- Email: [email protected]
0°-yield of gamma rays in the T(p, γ)4He reaction
Volume 18, number 3
0°-YIELD
]PHYSICS L E T T E R S
OF
GAMMA
RAYS
IN THE
1 September 1965
T(p, y)4He
REACTION
*
R. SCHRACK**, D. KOHLER, N. G. PUTTASWAMY and W. E. MEYERHOF
Department of Physics, Stanford University, Stanford, California Received 9 August 1965
P a s t e x p e r i m e n t a l s t u d i e s of the T(p,y) r e action [1-3] have indicated that the c a p t u r e p r o c e e d s m a i n l y by e l e c t r i c dipole e m i s s i o n , with s o m e e l e c t r i c quadrupole a d m i x t u r e , through s i n g l e t T+p i n t e r a c t i o n s . Both of t h e s e t y p e s of r a d i a t i o n would have z e r o yield at a 0 ° e m i s s i o n angle [1]. T r i p l e t T+p i n t e r a c t i o n s on the other hand would p r o d u c e g a m m a e m i s s i o n at 0 °. E x p e r i m e n t a l l y , the p r e s e n c e of 0°-yield in the T(p,7) r e a c t i o n has not b e e n c l e a r l y a s c e r t a i n e d [1,2]. A r e c e n t phase shift a n a l y s i s of the T(p, p), T(p, n) and 3He(n, n) r e a c t i o n up to 22 MeV in the 4He s y s t e m [4] has indicated s i n g l e t s and p and t r i p l e t p n u c l e a r i n t e r a c t i o n s in the T+p s y s t e m , but t h e r e is no evidence for a t r i p l e t s i n t e r a c t i o n beyond h a r d s p h e r e s c a t t e r i n g . The ~inglet s i n t e r a c t i o n gives r i s e to a 0 + s t a t e in He n e a r 20 MeV, which is now well e s t a b l i s h e d [5-9]. The state s e e m s to have isotopic spin T = 0 [10, 11]. It has b e e n shown [6] that a p wave i n t e r a c t i o n could explain r e s o n a n c e effects at 22 MeV in 4He which a p p e a r in 4He(e, e') [7], 4He(p,p') [8] and D(3He, 2p)W [9] r e a c t i o n s . T h i s is c o n s i s t e n t with c a l c u l a t i o n s of Sydlitz and W e r n t z [12], which i n d i c a t e that the state in q u e s t i o n should be 1% S = 0, T = 0. T(p, p) pol a r i z a t i o n m e a s u r e m e n t s also point to a 1- a s s i g n m e n t [13]. The e x i s t e n c e of h i g h e r lying, T = 1, s t a t e s in 4He c a n be i n f e r r e d f r o m phase shift a n a l y s i s by T o m b r e l l o [10] of 3He +p and T+n e l a s t i c s c a t t e r i n g and p o l a r i z a t i o n . On this b a s i s one would expect L = 1, S = 1, s t a t e s in 4 H e o f s p i n s 2, 1, a n d 0 n e a r 24, 26, and 2 8 M e V r e s p e c t i v e l y and an L = 1, S = 0, 1- state n e a r 30 MeV. We d e t e r m i n e d the 0O-yield of the T(p, ~) r e action as a m e a n s of studying higher lying s t a t e s of 4He, s i n c e it s e l e c t s the t r i p l e t T+p i n t e r a c * Supported in part by the National Science Foundation and by the U. S. Army Research Office (Durham). ** On educational leave from the National Bureau of Standards (1964-65).
tions [1]. A 14-keV thick T - Z r t a r g e t on 0 . 0 2 5 - c m thick s i l v e r backing [14] was b o m b a r d e d with p r o t o n s f r o m a 3-MeV Van de Graaff a c c e l e r a t o r . The g a m m a d e t e c t o r was a 5"-alia. × 6 " - l o n g sodium iodide c r y s t a l , p r o v i d e d with a p l a s t i c a n t i c o i n c i d e n c e shield and a n t i - p i l e u p c i r c u i t r y . A conical opening of 4.30 half angle in a 4" h e a v y -
u~ I.-
(a) L
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r-'t
n., ,.<
(b)
J uJ z z -r (,3 -% (/) I-Z
I
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0
L I00
I 200
300 CHANNEL
400
NUMBER
Fig. 1. Typical gamma-ray spectra from T(p,y).(a) At 46.4 o, Ep = 3.18 MeV. (b} At 0°, Ep = 3.18 MeV, before background subtraction. The shade(] region shows the part of the spectrum used in the cross section analysis. (c) Background at 0o, E D = 2.58 MeV, with collimator hole blocked by'4" long lead cylinder. 327
Volume 18, number 3
P H Y S I C S LE T T E RS
m e t block s e r v e d as c o l l i m a t o r . The d e t e c t o r a s s e m b l y could be r o t a t e d around the t a r g e t . In o r d e r to c a l i b r a t e the 0 ° c r o s s s e c t i o n and to co m p u t e the s i n g l e t c o n t r i b u t i o n [ ~ ( s i n 0 + a s i n a c o s 8) 2] [1] to the f o r w a r d y i e l d within the c o l l i m a t o r opening, the y ie ld w a s d e t e r m i n e d at 8.6 o and 46.4 °, as w e l l as 0 °. Fig. 1 shows the u p p e r end of ty p i c a l p u l s e height s p e c t r a : c u r v e (a) at 46.4 ° (Ep = 3.18 MeV), c u r v e (b) at 0 ° (E u = 3.18 MeV, no background s u b t r a c t e d ) , c u r v ~ (c) background at 0 ° (E n = 2.58 MeV) with a 4" long l e a d c y l i n d e r bloc~-king the c o l l i m a t o r opening. The shaded r e g i o n in c u r v e (10) was u s e d f o r the c r o s s s e c t i o n a n a l y sis. Fig. 2 g i v e s the 0 ° c r o s s s e c t i o n a f t e r s u b t r a c t i o n of the s p u r i o u s s i n g l e t yield. A ± 20% u n c e r t a i n t y in the c r o s s s e c t i o n c a l i b r a tion ha s not been included in the e r r o r b a r s . The solid dots show e s t i m a t e s of the 0 ° c r o s s s e c t i o n i n f e r r e d f r o m ref. 1. At the l o w e s t e n ergies, multiple Coulomb scattering gives a s m a l l c o n t r i b u t i o n to the 0 ° yield, w h o s e e s t i m a t e d magnitude is i n d ic a t e d by the dashed c u r v e . F o r w a r d Compton s c a t t e r i n g of the g a m m a r a y s in the t a r g e t backing c o n t r i b u t e s n e g l i g i b l y to the yield. The l o w e s t - e n e r g y triplet (nuclear) T+p i n t e r a c t i o n ev i d en t in p r e v i o u s p h a s e shift a n a l y s e s [4, 10] f r o m which any a p p r e c i a b l e g a m m a y i el d may be e x p e c t e d is that which g i v e s r i s e to the 1-, S = 1, T = 1 state e x p e c t e d n e a r 26 MeV in 4He (see fig. 3). T h e r e f o r e we a t t e m p t e d to fit the 0 ° T(p, y) c r o s s s e c t i o n with a s i n g l e - l e v e l B r e i t - W i g n e r f o r mula using the following l e v e l p a r a m e t e r s : r e s o n a n c e e n e r g y 26 MeV (i.e. e n e r g y at which the r e s o n a n c e p h as e shift is equal to 90°), r e duced widths ~2 u = ~2 n = 3 MeV, r a d i u s p a r a m e t e r 3.3 fm. Th~se v a l u e s a r e c l o s e to those e x p e c t e d f r o m the analog s t a t e s in 4H and 4Li [10]. The g a m m a - r a y width Fy was c h o s e n to give the b e s t fit to the data. An E3~ e n e r g y dependence was a s s u m e d f o r F7. The s o li d c u r v e in fig. 2 has been f i t t e d with F7 = 100 eV at the r e s o n a n c e e n e r g y . The r a t i o of F7 to the W e i s s k o p f e s t i m a t e f o r this a s s u m e d E1 t r a n sition would be equal to 0.03, which is well within the r a n g e for light n u c l e i [15]. It should be noted that in a s t r i c t LS coupling m o d e l the p r o p o s e d t r a n s i t i o n would be 5S forbidden, even if the 4He ground s t a t e has s o m e 5D a d m i x t u r e [16]. On the o t h e r hand, the t r a n s i tion would be in a c c o r d with the s e l e c t i o n r u l e A T = 1 r e q u i r e d f o r E1 t r a n s i t i o n s in s e l f conjugate nuclei. We intend to extend the c r o s s s e c t i o n m e a s 328
1 September 1965
2,5
A
2.0
w
7
0 la. 0
1.5
z v "o
1.0
b "o
0.5
0
~ 0
I
2
3
4 Ep
5
6
7
8
9
(10b.)
Fig. 2. Differential cross section in the lab. system for the T(p,~) reaction at 0° as a function of proton lab. energy. Effects of the singlet contribution have been subtracted. A + 20% uncertainty in the cross section calibration has not been included in the e r r o r bars. Coulomb scattering of the protons in the target material gives the estimated effects at low energies shown in dashed lines. The solid dots are taken from Per r y and Bame [1]. The solid curve assumes that the cross section is due to a 1-, S = 1, T= 1 resonance in 4He with a resonance energy at 26 MeV (but peaking at approximately 24 MeV). The r e s o n a n c e p a r a m e t e r s were chosen in accord with Tombrello's analysis of the analog s tates in 4H and 4 Li [10]. See text for the values used. u r e m e n t s to h i g h e r e n e r g i e s with our T a n d e m Van de G r a a f f a c c e l e r a t o r . At that t i m e the e n e r g y dependence of the 0 ° T ( p , r ) c r o s s s e c tion may indicate m o r e c l e a r l y w h e t h e r the p r o p o s e d explanation of the c r o s s s e c t i o n is correct. We would like to thank Dr. P e t e r Paul f o r the loan of a c o m p u t e r p r o g r a m to c a l c u l a t e B r e i t - W i g n e r r e s o n a n c e c u r v e s including l e v e l shifts and Dr. T. A. T o m b r e l l o f o r p e r -
Volume 18, n u m b e r 3
PHYSICS
LETTERS
1 S e p t e m b e r 1965 29,s////////C.s=o 27.7///////o-,s
~////////////////////,~ ~2s.7///////i-,s=1 s=,[ ~///////////////////~. ~24.0//////2-,s
)
~///////////////////~,
25.9////////I-,Sffil
-26//(,-,s= ,,T= ,)
'
=l
i
~////I/I//////////////~ -~3.845
24.5////////2-,S=1 ~//////////////////,~
D+D
22~/( I-,S=O,T =0) I 2o.sgs ~20.11 ~O+,SfO,T =0 >-0.577
H4
T+n
I
HeS+ n 19.913
I I
T-t.p
I
4 Li
19.795 He3+ p
I
.; ~
~ O+,(S=O),T=O He 4
Fig. 3. Level s y s t e m for A = 4. All e n e r g i e s a r e r e f e r r e d to the ground s t a t e of 4He. No Coulomb or m a s s c o r r e c tions have been applied to 4H and 4Li. The g a m m a t r a n s i t i o n s e e n in the p r e s e n t work has been tentatively a s s i g n e d as shown by the dashed line. See text for r e f e r e n c e s on level locations and a s s i g n m e n t s . m i s s i o n t o u s e s o m e of h i s r e s u l t s p r i o r to public ation.
References 1. J . E . P e r r y and S . J . B a m e , Phys. Rev. 99 (1955) 1368. 2. D.S. G e m m e l and G. A. J o n e s , Nucl. P h y s . 33 (1962) 102. 3. C.C. G a r d n e r and J. D. Anderson, P h y s . Rev. 125 (1962) 626; I.G. Main, Nuovo Cimento 26 (1962) 884. 4. W.E. Meyerhof and J . N . M e E l e a r n e y , Nuclear P h y s . (to be published). 5. C . W e r n t z , P h y s . Rev. 128 (1962) 1336; 133 (1964) B19. 6. W.E. Meyerhof, Rev. Mod. Phys. 37 (1965) 512. 7. R . F . F r o s c h and M . R . Y e a r i a n (private c o m m u n i c a tion).
8. L . E . Williams, P h . D . T h e s i s , U n i v e r s i t y of M i n n e sota (1965) (unpublished) ; Phys. Rev. L e t t e r s 15 (1965) 170. 9. P . D . P a r k e r , P . F . D o n o v a n , J . V . Kane and J . F . Mollenauer, P h y s . R e v . L e t t e r s 14 (1965) 15. 10. T . A . Tombrello, Nuclear Phys. (to be published). 11. R.W. Kavanagh, P . D . P a r k e r , and G.D. Symons, Bull. Am. P h y s . Soc. 8 (1963) 597. 12. P. Szydlik and C. Werntz, Phys. Rev. 138 (1965) B 8 6 6 13. C . A . K e l s e y , B.Hoop and P . V a n d e r Maat, Nuclear Phys. 51 (1964) 395. 14. T a r g e t obtained f r o m Oak Ridge National L a b o r a tory, Oak Ridge, T e n n e s s e e . 15. D.H. Wilkinson in: Nuclear Spectroscopy, ed..F. Ajzenberg-Selove (Academic P r e s s , New York, 1960) p. 852. 16. F o r a p p r o p r i a t e r e f e r e n c e s s e e D. Dixon in: Nuclear f o r c e s and the few-nucleon p r o b l e m , eds. T . C . Griffith and E. A. P o w e r ( P e r g a m o n P r e s s , New York, 1960) p.295.
329
0°-YIELD
]PHYSICS L E T T E R S
OF
GAMMA
RAYS
IN THE
1 September 1965
T(p, y)4He
REACTION
*
R. SCHRACK**, D. KOHLER, N. G. PUTTASWAMY and W. E. MEYERHOF
Department of Physics, Stanford University, Stanford, California Received 9 August 1965
P a s t e x p e r i m e n t a l s t u d i e s of the T(p,y) r e action [1-3] have indicated that the c a p t u r e p r o c e e d s m a i n l y by e l e c t r i c dipole e m i s s i o n , with s o m e e l e c t r i c quadrupole a d m i x t u r e , through s i n g l e t T+p i n t e r a c t i o n s . Both of t h e s e t y p e s of r a d i a t i o n would have z e r o yield at a 0 ° e m i s s i o n angle [1]. T r i p l e t T+p i n t e r a c t i o n s on the other hand would p r o d u c e g a m m a e m i s s i o n at 0 °. E x p e r i m e n t a l l y , the p r e s e n c e of 0°-yield in the T(p,7) r e a c t i o n has not b e e n c l e a r l y a s c e r t a i n e d [1,2]. A r e c e n t phase shift a n a l y s i s of the T(p, p), T(p, n) and 3He(n, n) r e a c t i o n up to 22 MeV in the 4He s y s t e m [4] has indicated s i n g l e t s and p and t r i p l e t p n u c l e a r i n t e r a c t i o n s in the T+p s y s t e m , but t h e r e is no evidence for a t r i p l e t s i n t e r a c t i o n beyond h a r d s p h e r e s c a t t e r i n g . The ~inglet s i n t e r a c t i o n gives r i s e to a 0 + s t a t e in He n e a r 20 MeV, which is now well e s t a b l i s h e d [5-9]. The state s e e m s to have isotopic spin T = 0 [10, 11]. It has b e e n shown [6] that a p wave i n t e r a c t i o n could explain r e s o n a n c e effects at 22 MeV in 4He which a p p e a r in 4He(e, e') [7], 4He(p,p') [8] and D(3He, 2p)W [9] r e a c t i o n s . T h i s is c o n s i s t e n t with c a l c u l a t i o n s of Sydlitz and W e r n t z [12], which i n d i c a t e that the state in q u e s t i o n should be 1% S = 0, T = 0. T(p, p) pol a r i z a t i o n m e a s u r e m e n t s also point to a 1- a s s i g n m e n t [13]. The e x i s t e n c e of h i g h e r lying, T = 1, s t a t e s in 4He c a n be i n f e r r e d f r o m phase shift a n a l y s i s by T o m b r e l l o [10] of 3He +p and T+n e l a s t i c s c a t t e r i n g and p o l a r i z a t i o n . On this b a s i s one would expect L = 1, S = 1, s t a t e s in 4 H e o f s p i n s 2, 1, a n d 0 n e a r 24, 26, and 2 8 M e V r e s p e c t i v e l y and an L = 1, S = 0, 1- state n e a r 30 MeV. We d e t e r m i n e d the 0O-yield of the T(p, ~) r e action as a m e a n s of studying higher lying s t a t e s of 4He, s i n c e it s e l e c t s the t r i p l e t T+p i n t e r a c * Supported in part by the National Science Foundation and by the U. S. Army Research Office (Durham). ** On educational leave from the National Bureau of Standards (1964-65).
tions [1]. A 14-keV thick T - Z r t a r g e t on 0 . 0 2 5 - c m thick s i l v e r backing [14] was b o m b a r d e d with p r o t o n s f r o m a 3-MeV Van de Graaff a c c e l e r a t o r . The g a m m a d e t e c t o r was a 5"-alia. × 6 " - l o n g sodium iodide c r y s t a l , p r o v i d e d with a p l a s t i c a n t i c o i n c i d e n c e shield and a n t i - p i l e u p c i r c u i t r y . A conical opening of 4.30 half angle in a 4" h e a v y -
u~ I.-
(a) L
-,j >n.. <[ m. I-
r-'t
n., ,.<
(b)
J uJ z z -r (,3 -% (/) I-Z
I
~j~ ~
r"-I
0
L I00
I 200
300 CHANNEL
400
NUMBER
Fig. 1. Typical gamma-ray spectra from T(p,y).(a) At 46.4 o, Ep = 3.18 MeV. (b} At 0°, Ep = 3.18 MeV, before background subtraction. The shade(] region shows the part of the spectrum used in the cross section analysis. (c) Background at 0o, E D = 2.58 MeV, with collimator hole blocked by'4" long lead cylinder. 327
Volume 18, number 3
P H Y S I C S LE T T E RS
m e t block s e r v e d as c o l l i m a t o r . The d e t e c t o r a s s e m b l y could be r o t a t e d around the t a r g e t . In o r d e r to c a l i b r a t e the 0 ° c r o s s s e c t i o n and to co m p u t e the s i n g l e t c o n t r i b u t i o n [ ~ ( s i n 0 + a s i n a c o s 8) 2] [1] to the f o r w a r d y i e l d within the c o l l i m a t o r opening, the y ie ld w a s d e t e r m i n e d at 8.6 o and 46.4 °, as w e l l as 0 °. Fig. 1 shows the u p p e r end of ty p i c a l p u l s e height s p e c t r a : c u r v e (a) at 46.4 ° (Ep = 3.18 MeV), c u r v e (b) at 0 ° (E u = 3.18 MeV, no background s u b t r a c t e d ) , c u r v ~ (c) background at 0 ° (E n = 2.58 MeV) with a 4" long l e a d c y l i n d e r bloc~-king the c o l l i m a t o r opening. The shaded r e g i o n in c u r v e (10) was u s e d f o r the c r o s s s e c t i o n a n a l y sis. Fig. 2 g i v e s the 0 ° c r o s s s e c t i o n a f t e r s u b t r a c t i o n of the s p u r i o u s s i n g l e t yield. A ± 20% u n c e r t a i n t y in the c r o s s s e c t i o n c a l i b r a tion ha s not been included in the e r r o r b a r s . The solid dots show e s t i m a t e s of the 0 ° c r o s s s e c t i o n i n f e r r e d f r o m ref. 1. At the l o w e s t e n ergies, multiple Coulomb scattering gives a s m a l l c o n t r i b u t i o n to the 0 ° yield, w h o s e e s t i m a t e d magnitude is i n d ic a t e d by the dashed c u r v e . F o r w a r d Compton s c a t t e r i n g of the g a m m a r a y s in the t a r g e t backing c o n t r i b u t e s n e g l i g i b l y to the yield. The l o w e s t - e n e r g y triplet (nuclear) T+p i n t e r a c t i o n ev i d en t in p r e v i o u s p h a s e shift a n a l y s e s [4, 10] f r o m which any a p p r e c i a b l e g a m m a y i el d may be e x p e c t e d is that which g i v e s r i s e to the 1-, S = 1, T = 1 state e x p e c t e d n e a r 26 MeV in 4He (see fig. 3). T h e r e f o r e we a t t e m p t e d to fit the 0 ° T(p, y) c r o s s s e c t i o n with a s i n g l e - l e v e l B r e i t - W i g n e r f o r mula using the following l e v e l p a r a m e t e r s : r e s o n a n c e e n e r g y 26 MeV (i.e. e n e r g y at which the r e s o n a n c e p h as e shift is equal to 90°), r e duced widths ~2 u = ~2 n = 3 MeV, r a d i u s p a r a m e t e r 3.3 fm. Th~se v a l u e s a r e c l o s e to those e x p e c t e d f r o m the analog s t a t e s in 4H and 4Li [10]. The g a m m a - r a y width Fy was c h o s e n to give the b e s t fit to the data. An E3~ e n e r g y dependence was a s s u m e d f o r F7. The s o li d c u r v e in fig. 2 has been f i t t e d with F7 = 100 eV at the r e s o n a n c e e n e r g y . The r a t i o of F7 to the W e i s s k o p f e s t i m a t e f o r this a s s u m e d E1 t r a n sition would be equal to 0.03, which is well within the r a n g e for light n u c l e i [15]. It should be noted that in a s t r i c t LS coupling m o d e l the p r o p o s e d t r a n s i t i o n would be 5S forbidden, even if the 4He ground s t a t e has s o m e 5D a d m i x t u r e [16]. On the o t h e r hand, the t r a n s i tion would be in a c c o r d with the s e l e c t i o n r u l e A T = 1 r e q u i r e d f o r E1 t r a n s i t i o n s in s e l f conjugate nuclei. We intend to extend the c r o s s s e c t i o n m e a s 328
1 September 1965
2,5
A
2.0
w
7
0 la. 0
1.5
z v "o
1.0
b "o
0.5
0
~ 0
I
2
3
4 Ep
5
6
7
8
9
(10b.)
Fig. 2. Differential cross section in the lab. system for the T(p,~) reaction at 0° as a function of proton lab. energy. Effects of the singlet contribution have been subtracted. A + 20% uncertainty in the cross section calibration has not been included in the e r r o r bars. Coulomb scattering of the protons in the target material gives the estimated effects at low energies shown in dashed lines. The solid dots are taken from Per r y and Bame [1]. The solid curve assumes that the cross section is due to a 1-, S = 1, T= 1 resonance in 4He with a resonance energy at 26 MeV (but peaking at approximately 24 MeV). The r e s o n a n c e p a r a m e t e r s were chosen in accord with Tombrello's analysis of the analog s tates in 4H and 4 Li [10]. See text for the values used. u r e m e n t s to h i g h e r e n e r g i e s with our T a n d e m Van de G r a a f f a c c e l e r a t o r . At that t i m e the e n e r g y dependence of the 0 ° T ( p , r ) c r o s s s e c tion may indicate m o r e c l e a r l y w h e t h e r the p r o p o s e d explanation of the c r o s s s e c t i o n is correct. We would like to thank Dr. P e t e r Paul f o r the loan of a c o m p u t e r p r o g r a m to c a l c u l a t e B r e i t - W i g n e r r e s o n a n c e c u r v e s including l e v e l shifts and Dr. T. A. T o m b r e l l o f o r p e r -
Volume 18, n u m b e r 3
PHYSICS
LETTERS
1 S e p t e m b e r 1965 29,s////////C.s=o 27.7///////o-,s
~////////////////////,~ ~2s.7///////i-,s=1 s=,[ ~///////////////////~. ~24.0//////2-,s
)
~///////////////////~,
25.9////////I-,Sffil
-26//(,-,s= ,,T= ,)
'
=l
i
~////I/I//////////////~ -~3.845
24.5////////2-,S=1 ~//////////////////,~
D+D
22~/( I-,S=O,T =0) I 2o.sgs ~20.11 ~O+,SfO,T =0 >-0.577
H4
T+n
I
HeS+ n 19.913
I I
T-t.p
I
4 Li
19.795 He3+ p
I
.; ~
~ O+,(S=O),T=O He 4
Fig. 3. Level s y s t e m for A = 4. All e n e r g i e s a r e r e f e r r e d to the ground s t a t e of 4He. No Coulomb or m a s s c o r r e c tions have been applied to 4H and 4Li. The g a m m a t r a n s i t i o n s e e n in the p r e s e n t work has been tentatively a s s i g n e d as shown by the dashed line. See text for r e f e r e n c e s on level locations and a s s i g n m e n t s . m i s s i o n t o u s e s o m e of h i s r e s u l t s p r i o r to public ation.
References 1. J . E . P e r r y and S . J . B a m e , Phys. Rev. 99 (1955) 1368. 2. D.S. G e m m e l and G. A. J o n e s , Nucl. P h y s . 33 (1962) 102. 3. C.C. G a r d n e r and J. D. Anderson, P h y s . Rev. 125 (1962) 626; I.G. Main, Nuovo Cimento 26 (1962) 884. 4. W.E. Meyerhof and J . N . M e E l e a r n e y , Nuclear P h y s . (to be published). 5. C . W e r n t z , P h y s . Rev. 128 (1962) 1336; 133 (1964) B19. 6. W.E. Meyerhof, Rev. Mod. Phys. 37 (1965) 512. 7. R . F . F r o s c h and M . R . Y e a r i a n (private c o m m u n i c a tion).
8. L . E . Williams, P h . D . T h e s i s , U n i v e r s i t y of M i n n e sota (1965) (unpublished) ; Phys. Rev. L e t t e r s 15 (1965) 170. 9. P . D . P a r k e r , P . F . D o n o v a n , J . V . Kane and J . F . Mollenauer, P h y s . R e v . L e t t e r s 14 (1965) 15. 10. T . A . Tombrello, Nuclear Phys. (to be published). 11. R.W. Kavanagh, P . D . P a r k e r , and G.D. Symons, Bull. Am. P h y s . Soc. 8 (1963) 597. 12. P. Szydlik and C. Werntz, Phys. Rev. 138 (1965) B 8 6 6 13. C . A . K e l s e y , B.Hoop and P . V a n d e r Maat, Nuclear Phys. 51 (1964) 395. 14. T a r g e t obtained f r o m Oak Ridge National L a b o r a tory, Oak Ridge, T e n n e s s e e . 15. D.H. Wilkinson in: Nuclear Spectroscopy, ed..F. Ajzenberg-Selove (Academic P r e s s , New York, 1960) p. 852. 16. F o r a p p r o p r i a t e r e f e r e n c e s s e e D. Dixon in: Nuclear f o r c e s and the few-nucleon p r o b l e m , eds. T . C . Griffith and E. A. P o w e r ( P e r g a m o n P r e s s , New York, 1960) p.295.
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