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Comment on application of statistical multi-step direct emission theory to a neutron-emitting reaction
V01ume 1408, num6er 5,6
PHY51C5 LE77ER5
14 June 1984
C0MMEN7 0 N APPL1CA710N 0 F 57A71571CAL MUL71-57EP D1REC7 EM15510N 7 H E 0 R Y 7 0 A NEU7R0N-EM1771N6 REAC710N
1. KUMA8E a, M. H A R U 7 A a, M. HYAKU7AKE a and M. M A 7 0 8 A 6
a Department 0fNuc1ear En91neer1n9, Kyu5hu Un1ver51ty, Fuku0ka 812, Japan 6 6raduate 5ch0010fEn91neer1n9 5c1ence5, Kyu5hu Un1ver51ty,Ka5u9a 816, Japan Rece1ved 20 Decem6er 1983
7he 5tat15t1ca1mu1t1-5tep d1rect em15510nthe0ry f0rmu1ated 6y Fe5h6ach, Kerman and K00n1n (FKK) wa5 app11ed t0 the ana1y5150f 14 MeV (n, n•) 5catter1n9 0n 93N6 and A9.1t 15 c0nc1uded that the FKK the0ry a51t 5tand5 d15a9ree5w1th exper1menta1 data, 6ecau5e 0f an0ma10u51y1ar9e mu1t1-5tepcr055 5ect10n5due t0 the re50nance-11ke 6ehav10ur 0f n0n-DW8A matr1x e1ement5 wh1ch are entered 1n the ca1cu1at10n.
7he 5tat15t1ca1 mu1t1-5tep d1rect em15510n the0ry ha5 6een f0rmu1ated 6y Fe5h6ach, Kerman and K00n1n (FKK) [1]. 80nett1 et a1. [2] app11ed the FKK the0ry f0r the ana1y515 0f 45 MeV (p, n) c0nt1nuum data, and they 06ta1ned 900d f1t5 t0 the exper1menta1 data. 1n th15 ana1y515 they u5ed the matr1x e1ement5 f0r 5ucce551ve tran51t10n5 0f the DW8A f0rm. H0wever, 1t ha5 6een p01nted 0ut [ 3 - 5 ] that the matr1x e1ement5 f0r 5ucce551ve tran51t10n5 1n the FKK f0rma115m 5h0u1d 6e 0f the type (~ (u+)1V[X(:•) 1 ) 1n5tead 0f the DW8A f0rm (~ ~-)[ V[ X~)1 ), where × are the d15t0rted wave5 0f the nuc1e0n, the 5uff1x (+)((-)) 5tand5 f0r an 0ut901n9 (1nc0m1n9) 5cattered wave, t11de 1nd1cate5 the t1me rever5ed 5tate5, and V 15 the f0rm fact0r. 7he n0n-DW8A matr1x e1ement can 6e ca1cu1ated w1th the DW8A c0de m0d1f1ed 6y u51n9 the re1at10n [3,4] (~(+) [ = 5 - 1 ( ~ ( - ) [ , where 5 15 the e1a5t1c 5catter1n9 5 matr1x e1ement. U51n9 the m0d1f1ed DW8A c0de, we ca1cu1ated the 14 MeV (n, n•) 5catter1n9 0n 93N6 and 107A9.7he 0pt1ca1 p0tent1a1 parameter5 91ven 6y W11m0re and H0d950n [6] were u5ed. 80nett1 et a1. [2] u5ed a m1cr05c0p1c f0rm fact0r 1n the ana1y515 0f (p, n) data. 1n the pre5ent ca1cu1at10n, h0wever, we u5ed the macr05c0p1c f0rm fact0r 0f the f0rm VLe/ (1 + e) 2 f0r the tran5ferred an9u1ar m0mentum L f0r the 5ake 0f 51mp11c1ty. 7h15 type 0f f0rm fact0r ha5 6een u5ed 1n the ana1y515 0 f ( p , p•) data 6y 7amura et a1. [7]. 272
51nce the pre5ent ca1cu1at10n wa5 a tr1a1 0ne, we d1d n0t carry 0ut the a6501ute n0rma112at10n and we adju5ted the va1ue 0f F L 50 a5 t0 f1t the exper1menta1 ma9n1tude 0f the cr055 5ect10n5 f0r 93N6.1n the ana1y515 f0r 107A9 we u5ed the ma55-num6er dependence VL cc A - 1 wh1ch wa5 06ta1ned 1n a prev10u5 w0rk [8] 6y u51n9 the exper1menta1 va1ue5 0f ~2 f0r 10w-1y1n9 2 + 5tate5 f0r var10u5 nuc1e1. 7he exper1menta1 [9] and ca1cu1ated ener9y 5pectra f0r 93N6 and 107A9 are 5h0wn 1n f195. 1 and 2, re5pect1ve1y. A5 15 5een 1n the f19ure5 the ca1cu1ated cr055 5ect10n5 f0r 93N6 repr0duce the exper1menta1 data we11, 6ut th05e f0r 107A9 d0 n0t, 6ecau5e 0f an an0ma10u51y 1ar9e c0ntr16ut10n 0f mu1t1-5tep pr0ce55e5. We exam1ned the rea50n f0r 5uch an an0ma1y and f0und that the an0ma1y 15 due t0 the re50nant1y 1ar9e va1ue 0f 154 [- 1 f0r the an9u1ar m0mentum 1 = 4 near 8 MeV a5 15 5een 1n f19.3.7heref0re we exam1ned the 6ehav10ur 0f E511-1 1n the ma55-num6er re910n 0f 0 250 and 1n the neutr0n ener9y ran9e 0 - 4 0 MeV, and f0und many ••re50nance5•• 1n the ener9y and ma55num6er p1ane. 7he e1a5t1c 5catter1n9 5 matr1x e1ement 5 t 15 expre55ed 6y the re1at10n 15112 = 1 - 71 , where 71 15 the tran5m15510n c0eff1c1ent. 7heref0re 1f the va1ue 0f 71 6ec0me5 c105e t0 1.0, the c0rre5p0nd1n9 va1ue 0f 1511-1 6ec0me5 very 1ar9e. 0.370-2693/84/$ 03.00 • E15ev1er 5c1ence Pu6115her5 8.V. (N0rth-H011and Phy51c5 Pu6115h1n9 D1v1510n)
V01ume 1408, num6er 5,6
PHY51C5 LE]•7ER5
14 June 1984
93N6(n,n• ) ~
°
~A9
°
k, • .
------
C7107AL FKK
......
,-,r(v) ~FKK
....
crc0Mp
•• ~ •,
>
~J-710
~ 0 d 9 5 0 n
0-707AL FKK -1-0Ce~/~:~"
//
,:1~--~-~-2
E v
tM "0
6 •~0
............
]
1
,
2
4
3.. 4
6
8
1
1
10
12
14
F19.3. Va1ue5 0f 1511-1 f0r 5evera1 part1a1 wave5 f0r 107A9 a5 a funct10n 0f neutr0n ener9y.
•
6
8
10
En•(MeV)
1L2
14
F19. 1. C0mpar150n 0f the exper1menta1 and ca1cu1ated ener9y 5pectrum f0r 93N6.7he c0ntr16ut10n5 0f 5tep5 u = 1-3 are 5h0wn.
7ran5m15510n c0eff1c1ent5 f0r neutr0n5 have 6een ca1cu1ated 6y L1ndner [ 1 0] w1th the n0n-10ca1 0pt1ca1 p0tent1a1 0 f Perey and 8ack. 7 h e y are 91ven 1n d1a9ram5 a5 funct10n5 0 f ma55 n u m 6 e r A and n e u t r 0 n en-
er9y E n. Re50nance-11ke 6ehav10ur 0 f 7• can 6e ea511y 5een 1n the d1a9ram5. ••Re50nance•• p051t10n5 0 f the va1ue5 0 f 71 f0r n e u t r 0 n ener91e5 6e10w 10 MeV were taken fr0m the d1a9ram5 and the c0rre5p0nd1n9 re50nance p051t10n5 0 f the va1ue5 0 f [511-1 are 5h0wn 1n f19.4 6y tr1an91e5. We ca1cu1ated the tran5m15510n c0eff1c1ent5 f0r n e u tr0n ener91e5 6 e t w e e n 1 0 and 40 MeV 1n ener9y 5tep5
0 A 10;
1=4
En•(MeV)
•, •
,
~
10
•
~
/
1
8ECCHE771-6REENLEE5 ( 5.0. 4-• ) L1NDNER
100
1
1°7A9 ( n, n•) f ~
; 102 ¢,
• •
------
0-707AL FKK
•,,
......
~
....
0•C 061P
//~---- ". .k.-r...
);
"6
"~0 10
..,;:;.<•..
v:1-"
--..x
V,,
,,
••,
~;~
d009~ %0•°-
5+ 05- 06* 06- 07+ 0 4* 0 4-
Lu 10 2 0
•
,~
0 040503-
L13 2
•• 3
,~
0:
E ••
$ E > :E
0
A3 A3
:3 h1 2
2~ 2 A 2
•,,
A0
A0
••
•0
1
P
6
1,
8
En•(MeV)
,6
t
F19. 2. C0mpar150n 0f the exper1menta1 and ca1cu1ated ener9y 5pectrum f0r A9.7he c0ntr16ut10n5 0f 5tep5 u = 1-4 are 5h0wn.
0
5101001
1.~02001
2~,0
300
MA55 NUM8ER F19.4.7he ••re50nance•• p051t10n5 0f the va1ue5 0f 1511-1 a5 funct10n5 0f ma55 num6er and neutr0n ener9y. 7he num6er5 1n the f19ure are the c0rre5p0nd1n9/-va1ue5. 273
V01ume 1408, num6er 5,6
PHY51C5 LE77ER5
7a61e 1 7he typ1ca1va1ue50f tran5m15510nc0eff1c1ent5 711n the re50nance5. 1
En(MeV)
3 4 5 6 7 9 10 11
16 12 24 26 28 34 40 36
A 20 95 35 80 80 200 240 235
71(+)
71(-) 0.9951
0.9949 0.9995 0.9986 0.9995 0.9999 0.9957
14 June 1984
7he re50nance-11ke 6ehav10ur 0f 1511- 1 de5cr16ed a60ve cau5e5 re50nance-11ke enhancement 0f mu1t1-5tep cr055 5ect10n5 0f F K K , 1n d15a9reement w1th the exper1. menta1 065ervat10n. 1t 5eem5 c1ear that the 5ame c0nc1u510n h01d5 a150 f0r 0ther neutr0n-em1tt1n9 react10n5 at the neutr0n ener9y 6e10w 40 MeV. 7he auth0r5 w0u1d 11ke t0 expre55 the1r 51ncere thank5 t0 Pr0fe550r M. Kawa1 0f the Department 0f Phy51c5 f0r va1ua61e 5u99e5t10n5 and many he1pfu1 d15cu5510n5.
0.9997
Reference5 0f 2 MeV and ma55-num6er 5tep5 0f 5 w1th the 0pt1ca1 p0tent1a1 0f 8ecchett1 and 6reen1ee5 [ 11] u51n9 the c0mputer pr09ram EL1E5E 11 [ 12]. 7he ••re50nance•• p051t10n5 0fthe va1ue5 0f 151[ - 1 are 5h0wn 6y 0pen c1rc1e5 1n f19.4.7he num6er51n the f19ure are the c0rre5p0nd1n9/-va1ue5, and the 5uffLx + and - c0rre5p0nd t0 the tran5m15510n5 f0r 1 + • and 1 - ~ 1n the 5p1n-0r61t c0up11n9, re5pect1ve1y. 7he typ1ca1 va1ue5 71 at the ••re50nance5•• are 5h0wn 1n ta61e 1.1t 15 1mp11ed that a11 the va1ue5 0f 1511- 2, t0 wh1ch the part1a1 cr055 5ect10n5 0f the/-wave are pr0p0rt10na1, at the ••re50nance5•• 115ted 1n ta61e 1 are 1ar9er than 100 1n 5p1te 0f the ca1cu1at10n f0r d15crete va1ue5 0fma55 num6er (AL1 = 5) and neutr0n ener9y (AE n = 2 MeV). 7he va1ue5 0f 15t 1- 2 at the 0ther ••re50nance5•• wh1ch are n0t 115ted 1n ta61e 1 are a150 1ar9er than 1 0 0 . 7 h e re50nance-11ke 6ehav10ur 0f 1511-1 15 06ta1ned w1th the 0pt1ca1 p0tent1a1 0f W11m0re and H0d950n, a1th09uh re50nance p051t10n5 5h1ft 5119ht1y 1n ma55 num6er and/0r neutr0n ener9y.
274
[ 1] H. Fe5h6ach, A.K. Kerman and 5. K00n1n, Ann. Phy5. (NY) 125 (1980) 429. [2] R. 80nett1, M. Camna510and L. C0111-M11a220,Phy5. Rev. C24 (1981) 71. [3 ] M. Kawa1, Pr1vate c0mmun1cat10n. [4] 7. 7amura, 7. Uda9awa and H. Len5ke, Phy5. Rev. C26 (1982) 379. [5] M.5. Hu55e1nand R. 80nett1, Phy5. Lett. 1128 (1984) 189. [6] D. W11m0reand P.E. H0d950n, Nuc1. Phy5. 55 (1964) 673. [7] 7. 7amura, 7. Uda9awa, D.H. Fen9 and K.-K. Kan, Phy5. Lett. 668 (1977) 109. [8] 1. Kuma6e, K. Fukuda and M. Mat06a, Phy5. Lett. 928 (1980) 15. [9] Y. 1r1e,M. Hyakutake, M. Mat06a, 1. Kuma6e and M. 50n0da, Mem. Fac. En9. Kyu5hu Un1v.37 (1977) 19. [10] A. L1nder, 1n5t1tutft1r Kernphy51kFrankfurt rep0rt 1KF-17 EANDC (E) 73 •U• (1966), unpu6115hed. [ 11 ] F.D. 8ecchett1 Jr. and 6.W. 6reen1ee5, Phy5. Rev. 182 (1969) 1190. [ 12] 5.19ara51, JAER1-1169 (1968).
PHY51C5 LE77ER5
14 June 1984
C0MMEN7 0 N APPL1CA710N 0 F 57A71571CAL MUL71-57EP D1REC7 EM15510N 7 H E 0 R Y 7 0 A NEU7R0N-EM1771N6 REAC710N
1. KUMA8E a, M. H A R U 7 A a, M. HYAKU7AKE a and M. M A 7 0 8 A 6
a Department 0fNuc1ear En91neer1n9, Kyu5hu Un1ver51ty, Fuku0ka 812, Japan 6 6raduate 5ch0010fEn91neer1n9 5c1ence5, Kyu5hu Un1ver51ty,Ka5u9a 816, Japan Rece1ved 20 Decem6er 1983
7he 5tat15t1ca1mu1t1-5tep d1rect em15510nthe0ry f0rmu1ated 6y Fe5h6ach, Kerman and K00n1n (FKK) wa5 app11ed t0 the ana1y5150f 14 MeV (n, n•) 5catter1n9 0n 93N6 and A9.1t 15 c0nc1uded that the FKK the0ry a51t 5tand5 d15a9ree5w1th exper1menta1 data, 6ecau5e 0f an0ma10u51y1ar9e mu1t1-5tepcr055 5ect10n5due t0 the re50nance-11ke 6ehav10ur 0f n0n-DW8A matr1x e1ement5 wh1ch are entered 1n the ca1cu1at10n.
7he 5tat15t1ca1 mu1t1-5tep d1rect em15510n the0ry ha5 6een f0rmu1ated 6y Fe5h6ach, Kerman and K00n1n (FKK) [1]. 80nett1 et a1. [2] app11ed the FKK the0ry f0r the ana1y515 0f 45 MeV (p, n) c0nt1nuum data, and they 06ta1ned 900d f1t5 t0 the exper1menta1 data. 1n th15 ana1y515 they u5ed the matr1x e1ement5 f0r 5ucce551ve tran51t10n5 0f the DW8A f0rm. H0wever, 1t ha5 6een p01nted 0ut [ 3 - 5 ] that the matr1x e1ement5 f0r 5ucce551ve tran51t10n5 1n the FKK f0rma115m 5h0u1d 6e 0f the type (~ (u+)1V[X(:•) 1 ) 1n5tead 0f the DW8A f0rm (~ ~-)[ V[ X~)1 ), where × are the d15t0rted wave5 0f the nuc1e0n, the 5uff1x (+)((-)) 5tand5 f0r an 0ut901n9 (1nc0m1n9) 5cattered wave, t11de 1nd1cate5 the t1me rever5ed 5tate5, and V 15 the f0rm fact0r. 7he n0n-DW8A matr1x e1ement can 6e ca1cu1ated w1th the DW8A c0de m0d1f1ed 6y u51n9 the re1at10n [3,4] (~(+) [ = 5 - 1 ( ~ ( - ) [ , where 5 15 the e1a5t1c 5catter1n9 5 matr1x e1ement. U51n9 the m0d1f1ed DW8A c0de, we ca1cu1ated the 14 MeV (n, n•) 5catter1n9 0n 93N6 and 107A9.7he 0pt1ca1 p0tent1a1 parameter5 91ven 6y W11m0re and H0d950n [6] were u5ed. 80nett1 et a1. [2] u5ed a m1cr05c0p1c f0rm fact0r 1n the ana1y515 0f (p, n) data. 1n the pre5ent ca1cu1at10n, h0wever, we u5ed the macr05c0p1c f0rm fact0r 0f the f0rm VLe/ (1 + e) 2 f0r the tran5ferred an9u1ar m0mentum L f0r the 5ake 0f 51mp11c1ty. 7h15 type 0f f0rm fact0r ha5 6een u5ed 1n the ana1y515 0 f ( p , p•) data 6y 7amura et a1. [7]. 272
51nce the pre5ent ca1cu1at10n wa5 a tr1a1 0ne, we d1d n0t carry 0ut the a6501ute n0rma112at10n and we adju5ted the va1ue 0f F L 50 a5 t0 f1t the exper1menta1 ma9n1tude 0f the cr055 5ect10n5 f0r 93N6.1n the ana1y515 f0r 107A9 we u5ed the ma55-num6er dependence VL cc A - 1 wh1ch wa5 06ta1ned 1n a prev10u5 w0rk [8] 6y u51n9 the exper1menta1 va1ue5 0f ~2 f0r 10w-1y1n9 2 + 5tate5 f0r var10u5 nuc1e1. 7he exper1menta1 [9] and ca1cu1ated ener9y 5pectra f0r 93N6 and 107A9 are 5h0wn 1n f195. 1 and 2, re5pect1ve1y. A5 15 5een 1n the f19ure5 the ca1cu1ated cr055 5ect10n5 f0r 93N6 repr0duce the exper1menta1 data we11, 6ut th05e f0r 107A9 d0 n0t, 6ecau5e 0f an an0ma10u51y 1ar9e c0ntr16ut10n 0f mu1t1-5tep pr0ce55e5. We exam1ned the rea50n f0r 5uch an an0ma1y and f0und that the an0ma1y 15 due t0 the re50nant1y 1ar9e va1ue 0f 154 [- 1 f0r the an9u1ar m0mentum 1 = 4 near 8 MeV a5 15 5een 1n f19.3.7heref0re we exam1ned the 6ehav10ur 0f E511-1 1n the ma55-num6er re910n 0f 0 250 and 1n the neutr0n ener9y ran9e 0 - 4 0 MeV, and f0und many ••re50nance5•• 1n the ener9y and ma55num6er p1ane. 7he e1a5t1c 5catter1n9 5 matr1x e1ement 5 t 15 expre55ed 6y the re1at10n 15112 = 1 - 71 , where 71 15 the tran5m15510n c0eff1c1ent. 7heref0re 1f the va1ue 0f 71 6ec0me5 c105e t0 1.0, the c0rre5p0nd1n9 va1ue 0f 1511-1 6ec0me5 very 1ar9e. 0.370-2693/84/$ 03.00 • E15ev1er 5c1ence Pu6115her5 8.V. (N0rth-H011and Phy51c5 Pu6115h1n9 D1v1510n)
V01ume 1408, num6er 5,6
PHY51C5 LE]•7ER5
14 June 1984
93N6(n,n• ) ~
°
~A9
°
k, • .
------
C7107AL FKK
......
,-,r(v) ~FKK
....
crc0Mp
•• ~ •,
>
~J-710
~ 0 d 9 5 0 n
0-707AL FKK -1-0Ce~/~:~"
//
,:1~--~-~-2
E v
tM "0
6 •~0
............
]
1
,
2
4
3.. 4
6
8
1
1
10
12
14
F19.3. Va1ue5 0f 1511-1 f0r 5evera1 part1a1 wave5 f0r 107A9 a5 a funct10n 0f neutr0n ener9y.
•
6
8
10
En•(MeV)
1L2
14
F19. 1. C0mpar150n 0f the exper1menta1 and ca1cu1ated ener9y 5pectrum f0r 93N6.7he c0ntr16ut10n5 0f 5tep5 u = 1-3 are 5h0wn.
7ran5m15510n c0eff1c1ent5 f0r neutr0n5 have 6een ca1cu1ated 6y L1ndner [ 1 0] w1th the n0n-10ca1 0pt1ca1 p0tent1a1 0 f Perey and 8ack. 7 h e y are 91ven 1n d1a9ram5 a5 funct10n5 0 f ma55 n u m 6 e r A and n e u t r 0 n en-
er9y E n. Re50nance-11ke 6ehav10ur 0 f 7• can 6e ea511y 5een 1n the d1a9ram5. ••Re50nance•• p051t10n5 0 f the va1ue5 0 f 71 f0r n e u t r 0 n ener91e5 6e10w 10 MeV were taken fr0m the d1a9ram5 and the c0rre5p0nd1n9 re50nance p051t10n5 0 f the va1ue5 0 f [511-1 are 5h0wn 1n f19.4 6y tr1an91e5. We ca1cu1ated the tran5m15510n c0eff1c1ent5 f0r n e u tr0n ener91e5 6 e t w e e n 1 0 and 40 MeV 1n ener9y 5tep5
0 A 10;
1=4
En•(MeV)
•, •
,
~
10
•
~
/
1
8ECCHE771-6REENLEE5 ( 5.0. 4-• ) L1NDNER
100
1
1°7A9 ( n, n•) f ~
; 102 ¢,
• •
------
0-707AL FKK
•,,
......
~
....
0•C 061P
//~---- ". .k.-r...
);
"6
"~0 10
..,;:;.<•..
v:1-"
--..x
V,,
,,
••,
~;~
d009~ %0•°-
5+ 05- 06* 06- 07+ 0 4* 0 4-
Lu 10 2 0
•
,~
0 040503-
L13 2
•• 3
,~
0:
E ••
$ E > :E
0
A3 A3
:3 h1 2
2~ 2 A 2
•,,
A0
A0
••
•0
1
P
6
1,
8
En•(MeV)
,6
t
F19. 2. C0mpar150n 0f the exper1menta1 and ca1cu1ated ener9y 5pectrum f0r A9.7he c0ntr16ut10n5 0f 5tep5 u = 1-4 are 5h0wn.
0
5101001
1.~02001
2~,0
300
MA55 NUM8ER F19.4.7he ••re50nance•• p051t10n5 0f the va1ue5 0f 1511-1 a5 funct10n5 0f ma55 num6er and neutr0n ener9y. 7he num6er5 1n the f19ure are the c0rre5p0nd1n9/-va1ue5. 273
V01ume 1408, num6er 5,6
PHY51C5 LE77ER5
7a61e 1 7he typ1ca1va1ue50f tran5m15510nc0eff1c1ent5 711n the re50nance5. 1
En(MeV)
3 4 5 6 7 9 10 11
16 12 24 26 28 34 40 36
A 20 95 35 80 80 200 240 235
71(+)
71(-) 0.9951
0.9949 0.9995 0.9986 0.9995 0.9999 0.9957
14 June 1984
7he re50nance-11ke 6ehav10ur 0f 1511- 1 de5cr16ed a60ve cau5e5 re50nance-11ke enhancement 0f mu1t1-5tep cr055 5ect10n5 0f F K K , 1n d15a9reement w1th the exper1. menta1 065ervat10n. 1t 5eem5 c1ear that the 5ame c0nc1u510n h01d5 a150 f0r 0ther neutr0n-em1tt1n9 react10n5 at the neutr0n ener9y 6e10w 40 MeV. 7he auth0r5 w0u1d 11ke t0 expre55 the1r 51ncere thank5 t0 Pr0fe550r M. Kawa1 0f the Department 0f Phy51c5 f0r va1ua61e 5u99e5t10n5 and many he1pfu1 d15cu5510n5.
0.9997
Reference5 0f 2 MeV and ma55-num6er 5tep5 0f 5 w1th the 0pt1ca1 p0tent1a1 0f 8ecchett1 and 6reen1ee5 [ 11] u51n9 the c0mputer pr09ram EL1E5E 11 [ 12]. 7he ••re50nance•• p051t10n5 0fthe va1ue5 0f 151[ - 1 are 5h0wn 6y 0pen c1rc1e5 1n f19.4.7he num6er51n the f19ure are the c0rre5p0nd1n9/-va1ue5, and the 5uffLx + and - c0rre5p0nd t0 the tran5m15510n5 f0r 1 + • and 1 - ~ 1n the 5p1n-0r61t c0up11n9, re5pect1ve1y. 7he typ1ca1 va1ue5 71 at the ••re50nance5•• are 5h0wn 1n ta61e 1.1t 15 1mp11ed that a11 the va1ue5 0f 1511- 2, t0 wh1ch the part1a1 cr055 5ect10n5 0f the/-wave are pr0p0rt10na1, at the ••re50nance5•• 115ted 1n ta61e 1 are 1ar9er than 100 1n 5p1te 0f the ca1cu1at10n f0r d15crete va1ue5 0fma55 num6er (AL1 = 5) and neutr0n ener9y (AE n = 2 MeV). 7he va1ue5 0f 15t 1- 2 at the 0ther ••re50nance5•• wh1ch are n0t 115ted 1n ta61e 1 are a150 1ar9er than 1 0 0 . 7 h e re50nance-11ke 6ehav10ur 0f 1511-1 15 06ta1ned w1th the 0pt1ca1 p0tent1a1 0f W11m0re and H0d950n, a1th09uh re50nance p051t10n5 5h1ft 5119ht1y 1n ma55 num6er and/0r neutr0n ener9y.
274
[ 1] H. Fe5h6ach, A.K. Kerman and 5. K00n1n, Ann. Phy5. (NY) 125 (1980) 429. [2] R. 80nett1, M. Camna510and L. C0111-M11a220,Phy5. Rev. C24 (1981) 71. [3 ] M. Kawa1, Pr1vate c0mmun1cat10n. [4] 7. 7amura, 7. Uda9awa and H. Len5ke, Phy5. Rev. C26 (1982) 379. [5] M.5. Hu55e1nand R. 80nett1, Phy5. Lett. 1128 (1984) 189. [6] D. W11m0reand P.E. H0d950n, Nuc1. Phy5. 55 (1964) 673. [7] 7. 7amura, 7. Uda9awa, D.H. Fen9 and K.-K. Kan, Phy5. Lett. 668 (1977) 109. [8] 1. Kuma6e, K. Fukuda and M. Mat06a, Phy5. Lett. 928 (1980) 15. [9] Y. 1r1e,M. Hyakutake, M. Mat06a, 1. Kuma6e and M. 50n0da, Mem. Fac. En9. Kyu5hu Un1v.37 (1977) 19. [10] A. L1nder, 1n5t1tutft1r Kernphy51kFrankfurt rep0rt 1KF-17 EANDC (E) 73 •U• (1966), unpu6115hed. [ 11 ] F.D. 8ecchett1 Jr. and 6.W. 6reen1ee5, Phy5. Rev. 182 (1969) 1190. [ 12] 5.19ara51, JAER1-1169 (1968).