i

20

o

I

,

40

I

GO

T A N " l t;

(a) I

re

$

3

1.2

t¢

'

I

'

i

I

'

~

i

1

'

I

'

I

'

I

'

I

,

I

t

mw

Z

I~JG4 PI

o

i/2 cosl~

I

0

20

40 60 TAN " l t

I 80

(b) F i g . 7. (a), (b): R e l a t i v e c o i n c i d e n c e r a t e f o r t h e 7.6 a n d 2.84 M e V c a s c a d e r a d i a t i o n a s a f u n c t i o n o f a n g l e f o r t r i p l e c o r r e l a t i o n m e a s u r e m e n t s a t t h e 630 k e V r e s o n a n c e . (a'), Co'): C o r r e l a t i o n c o e f f i c i e n t s A s a n d / 1 t a s a f u n c t i o n o f t h e c h a n n e l s p i n p a r a m e t e r t a t t h e 630 k e V r e s o n a n c e .

For geometry A this corresponds to 0.00 < t < 0.32 for the channel spin parameter in the calculated correlation function and 0.52 < t < 0.75 for geometry B. Once again, the statistical errors did not allow a meaningful value for the coefficient to the P4 term. For the range of t found for geometry B,

ANGULAR CORRELATI ON S T U D I E S

85

0.002 < A~ero < 0.013 should have been observed. The least square fits to the data and plots of the angular correlation coefficients as a function of channel spin parameter t are shown in fig. 7. These values found f o r the channel spin parameters are j u s t outside one standard deviation of the previously determined values of 0.46 < t < 0.53 for 10.4 MeV distribution, 0.46 < t < 0.50 for 1.78 MeV distribution, 0.36 < t ~ 0.51, 0.40 ~ t ~ 0.51, for geometry A and B, respectively, in the 10.4-1.78 MeV triple correlation. It is felt that these results do not unduly weaken the 3- -+ 4+ -~ 2+ spin sequence for this cascade since this correlation experiment was difficult to perform and the value of A~ is relatively insensitive to the magnitude of t (see fig. 7). 4.2.3. The 326 keV resonance With the spin for the first and second excited states determined, the capture state spin of the 326-keV resonance (Ex = 11.90 MeV) could be obtained through angular distributions of the 7.3 and 2.84 MeV components of this cascade. The measured distributions are 7 . 2 8 : 1 nt- (0.287-1- 0.017 ) P~, 2.84: 1 ~ (0.248q-O.O23)P2, where approximately 3000 counts were recorded at each angle. Since the distributions are not isotropic, p-wave proton capture was assumed with 1% 2-, 3- and 4 - as the possible spins and parity for the 11.90 MeV level. Results presented in table 5 show that only a spin of 4 is consistent with the observed TABLE

Double

correlations

5

at 326 keV resonance 2.84 MeV

7.28 MeV

Spinsequence

A, = Qs as/ao; Qs = 0.910 • AsexP = 0.287q-0.017

1 - --~ 4 + --~ 2 + 2 - -~- 4 + - ~ 2 + 3---+4+-+2+ 4 + --~ 4 + --~ 2 +

A t = 0.023 --0.182 < A, < --0.130 --0.091 < A s < 0.114 Yes?: . 4 , = 0.250

A s = Q,s as/ao; Qs = 0 . 9 1 0

AsexP =

0.248~0.023

No: No: No:

Yes: A s = 0.217

C o r n ~arison b e t w e e n e x p e r i m e n t a l l y o b s e r v e d A I ~ p c o e f f i c i e n t a n d p r e d i c t e d A , c o e f f i c i e n t s f o r t h e 7 . 2 8 - 2 . 8 4 - 1 . 7 8 M e V c a s c a d e . ~ [ a o is t h e p o i n t c o u n t e r c o r r e l a t i o n c o e f f i c i e n t a n d A s t h e f i n i t e counter correlation coefficient.

distributions. A question .mark is placed after the "Yes" in the 7.28 MeV column because the value of A s is outside the range of experimental error. Once again the over-correction of the geometry is assumed to be partially at

86

J . I . V A L E R I O A N D E. B. N E L S O N

fault since only counts in the total capture peak of the 7.28 MeV line were summed at each angle. Also, contributions of the high energy edge of the 6.8 MeV line will tend to contribute more at this resonance t h a n at the 405 keV resonance since the energy of the primary de-excitation gamma ray is about 80 keY lower, while the energy of the 6.8 MeV gamma ray does not change with bombarding energy. 4.3. THE

3.4-6.8-1.78

MeV

CASCADE

The 3.4-6.8-1.28 MeV cascade discovered by coincidence work at the 405 keV resonance is difficult to study because it is quite weak. A shift in energy of the 3.31 MeV line to 3.40 MeV at the proton energy was increased from 326 keV to 405 keV demonstrates that this line is the first member of the cascade from the capture state to the 8.59 MeV level. Hinds and Middleton have shown a proton orbital capture of zero in the Al~(I-Ie8, d)Si 2s reaction for this level with the consequence that 2+ and 3+ aret:he spins and parity possible. Since the capture state (Ex = 11.98 MeV) has a 4-~ assignment, 3+ is the .most probable assignment for this level, assuming that an E1 transition is competing with the higher intensity E1 transition from the capture state to the 4.62 MeV level. The 3.4-6.8 MeV triple correlation was measured in geometry A with 400 to 600 counts observed at each angle. The measured result is 1--

(0.130+0.051) Pz-

Although the data are somewhat poor statistically, the sign and magnitude of the P2 coefficient is qualitatively in agreement with the predicted correlation obtained with the proposed spin sequence, provided the mixing parameter associated with the 6.8 MeV radiation is allowed to assume a value in the ranges -oo < ~ . < 0 . 2 8 or 1 2 < ~ < +oo.

5. Summary

It has been the central purpose of this paper to establish the spin of the second excited state of Si ~s by a series of interlocking self-consistent experiments. Since a triple cascade from resonant capture states through the second and then the first excited state was the only means of studying the second excited state, one must place the spins and parities of the capture state and first excited state on a firm foundation. The parity of the first excited state was established as even b y Rubin's work on A127{d, n)Si s8 reaction and the spin was limited to 2 or 3. Previous workers have found that a spin 9 f two for this state was consistent with angallar distribution measurements and agreed with nuclear systematics. The 10.4-1.78 triple correlation at the 630 keV resonance has definitely confirmed this assignment.

ANGULAR CORRELATION STUDIES

~7

Parities of the capture states of the resonances studied are determined b y the orbital momentum of the captured proton because A1~7 is known to have even parity. Since all observed double correlations were anisotropic, s-wave protons are excluded. Many double and triple correlations for both the 630 and 405 keV resonances were computed on the assumption of d-wave proton capture. A consistent set could not be found to explain all the experimental results. Consequently, it was assumed that the resonances studied proceed by p-wave protons with negative parity assigned to the capture states. With both the spin and parity of the 1.78 MeV level established and the parity of the capture state known, the problem of determining the spin of the 4.62 MeV level is less difficult. Preliminary spin assignments for the capture states and the 4.62 MeV level are based upon measured double correlations. The entire spin sequence for the triple cascade has then been confirmed by a series of triple correlations. Correlation functions for the 7.36-2.84 MeV triple correlation at the 405 keV resonance have been computed with an assumed spin of 2, 3 or 4 for the 4.62 MeV level and 4- for the capture state. Although a set of mixing parameters could be found to explain the observed correlation with a spin of 2 or 3 for the second excited state for one geometry, it was not possible to obtain mutually consistent correlations for both geometries A and B. Furthermore since Hinds and Middleton have shown the parity of the 4.62 MeV level to be even, it is highly improbable t h a t finite mixing ratios could be observed both in the first and second transitions because only M1-E2 multipolarities are known to mix perceptibly. The interlocking network of double and triple correlations performed on the triple cascade strongly establishes the spin sequence at the 405 keV resonance to be 4- -+ 4 + -+ 2 + --~ 0 + and at the 630 keV resonance to be 3- -~ 4 + --~ 2 + --~ 0 +. With the determination of J~ = 4 + for the 4.62 MeV level, double correlations at the 326 keV resonance permitted a unique assignment of 4- for the Capture state. This confirms the less precise measurement by D. G. Fitzgerald 15) and agrees with the recent 0 ° to 90 ° anisotropy determination b y K. Okano 9).

References 1) 2) 3) 4)

R. Tangen, K. Nordske Vidensk. Selsk. Skr. (1946) S. E. H u n t and W. M. Jones, Phys. Rev. 89 (1953) 1283 K. J. Brostrom, T. Huus and R. Tangen, Phys. Rev. 71 (1947) 661 F. C. Shoemaker, J. E. Faulkner, G. M. Bouricius, S. G. K a u f m a n n and F. P. Mooring, Phys. Rev. 83 (195]) 1011 5) J. G. Rutherglen, P. J. Grant, F. C. Flack and W. M. Deuchars, Proc. Phys. Soc. 67 (1954) 101 6) J. G. Rutherglen and R. D. Smith, Proc. Phys. Soc. 66 (]953) 800 7) H. E. Gore, E. B. Paul, G. A. Bartholomew and A. E. Litherland, Phys. Rev. 94 (1954) 749

88

8) 9) ]0) 11) 12) 13) 14) 15)

Jr. I . V A L E R I O

AND

E.

B.

NELSON

J. I. Valerio, P h . D . dissertation, State University of Iowa (1960) K. Okano, J. Phys. Soc. Japan 15 (1960) 28 P. M. Endt and A. Heyligers, Physica 26 (1960) 230 P. M. E n d t and C. M. B r i m s , Rev. Mod. Phys. 29 (1957) 683 S. Hinds and R. Middleton, Proc. Phys. Soc. 7b (1960) 545 M. E. Rose, Phys. Rev. 91 (1953) 610 A. G. Rubin, Phys. Rev. 108 (1957) 62 D. G. Fitzgerald, M. S. thesis, State University of Iowa {L959)