The reaction 19F(d, pγ)20F

Nuclear Physics 59 (1964) 257--273; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

THE REACTION

tgF(d, p?)2°F

P. R. CHAGNON t Physics Department, The University of Notre Dame, Notre Dame, Indiana, U.S.A Received 31 March 1964 Abstract: With a deuteron energy of 0.47 MeV, proton- and gamma-ray spectra and gamma-gamma and proton-gamma coincidences in 19F(d, p~)2°F have been studied. A decay scheme for excited levels up to 3.5 MeV has been deduced. Proton-gamma directional correlations through some of the low-lying levels have been measured and have been analysed in terms of the distortedwave theory of direct interactions. The results are consistent with the former assignment of J = 1+ for the 1.06 MeV level, and permit a new assignment o f J = 2+ to be made for the 1.31 MeV level. For the first-excited level at 0.65 MeV, relations between the spin and the quadxupoledipole mixing ratio have been found. E

NUCLEAR REACTIONS FXg(d,lY/), Ea = 0.47 MeV; measured 7,),-coin, d, P'7'(e,~p). FXg(d,n), Fl°(d, p), FXg(d,~¢), Ea = 0.23-0.5 MeV; measured o'. F 2° deduced levels, J, •, ~ (E2/M1). 1. Introduction

Progress in the i n t e r p r e t a t i o n o f nuclear structure in the 2s, l d shell suggests t h a t it w o u l d be desirable t o have e x p e r i m e n t a l i n f o r m a t i o n a b o u t the levels o f o d d nuclei with f o u r particles in this shell, such as Z°F. This investigation was u n d e r t a k e n p r i m a r i l y with t h e objective o f d e t e r m i n i n g spins o f low-lying levels in 2°F. These levels are r e a d i l y excited t h r o u g h the r e a c t i o n 19F(d, p ) 2 ° F , Qo = 4.37 MeV. F r o m p r e v i o u s (d, p ) e x p e r i m e n t s 1, 2) the p o s i t i o n s o f m a n y levels have been d e t e r m i n e d a n d their p o s s i b l e spins have been restricted u s u a l l y to a choice o f three values. I n the p r e s e n t w o r k d, p? d i r e c t i o n a l c o r r e l a t i o n m e a s u r e m e n t s have been m a d e which in s o m e cases p e r m i t f u r t h e r restrictions to be placed on the spins.

2. Experimental Procedure D e u t e r o n b e a m s o f u p to 500 keV were p r o v i d e d b y a s m a l l V a n de G r a a f f accelerator. Fig. 1 shows schematically the g e o m e t r y used. M o s t o f the experiments were c a r r i e d o u t with t h i c k P b F 2 targets e v a p o r a t e d on 0.5 m m t h i c k c o p p e r backings. W i t h b e a m currents o f 3 # A over a n a r e a o f 0.1 c m 2 the P b F 2 showed slight losses in yield over p e r i o d s o f a b o u t 1 h. Each target b a c k i n g c o u l d be m o v e d so as t o expose f o u r fresh t a r g e t a r e a s to the b e a m w i t h o u t b r e a k i n g v a c u u m , so t h a t u n i n t e r r u p t e d r u n s o f several h o u r s were possible. A n Ortec surface b a r r i e r d e t e c t o r 300 m m 2 in + The work described in sects. 2-4 was done at the University of Michigan and was supported by the U . S . A . E . C . 257

258

P.R. CHAGNON

area was used as the proton detector; this was covered with a nickel foil 3 rag" c m - 2 thick which completely absorbed the scattered deuterons while permitting the observa-

A

\'

SCALE

I

0

t

I

I

2

I

3 cm

I

4

P

5

~J'J~'~

Fig. 1. Schematic representation of the experimental arrangement. The deuteron beam entering from the left is collimated by aperture A and impinges on target material T deposited on thick backing B. The sensitive area S of the particle detector is covered by nickel foil F held in place by the protective cap C which does not restrict the solid angle. Scintillation crystal N is shown in the reaction plane. It may be rotated about an axis perpendicular to the plane of the drawing. The particle detector may be rotated about the target chamber axis and the target chamber may be rotated about the beam axis.

kdlk p

~÷)P Fig. 2. The coordinate system. The polar axis is defined by kd × kp and azimuthal angles are measured from kd. t i o n o f p r o t o n p e a k s as l o w a s 1 M e V i n e n e r g y . T h e ~ - r a y d e t e c t o r w a s a 7.6 x 7.6 crn N a I ( T 1 ) s c i n t i l l a t i o n c o u n t e r a n d w a s u n s h i e l d e d . F o r ~-7 c o i n c i d e n c e m e a s u r e m e n t s a second such counter

12.7 x 10.2 c m w a s u s e d .

THE REACTION 19F(d, p~,)~°F

259

The proton counter could be rotated about the axis of the chamber, the target chamber could be rotated about the beam axis and the gamma-ray counter about an axis fixed in the laboratory so that measurements could be made with the gamma-ray counter both in and out of the reaction plane. Fig. 2 illustrates the coordinate system to which all angles are referred. It is identical to the coordinate system of Fletcher et al. 3) except that the (d, p) reaction angle is called 95p rather than Oap. With this choice of axes, 0p is always ½zc,~bp is always positive and the nuclear recoil direction ~bR is always negative. Here the angles (095) are used in context to denote either the direction of a radiation or of the centre of the corresponding detector; geometrical corrections are treated separately in the appendix. After each directional correlation was measured, corrections for y-ray absorption and for eccentricity of the apparatus were obtained by preparing radioactive sources of appropriate y-ray energy on standard target backings and measuring the y-ray intensity at every angle used in the correlation. The transmission thus measured showed characteristic dips of the order of 10 ~ when the y-ray counter passed behind the proton detector or in the plane of the target backing. No intensity corrections were applied to the particle detector since the reaction intensity was measured with this counter itself. The small bombarding energy available resulted in low yields, which was to some extent offset by the possibility of excluding scattered deuterons from the detector, allowing relatively high currents to be used, and by the feasibility of using thick targets without incurring excessive line widths. The experiments consisted of a general survey of ),-ray transitions through p? and ?y coincidence measurements over the whole range of excitation energy available, followed by py directional correlations through the 0.65, 0.99, 1.06 and 1.31 MeV excited levels of 20 F. For the VYcoincidences a conventional fast-slow system with a one parameter multichannelanalyser was used, while the py coincidence and correlation data were recorded on a Nuclear Data model 150-FM two-parameter analyser. In this case no external coincidence system was required as the resolving time of the analyser, about 1.3 #sec, was adequate to keep the chance coincidence rate below 30 ~ in the worst case. As most of the low-lying 2°F levels are excited by In = 2 stripping, directional correlation measurements were made with the y-ray detector moving in all three coordinate planes, in accordance with the recommendation of Huby, Refai and Satchler 4). Aside from the reaction under study, additional intense peaks from 19F(d, 001vO were evident in the coincidence spectra, while the singles spectra were partially obscured by the products of several reactions, principally 19F(d, ny)2°Ne and those originating in (12'~aC+d) and (2H+d). These background reactions restricted the range of proton angles for which good spectra could be obtained, and made it impossible to monitor the reaction rate directly. Rather the intensity was monitored by a separate single-channel analyser connected to the particle counter and set on

260

P.R.

CHAGNON

the prominent ground-state a-particle peak of 19F(d, ~)170 which falls at about 8 MeV, beyond all other particle groups.

3. Survey Experiments Relative yields of the 1.63 MeV 2°Ne y-ray from 19F(d, n)2ONe* and from tgF (d, p)2°F(fl)2°Ne* were measured over the deuteron energy range 400 to 500 keV, with a thick Teflon target, by observing with a 20-channel time analyser the growth

leF (d p)2°F ,9 F (d, p)Z°F(/~)2°Ne* 'gF (d, ~) u70

/

/

7

I-

z >(¢: <~

¢3 .J ta >-

2 BOMBARDING ENERGY (keV)

Fig. 3. Relative yields of the X°F(d, p) and 19F (d, co) reactions.

and decay of this y-ray with beam on and beam off. In this range the yields from the two reactions were found to be equal within __ 10 7o. In the same type of measurement at Ea = 1.05 MeV, Thompson s) has reported that the yield of zgF(d, p)Z°F is by far the larger. Relative yields of 19F(d, po)Z°F and 19F(d, c%)170 at a reaction angle of 90 ° have also been measured from E a = 230 to 470 keV. These are shown in fig. 3 where the intensity scale has been adjusted to match the Po and the y-ray measurements. The ratio of (d, e) to (d, p) yield varies only slowly with energy, justifying the use of the eo peak as an intensity monitor. At 470 keV the total production of Z°F from a thick PbF2 target is approximately 2 x 10-it reactions/deuteron.

THE REACTION 10F(d, p},)tOr

261

From the (d, p) yield curve one finds a mean deuteron kinetic energy of 448 keV when the beam energy is 470 keV, as in the correlation experiments. It may readily be seen that the use of thin targets would not appreciably have reduced the energy spread, as most of the reactions take place very near the surface of the target.

4.374

'gF + d - p

T

-- 4.28 4.31 4.08 3.96 3.68

;5.~59 t,°0 ~ :~.47 3.53 30 30

40

SO 40

3.18 tn= I Ln,3

2.97 2.87

2.20 Ln=2 2.05 tr,=Z - 1.97 1.85

30

10

I

90 0

Ln--2

1.31

(to:o) --0.9g L06 (Ln:2) t,:Z 0.830.65 i IO i 90 Ln=Z

Ln=2:

(I*)

J,2 +

Fig. 4. The k n o w n energy levels o f =°F up to 5 MeV taken from ref. x) together with the 7-ray transitions identified in this work. Branching ratios are qualitative estimates only.

The background problems mentioned above precluded the quantitative measurement of proton angular distributions. Qualitatively, none of the proton groups showed sharp forward peaking but in general a rise in intensity toward the backward direction was observed. This would appear to be consistent with the results of One et al. 6) and Seward et aL 7). In the P7 coincidence spectra several well-defined peaks were observed which have been identified as transitions between known 2°F levels; the transition scheme is shown in fig. 4. For the levels below 2.2 MeV this is in agreement with the results of

262

1'. R. CHAGNON

Gorodetzky et aL s). The transition from the 0.99 to the 0.65 MeV level has not been observed directly. The cascades originating at the 3.49 and 3.53 MeV levels jointly were confirmed by ?7 coincidences but the two levels could be resolved from each other only in the P7 spectra. In fig. 4 the tentative spin assignment J = 1 + comes from the 2 ° 0 beta decay experiment of Goldhaber et al. 9). The (d, p) reaction to the 0.83 MeV level was not observed. This region of the spectrum is partially obscured by the (d, ~) reaction leading to the 0.87 MeV level of 170. The only evidence observed relating to the 0.83 MeV level was the 1.37-0.83 MeV 77 cascade from the 2.20 MeV level.

4. Directional Correlations With the two-parameter analyser, d, P7 angular correlations through the 0.65, 0.99, 1.06, and 1.31 MeV levels were measured simultaneously. Four series of runs were made: in the first three the proton angle ~bp was fixed at 135 ° and the y-ray counter moved in the three coordinate planes (fig. 2), while in the fourth points were taken in the reaction plane only but with q~p = 90 °. Each point of each correlation corresponded to an integrated deuteron beam o f about 30 m C and contained f r o m 100 to 1000 counts in each coincidence peak. Some of the data are illustrated in figs. 5 and 6. After corrections for y-ray absorption and for chance coincidences were made, the data for ~bp = 135 ° were fitted by least-squares to the expression

~(0~%) = -40o [1 +y~ A~± C,~= (0~%)],

(1)

kq

with k = 2, 4 and q = 0, 2 . . . k. The Ck~+ are the real and imaginary parts of the spherical harmonics normalized as in ref. lO)

Ckq+ = ½(4n/(2k+ 1))~(Ykq+ Yk,-~), Ckq- = (1/2i)(4zc/(2k + l))~(Ykq-- Yk,-q), Cko = PR(COSoa). A Cartesian rather than polar form was chosen in order to simplify the least-squares fitting procedure *. However, the phase angles 2q~o and 4qbx, where Ak2 = ]Akz] exp(--i2~oo) and Ak4 = [Ak4]exp(--i4qh ) are useful in making comparisons with theoretical calculations. These are listed along with the Akq in table 1. The angles listed are referred to the recoil axis not the beam axis. * For points restricted to the three coordinate planes, Caz_and C~2_are not linearly independent functions, hence the 42- term had to be omitted from the least-squares fits. The coefficient listed as A~_ in table 1 is really a linear combination of the Aza_and A42- occurring in eq. (1). As the corresponding theoretical coefficientsd2~ and ~2 are proportional to each other, this caused no difficulty except insofar as the geometrical corrections applicable to the two terms are different.

REACTION 19F(d, pT)tOF

THE

180"

90 ° I

I

0°

I

I

I

263

0°

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90 °

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I

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--,.,8

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¢j•y=O

1.2-

18(

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1.2

~='~"

/>

°°°

~"~" o o

1.0

-I.0

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0.8

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1.20

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e,.,o-

0.8-

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i

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Q

0

_~,

t

-

0

\oo~ o'S ~oj

C~p=135'*

_ 180o

/ ~

1.0-

-0.8

/ \

0

/

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i

(~

~

t

1

I

I o 90

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.

1.2-

1.0-

0.8-

~ = 9(3"

I

-180 •

I

I

-90"

|

•

I

I

90 =

I

I

180o

Fig. 5. Directional P7 correlations through the 0.65 MeV level. The three upper graphs show points in the three coordinate planes, with ~p = 135 °. The solid curves are a single least-squares fit. The bottom graph is for ~p = 90 °, in the reaction plane only, with the scale displaced by the difference in recoil angles. The solid curve is a separate least-squares fit.

264

v. R, CHAGNON

In each case additional least-squares fits were made to expression (1) with k restricted to 2. The criterion of Rose 11) was then applied to determine whether k = 4 terms should be considered significant. Values of Ak~are given in table 1 and were retained in the analysis below, to the next higher order than that satisfying Rose's criterion. Data taken with ~bp = 90 ° covered only the reaction plane. In this case a simple Fourier series ~(q~) = A o [ 1 + ~ (Aq+ cos q~%+A~_sin qq~)] (2) q <

180"

J

~r

1.2-

],

8r 90 ° J

r

]

0° I

I

(2# I

~' 180"

90 °

I

]

I

I

~r

=0

(j~p =135 .

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o

o

o

I =90"

-I.2

(~)p = l~350 -I.0

1.0-

o

0.8-

X

\

/

\

0.8

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,2-1

/

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0.8

8y=90

=

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!q I

-180"

I

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- 90 °

I

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•

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90*

180*

1.2 o

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o

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1.0 o

0.8

8y=90.

o

~=9o-- 180 °

,

~,, I

__~Oe

* I

~)0

I

'

9~

'

I

180 °

Fig. 6. Directional (pr) correlations through theol.31 MeV level. The arrangement is as in fig. 5.

THE REACTION x'r(d, pr)*°F

265

was used, with q = 2 and 4. All of the expansion coefficients relating to a given level are used together in the analysis below. TABLE 1 The experimental coefficients A~ ~ of expression (1) and A a~ of expression (2) for the p7 directional correlations Ex(MeV)

0.65

0.99

A~o A21+ A21- a) A4o A4~+ A44+ A4~2ffo(deg) 4~i(deg)

0.1194-0.011 --0.1544-0.012 0.2544-0.016 0 4-0.02 0.01 4-0.01 0 4-0.02 --0.03 4-0.02 3 4-2.5

0 =1=0.04 0 4-0.04 --0.054-0.04

A2+ Ae_ A4+ A4_

0.032=[=0.010 0.0634-0.010 0.01 4-0.01 --0.0154-0.010

0 4-0.02 --0.054-0.03

1.06 --0.024-0.03 --0.04=1=0.03 --0.02=1=0.03

0.044-4-0.04 0.01 4-0.04

1.31 -----

0.054- 0.03 0.064- 0.04 0.144- 0.04 0.104- 0.04 0.064- 0.02 0.064- 0.04 0.024- 0.06 -- 23 4-18 136 4-48

-- 0.045::t= 0.035-4-- 0.05 40.054-

0.04 0.04 0.03 0.04

a) See footnote in text.

5. Analysis 5.1. DETERMINATION O F THE ~7tFk

The analysis of d, p~ directional correlations has been extensively discussed by Satchler et aL 4, 1o, 12, 13). It has been shown that in the plane-wave limit the correlation is equivalent to that between the gamma-ray and a neutron entering along the nuclear recoil axis. That this limiting case does not apply to the present experiment is evident in fig. 5, where the anisotropy is reduced by a factor of 3 when the proton angle is changed from 135° to 90 ° . This figure also illustrates the remark 12) that the shift of the symmetry axis away from the recoil axis may be small even though distrotion effects are appreciable. The form of the point angular correlation, for l. = 2 and for a fixed proton angle, has been given x2,13) as =

(3) kq

where the Fk are the gamma-ray angular correlation factors and in general include multipole mixing F k = (1 + ¢52)- 1[Fk(LLJf j ) + 2tSFk(LL,Jfj) + t52Fk(L,L, jr j)],

(4)

where 6 is the ~-ray amplitude mixing ratio, Fk(LxL2JtJ) are the coefficients tabulated by Ferentz and Rosenzweig 14), L and L' are the multipole orders (here 1 and 2),

266

P. R. CHAGNON

Jf is the final-state spin (here 2 for the 2 ° F ground level) and J i s the spin of the intermediate state (excited level). The rik are analogous coefficients for spin ½ particles, introduced and tabulated by Satchler 1o) and include mixtures in the transferredneutron partial waves rik = (1 +X2) -1 [rlg(JnJ, . .Ji J). +.2Xrik(JnJn . Si J) + x 2rik(a,.... Jn J~ J) ],

(5)

where x is the partial-wave amplitude mixing ratio, j . and j., are the total angular momenta of the transferred neutron partial waves, and Ji is the spin of the target nucleus. In the present experiment J~ = ½ so that partial-wave mixtures occur only for J = l.. Mixtures of different l, have not been considered in the following. The aVkqin eq. (3) are the statistical tensors describing the distortion effects and are calculable from optical-model potentials 23). With the coordinate system chosen as in fig. 2, k and q take on only even values but the dkq are complex. They transform like spherical tensors so that expression (3) is always real. It is shown in the appendix that the calculated experimental angular correlation may be expressed as W(0~'(Pr; (PP) = 2 rikFkCkObkq((pp)Ckq(Ort~y)'

kq

(6)

with q taking on positive and negative even values where now (0~br) denotes the centre of the v-ray detector, and ~bp of the proton detector, rather than the actual directions of emission. The Cko are the usual gamma-ray detector correction factors (Jk of ref. 11)) and the bkq are essentially the CVkq,expressed in laboratory coordinates and averaged over the proton detector. Explicitly eq. (6) may be written, setting rio = F 0 = Coo = b o o = 1, as = 1 + c2 0 ri2 F2 [b2 0 C2 0(0~ cp~)+ 2b2 2 + C2 2 + (0~ cp~)- 2b2 2- C2 2- (0~ ~P~)]

+C4ori4F4[b4oC4o(O~q~)+... ], (7) where bkq+ and bk~- denote the real and imaginary parts of bkq. Thus the values of q2F2 and ri4F4 may be determined if the ak~ are known. For the 19F(d, pv) 2OF reaction, values of the distortions a~kqhave been calculated 15) by Satchler using potentials for the incident deuteron taken from elastic scattering or from (d, p) experiments on neighbouring nuclei, e.g. (1 s O + d) and for the outgoing proton taken from the comprehensive work of Percy x6). As Satchler provided calculations for several combinations of potentials and cutoff radii, the following procedure was adopted to determine the most suitable distorted-wave parameters. First a qualitative selection was made on the basis of the phase angles 2~bo and 4tkx only, because these do not depend on the rikFk and are only slightly altered by geometrical corrections. For each of the eight combinations selected in this way, the bkq were computed as described in the appendix. Then a least-squares fit was made of the experimental Akq+ and Aq± of eqs. (1) and (2) to the corresponding quantities in eq. (7), e.g. A2o to ri2F2b2oc2o, A44_ to -2q4F4b44_e4o, etc. In each of these fits,

TIlE REACTION 19r(d, p~,)2°F

267

all of the experimental coefficients for both proton angles and for the two excited levels Ex = 0.65 and Ex = 1.31 MeV were matched to the set of bk~ computed from one potential, the only adjustable parameters being the angular correlation factors t h F ~ for the two levels, and the normalization factor Ao/Aoo. Some sets of optical-model parameters yielding good overall fits, together with the value of X2 for each fit and the resulting coefficients rhF k are given in table 2. It may be noted that (a) although the first two potentials are rather different they yield nearly identical values of ~hFk and (b) if the same parameters are used to fit individual sets of data, consistent values of r/kF~ are obtained. Of course in that case the individual fits are better. The latter point is distinctly different from the planewave treatment, which gives disparate values of ~hFk for ~bp = 90 ° and q~p = 135 °. TABLE 2 The optical model parameters in the notation of ref. is) and the resulting angular correlation factors Potential label

M3 a)

B3 b)

B3

Cutoff radius (fm)

4.8

4.5

4.1

Deuteron V(MeV) W(MeV) re(fro) re(fm) a(fm) ro(fm ) a'(fm) W'(MeV)

69 15 1.46 1.3 0.63 0 0 0

100 0 1.0 1.3 0.9 1.55 0.5 80

Proton V(MeV) W(MeV) r0(fm) rc(fm ) a(fm) r0(fm ) a'(fm) W'(MeV)

55 0 1.25 1.25 0.65 1.25 0.47 3D

55 0 1.25 1.25 0.65 1.25 0.47 30

Z2 rhF2(0.65 ) r/4F4(0.65 ) ~hF2(1.31) r/~F4(1.31)

3.1 --0.2924-0.02 0 -4-0.03 0.03 4-0.05 0.17 4-0.06

a) from 180(d, p)1'O at 7 MeV (ref. iv)). b) from (160+d), modified is).

3.3 --0.290={=0.02 0 -4-0.03 0.03 -4-0.05 0.18 4-0.06

3.9 --0.2944-0.025 0 -4-0.03 0.03 -4-0.05 0.18 4-0.06

268

P.R. CHAGNON

The uncertainties in rhFk listed in table 2 are those arising from the poorness of the overall fit and are appreciably larger than the propagated experimental errors. 5.2. INTERPRETATION OF THE r/kFk Levels formed by 1n = 2 stripping on 19F m a y have spins 1 +, 2 + or 3 +. I f J = 1 or 3, the neutron partial wave must be pure d t or d t respectively. In these cases the values of ~/k are known 1o) so that the experimental values o f FR m a y be determined. These are to be compared with the values of F k as functions o f J and 6 as given by eq. (4). This m a y be done most readily by the graphical method of Arns and Wiedenbeck is). In the case J = 2, both dj and d~ partial waves are permissible, and the experimental values of rlkFk must be compared with the product of expressions (4) and (5). The method given by Arns and Wiedenbeck for double mixtures in ?-V correlations is readily adapted to this case, as illustrated in fig. 7. for the 1.31 MeV level. In this graphical analysis Qp represents the fractional intensity contributed by the higher jn value, Qp = x2/(1 "[-X2) in analogy with the fractional quadrupole intensity Qr = fi2/( 1 +fi2) for the v-rays. One point o f difference with the V-? case should be noted: as the r/4 ellipse is non-degenerate, one must, in projecting points with a given Qp f r o m the ~/2 to the r/, ellipse, connect only points having the same sign of the mixing ratio x. 6. Results and Discussion

6.1. THE 0.65 MeV LEVEL Taking as experimental values r / 2 F 2 = -0.2914-0.02 and r/4F 4 = 04-0.03, it is possible to find values of Qp and Qv for all t ~ e e spin choices J = 1, 2, 3. These are listed in table 3. The three spin choices correspond to quite different values of the TABLE 3 Values of the mixing parameters for the formation and decay of the 0.65 MeV level in laF(d, pT)~°F Spin (J)

3

Jn

Fractional intensities

1

]

0.10 ~ Qr ~ 0.14, ~5 > 0 or 0.99 _~Q? ~1.0 , tS>0

2

~,~

0.27 ~ a~ < 0.44, tS<0 or 0.92 ~ Q? ~ 0.98, t5 < 0 with 0_~Qp___0.03 or 0.89 ~ Qp ~ 1.0 , x < 0

~

0 <: Q? _~ 0.0016, d ~

o

quadrupole fractional intensity Qr. For J = 1 or 3 one would expect Qr to be within a few orders o f magnitude of the single particle estimate which is about 10 -4. This makes the choice J = 3 far more attractive than J = 1. The latter is unlikely also

TI-IE

REACTION

19F(d) p~,)~°r

269

in view of the lack of a fl-ray branch to this level in the decay of 2 oO (re£ 9)). For the choice J = 2 however, the mixing ratios listed are not improbable as the E2 transition rate may be greatly enhanced by collective effects. It should be pointed out that a separate measurement of the mixing ratio for this transition would now be sut]Scient to determine the spin. 6.2. THE 0.99 A N D 1.06 MeV LEVELS

The angular correlations through both of these levels are not distinguishable from isotropic. For the 1.06 MeV level this is consistent with the stripping result 1, 2) In = 0 and with either J = 0 or J = 1. Goldhaber et al. 9) have made the tentative assignment J = 1 + on the basis on t h e f t value for 2°0//-decay. The present data for the 0.99 MeV level are poor as the doublet was barely resolved. The anisotropy is

I I I ; ;

0.5 ,,

1 Qp

-I

t I J 1 1 1

't

I

I

/

o.s o .....

~L~~ ~(~0~

~Qp

l -~

-Z l

l

l

,i

l

8-0~ J

I'Q>. Fig. 7. The graphical analysis of the data for the 1.31 MeV level and J = 2. The hyperbolae representing the experimental values arc drawn for one standard deviation above and below the mean values. Only that branch of each hyperbola which leads to a solution is shown.

270

P.R.

CHAGNON

certainly not large, as indicated in table 1, but any of the spin choices J = 1, 2, 3 could give nearly-isotropic correlations for certain mixing ratios. Rout et aL 2) have expressed disagreement with the earlier stripping assignment for these two levels, as quoted here. 6.3. THE 1.31 MeV LEVEL Here again the stripping value is l, = 2, but in this case the experimental values q2F2 = 0.03+0.05 and ~/4F4 = 0.17+_.0.07 cannot occur with J = 1 or 3. For J = 2, L31

2~

(¢)

1.06 0.99 0.83

(z+,3'-:

0.65

E2

0

2¢

':F,, Fig. 8. The low-lying levels of 2°F. the fractional intensities are 0.97 < Qr < 1.0, and either 0.01 < Qp =< 0.12 or 0.73 = Qp =< 0.89 (cf. fig. 7). The large value of Q~ is not unreasonable for a 2 + --, 2 ÷ transition if the levels are collective in nature. As a rough comparison, the DavydovFilippov 19) estimate for a transition between the second and first 2 + excited levels in an even nucleus with Z = 9 and E~ = 1.31 MeV is Q~ ~ 0.4. The results are summarized in fig. 8. 6.4. DISCUSSION In a recent paper Kurath 20) has suggested that as a first approximation the lowlying levels of Z°F may be regarded as formed of collective K = 1 and K = 2 bands of the Nilsson model, with strong band mixing. On this basis he was able to compute the magnetic moment of the ground level in good agreement with experiment. It is not possible, however, to reconcile the present results with the spectrum predicted by Kurath. I f one assumes that the 0 and 1.31 MeV levels are the members of the I = 2, K = 1 and 2 doublet, the energy difference (or the moment of inertia) is wrong by a factor of 2. Slightly more band mixing than used by K u r a t h would bring an I = 3 level into the r61e of first excited level, but would increase the discrepancy

THE REACTION l a F ( d , I ~ ) 2 ° F

271

mentioned above. As Kurath suggests, particle excitations should be taken into account in discussing the excited levels. A thorough analysis of the stripping results has been made by Dazai 23), who assigned J = 3 + to the first excited level on the basis of the reduced width. The author wishes to express his appreciation for helpful and stimulating discussions with Professor K. T. Hecht, who suggested the problem, with Professor M. L. Wiedenbeck, in whose laboratories the experiments were carried out, with Dr. R. M. Woods, Jr. and Dr. Michel Martin. Much of the computer coding was done by William Greenberg. William Greenberg, Victoria Levis, Dennis Lollar, A. B. Miller, William Miller, Betram Pohl, Kenneth Weaver, Katherine Yakes and John Yoder assisted in taking data. Special thanks are due to Dr. G. R. Satchler of the Oak Ridge National Laboratory who suggested the distorted-wave potentials and computed the distortions.

Appendix GEOMETRICAL CORRECTIONS Geometrical corrections to angular correlation measurements involving a collimated beam and two axially-symmetric detectors have been discussed in a previous paper21). The coordinate systems and notation of ref. 21) will be used in this section, with subscript 1 denoting the proton, and 2 the ?-ray, coordinates. In the present case the dependence of the angular correlations on proton angle has not been explored fully. It is desired to determine the geometrical corrections using the computed variations of the distortions akq with reaction angle. In so doing it is necessary to take into account that the point correlation, eq. (3), is given in a coordinate system, say x"y"z", whose x"y"-plane is defined by the actual direction of emission of the proton and the beam axis, while the laboratory xy-plane is defined by the centre of the proton detector and the beam axis. If the proton is emitted in direction (01~1) relative to the proton detector (see fig. 1 of ref. 21)), the x"y"z" coordinate system is related to the xyz system by a rotation through an angle fl, where tg fl = -sin/)1 cos ~pl/(sin • cos/)1 +cos ~ sin/)1 sin ~Pl),

(A.1)

where ~ is the angle from the beam axis to the centre of the proton detector. The actual (d, p) reaction angle ~b'p'is given by cos ~ ' = cos ~ cos/)1 - sin ~ sin/)1 sin ~1.

(A.2)

The point correlation of eq. (3) becomes in laboratory coordinates t ! tl W(/)2(,02, r.pp fl) = 2 qkFkdk~/((PP ) E n.~ *k (--½It, fl, ½g)Ck.(/)2, tp2). , .

¢t

kq

I~

Substituting for the rotation matrix elements

o*~(-½=,/~, ½=) = (i)"-'d~,~),

(A.3)

272

p . R . CHAGNON

rearranging factors and interchanging indices bt and q one obtains

w = ~, rlkFk • (i)q-~aku(q~)dk~(fl)Ckq(~'2tP'2).

kq

(A.4)

A convenient expression for the elements dff~is quoted by Feingold ond Franke122). In eq. (A.3) the index # takes on odd as well as even values from - k to k, consequently after the interchange of indices, q in eq. (A.4) takes on odd values also while the sum on # is over even values only. In the integration over the axiallysymmetric detector, below, the odd q terms vanish. Following ref. 21) the experimental correlation ~ may be written ~(~tp; 4 ) = f d ~ l d O

2 El(~l~ol)E2(#2tP2)

,, k ~qkFiCkq(~'2q>'2)~, (,)• q-t~ dka(q~p)d~(fl),

kq

#

or

~(0q~; 4) = ~ rlkFkCkobk~(~)C~(Oq?) ,

kq

(A.5)

which is eq. (6) of the text, where Cko is the usual correction factor for the gammaray detector 11, 21, 22) and ¢t k bk~(~) = f d a l E1 ( 0 l i p 1 ) ) " (t)• q--/t t~ku(tpv)d~u(fl).

(A.6)

Fortunately the Oak Ridge computer code SALLY which is used to calculate the distortions gives as output a complete table of dkq versus reaction angle (here 4~p'). A computer code has been written to perform integration (A.6) numerically, for each point in detector coordinates (01t~,) evaluating (op' and fl from expressions (A.1) and (A.2), and interpolating ~kq(~bp) from the tables of code - SALLY output. For the experiments described above where the proton detector solid angle was (0.02)47r, the values of bkq differed from the corresponding a~kqby 10% to 20%. References 1) T. Lauritsen and F. Ajzenberg-Selove, Energy levels of light nuclei, issued as 1961 Nuclear Data Sheets (1962) 2) V. M. Rout, W. M. Jones and D. G. Waters, Nuclear Physics 45 (1963) 369 3) N. R. Fletcher, D. R. Tilley and R. M. Williamson, Nuclear Physics 28 (1962) 18 4) R. Huby, M. Y. Refai and G. R. Satchler, Nuclear Physics 9 (1958) 94 5) L. C. Thompson, Phys. Rev. 96 (1954) 369 6) K. One et al., J. Phys. Soc. Japan 14 (1959) 117 7) F. D. Seward, I. Slaus and H. W. Fulbright, Phys. Rev. 107 (1957) 159 8) S. Gorodetzky, T. Muller, G. Bergctolt and M. Port, Congres Int. de Phys. Nucl6aire, 1958 (Dunod, Paris, 1959) p. 885 9) G. Scharff-Goldhaber, A. Goodman and M. G. Silbert, Phys. Rev. Lett. 4 (1960) 25 10) G. R. Satchler, Prec. Phys. Soc. A66 (1953) 1081 11) M. E. Rose, Phys. Rev. 91 (1953) 610 12) G. R. Satchler and W. Tobocman, Phys. Rev. 118 (1960) 1566 13) R. H. Bassel, R. M. Drisko and G. R. Satchler, Oak Ridge National Laboratory Report ORNL-3240, unpublished

THE REACTION 18F(d, pT)20F

14) 15) 16) 17) 18) 19) 20) 21) 22) 23)

273

M. Ferentz and N. Rosenzweig, Argonne National Laboratory Report ANL-5324, unpublished G. R. Satchler, private communication F. G. Perey, Phys. Rev. 131 (1963) 745 G. Wickenberg, S. Hjorth, N. G. E. Johansson and B. Sjogren, Ark. Fys. 25 0963) 191 R. G. Arns and M. L. Wiedenbeck, Phys. Rev. 111 (1958) 1631 A. S. Davydov and G. P. Filippov, Nuclear Physics 8 (1958) 237 D. Kurath, Phys. Rev. 132 0963) 1147 P. R. Chagnon, Nucl. Instr., to be published A. M. Feingold and S. Frankel, Phys. Rev. 97 '(1955) 1025 T. Dazai, Prog. Theor. Phys. Osaka 27 (1962) 433