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The (t, p) reaction as a means of distinguishing among optical model potentials satisfying triton elastic scattering
Volume 18, number 2
PHYSICS LETTERS
m o d e l of Sliv to i n v e s t i g a t e t h i s effect for M1 r a diation in the L1 subsheLl with a t o m i c n u m b e r v a r y i n g , and M1 r a d i a t i o n in the L2 s u b s h e l l with e n e r g y v a r y i n g . The d i s a g r e e m e n t with Sliv f o r M1 v e r s u s Z in the L1 s u b s h e l l was r e d u c e d to l e s s than 1% f o r Z --< 90. The a g r e e m e n t was i m p r o v e d f o r M1 v e r s u s K in the L2 s u b s h e l i below 200 keV. The d i s c r e p a n c y above 500 keV w a s i n c r e a s e d . A l e s s e x t e n s i v e C o m p a r i s o n f o r the E1 and M2 m u l U p o l e s i n d i c a t e s c o m p a r a b l e a g r e e m e n t with the v a l u e s of Sliv. In the r a n g e of e n e r g i e s and a t o m i c n u m b e r s m o s t often o c c u r r i n g in e x p e r i m e n t s the v a l u e s of Sliv and Band and t h o s e we o b t a i n e d a g r e e r e a s o n a b l y weU.
15 August 1965
References 1. L.A. Sliv, I.M. Band, Coefficients of internal conversion of gamma radiation, Part H: L-shell (USSR Academy of Sciences, 1958). 2. M.E.Rose, Internal cenversion coefficients (NorthHolland Publ. Comp., Amsterdam, 1958). 3. T. Novakov, J.M. Hollander, UCRL-11400 (1964). 4. R.Hager, E.Seltzer 1965, to be published. 5. K.Sisgbahn, Alpha, Beta, G~mma-Ray Spectroscopy (North-Holland Publ. Comp., Amsterdam, 1965). 6. F.Herman, S.Skillman, Atomic struct~lre calculations (Prentice Hall inc., New Jersey, 1963). 7. D.C.Slater, Phys.Rev. 81 (1951) 385. 8. D.C. Slater, Quantum theory of atomic structure (McGraw Hill, New York, 1960)Vol.2, Ch. 17. 9. P. Henrici, Discrete variable methods in ordinary differential equations (John Wiley, New York, 1962). 10. Such a correcter formula can be derived from f o r mulae of p. 165 of M. E. Rosets Relativistic electron theory (John Wiley, New York, 1961). 11. R.H.Good J r . , Phys.Rev. 90 (1953) 131. 12. E. Seltzer, Thesis, Caltech (1965).
The a u t h o r s w i s h to thank P r o f e s s o r F e l i x Boelun f o r his i n t e r e s t and s u p p o r t .
T H E (t,p) R E A C T I O N AS A MEANS OF DISTINGUISHING OPTICAL MODEL POTENTIALS SATISFYING TRITON ELASTIC
AMONG SCATTERING
R. N. GLOVER A . W . R . E . Aldermaston, Berkshire * and
A. D. W. JONES Nuclear Physics Laboratory, Oxford Received 5 June 1965
In a r e c e n t c o m m u n i c a t i o n [1] f o u r s e t s of p a rameters describing triton elastic scattering were r e p o r t e d f o r e a c h n u c l e u s studied. We have u s e d t h e s e p o t e n t i a l s f o r DWBA a n a l y s t s of the r e a c t i o n s I 2 c ( t , p)14C and 160(t, p)l-80. Fig. 1 shows the e x p e r i m e n t a l d a t a of Middleton and P u l l e n [2], and the t h e o r e t i c a l f i t s f o r e a c h s e t of e l a s t i c s c a t t e r i n g p a r a m e t e r s f o r l e v e l s of known conf i g u r a t i o n giving a r a n g e of a n g u l a r m o m e n t u m t r a n s f e r v a l u e s L = 0 to L ffi 4. The t h e o r e t i c a l d i s t r i b u t i o n s a r e c l e a r l y s e n s i t i v e to the s e t of t r i t o n p a r a m e t e r s u s e d . The e x p e r i m e n t a l d i s t r i b u t i o n s a r e r e a s o n a b l y f i t t e d u s i n g the p o t e n t i a l s b a s e d on a w e l l depth U ~ 150 MeV. C a l c u l a t i o n s f o r p o t e n t i a l s with U ~ 200 MeV a r e s i m i l a r . In c o n t r a s t the p o t e n t i a l s with U ~ 50 MeV p r o d u c e az'x~z~ d i s t r i b u t i o n s in m a r k e d d i s a g r e e m e n t with e x p e r i m e n t , while t h o s e with U ~ 100 MeV l e a d to s o m e a g r e e m e n t f o r t r a n s i t i o n s with
s m a l l L - v a l u e s , but no a g r e e m e n t for h i g h e r v a l u e s , L = 3 and L = 4. Thus the (t, p) r e a c t i o n d i s c r i m i n a t e s a g a i n s t c e r t a i n o p t i c a l potenH~]s which s a t i s f y t r i t o n e l a s t i c s c a t t e r i n g . F r o m e x p e r i e n c e with DWBA a n a l y s i s of (d, p) r e a c t i o n s i t i s known that the a p ~ l * ~ d i n t r t b u t i o u s a r e r a t h e r i n s e n s i t i v e to the c h o i c e of d e u t e r o n p o t e n t i a l . We have v e r i f i e d that t h i s i n s e n s i t i v i t y a l s o a p p l i e s to (t, d) r e a c t i o n s by DWBA a n a l y s i s of the r e a c t i o n s 12C(t, d)13C and 26Mg(t, d)27Mg. Significant d e p e n d e n c e of DWBA c a l c u l a t i o n s on the o p t i c a l p o t e n t i a l u s e d s e e m s , a t p r e s e n t , to be unique to the (t, p) r e a c t i o n . The e x p e r i m e n t a l d a t a for the above (t, p) r e a c t i o n s and the DWBA a n a l y s i s a r e in a g r e e m e n t only if a m i n i m u m well depth of 150 MeV i s used. Such a depth i s a p p r o z * On temporary leave of absence at Nuclear Research Center tDemocritus,, Athens, Greece.
165
Volume 18, number 2
80
PHYSICS LETTERS
"•
20
..\
14C 6.58 MeV !! $
00
\\ \\
40
60
-..
L = 0 p8 s 2
15 August 1965
~
~, /"~', L=3p9d
io\
I0
14C 6.72 MeV
14C 6.09 MeV L=lp9s
\./
40
ZO 20
$0
60
90
IL)O
I$0
l $0
180
I 60
I 90
I IZO
I I$0
//
0
160
/:.°
_/ \; ~/
0
"-...
//~
1 30
O
oo o J 60
] 90
I ,, IZO
I ISO
:lllO
A
180 1.98 MeV
t~
180 3.55 MeV
6
L=2d 2
/'
/ 15
Triton potentials (r = 1.4 fro).
I
12C
10
:\I~.
...... ..-.J/ 160
o
50
00
90
IlO
I$O
160'
0
"//
30
00
gO
leo
I$0
U (MeV)
W (MeV)
a (fro)
58.4 102.4 160.5 232.3 50.6 93.8 146.8 209.3
14.1 13.9 17.6 22.3 10.7 14.7 18.4 21.3
0.77 0.69 0,63 0.58 0.75 0.62 0.55 0.52
160
Oc. m .
Fig. 1. DWBA angular distributions for (t, p) reactions for the levels and configurations indicated. The potentials are distinguished as follows: U~ 50 MeV - . -, U ~ 1 0 0 MeV - - - , U ~ 150 MeV ~ . Experimental data are represented by open circles. Note that in contrast to the plane wavp analysis of Middleton and Pullen the DWBA analysis gives L-values in agreement with the known 'eC spins. i m a t e l y equal to the s u m of the potenUals of the c o n s t i t u e n t nucleons. The p r e s e n t r e s u l t s a r e t h e r e f o r e a s t r o n g piece of evidence in favour of such t r e a t m e n t of composite p a r t i c l e s . Detailed a n a l y s i s of all (t, p) data taken at A l d e r m a s t o n i s in p r o g r e s s . P r e l i m i n a r y r e s u l t s s u g g e s t that the potential with U ~ 50 MeV is g e n e r a l l y unacceptable. We a r e i n d e b t e d t o Mr. M. J. L. Yates for the use of his c o m p u t e r p r o g r a m m e b a s e d on the dou* * * * *
166
ble s t r i p p i n g t h e o r y of Rook and M i t r a [3]. One of us (ADWJ) i s g r a t e f u l to the C o m m i s s i o n e r s for the Exhibition of 1851 for a Senior Studentship.
References I. R.N.Glover and A.D.W.Jones, Physics Letters 16 (1965) 69. 2. R.Middleton and D.J.Pullen, Nuclear Phys.51 (1964) 63. 3. J.R. Rook and D. Mitts, Nuclear Phys. 51 (1964) 96.
PHYSICS LETTERS
m o d e l of Sliv to i n v e s t i g a t e t h i s effect for M1 r a diation in the L1 subsheLl with a t o m i c n u m b e r v a r y i n g , and M1 r a d i a t i o n in the L2 s u b s h e l l with e n e r g y v a r y i n g . The d i s a g r e e m e n t with Sliv f o r M1 v e r s u s Z in the L1 s u b s h e l l was r e d u c e d to l e s s than 1% f o r Z --< 90. The a g r e e m e n t was i m p r o v e d f o r M1 v e r s u s K in the L2 s u b s h e l i below 200 keV. The d i s c r e p a n c y above 500 keV w a s i n c r e a s e d . A l e s s e x t e n s i v e C o m p a r i s o n f o r the E1 and M2 m u l U p o l e s i n d i c a t e s c o m p a r a b l e a g r e e m e n t with the v a l u e s of Sliv. In the r a n g e of e n e r g i e s and a t o m i c n u m b e r s m o s t often o c c u r r i n g in e x p e r i m e n t s the v a l u e s of Sliv and Band and t h o s e we o b t a i n e d a g r e e r e a s o n a b l y weU.
15 August 1965
References 1. L.A. Sliv, I.M. Band, Coefficients of internal conversion of gamma radiation, Part H: L-shell (USSR Academy of Sciences, 1958). 2. M.E.Rose, Internal cenversion coefficients (NorthHolland Publ. Comp., Amsterdam, 1958). 3. T. Novakov, J.M. Hollander, UCRL-11400 (1964). 4. R.Hager, E.Seltzer 1965, to be published. 5. K.Sisgbahn, Alpha, Beta, G~mma-Ray Spectroscopy (North-Holland Publ. Comp., Amsterdam, 1965). 6. F.Herman, S.Skillman, Atomic struct~lre calculations (Prentice Hall inc., New Jersey, 1963). 7. D.C.Slater, Phys.Rev. 81 (1951) 385. 8. D.C. Slater, Quantum theory of atomic structure (McGraw Hill, New York, 1960)Vol.2, Ch. 17. 9. P. Henrici, Discrete variable methods in ordinary differential equations (John Wiley, New York, 1962). 10. Such a correcter formula can be derived from f o r mulae of p. 165 of M. E. Rosets Relativistic electron theory (John Wiley, New York, 1961). 11. R.H.Good J r . , Phys.Rev. 90 (1953) 131. 12. E. Seltzer, Thesis, Caltech (1965).
The a u t h o r s w i s h to thank P r o f e s s o r F e l i x Boelun f o r his i n t e r e s t and s u p p o r t .
T H E (t,p) R E A C T I O N AS A MEANS OF DISTINGUISHING OPTICAL MODEL POTENTIALS SATISFYING TRITON ELASTIC
AMONG SCATTERING
R. N. GLOVER A . W . R . E . Aldermaston, Berkshire * and
A. D. W. JONES Nuclear Physics Laboratory, Oxford Received 5 June 1965
In a r e c e n t c o m m u n i c a t i o n [1] f o u r s e t s of p a rameters describing triton elastic scattering were r e p o r t e d f o r e a c h n u c l e u s studied. We have u s e d t h e s e p o t e n t i a l s f o r DWBA a n a l y s t s of the r e a c t i o n s I 2 c ( t , p)14C and 160(t, p)l-80. Fig. 1 shows the e x p e r i m e n t a l d a t a of Middleton and P u l l e n [2], and the t h e o r e t i c a l f i t s f o r e a c h s e t of e l a s t i c s c a t t e r i n g p a r a m e t e r s f o r l e v e l s of known conf i g u r a t i o n giving a r a n g e of a n g u l a r m o m e n t u m t r a n s f e r v a l u e s L = 0 to L ffi 4. The t h e o r e t i c a l d i s t r i b u t i o n s a r e c l e a r l y s e n s i t i v e to the s e t of t r i t o n p a r a m e t e r s u s e d . The e x p e r i m e n t a l d i s t r i b u t i o n s a r e r e a s o n a b l y f i t t e d u s i n g the p o t e n t i a l s b a s e d on a w e l l depth U ~ 150 MeV. C a l c u l a t i o n s f o r p o t e n t i a l s with U ~ 200 MeV a r e s i m i l a r . In c o n t r a s t the p o t e n t i a l s with U ~ 50 MeV p r o d u c e az'x~z~ d i s t r i b u t i o n s in m a r k e d d i s a g r e e m e n t with e x p e r i m e n t , while t h o s e with U ~ 100 MeV l e a d to s o m e a g r e e m e n t f o r t r a n s i t i o n s with
s m a l l L - v a l u e s , but no a g r e e m e n t for h i g h e r v a l u e s , L = 3 and L = 4. Thus the (t, p) r e a c t i o n d i s c r i m i n a t e s a g a i n s t c e r t a i n o p t i c a l potenH~]s which s a t i s f y t r i t o n e l a s t i c s c a t t e r i n g . F r o m e x p e r i e n c e with DWBA a n a l y s i s of (d, p) r e a c t i o n s i t i s known that the a p ~ l * ~ d i n t r t b u t i o u s a r e r a t h e r i n s e n s i t i v e to the c h o i c e of d e u t e r o n p o t e n t i a l . We have v e r i f i e d that t h i s i n s e n s i t i v i t y a l s o a p p l i e s to (t, d) r e a c t i o n s by DWBA a n a l y s i s of the r e a c t i o n s 12C(t, d)13C and 26Mg(t, d)27Mg. Significant d e p e n d e n c e of DWBA c a l c u l a t i o n s on the o p t i c a l p o t e n t i a l u s e d s e e m s , a t p r e s e n t , to be unique to the (t, p) r e a c t i o n . The e x p e r i m e n t a l d a t a for the above (t, p) r e a c t i o n s and the DWBA a n a l y s i s a r e in a g r e e m e n t only if a m i n i m u m well depth of 150 MeV i s used. Such a depth i s a p p r o z * On temporary leave of absence at Nuclear Research Center tDemocritus,, Athens, Greece.
165
Volume 18, number 2
80
PHYSICS LETTERS
"•
20
..\
14C 6.58 MeV !! $
00
\\ \\
40
60
-..
L = 0 p8 s 2
15 August 1965
~
~, /"~', L=3p9d
io\
I0
14C 6.72 MeV
14C 6.09 MeV L=lp9s
\./
40
ZO 20
$0
60
90
IL)O
I$0
l $0
180
I 60
I 90
I IZO
I I$0
//
0
160
/:.°
_/ \; ~/
0
"-...
//~
1 30
O
oo o J 60
] 90
I ,, IZO
I ISO
:lllO
A
180 1.98 MeV
t~
180 3.55 MeV
6
L=2d 2
/'
/ 15
Triton potentials (r = 1.4 fro).
I
12C
10
:\I~.
...... ..-.J/ 160
o
50
00
90
IlO
I$O
160'
0
"//
30
00
gO
leo
I$0
U (MeV)
W (MeV)
a (fro)
58.4 102.4 160.5 232.3 50.6 93.8 146.8 209.3
14.1 13.9 17.6 22.3 10.7 14.7 18.4 21.3
0.77 0.69 0,63 0.58 0.75 0.62 0.55 0.52
160
Oc. m .
Fig. 1. DWBA angular distributions for (t, p) reactions for the levels and configurations indicated. The potentials are distinguished as follows: U~ 50 MeV - . -, U ~ 1 0 0 MeV - - - , U ~ 150 MeV ~ . Experimental data are represented by open circles. Note that in contrast to the plane wavp analysis of Middleton and Pullen the DWBA analysis gives L-values in agreement with the known 'eC spins. i m a t e l y equal to the s u m of the potenUals of the c o n s t i t u e n t nucleons. The p r e s e n t r e s u l t s a r e t h e r e f o r e a s t r o n g piece of evidence in favour of such t r e a t m e n t of composite p a r t i c l e s . Detailed a n a l y s i s of all (t, p) data taken at A l d e r m a s t o n i s in p r o g r e s s . P r e l i m i n a r y r e s u l t s s u g g e s t that the potential with U ~ 50 MeV is g e n e r a l l y unacceptable. We a r e i n d e b t e d t o Mr. M. J. L. Yates for the use of his c o m p u t e r p r o g r a m m e b a s e d on the dou* * * * *
166
ble s t r i p p i n g t h e o r y of Rook and M i t r a [3]. One of us (ADWJ) i s g r a t e f u l to the C o m m i s s i o n e r s for the Exhibition of 1851 for a Senior Studentship.
References I. R.N.Glover and A.D.W.Jones, Physics Letters 16 (1965) 69. 2. R.Middleton and D.J.Pullen, Nuclear Phys.51 (1964) 63. 3. J.R. Rook and D. Mitts, Nuclear Phys. 51 (1964) 96.