The 16O(d, n)17F reaction at Ed = 8.0 and 9.3 MeV

- ~

Nuclear Physics A137 (1969) 531--544; ~ ) North-Holland Publishin~l Co., Amsterdam Not to be reproduced by photopriut or microfilm without written permission from the publisher

1 6 0 ( d , n)1~F R E A C T I O N AT E d = 8.0 AND 9.3 MeV

THE

S. T. T H O R N T O N t

University ol Wisconsin, Madison, Wisconsintt Received 4 August 1969 Abstract: The reaction 160 (d, n) ~7F was investigated by the neutron time-of-flight method at Ed = 8.0

and 9.3 MeV. Absolute angular distributions were obtained for the transitions to the ground and first excited states in 17E. Excited states in 17E at Ex = 3.10 and 3.86 MeV were identified. No evidence was found in 17F for the mirror level of the 5.22 MeV state in 170. The distorted wave method analysis of 160(d, p)170 and 160(d, n)lTF ground state and first excited state transitions yielded spectroscopic factors near 0.9. E I

I

N U C L E A R REACTIONS 160(d, n), E = 8.0, 9.3 MeV; measured a(En, 0). 17F levels deduced S. Natural target.

1. Introduction

The mirror nuclei 170 and 17F' have been the object of many experimental and theoretical investigations. In the simple shell-model the low-lying states of 170 and 17F are considered as having one nucleon outside the doubly magic closed shell nucleus 160. However, the true situation may be much more complex. Brown and Green 1) found that the low-lying even-parity states of 170 are described by mixing the usual states in the spherical shell model with deformed states obtained from an excited deformed core. Zuker, Buck and McGrory 2) found that the first two levels of 170 and XVF are well described by direct coupling of d~ and s~ nucleons to the 160 ground state. However, the 160 ground state was a highly correlated nucleus, composed of four nucleons moving outside a 12C core. Birkholz and Beck 3) concluded that several features of the excitation spectra of 17O and 17F may be accounted for by coupling an extra nucleon to the ground state and low-lying collective states of the 160 core. Brown et al. 4) concluded that the coupling of the extra nucleon in 170 with the odd-parity vibrations of 160 will shift an appreciable part (20 %) of the singleparti~le strength to levels several MeV away from the low-lying states. The 1 6 0 ( d , p ) 1 7 0 reaction has recently been experimentally studied by three groups 5- 7) who analysed the data using the distorted wave method. Earlier, several t U.S. Atomic Energy Commission Postdoctoral Fellow. Present address: Department of Physics, University of Virginia, Charlottesville, Virginia. tt Work supported in part by the U.S. Atomic Energy Commission. 531

532

S.T. THORNTON

groups analysed the 160(d, p)170 reaction with the Butler stripping theory. Alty et al. 5) recently reported spectroscopic factors of' about 0.6 for the transitions to the ground state and first excited state of 170. More recently, however, a study of the same reaction by Naqib and Green 6) and by deforest 7) gave spectroscopic factors nearer to 1.0. One of the objects of the present experiment was to determine the spectroscopic factors for the corresponding (d, n) transitions to the mirror states in 17F. After the present work was completed an experiment by 0liver et al. s) on 160(d, n)17F at Ed = 7.73, ll and 12 MeV was published. States in 17F at 0.0, 0.5, 3.1, 3.8, 4.4, 4.6, 4.8 and 5.6 MeV were reported. A broad state at 4.69 MeV is known to exist in 17F, but the states at 4.4, 4.6, and 4.8 MeV were reported for the first time. Spectroscopic factors near 1.0 were determined for the ground and first excited state transitions. Previously an 160(d, n)lTF experiment at E d = 7.7 MeV was reported by Knoll et aL 9), but no angular distributions were measured. Yaramis 1o) measured absolute differential cross sections for the 160(d, n)17F reaction for E d = 5.0 MeV to the ground and first excited states of 17F and analysed the data using the Butler stripping theory. One object of the present experiment was to identify as many states as possible in 17F. The energy level parameters of 170 and 17F nearly coincide through about the first ten excited levels (6 MeV excitation energy) except for a state at 5.22 MeV in 170 of unknown spin and parity. The mirror state in lVF has not been identified. The state in 170 is weakly excited 7) in 160(d, p)170, but is strongly excited 11,12) in the reactions I4N(~, p)170, 13C(6Li, d)170, and 13C(7Li, t)170. The state has never been seen in n + 160 elastic scattering. The particle width of the state cannot be more than a few keV [ref. 13)]. If the cross section were as large in the 160(d, n)lTF reaction as in the 160(d, p)17 O mirror reaction, it would be experimentally feasible to identify the neutrons going to the mirror state in 17F.

2. Experimental method Pulsed deuterons were obtained from the University of Wisconsin tandem accelerator. Neutron spectra were obtained by the neutron time-of-flight method. Details of the experimental apparatus and procedure have been previously described14). Recent additions include a direct extraction ion source, an ORTEC model 268 fast zero crossing discriminator-preamp base for the 58 AVP photo-multiplier tube, and the use of a DDP-124 on-line computer. A flight path of three meters for the neutrons was used. The NE 213 liquid ~cintillator coupled to the photomultiplier was 2.5 cm deep with a diameter of 10.2 cm. Pulse shape discrimination was used to separate neutrons and gamma rays. The lowenergy neutron bias was 0.5 MeV. The efficiency of the neutron detector was measured previously at the same neutron energy bias using the T(p, n)3He and D(d, n)3He reactions 15). The D(d, n)3He reaction angular distribution was measured at

160(d, n) 17F REACTION

533

E d = 5.0 and 5.8 MeV in the present experiment to check the neutron detection efficiencies. Both neutron and gamma spectra were recorded in 1024 channels and put on magnetic tape after each run. Thus the n- 7 discrimination and the intensity of the debunched beam could be checked and appropriate corrections applied. The 02 gas was contained in a cylindrical cell 2.75 cm long by 1.5 cm diameter. The gas was separated from the high vacuum by a 2.5 pm Mo foil. The beam was stopped at the end of the gas cell by a gold backstop. Data were taken with and without 02 gas, and the background runs were subtracted to obtain the neutron spectra from the 02 gas. Neutrons not coming from the target were shown to have an insignificant time correlation by taking neutron spectra with a brass shadow cone between target and detector. The only observed neutron spectra impurities were occasionally very small peaks probably from 12C. Natural 02 of purity greater than 99.9 ~o was used at a pressure of 175 Torr. The total target thickness for 9.3 MeV deuterons was 65 keV. The width of the neutron peaks was as low as 1.2 nsec F W H M , but was typically 1.5 nsec. Average beam currents were as high as 500 nA, but were usually limited to 100 nA by electronic dead time loss considerations. Neutron spectra were taken for deuteron bombarding energies at the center of the target of 8.00 and 9.30 MeV. Angular distributions between 0 ° and 140 ° were taken in steps of 10°.

3. Experimental results A neutron time-of-flight spectrum for Ed = 8.0 MeV at a lab angle of 41 ° is shown in fig. 1. The two gamma-ray peaks 71 and 72 are from gammas that escape the n-7 discrimination. The peaks are 250 nsec apart and are used to calibrate the time scale. Zero time is 10 nsec to the right of 71 and time proceeds to the left towards 72 where the cycle starts over. The beam is pulsed at 4 MHz, but the stop count rate to the time to amplitude converter is only 2 MHz. The neutron energy is shown at the bottom. Neutron transitions to the ground and first excited states (0.50 MeV) of 17 F are strong and are seen at every angle. Fig. 1 shows clear evidence for excited states at 3.10 and 3.86 MeV. These neutrons were also seen at most other angles, qhe angular distributions of transitions to the states at 3.10 and 3.86 MeV were not extracted since the transitions were weak. Neutrons going to the suspected peak near 5.22 MeV in 17 F would not be seen for Ed = 8.0 MeV. In the neutron spectra at Ed = 9.3 MeV, no peak was seen at any scattering angle due to the mirror level in 17 F of the 5.22 MeV level in 170. It is estimated that if the level is narrow and does exist in 17F, the differential cross section for the (d, n) transition must be less than 1 mb/sr at all angles for Ed = 9.3 MeV. The corresponding cross section in the 160(d, p6)170 reaction was as large as 6 mb/sr at the energies at which deForest 7) measured. The highest energy in these measurements was 8.55 MeV, and no 160(d, P6)170 data are available at Ed = 9.3 MeV. DeForest 7)found

534

S.T. THORNTON

800 -

I

ig.s.)

nTF(g's') ZeO(d,n)lrF Ed =8.00 MeV

700 x

(gLA8 = 41 * FLIGHT PATH = 3 m

600

d Z Z

500-

-r 40003 I--- 300Z :Z) 0 200C)

17F(O.50 )

I00~,,,

+_ 200

~'2 •

nlF(3.86)

~

'TF(&IO)

,

300

,t+~

400

500

600

CHANNEL '

I

.

.

.

.

.

800

.

Jk

900

IOOo

NUMBER

I

1.0

.

700

I

1.5

I

2.0

I

3.0

I

I

P

I

4,0 5,06.0 gOlO.O

NEUTRON ENERGY (MeV) Fig. 1. Neutron time-of-flight spectrum for Ea = 8.0 MeV. The time calibration is 0.40 nsec/¢hannel.

I

100 50'

i

i

~

i

160(d, no)17f ~..~'~, ~' /

\

,

i

i

160 Id,pa)170

E d = 8.0 MeV ~. ~ Rosen tl. - - . Watson

N~'i, ~'N.

i

E d : 7.85 MeV 13" - - Rosen '-" - - - Watson

~ e .

S:1.0

~,

Zi

S =1.0

10

5

1

i

i

iI

i

i

i

I

i

.....

~

i

i

i

i

i

i

i

~100

b 50 "o

20

~

\

.~',.

160(d, no)17F

160(d, po)170

E d = 9.3 MeV • -Rosen n. - - - Watson S : 1.0

E d = 8.55MeV ~- - - R o s e n

",// _~/,

~.\, x~,,

" --- watson s:,.o

10 ",,

10

2'o ~'o

go

8'o ,;o

,do ~;~'o ,;o ,8o0

Oc.m. (DEGREES)

2b

,'o

go

t

8'0 ,do ,2o

I

,,o

I

,+o ,80

Oc.m. (DEGREES)

Fig. 2. Centre-of-mass angular distributions for l~O(d, no)lTF at Ea = 8.0 and 9.3 MeV (data from present experiment) and for 160(d, po)lTO at Ed = 7.85 and 8.55 M e V [data from deForest 7)]. The lines are distorted wave predictions using the deuteron potential of Satchler 7) and the nucleon potentials of Rosen zg) and W a t s o n 22).

160(d, n)lTF REACTION

535

that the yield oscillated rapidly with energy. I f the suspected level were broad in ~7F, it would be difficult to detect the level in a neutron time-of-flight experiment. For example, the (d, n) transitions to the fourth (4.69 MeV) and fifth (5.10 MeV) excited states are not detected, probably because the peaks are spread out over too large an energy region in the neutron time-of-flight spectrum.

200 ~ ! \ 100

160(d'nl)17F Ed : 8 . 0 M e V I"I' - - Rosen • --- Watson S:l.O

50 ~ 20 I 10

60(d,P1)170 Ed : 7,85MeV ~ :

I

r --S:I.O

•• •

Rosen Watson

5 2

.

~J'

%

i •

1 "E" 0.5 ..o 0.2 E 0.1

I

I

I,,

I

~

200 b 100 "1o 50

I

I

I

I

160(d, n1)17F Ed 9.3 M e V ~s

n' ~

20 ~ 10 5

~ i~°

1

i

i

\

~

i

I

i

i

i

160(d'Pl )170 Ed : 8.55MeV p: - - Rosen --- Watson

~ V~

Rosen

' --- W a t s o n S:I.O

~

L

S:I.0 \

••

•

"'''"

"

" •

"'"

0.5 0,2 0.1

20

40

60

80 100 120 Oc.=. (DEGREES)

140 160 ;80

2'o

4'o

I

~o

i

8b ;do ;20 Oc.m.(DEGREES)

i

;~o

i

;60

;80

Fig. 3. Centre-of-mass angular distributions for 160(d, nl)lTF at Ea = 8.0 and 9.3 MeV (data from present experiment) and for 160(d, p l ) l T O at Ea = 7.85 and 8.55 MeV [data from deForest 7)]. T h e l i n e s are d i s t o r t e d w a v e p r e d i c t i o n s u s i n g t h e d e u t e r o n p o t e n t i a l o f S a t c h l e r 7) a n d t h e n u c l e o n p o t e n t i a l s o f R o s e n 19) a n d W a t s o n 22).

States at 5.67 and 5.68 MeV are known to exist in 17F. A peak in the neutron spectra for Ed = 9.3 MeV at several angles probably corresponds to neutrons going to one or both of these states. The resolution was not sufficient to separate the peaks. No neutrons were seen due to states at 4.4, 4.6, and 4.8 MeV as reported by Oliver

et al. 8). The angular distributions at Ed = 8.0 and 9.3 MeV for the x60(d, n)lTF ground and first excited state transitions are shown in figs. 2 and 3. The data are tabulated in table 1. The uncertainty in the absolute differential cross sections is estimated to be

536

s.r. THORNTON

__+15 %. This u n c e r t a i n t y is primarily due to uncertainties in the n e u t r o n detector efficiency a n d in separating the n e u t r o n spectrum peaks of no a n d n 1 .

TABLE 1 Centre-of-mass differential cross sections for 160(d, n)17F a)

160(d, no)17F Ea = 8.0 MeV

0.... (deg) 0.5 11.5 22.0 33.3 44.1 54.8 65.3 75.8 86.0 95.7 106.0 115.8 125.3 134.8 144.0

160(d, nl)17F

.Ea = 9.3 MeV

Ed = 8.0 MeV

do/dO (mb/sr)

0.... (deg)

dcr/d.Q (mb/sr)

33.6 38.3 43.5 43.2 30.8 17.1 9.45 6.60 6.05 6.34 6.60 6.50 5.95 5.20 3.54

1.0 11.9 21.0 22.9 33.7 44.5 55.2 65.7 76.1 86.4 96.4 106.3 116.1 125.6 135.1 144.4

31.6 35.4 36.8 36.4 29.7 16.3 7.55 4.45 4.13 4.25 4.25 4.48 4.91 5.34 5.15 4.48

0.... (deg) 0.5 11.5 22.0 33.4 44.3 55.0 65.7 76.0 86.4 96.4 106.3 116.0 125.6 135.0 144.2

Eo = 9.3 MeV

dtr/dO (mb/sr)

0.... (deg)

dtx/d-Q (mb/sr)

183.0 110.0 32.2 9.35 10.1 7.56 3.87 2.08 2.49 3.56 3.50 3.02 2.79 2.61 2.18

1.0 12.0 21.1 23.0 33.9 44.8 55.5 66.1 76.5 86.8 96.7 106.6 116.3 125.8 135.2 144.5

164.0 85.0 22.4 16.1 7.08 8.41 5.38 3.25 2.69 2.83 2.46 2.03 1.68 1.58 1.75 1.60

a) Absolute uncertainty in cross section is estimated to be ~ 15 %.

4. Analysis I n a d d i t i o n to the 160(d, n)~ 7F data from the present experiment, the x6 0 ( d , p)~ vO reaction data were analysed since the methods a n d results should be similar. It is interesting to determine if similar optical-model parameters give satisfactory fits to both reactions using the distorted wave method. If this is the case, a test can be made whether the spectroscopic factor S is the same for the (d, n) a n d (d, p) reactions. 4.1. OPTICAL-MODEL PARAMETERS The optical-model parameters from which the distorted waves in the entrance a n d exit channels m a y be calculated are determined by elastic scattering data. The opticalmodel potential used in the present distorted wave analysis had the form U ( r ) = Uc(r ) - V(I +eX) -1 +4iWD ~x (1 +eX') -1

_ _

r

_

dr

•

(1)

16 0 (d, n) ~7F REACTION

537

where x = (r-ro.4~)/a,

x' = (r-r~A~)/a '

and Xtt

It

~-

t!

= ( r - - r o . 4 )/a .

The C o u l o m b p o t e n t i a l , Uc(r), is t h a t o f a u n i f o r m l y c h a r g e d sphere o f r a d i u s rc A~. T w o sets o f d e u t e r o n p o t e n t i a l s were used to analyse the data. The first set was d e t e r m i n e d by Satchler as r e p o r t e d by d e F o r e s t 7). Satchler analysed d e F o r e s t ' s 1 6 0 ( d , d ) 1 6 0 elastic scattering d a t a at 6.00, 6.35, 6.90, 7.48, 7.85 a n d 8.55 M e V a n d r e c o m m e n d e d an average p o t e n t i a l t h r o u g h o u t the energy range r a t h e r t h a n the " b e s t fit" p o t e n t i a l for each energy. In the average potential the surface p o t e n t i a l W o was the only p a r a m e t e r t h a t varied with energy, (2)

W o = 1.5+0.425 Ed,

where E a is the l a b d e u t e r o n b o m b a r d i n g energy. The o p t i c a l - m o d e l p a r a m e t e r s are given in table 2. This p o t e n t i a l is representative ot d e u t e r o n optical potentials in the light nuclei 16). TABLE 2

Optical-model potential parameters used in entrance and exit channels ParV r ticle (MeV) (fin)

a (fm)

109

1.0

0.8

d 117.6

1.0

0.6

d

WD (MeV) 1.5.1. 0.425Ea ") 4.9

r' (fm)

a' (fro)

Vs.o. (MeV)

r" (fm)

a" (fm)

rc (fm)

Ref.

1.9

0.6

6.0

1.0

0.8

1.3

7)

1.9

0.6

7.5

1.1

0.37

1.3

n 49.31.25 0.33E. b)

0.65 5.75

1.25

0.7

5.5

1.25

0.65

present result 19)

n 48.01.27 0.29Enb)

0.66 9.6

1.27

0.47

7.2

1.27

0.66

zo)

n 61.61.14 0.3En b) p 53.8-1.25 0.33Ep°) p 62.8-1.14 0.3Ep c)

0.57 0.59-t0.64En b) 0.65 7.5

1.14

0.5

5.5

1.14

0.57

22)

1.25

0.7

5.5

1.25

0.65

1.07

19)

0.57 0.37"1" 0.64Ep ¢)

1.14

0.5

5.5

1.14

0.57

1.07

2z)

a) E~ = lab deuteron incident energy. b) E, = c.m. neutron incident energy. c) Ep = c.m. proton incident energy.

Recently B j o r k h o l m a n d H a e b e r l i 17) have m e a s u r e d the vector p o l a r i z a t i o n iT11 for 1 6 0 ( d , d o ) 1 6 0 at Ed = 8.0 MeV. W i t h p o l a r i z a t i o n d a t a it m a y be possible to i m p r o v e Satchler's p o t e n t i a l s t h a t were d e t e r m i n e d only f r o m scattering cross sections.

53/S

S. T. THORNTON

The optical-model search computer program S N O O P Y developed by Schwandt is) was used to fit simultaneously the iT~1 data at 8.0 MeV and the 7.85 MeV differential cross-section data. The result is given in table 2. All parameters were allowed to vary during one search or another to determine the new potential. In fig. 4 is shown 10.0

i

]

i

i

7.0

160(d ' d0 )160

4.0

Eel: 7,85"MeV --Satchler ---

~

i

~ /

.

Potenhal

Present

i

/

/

. j _ , , , .o'x. v ~"" * "'.. oJ

/

•

2.0 I

".,,.

it

Xl

1.0 0.7

0.4 0.2

~o.~

10.0 c~ 7.0 b 4.0

I

I

I

I

I

I

f

I

J

i

i

,

i

i

,

,

160(d, d0)160 = 8.55 MeV Ed--Satchler

---Present

2.0

"

" ; -~ - - " ' ~ " y

Potential

,~

,;

"

s

Ii

II

I

"'~ "

/

'

,

"l~

1.0 0.7 0,4

g

0.2

O. 1

20

4qO

610

[

q

I

80 I00 120 Oc.m. (DEGREES)

1

140

160 180

Fig. 4. The ratio of elastic scattering to pure Rutherford scattering. The data are from deForest 7). The lines are the optical-model fits to the data. deForest's elastic scattering 160(d, d0)X 60 data at 7.85 and 8.55 MeV with the opticalmodel predictions from the potential o f Satchler 7) and the new potential. Both potentials satisfactorily fit the data, the new potential being perhaps a little better at the backward angles. The optical-model predictions for iTt ~ are shown in fig. 5 for the 8.0 MeV data o f Bjorkholm and Haeberli 17). Since Satchler's potential was not based on the data, the values calculated from it can be considered a prediction.

160(d, n) t 7F REACTION

539

Most of the distorted wave calculations were made with the deuteron potential of Satchler 7). The new potential was not much more successful in fitting the 160(d, do)t60 elastic scattering data. Satchler's potential was an average potential over a 2.5 MeV energy range and probably tends to smooth out fluctuations. No elastic scattering data were available for n + ~7F or p + t 70. Therefore opticalmodel parameters had to be taken either from data on nearby nuclei or from parameters that are determined from a wide range of nuclei and energy. Neither method has been very successful for the light nuclei. In the present work the neutron and

;

I

o.6 -

i

I

'

I

'

I

'

'

I

i

I

I

160 (d,do)160 E d : 8.OMeV - - Satchler --- Present Pote'ntial

0.4

0.2

•

•

PI

-o.2

-\',

i _ /

I

"'- "

I

•

-

-

-0.4 _

:

I

-

-0.6

I 0

I 20

I

i 40

i

I 60

I

I 80

"~

I

i

I00

I 120

l

I 140

l

I 160

L 180

8c.m. (DEGREES)

Fig. 5. The data points for the iTlt angular distribution are from Bjorkholrn and Haeberli 17). The lines are the optical-model predictions (Satchler 7)) and fits (present potential) to the data.

proton optical-model parameters used were from general parameter sets. Well-known potentials for neutrons are those of Rosen t9) and Perey and Buck zo), and for protons those of Rosen tg) and Perey z~). These potentials were used along with potentials for protons and neutrons recently determined by Watson 22). Watson used data on light nuclei so that the potentials should be especially suitable for the 160(d, p)lTo and 160(d, n ) t 7 F distorted wave analysis. The neutron and proton optical-model potentials are shown in table 2. Optical-model potentials for the bound state particle consisted of the real central and spin orbit terms with the real central depth adjusted in the distorted wave analysis to fit the binding energy of the particle. The same shape of the optical-model potential was used in the bound state as for the nucleon in the exit channel.

540

S. T. THORNTON

4.2. DISTORTED W A V E ANALYSIS

The distorted wave method is often used in the analysis of direct reactions to determine the transferred orbital angular momentum and the spectroscopic factor. Much work has been performed on (d, p) reactions, but because of the greater experimental difficulties, (d, n) reactions have received less attention. The low-lying states of 17 0 and 17F are fairly well understood in the framework of the shell model.

200 ~

160(d

100

E d : 8.0 MeV ,d - - Satchler u: ___ Present Potential S : 1.0

50 20

,nl)T7F

~

10 % J

5

•

,,

2 1 "D

0.5

r', 0.2 E 0.1

I

I

I

200 " % " ~ ~ b

I

I

I

I

I

160(d'Pl)170 E d : 7.85MeV d" - - S a t c h l e r " - - - Present Potential S:1.0

lOO 50 20 °°';-'t

lO 5 2 1 0.5 0.2 0.I 0

~ 20

4'0

60'

' 12'0 8b 100 0c,m. (DEGREES)

' 140

160

180

Fig. 6. Centre-of-mass angular distributions for x60(d, nl)a7F (present data) and a60(d, pt)170 (deForest's 7) data). The lines are distorted wave predictions comparing the present deuteron potential and Satchler's 7). The nucleon potentials are from Rosen 19).

The ground state should be a ld~ state and the first excited state should be a 2s~ state 23). Since the ground state of t 6 0 is 0 +, all the angular momentum quantum numbers are assumed to be known for the stripping transitions. Thus by comparing the experimental differential cross section with that predicted by the distorted wave method, an estimate of the spectroscopic factor can be made.

160(d, n)lTF REACTION

541

The distorted wave calculations for the present analysis were made primarily with the distorted wave computer code DWUCK24). Finite range 25-27) and nonlocal 2a) effects were included by the local energy approximation. The non-locality range used was fl = 0.54 fm for deuterons and fl = 0.85 fm for the nucleons. Typically the non-locality correction was applied to the bound state as well as the entrance and exit channels. The results are shown in figs. 2 and 3 for the 160(d, n)lTF and 160(d, p)l 70 reactions. The curves shown are for a spectroscopic factor of 1. The neutron potentials of Rosen 19) and Perey and Buck 2o) gave similar elastic scattering and distorted wave stripping results for 160(d, n)lTF. Therefore, all the calculations shown are for nucleon optical-model potentials proposed by Rosen 19) or Watson 22). The results shown give the overall impression that the potentials of Rosen 19) are more successful in fitting the data than those of Watson 22). In fig. 6 a comparison is made of the deuteron potentials of Satchler 7) and the new potential for the transitions to the first excited states of 17 F and 170. TABLE 3 Absolute spectroscopic factors a)

Reaction 160(d, n)lTF 160(d, n)tTF a60(d, p)tTO 160(d, p)170 average S

Ed (lab) (MeV)

Ground state transition

First excited state transition

8.00 9.30 7.85 8.55

0.84 0.77 1.01 0.99 0.90

0.93 0.96 0.93 0.86 0.92

a) Calculated with deuteron potentials of Satchler 7) and nucleon potentials of Rosen 19). Finite range and non-local corrections were made. Distorted wave predictions agreed well with the 8.0 MeV 160(d, p0)17 0 analysing power data of Bjorkholm and Haeberli 17). The distorted wave predictions using the present deuteron potential agreed slightly better with the data than those using the potential of Satchler 7). No set of deuteron and nucleon potentials was successful in giving the shape of the 8.0 MeV 160(d, Pl)17 0 analysing power data of Bjorkholm and Haeberli t7) or of the 160(d, p~)170 polarization data of Evans 29) at 7.0, 8.2, and 9.55 MeV. In order to fit the 160(d, p 1) 17O polarization data, effects such as compound nucleus contributions will probably have to be taken into account. In order to extract spectroscopic factors, the normalisation factor D 2, defined by Satchler 30), was set equal to 1.65× 104 MeV 2 " fm 3. The isospin ClebschGordan factor, C 2, is equal to 1. The resulting spectroscopic factors are given in table 3. At deuteron energies near 8.0 MeV and for a nucleus as light as 160, compound nucleus contributions may be significant. No Hauser-Feshbach calculations were performed for the present analysis. Such an analysis has been made below 3 MeV

542

S. T. THORNTON

by Dietzsch et aL 31). For the x60(d, n 0) t 7F reaction Dietzsch et aL a 1) found about 10 ~ for the compound nucleus contribution at the forward peak. The compound nucleus contribution was always smaller than 3 mb/sr, and was generally isotropic 31). The compound nucleus contribution can be estimated for the present analysis. If the interference between the compound and direct contributions is assumed to cancel, the Hauser-Feshbach calculation for the compound nucleus contribution alone is symmetric about 90 ° in the centre of mass. Therefore an upper limit can be determined for the compound nucleus contribution at the forward peak from the corresponding experimental cross section at backward angles. The compound nucleus contribution can be neglected for the transition to the first excited state, but the contribution may be appreciable for the ground state. From fig. 2 the upper limit for the compound nucleus contribution at the forward peak f o r 1 6 0 ( d , n0)lTF and 1 6 0 ( d , p o ) l 7 0 is about 10 ~ . Thus an estimate for the compound nucleus correction is 5 + 5 ~ . The spectroscopic factors for the ground state transitions given in table 3, therefore, have been lowered by 5 ~o to take into account this effect. TABLE 4 C o r r e c t i o n effects in distorted wave analysis for 160(d, no)lTF reaction at Ed = 8.0 M e V Local or non-local potentials entrance a n d bound exit channels state non-local non-local non-local non-local local local local local

non-local non-local local local local local non-local non-local

Zero or finite range

finite zero finite zero finite zero finite zero

Effect o n spectroscopic factor ( ~ ) standard -- 1 + 15 ÷ 15 + 4 + 11 -- 1 -- 4

The 1 6 0 ( d , no) 17F distorted wave calculations at Ed = 8.0 MeV were also performed with the code JULIE 32) using Satchler's deuteron potential 7) and Rosen's nucleon potentials 19). Several variations with and without finite range, non-local and spin-orbit terms were calculated with both D W U C K and JULIE. No significant differences in the predicted magnitudes or shapes of the cross section were found between the two computer codes. The effects of finite range and non-locality are compared in table 4 for the i60(d, no)17F reaction at Ea = 8.0MeV. The calculations were performed by D W U C K with the optical-model potentials of Satchler 7) and Rosen 19). The standard configuration is the calculation including finite range and non-locality in the entrance, exit, and bound particles. The number given is the percentage correction to be applied to the spectroscopic factor resulting from the standard configuration. The difference between the zero range and finite range calculations is seen to be small.

160(d, n)17F REACTION

543

There is also little change in the shape of the angular distribution which is a general result ao). The effects of non-locality are pronounced. It is unclear whether the bound state potential should have the non-local correction applied 33). If it is not used the spectroscopic factor is increased by 15 ~ . 5. Discussion

No evidence was found in 17F for the mirror level of the 5.22 MeV level in 170. A promising reaction to investigate would be 14N(~, n)l 7F. This is the analog of the 14N(~,p)170 in which the 5.22 MeV state is strongly excited 11). The average of the spectroscopic factors for the 160(d, n)17F and 160(d, p)XTO reactions at the various deuteron energies were S = 0.90 for the ground state transitions and S = 0.92 for the first excited state transitions. The spectroscopic factors for the (d, ni) and (d, Pl) transitions were similar, but the spectroscopic factor for (d, Po) was about 20 ~ higher than that for (d, no). This difference is not particularly disturbing because of the uncertainty in determining spectroscopic factors and the lack of a proper compound nucleus correction. In addition, it was shown for the 160(d, no)lVF reaction at Ed = 8.0 MeV that using a local instead of a non-local potential for the bound state increased S by 15 ~ . Thus, there is clearly an uncertainty of at least _ 20 ~o in S. Previous investigators of these reactions have similarly found spectroscopic factors near 1.0. Dietzsch et al. aa) at much lower energies found S = 0.8-1.25 for the (d, no), (d, nl), (d, Po) and (d, p~) reactions. In an investigation of the 160(d, p)170 reaction for Ed = 6.0 to 11.0 MeV, Naqib and Green 6) found S = 0.8-1.0 for the ground state transition and S "nearly 1.0" for the first excited state transitions. Naqib and Green 6) corrected earlier results of Alty et al. 5) who had found rather small spectroscopic factors. Oliver et al. s) found spectroscopic factors near 1.0 for (d, no) and (d, nl). The results of the various experiments indicate spectroscopic factors for the two transitions in the range S = 0.9 to 1.0. The uncertainties associated with determining spectroscopic factors are, however, still too great to test the calculation of Brown et al. 4) according to which 20 ~o of the simple single-particle levels may be depleted. The author would like to thank Professor H. H. Barschall for his help and interest in this experiment. Appreciation is due R. R. Borchers and R. G. Kerr for their help with the time-of-flight apparatus and W. J. Thompson and G. R. Satchler for enlightening discussions. The experimental help of L. N. Rothenberg, J. C. Davis, F. T. Noda, D. G. Schuster, T. G. Masterson, and R. L. Hagengruber is gratefully acknowledged. Thanks are due to B. M. Preedom for performing the distorted wave calculations with JULIE. The author acknowledges support from a National Science Foundation grant at the University of Virginia where this manuscript was partially prepared.

544

S. T. THORNTON

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23)

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