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Medium energy reactions and scattering
Gugelot, P . C . 1956
Physica X X l I 1019-1026 A m s t e r d a m Nuclear R e a c t i o n s Cpnference
MEDIUM IENERGY REACTIONS AND SCATTERING by P. C. GUGELOT *) Instituut voor kernphysisch Onderzoek, Amsterdam, Nederland Synopsis T h e i n t e r p r e t a t i o n of elastic p r o t o n s c a t t e r i n g leads to t h e a s s u m p t i o n of a nuclear a b s o r p t i o n p o t e n t i a l which varies b e t w e e n 2 MeV and 10 MeV. T h e corresponding m e a n free p a t h of a nucleon in nuclear m a t t e r is t h e n of the same order of m a g n i t u d e as t h e nuclear dimension. This result bears s t r o n g l y on t h e i n t e r p r e t a t i o n of inelastic p r o t o n s c a t t e r i n g and on p r o t o n or n e u t r o n induced reactions. T h e picture of t h e c o m p o u n d nucleus which depends on a strong, u n h a m p e r e d i n t e r a c t i o n b e t w e e n inc o m i n g nucleon and nucleus m a y h a v e to be changed. N o t only t h e p r o t o n surface i n t e r a c t i o n has to be t a k e n into account, b u t one m a y h a v e to consider t h e t r a n s p a r e n c y of t h e t a r g e t nucleus such t h a t t h e (p, p') reaction becomes p a r t i c u l a r l y probable if t h e residual states are similar to t h e initial states. On_the nfh~r h a n d if fh.e finn.| s t a t e c a n n o t h a v e a n y r e s e m b l a n c e to t h e initial s t a t e as for instance for (p, ~) reactions one would e x p e c t t h e shape of t h e s p e c t r u m to differ f r o m t h e p r o t o n s p e c t r u m for inelastic scattering. T h e w i d t h for the reemission of fast protons m a y be greater b y several orders of m a g n i t u d e t h a n t h e w i d t h for t h e emission of fast ~-particles. T h e ratio of t h e w i d t h s reduces to a b o u t one for low emission energy.
Recent experimental results have changed our views about nuclear reactions. The strong interaction model has to be modified and amended. This new information provides also a more general picture for the understanding of nuclear structure. The experiments which contributed to this development are in the first place proton elastic scattering data which are interpreted by M e l k a n o f f , M o s z k o w s k i , N o d v i k and S a x o n 1). Using an optical model these authors were able to obtain fairly good agreement between theoretical and experimental angular distributions for a potential of the form:
u = -(v
+ iw)/(1 + eCr-R~/a)
(I)
R = 1.33 × 10-13Al/3cm a = 0.5 × 10-13cm The values for V and W axe energy dependent, as shown in Fig. 1 and Fig. 2. These parameters present the best fit to the experimental data for the *) Paper read at the Amsterdaln Nuclear Reactions Conference on J u l y 2nd, 1956.
-
-
1019-
1020
P . C . GUGELOT
assumed potential. A change in the shape of U or the inclusion of spin orbit forces m a y have the result that one obtains somewhat different values for radius and potential depth. A spin orbit force has been assumed by F e r n b a c h 2) for the interpretation of elastic neutron scattering.
SO
".,-o.
~ .
~ ~
.
40
""
3C
V MeV
20 I0 0 0
E MtV
Fig. 1. R e a l p a r t of nuclear p o t e n t i a l as a f u n c t i o n of the e n e r g y of the i n c i d e n t proton. The points are calculated in ref. 1 from e x p e r i m e n t s at 5.25 MeV 10),~at 17 MeV lz) and a t 31.5 MeV l~).
20
W
IO
o
o
,~
E McV
2b
3'0
Fig. 2. I m a g i n a r y p a r t of nuclear p o t e n t i a l as a f u n c t i o n of t h e i n c i d e n t p r o t o n energy. T h e t h e o r e t i c a l c u r v e is f r o m ref. 3.
The value of the real part of the scattering potential is in agreement with the ~ e w s obtained from shell structure. The decrease of potential with increasing proton energy can be made plausible by the decreasing nucleonnucleon forces. The curve in Fig. 2 is calculated by L a n e and W a n d e l s) on the basis of a semi-classical picture in which the nucleons are supposed
M E D I U M E N E R G Y REACTIONS AND S C A T T E R I N G
1021
to move in a Fermi-gas in which the number of collisions is restricted b y the action of the Pauli principle. The value of W, the absorptive part of the potential, is related to the mean free path of nucleons in nuclear matter,
A = (1/K)(e + V)/W K is the wave number of the nucleon inside the potential. For e = 20 MeV, one obtains A = 8 x 10-Is cm; a proton beam passing through a heavy nucleus is attenuated to about 1/e of its intensity.This value for the mean free path does not make possible an interpretation of reactions in terms of a compound nucleus. This does not mean, however, that one should discard the compound nucleus hypothesis completely. The reflection at the nuclear boundary will probably cause a low energy nucleon to traverse a nucleus m a n y times. .For the elastic scattering of a-particles the situation is as yet much less clear. Though good experimental information is available, nobody has carried out a detailed analysis b y using the optical model. An attempt to use a Born approximation for the interpretation of a-scattering b y magnesium yielded some useful information 4). An interaction potential of only 5 MeV was found b y this method. However, Henley observed that an opaque disc of the same radius gave also a satisfactory flt is). The nucleons eliminated from the incident channel will produce reacUons. On account of the long free path, a nucleon will produce reactions of the type in which only one nucleon is excited and the incident or exchanged nucleon is escaping with reduced energy. We would like to call these collisions inside the nucleus without the whole nucleus taking part "direct volume interactions". In this type of interactions one would expect that only few levels of the nucleus are excited, levels which can be represented b y A -- 1 nucleons in their normal states and one nucleon excited. This effect m a y have as a consequence the appearance of a giant resonance. Some experimental information shows that this m a y be the case 5). A compound nucleus can still be formed either in more complicated collisions, depending on many body interactions or, if so much energy is available that still other particles can escape after the initial direct interaction. We m a y be able to demonstrate the direct interaction with protons b y comparing the ratio of proton emission to a-emission in reactions of the kind X(x, y)Y in which x is a proton, y a proton or a-particle and Y the residual nucleus which should be preferably the same in the proton and ~-particle reactions. We assume that' a-particles are less liable to make direct interactions if large angles of scattering are considered. In the compound nucleus formalism,
F~ v = davy / ev Sv = constv o~v(E) de-----~l
1022
P.c. G U G E L O T
we find ~. ~
F~,/const~. F~Jconsta
OJvl(E)
r~y2(E)
ey is the energy of the emitted particle y; Sy is the geometrical cross-section times barrier penetration probability for particle y;
i
x
Rh(p,a)Ru
o
Ni(p,p')Ni Ni(p,a)Go
Fe (p,p')Fe o Co(p,a)Fe AI (p,#)AI
(
fi_~p (a
AI ( p , a ) M g
t
tO
Excitation Energy
MeV Fig. 3. R a t i o of " S t i c k i n g p r o b a b i l i t i e s " for t h e r e a c t i o n s X ( p , p) Y a n d Z (p, =) Y vs. e x c i t a t i o n energy. T h i s r a t i o s h o u l d b e one, if t h e s t a t i s t i c a l t h e o r y of n u c l e a r r e a c t i o n s is valid. 0.1 m .o¢ t,t t- .0~ to -, .07
D6
I
bl "~]"~'O3 .02 I
I
I
/
I
10°20"30°40 °
60 ° 90 ° C.M. A N G L E
120°
i50 °
180"
Fig. 4. A n g u l a r d i s t r i b u t i o n of =-particles e x c i t i n g t h e g r o u n d s t a t e of 100Ru f r o m t h e r e a c t i o n 103Rh (p, a) 100Ru. T h e s t r o n g f o r w a r d p e a k i n g of t h e cross-section s u g g e s t s t h a t t h e =-particles a r e p r o d u c e d in d i r e c t i n t e r a c t i o n s . E x p e r i m e n t a l w o r k f r o m ref. 6.
1023
MEDIUM ENERGY REACTIONS AND SCATTERING
oJv is the level density of the residual nucleus Y of which the excitation energy is E. The ratio ~p,/~ = 1 if Y1 and Y2 are the same residual nuclei. Fig. 2 shows that only for large excitation energy in the residual nucleus ~p,/~ m 1. That the statistical theory is 6lily valid for large energy transfer is also borne out b y the observed angular distributions of reaction products. The particles "evaporating" with low energy show almost isotropic angular distributions. The angular distribution of fast emitted particles is always in the forward direction. Fig. 4 shows that ]ast ~-particles are also the product of direct interactions, since the angular distribution is forward directed for those ~-particles which leave 100Ru in the ground state after the reaction lO3Rh (p, ~) 100Ru. These experiments were carried out by P. B r a d y s). ! t
200
~160 ~120
~ 80 le ~
40
b 0
0
2
I
40
0
60
I
GO
tO0
|
IL;~
140
I
160
180
0- sc~)ttcrlng angle Fig. 5. A n g u l a r distribution of inelastically scattered neutrons in the energy i n t e r v a l from 4 MeV to 12 MeV from Bi (n, n'), incident n e u t r o n energy 14MeV. T h e e x p e r i m e n t a l points are o b t a i n e d b y R o s e n and S t e w a r t 18). The theoretical c u r v e is calculated b y B r o w n and M u i r h e a d 7).
B r o w n and M u i r h e a d 7) started a simple theoretical treatment for the calculation of the emission spectra b y making use of the classical ideas of G o l d b e r g e r in his calculation of the mean free path. The cross-section alp for the collision of an incoming neutron with protons inside a nucleus is written as GIp = GI
ai
is the interaction cross-section of the incident neutrons x(~l) is the cross-section for a collision of a neutron of momentum Pl with a free nucleon is a factor which reduces the magnitude of x(pl) inside the nucleus through the operation of the Pauli principle and is the density of the nucleons inside the nucleus.
1024
P . C . GUGELOT
The theoretical results are compared to many experimental data. Fig. 5 and Fig. 6 show two of these comparisons. The agreement of this extremely classical calculation with experimental data is good. It is not understood w h y wave aspects like diffraction can be neglected.
(Mcv)'~ t10-~
}I}
IA9
'"
t" .~
I
• 60°
I.
o iso"
,o-'
i o .4
o°e iso"
•
OOOoel °
id s
J [4 4
~ I2 6
EXCITATION ENERGY",,,~t¢v. LO 8 6 4 8
|0
12
2
14 t6 EMev.
0 18
Fig. 6. Comparison of the experimental data from Ag (p, p') (ref. 14) and the theoretical curves of ref. 7. The data are presented in such a way that the ordinate is proportional to the level density if the statistical theory of nuclear reactions can be applied.
Finally I would like to point to another sort of direct interaction in which the nucleus takes part in a collective mode. One example m a y be the emission of energetic 7-rays after the capture of high energy protons. This reaction has been discussed b y B e c k s). Another example is the excitation of Bohr-Mottelson surface oscillations b y the inelastic scattering of co-particles as represented in Fig. 7 ( B o h r - M o t t e l s o n direct interaction 4)). One m a y deduce the nuclear quadrupole moment from such measurements. The angular distribution of 18 MeV protons exciting the 1.37 MeV level of 24Mg (Fig. 8) shows that an interpretation in the same terms as the ~-
MEDIUM
ENERGY
REACTIONS
AND
SCATTERING
1025
particle scattering (Fig. 7) is not possible 9). Direct v o l u m e i n t e r a c t i o n m a y h a v e to be t a k e n into a c c o u n t to explain the d a t a of Fig. 8. 24Mg {a,a,) Mg '.~7M~N Ea "42 MeV
mb/stera~
m[j.(oR~ ~ . ~,v 5,'~ .2 2,),O"~:r. t
2o | IO
( Ls 2 1.0.
o o
=
0.2 0.1
' ;o'
~o'
~o
eb'
,~o
ec~
Fig. 7. Angular distribution of =-particles from the reaction 24Mg (,',od) exciting the 1.37 MeV level in ~4Mg. The angular distribution is fitted to the square of the spherical Bessel-function of order two. The magnitude of the cross-section fixes the product of intrinsic quadrupole moment and surface interaction potential.
mbLsterad 24Mg lp.t~) Mg~57Mw Ep'18 MeV z R.6,0,$¢m [,, OR)].
8O
,) 4
t
(, t
~
t
i
3 2
//ss-% ~*'z i
t
Gem
Fig. 8. Angular distribution of protons from the reaction ~4Mg (p, p') exciting the 1.37 MeV level. [7'3(QR)]g does not fit the experimental curve. The Bohr-Mottelson surface interaction would predict the cross-section to be ten times larger. Physica XXII
65
1026
MEDIUM ENERGY REACTIONS AND SCATTERING
Summarizing these considerations we found that the optical model helped us in making plausible that interactions can occur which cannot be described by a compound nucleus formalism. The direct type of interactions are a new tool to investigate the nucleus and special attention has to be given to their theoretical and experimental studies at the moment.
Short communications directly /ollowing this paper were read by Cohen p. zi25 and Bleuler, p. zz27 o/ this volume. Received 12-7-56.
REFERENCES 1) M e l k a n o f f , M. A., M o s k o w s k i , S. A., N o d v i k , J. and S a x o n , D. S., Phys. Rev. 101 (1956) 507. 2) C u l l e r , G., F e r n b a c h , S. and S h e r m a n , N., Phys. Rev.101, (1956) 1047; B j o r k l u n d , F. E., F e r n b a c h , S. and S h e r m a n , N., Phys. Rev. 101 (1956) 1832. In this paper the authors obtain a very good fit to the 14 MeV neutron scattering data by making use of an absorptive surface. 3) L a n e , A. M. and W a n d e l , C. F., Phys. Rev. 98 (1955) 1524. 4) G u g e l o t , P. C. and. R i c k e y , M., Phys. Rev. 101 (1956) 1613. 5) G u g e l o t, P. C., "Statistical Aspects of the Nucleus", B N L 331 (C-21). The cross-section for the inelastic scattering of protons from Ag shows fluctuations which m a y indicate giant resonances. 6) B r a d y , P., Princeton University (unpublished work). 7) B r o w n , G. and M u i r h e a d , H., to be published. (We t h a n k the authors for sending us their results prior to publication.) 8) B e c k , F., On the calculation of (n, y) cross section, short communication. G u g e l o t , P. C., unpublished. 9) G u g e l o t , P. C. and P h i l l i p s , P. R., Phys. Rev. 101 (1956) 1614. 10) B r o m l e y , D. A. and W a l l , N. S., Phys. Rev. 99 (1955) 1029. 11) D a y t o n , I. E. and S c h r a n k , G., Phys. Rev. 101 (1956) 1358. 12) K i n s e y , B. B., Phys. Rev. 99 (1955) 332. 13) R o s e n , L. and S t e w a r t , L. Phys. Rev. 99 (1955) 1052. 14) G u g e l o t , P. C., Phys. Rev. 93 (1954) 425. 15) H e n l e y , E. M., Private communication.
Physica X X l I 1019-1026 A m s t e r d a m Nuclear R e a c t i o n s Cpnference
MEDIUM IENERGY REACTIONS AND SCATTERING by P. C. GUGELOT *) Instituut voor kernphysisch Onderzoek, Amsterdam, Nederland Synopsis T h e i n t e r p r e t a t i o n of elastic p r o t o n s c a t t e r i n g leads to t h e a s s u m p t i o n of a nuclear a b s o r p t i o n p o t e n t i a l which varies b e t w e e n 2 MeV and 10 MeV. T h e corresponding m e a n free p a t h of a nucleon in nuclear m a t t e r is t h e n of the same order of m a g n i t u d e as t h e nuclear dimension. This result bears s t r o n g l y on t h e i n t e r p r e t a t i o n of inelastic p r o t o n s c a t t e r i n g and on p r o t o n or n e u t r o n induced reactions. T h e picture of t h e c o m p o u n d nucleus which depends on a strong, u n h a m p e r e d i n t e r a c t i o n b e t w e e n inc o m i n g nucleon and nucleus m a y h a v e to be changed. N o t only t h e p r o t o n surface i n t e r a c t i o n has to be t a k e n into account, b u t one m a y h a v e to consider t h e t r a n s p a r e n c y of t h e t a r g e t nucleus such t h a t t h e (p, p') reaction becomes p a r t i c u l a r l y probable if t h e residual states are similar to t h e initial states. On_the nfh~r h a n d if fh.e finn.| s t a t e c a n n o t h a v e a n y r e s e m b l a n c e to t h e initial s t a t e as for instance for (p, ~) reactions one would e x p e c t t h e shape of t h e s p e c t r u m to differ f r o m t h e p r o t o n s p e c t r u m for inelastic scattering. T h e w i d t h for the reemission of fast protons m a y be greater b y several orders of m a g n i t u d e t h a n t h e w i d t h for t h e emission of fast ~-particles. T h e ratio of t h e w i d t h s reduces to a b o u t one for low emission energy.
Recent experimental results have changed our views about nuclear reactions. The strong interaction model has to be modified and amended. This new information provides also a more general picture for the understanding of nuclear structure. The experiments which contributed to this development are in the first place proton elastic scattering data which are interpreted by M e l k a n o f f , M o s z k o w s k i , N o d v i k and S a x o n 1). Using an optical model these authors were able to obtain fairly good agreement between theoretical and experimental angular distributions for a potential of the form:
u = -(v
+ iw)/(1 + eCr-R~/a)
(I)
R = 1.33 × 10-13Al/3cm a = 0.5 × 10-13cm The values for V and W axe energy dependent, as shown in Fig. 1 and Fig. 2. These parameters present the best fit to the experimental data for the *) Paper read at the Amsterdaln Nuclear Reactions Conference on J u l y 2nd, 1956.
-
-
1019-
1020
P . C . GUGELOT
assumed potential. A change in the shape of U or the inclusion of spin orbit forces m a y have the result that one obtains somewhat different values for radius and potential depth. A spin orbit force has been assumed by F e r n b a c h 2) for the interpretation of elastic neutron scattering.
SO
".,-o.
~ .
~ ~
.
40
""
3C
V MeV
20 I0 0 0
E MtV
Fig. 1. R e a l p a r t of nuclear p o t e n t i a l as a f u n c t i o n of the e n e r g y of the i n c i d e n t proton. The points are calculated in ref. 1 from e x p e r i m e n t s at 5.25 MeV 10),~at 17 MeV lz) and a t 31.5 MeV l~).
20
W
IO
o
o
,~
E McV
2b
3'0
Fig. 2. I m a g i n a r y p a r t of nuclear p o t e n t i a l as a f u n c t i o n of t h e i n c i d e n t p r o t o n energy. T h e t h e o r e t i c a l c u r v e is f r o m ref. 3.
The value of the real part of the scattering potential is in agreement with the ~ e w s obtained from shell structure. The decrease of potential with increasing proton energy can be made plausible by the decreasing nucleonnucleon forces. The curve in Fig. 2 is calculated by L a n e and W a n d e l s) on the basis of a semi-classical picture in which the nucleons are supposed
M E D I U M E N E R G Y REACTIONS AND S C A T T E R I N G
1021
to move in a Fermi-gas in which the number of collisions is restricted b y the action of the Pauli principle. The value of W, the absorptive part of the potential, is related to the mean free path of nucleons in nuclear matter,
A = (1/K)(e + V)/W K is the wave number of the nucleon inside the potential. For e = 20 MeV, one obtains A = 8 x 10-Is cm; a proton beam passing through a heavy nucleus is attenuated to about 1/e of its intensity.This value for the mean free path does not make possible an interpretation of reactions in terms of a compound nucleus. This does not mean, however, that one should discard the compound nucleus hypothesis completely. The reflection at the nuclear boundary will probably cause a low energy nucleon to traverse a nucleus m a n y times. .For the elastic scattering of a-particles the situation is as yet much less clear. Though good experimental information is available, nobody has carried out a detailed analysis b y using the optical model. An attempt to use a Born approximation for the interpretation of a-scattering b y magnesium yielded some useful information 4). An interaction potential of only 5 MeV was found b y this method. However, Henley observed that an opaque disc of the same radius gave also a satisfactory flt is). The nucleons eliminated from the incident channel will produce reacUons. On account of the long free path, a nucleon will produce reactions of the type in which only one nucleon is excited and the incident or exchanged nucleon is escaping with reduced energy. We would like to call these collisions inside the nucleus without the whole nucleus taking part "direct volume interactions". In this type of interactions one would expect that only few levels of the nucleus are excited, levels which can be represented b y A -- 1 nucleons in their normal states and one nucleon excited. This effect m a y have as a consequence the appearance of a giant resonance. Some experimental information shows that this m a y be the case 5). A compound nucleus can still be formed either in more complicated collisions, depending on many body interactions or, if so much energy is available that still other particles can escape after the initial direct interaction. We m a y be able to demonstrate the direct interaction with protons b y comparing the ratio of proton emission to a-emission in reactions of the kind X(x, y)Y in which x is a proton, y a proton or a-particle and Y the residual nucleus which should be preferably the same in the proton and ~-particle reactions. We assume that' a-particles are less liable to make direct interactions if large angles of scattering are considered. In the compound nucleus formalism,
F~ v = davy / ev Sv = constv o~v(E) de-----~l
1022
P.c. G U G E L O T
we find ~. ~
F~,/const~. F~Jconsta
OJvl(E)
r~y2(E)
ey is the energy of the emitted particle y; Sy is the geometrical cross-section times barrier penetration probability for particle y;
i
x
Rh(p,a)Ru
o
Ni(p,p')Ni Ni(p,a)Go
Fe (p,p')Fe o Co(p,a)Fe AI (p,#)AI
(
fi_~p (a
AI ( p , a ) M g
t
tO
Excitation Energy
MeV Fig. 3. R a t i o of " S t i c k i n g p r o b a b i l i t i e s " for t h e r e a c t i o n s X ( p , p) Y a n d Z (p, =) Y vs. e x c i t a t i o n energy. T h i s r a t i o s h o u l d b e one, if t h e s t a t i s t i c a l t h e o r y of n u c l e a r r e a c t i o n s is valid. 0.1 m .o¢ t,t t- .0~ to -, .07
D6
I
bl "~]"~'O3 .02 I
I
I
/
I
10°20"30°40 °
60 ° 90 ° C.M. A N G L E
120°
i50 °
180"
Fig. 4. A n g u l a r d i s t r i b u t i o n of =-particles e x c i t i n g t h e g r o u n d s t a t e of 100Ru f r o m t h e r e a c t i o n 103Rh (p, a) 100Ru. T h e s t r o n g f o r w a r d p e a k i n g of t h e cross-section s u g g e s t s t h a t t h e =-particles a r e p r o d u c e d in d i r e c t i n t e r a c t i o n s . E x p e r i m e n t a l w o r k f r o m ref. 6.
1023
MEDIUM ENERGY REACTIONS AND SCATTERING
oJv is the level density of the residual nucleus Y of which the excitation energy is E. The ratio ~p,/~ = 1 if Y1 and Y2 are the same residual nuclei. Fig. 2 shows that only for large excitation energy in the residual nucleus ~p,/~ m 1. That the statistical theory is 6lily valid for large energy transfer is also borne out b y the observed angular distributions of reaction products. The particles "evaporating" with low energy show almost isotropic angular distributions. The angular distribution of fast emitted particles is always in the forward direction. Fig. 4 shows that ]ast ~-particles are also the product of direct interactions, since the angular distribution is forward directed for those ~-particles which leave 100Ru in the ground state after the reaction lO3Rh (p, ~) 100Ru. These experiments were carried out by P. B r a d y s). ! t
200
~160 ~120
~ 80 le ~
40
b 0
0
2
I
40
0
60
I
GO
tO0
|
IL;~
140
I
160
180
0- sc~)ttcrlng angle Fig. 5. A n g u l a r distribution of inelastically scattered neutrons in the energy i n t e r v a l from 4 MeV to 12 MeV from Bi (n, n'), incident n e u t r o n energy 14MeV. T h e e x p e r i m e n t a l points are o b t a i n e d b y R o s e n and S t e w a r t 18). The theoretical c u r v e is calculated b y B r o w n and M u i r h e a d 7).
B r o w n and M u i r h e a d 7) started a simple theoretical treatment for the calculation of the emission spectra b y making use of the classical ideas of G o l d b e r g e r in his calculation of the mean free path. The cross-section alp for the collision of an incoming neutron with protons inside a nucleus is written as GIp = GI
ai
is the interaction cross-section of the incident neutrons x(~l) is the cross-section for a collision of a neutron of momentum Pl with a free nucleon is a factor which reduces the magnitude of x(pl) inside the nucleus through the operation of the Pauli principle and is the density of the nucleons inside the nucleus.
1024
P . C . GUGELOT
The theoretical results are compared to many experimental data. Fig. 5 and Fig. 6 show two of these comparisons. The agreement of this extremely classical calculation with experimental data is good. It is not understood w h y wave aspects like diffraction can be neglected.
(Mcv)'~ t10-~
}I}
IA9
'"
t" .~
I
• 60°
I.
o iso"
,o-'
i o .4
o°e iso"
•
OOOoel °
id s
J [4 4
~ I2 6
EXCITATION ENERGY",,,~t¢v. LO 8 6 4 8
|0
12
2
14 t6 EMev.
0 18
Fig. 6. Comparison of the experimental data from Ag (p, p') (ref. 14) and the theoretical curves of ref. 7. The data are presented in such a way that the ordinate is proportional to the level density if the statistical theory of nuclear reactions can be applied.
Finally I would like to point to another sort of direct interaction in which the nucleus takes part in a collective mode. One example m a y be the emission of energetic 7-rays after the capture of high energy protons. This reaction has been discussed b y B e c k s). Another example is the excitation of Bohr-Mottelson surface oscillations b y the inelastic scattering of co-particles as represented in Fig. 7 ( B o h r - M o t t e l s o n direct interaction 4)). One m a y deduce the nuclear quadrupole moment from such measurements. The angular distribution of 18 MeV protons exciting the 1.37 MeV level of 24Mg (Fig. 8) shows that an interpretation in the same terms as the ~-
MEDIUM
ENERGY
REACTIONS
AND
SCATTERING
1025
particle scattering (Fig. 7) is not possible 9). Direct v o l u m e i n t e r a c t i o n m a y h a v e to be t a k e n into a c c o u n t to explain the d a t a of Fig. 8. 24Mg {a,a,) Mg '.~7M~N Ea "42 MeV
mb/stera~
m[j.(oR~ ~ . ~,v 5,'~ .2 2,),O"~:r. t
2o | IO
( Ls 2 1.0.
o o
=
0.2 0.1
' ;o'
~o'
~o
eb'
,~o
ec~
Fig. 7. Angular distribution of =-particles from the reaction 24Mg (,',od) exciting the 1.37 MeV level in ~4Mg. The angular distribution is fitted to the square of the spherical Bessel-function of order two. The magnitude of the cross-section fixes the product of intrinsic quadrupole moment and surface interaction potential.
mbLsterad 24Mg lp.t~) Mg~57Mw Ep'18 MeV z R.6,0,$¢m [,, OR)].
8O
,) 4
t
(, t
~
t
i
3 2
//ss-% ~*'z i
t
Gem
Fig. 8. Angular distribution of protons from the reaction ~4Mg (p, p') exciting the 1.37 MeV level. [7'3(QR)]g does not fit the experimental curve. The Bohr-Mottelson surface interaction would predict the cross-section to be ten times larger. Physica XXII
65
1026
MEDIUM ENERGY REACTIONS AND SCATTERING
Summarizing these considerations we found that the optical model helped us in making plausible that interactions can occur which cannot be described by a compound nucleus formalism. The direct type of interactions are a new tool to investigate the nucleus and special attention has to be given to their theoretical and experimental studies at the moment.
Short communications directly /ollowing this paper were read by Cohen p. zi25 and Bleuler, p. zz27 o/ this volume. Received 12-7-56.
REFERENCES 1) M e l k a n o f f , M. A., M o s k o w s k i , S. A., N o d v i k , J. and S a x o n , D. S., Phys. Rev. 101 (1956) 507. 2) C u l l e r , G., F e r n b a c h , S. and S h e r m a n , N., Phys. Rev.101, (1956) 1047; B j o r k l u n d , F. E., F e r n b a c h , S. and S h e r m a n , N., Phys. Rev. 101 (1956) 1832. In this paper the authors obtain a very good fit to the 14 MeV neutron scattering data by making use of an absorptive surface. 3) L a n e , A. M. and W a n d e l , C. F., Phys. Rev. 98 (1955) 1524. 4) G u g e l o t , P. C. and. R i c k e y , M., Phys. Rev. 101 (1956) 1613. 5) G u g e l o t, P. C., "Statistical Aspects of the Nucleus", B N L 331 (C-21). The cross-section for the inelastic scattering of protons from Ag shows fluctuations which m a y indicate giant resonances. 6) B r a d y , P., Princeton University (unpublished work). 7) B r o w n , G. and M u i r h e a d , H., to be published. (We t h a n k the authors for sending us their results prior to publication.) 8) B e c k , F., On the calculation of (n, y) cross section, short communication. G u g e l o t , P. C., unpublished. 9) G u g e l o t , P. C. and P h i l l i p s , P. R., Phys. Rev. 101 (1956) 1614. 10) B r o m l e y , D. A. and W a l l , N. S., Phys. Rev. 99 (1955) 1029. 11) D a y t o n , I. E. and S c h r a n k , G., Phys. Rev. 101 (1956) 1358. 12) K i n s e y , B. B., Phys. Rev. 99 (1955) 332. 13) R o s e n , L. and S t e w a r t , L. Phys. Rev. 99 (1955) 1052. 14) G u g e l o t , P. C., Phys. Rev. 93 (1954) 425. 15) H e n l e y , E. M., Private communication.