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The (n, d) reaction on Fe54
1.D.1 : I.E.1 : 2.B:2.G
Nuclear Physics 36 (1962) 471--475; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
T H E (n, d) R E A C T I O N O N Fe s4 G. B A S S A N I , L. COLLI, E. G A D I O L I and I. I O R I
Istituto di Fisica dell'Universitg, Milano and
Laboratori CISE, Milano * Received 10 April 1962 The a n g u l a r distribution of deuterons from the pick-up reaction Fe54(n, d)Mn ~3 t a k e n at incident n e u t r o n energy of 14 MeV is presented; only high energy deuterons h a v e been considered. These d e u t e r o n s correspond to t w o levels of the residual nucleus Mn 5a, t h a t is the ground state and the first excited level at 0.39 MeV, which c a n n o t be separated. The results can be interpreted b y m e a n s of Satchler's calculation using distorted wave B o r n a p p r o x i m a tion, a t t r i b u t i n g a p a r t of the transition to a pick-up reaction with transferred a n g u l a r m o m e n t u m l = 1. This shows t h a t the first excited level of Mn 63 m u s t have spin {}.
Abstract:
1. I n t r o d u c t i o n Direct reactions have received an increasing attention in the last few years due to the fact that they may give some information on nuclear structure. This quality of direct effects is connected with the fact that they are single particle processes, and therefore are of relatively simple interpretation. From this point of view, we have studied some (n, d) reactions 1-4), involving in particular the nuclei 4) between Sc 45 and Ni ~°. All these nuclei have, according to the shell model, a very similar proton configuration. In fact, from Sc to Ni, they fill progressively the orbit ft, Sc having only one proton in this orbit and Ni eight. For these nuclei, the deuteron spectra emitted forward following bombardment with 14 MeV neutrons were measured. Of particular interest was the comparison of the cross sections of the deuteron peaks of maximum energy, at which the residual nucleus is left in the ground state. From this comparison we have derived some indications of the validity of the shell model with j-j coupling as was discussed in the work quoted above. All previous conclusions were based on the hypothesis that the mechanism of the (n, d) reaction is that of pick-up, according to which the incident neutron snatches a proton off the target nucleus without interacting with the nucleus as a whole. This is therefore a typical case of direct interaction, which is well described by Butler theory to the first approximation. t W o r k done u n d e r the research c o n t r a c t E U R A T O M - C N E N . 471
472
G. BASSANI
gt al.
Many recent experimental results have, however, demonstrated that there exist systematic deviations from the predictions of Butler's theory, and some doubt always arises as to the validity of the theory in the particular cases concerned. A basic check of what has been stated above, both with regard to the hypotheses of the configuration of protons as expected on the basis of the shell model and the validity of Butler's theory, can be made by measuring the angular distribution of the deuterons emitted in the reaction. According to the above theory, this distribution is in fact determined by the orbit of the shell model on which the proton in the nucleus lies. With this in mind, we have begun the measurement of the angular distribution of deuterons of maximum energy emitted by the elements examined in the above quoted work. The present work reports the results obtained for Fe 54.
2. Experimental Apparatus The experimental apparatus is the same one used in the previous work 4). The deuterons are detected by means of a telescopic unit of proportional counters and a scintillator in coincidence. By measuring the energy loss in a proportional counter the separation of particles of different mass is achieved. Therefore, the measurements are not affected by the protons emitted in the (n, p) reaction on the same nucleus. The energy resolution of the system is 5 %. The measurements are carried out taking the pulse energy spectrum at 10 angles between 7 ° and 120 °, with an average angular opening varying from 10 ° to 15 °. In the spectra thus obtained, the peak corresponding to the deuterons of maximum energy is experimentally identified (fig. 1) and the number of deuterons contained in the peak is calculated. The result of the angular distribution so obtained is shown in fig. 2.
3. Discussion The ground state of Mn 5~ has spin ~, as foreseen by the shell model, and the first excited level at 0.38 MeV has unknown spin value 5). We m a y note at once that the energy resolution of our measurement is not such as to enabel us to discriminate between these two levels and therefore both levels could contribute to the measured peaks. In the pick-up theory, the transition obey the angular momentum conservation law expressed by the formula:
(J~n+Jtln+ S)max~ l ~ (Jln+J~ln+ S)mln. where Jln and Jnn are the angular momenta of the initial and final states, S is the proton spin, and l is the transferred angular momentum.
THE (n, d) REACTION ON Fe64
473
Number orj pulses per channel 9 = 15 °
7060X
50XX X
40-
X
30xx
x
x x
X
20-
x x
x x~
10-
x x)~
2'0
3'0
4'0
5'0
xx
x
6'0
Channels
Fig. 1. E n e r g y s p e c t r u m of d e u t e r o n s f r o m t h e Fe 6¢(n, d )Mn 6s reaction a t 15 °. The p e a k of d e u t e r o n s oI m a x i m u m energy is p r o m i n e n t .
mb str
54
Fe (..d)
4-
26
n
2B
3 ~
/,,, /
2-
i
j'
1-
i ,,'--~
/ o
.
.
.
.
.
.
":,-.-,-'
+
+
. . . .
(3° 10° 20 o 30°40 ° 50° 600 70 o BOo 90 ° 100e110° 120°
- -
0 C.M.
Fig. 2. A n g u l a r d i s t r i b u t i o n s of d e u t e r o n s of m a x i m u m energy f r o m the Fei4(n, d)Mn 8a reaction. P o i n t s are e x p e r i m e n t a l results. B a r s on each p o i n t s h o w t h e statistical errors. The d o t t e d curve is calculated b y Satchler using a distorted w a v e - B o r n a p p r o x i m a t i o n and a s s u m i n g transferred a n g u l a r m o m e n t u m I = 3. The curve d r a w n in fullis obtained t a k i n g 68 % of l = I t r a n s i t i o n plus 32 % of 1 : 3.
474
G. B A S S A N I
et al.
Due to this limitation, the l = 3 value is the only one p e r m i t t e d for the transition to the Mn 53 g r o u n d state, because Jtn = 0 and Jnn 7 The angular distribution proposed b y Butler's t h e o r y for the transition to the g r o u n d state is a curve with a m a x i m u m at 40 ° and therefore in complete disagreement with the e x p e r i m e n t a l results. Satchler 6) has r e c e n t l y calculated the angular distribution e x p e c t e d on the basis of the d i s t o r t e d wave Born a p p r o x i m a t i o n for a reaction v e r y similar to the one studied b y us, viz. the FeS~(n, d)Mn 55 reaction. Using these calculations, we find for the transition with l = 3, the d o t t e d curve shown in fig. 2, which presents a m a x i m u m at 32 °. The curve is arbitrarily normalized. Comparing the part of the angular distribution at small angles with the curve calculated for other values of l, one finds t h a t the m a x i m u m at ~ 1 5 ° coincides r a t h e r well with the calculations for a transition with a transferred angular m o m e n t u m l = 1. In fact, taking 68 °/o of the 1 = 1 transition, and 32 °/o of the l = 3 transition, we obtain the full curve of fig. 2. T h e agreement of this curve with the e x p e r i m e n t a l points seems to verify the presence of the l = 1 transition. Considering now the restrictions given b y the angular m o m e n t u m conservation laws, one can see t h a t the only possibility of having an l = 1 transition is t h a t the J value of the final nucleus is 3. So, given the g r o u n d state spin of 7, we m u s t a t t r i b u t e the value { to the first excited level at 0.38 MeV. T h e r e seems to be no other possibility for explaining the presence of the value l = 1, if we w a n t to ~:~p the hypothesis of a pure pick-up mechanism. As for the possibility tb~* the first excited level has J = { the following m a y be observed: examining .'~e level spectra of nuclei with the p r o t o n and n e u t r o n configuration similaI to the one of Mn 53, we find t h a t the first excited level above the { g r o u n d state has in some cases J = { and in others J - 2 . 3 Therefore, the assignment does not seem to be unlikely at all. It m a y be n o t e d t h a t even a small part of the p l configuration mixing is easily detectable, because a transition with l = 1, is, in absolute value, an order of m a g n i t u d e higher t h a n the one with l = 3. Finally, following this m e a s u r e m e n t , we should re-examine some of the conclusions drawn from the a b o v e - q u o t e d work, in which the transition probabilities were discussed for deuterons of m a x i m u m e n e r g y in the case of nuclei from Sc .5 to Ni 6° made on the simple l = 3 hypothesis. It is quite clear from the present m e a s u r e m e n t t h a t the presence of the transition with l -7- 1 changes the value of the specroscopic factor calculated on the basis of the hypothesis t h a t the transition has p u r e l y l ----- 3. B u t this fact does not substantially alter the agreement between the theoretical predictions and the e x p e r i m e n t a l results, since t h a t agreement was qualita--
2"
THE (n, d) REACTION ON Fes4
475
tive within a factor of 2, and therefore remains such; it shows, however, t h a t the study of the angular distribution of deuterons emitted in these reactions would be necessary in order to obtain more detailed information concerning the nuclear structure of the residual nuclei. References 1) 2) 3) 4) 5)
L. Colli, F. Cvelbar, S. Micheletti a n d M. Pignanelli, N u o v o Cim. 13 (1969) 868 L. Colli, F. Cvelbar, S. Micheletti a n d M. Pignanelli, N u o v o Cim. 14 (1959) 1220 L. Colli, M. G. Marcazzan, F. Merzari, P. G. Sona a n d F. Tonolini, N u o v o Cim. 16 (1960) 991 L. Colli, I. Iori, S. Micheletti a n d M. Pignanelli, N u o v o Cim. 20 (1961) 94 L a n d o l t - B 6 r n s t e i n , N u m e r i c a l d a t a a n d f u n d a m e n t a l relationship in science a n d t e c h n o l o g y , n e w series, G r o u p I, Vol. I (Springer-Verlag, Berlin, 1961) 6) R. Satchler, p r i v a t e c o m m u n i c a t i o n
Nuclear Physics 36 (1962) 471--475; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
T H E (n, d) R E A C T I O N O N Fe s4 G. B A S S A N I , L. COLLI, E. G A D I O L I and I. I O R I
Istituto di Fisica dell'Universitg, Milano and
Laboratori CISE, Milano * Received 10 April 1962 The a n g u l a r distribution of deuterons from the pick-up reaction Fe54(n, d)Mn ~3 t a k e n at incident n e u t r o n energy of 14 MeV is presented; only high energy deuterons h a v e been considered. These d e u t e r o n s correspond to t w o levels of the residual nucleus Mn 5a, t h a t is the ground state and the first excited level at 0.39 MeV, which c a n n o t be separated. The results can be interpreted b y m e a n s of Satchler's calculation using distorted wave B o r n a p p r o x i m a tion, a t t r i b u t i n g a p a r t of the transition to a pick-up reaction with transferred a n g u l a r m o m e n t u m l = 1. This shows t h a t the first excited level of Mn 63 m u s t have spin {}.
Abstract:
1. I n t r o d u c t i o n Direct reactions have received an increasing attention in the last few years due to the fact that they may give some information on nuclear structure. This quality of direct effects is connected with the fact that they are single particle processes, and therefore are of relatively simple interpretation. From this point of view, we have studied some (n, d) reactions 1-4), involving in particular the nuclei 4) between Sc 45 and Ni ~°. All these nuclei have, according to the shell model, a very similar proton configuration. In fact, from Sc to Ni, they fill progressively the orbit ft, Sc having only one proton in this orbit and Ni eight. For these nuclei, the deuteron spectra emitted forward following bombardment with 14 MeV neutrons were measured. Of particular interest was the comparison of the cross sections of the deuteron peaks of maximum energy, at which the residual nucleus is left in the ground state. From this comparison we have derived some indications of the validity of the shell model with j-j coupling as was discussed in the work quoted above. All previous conclusions were based on the hypothesis that the mechanism of the (n, d) reaction is that of pick-up, according to which the incident neutron snatches a proton off the target nucleus without interacting with the nucleus as a whole. This is therefore a typical case of direct interaction, which is well described by Butler theory to the first approximation. t W o r k done u n d e r the research c o n t r a c t E U R A T O M - C N E N . 471
472
G. BASSANI
gt al.
Many recent experimental results have, however, demonstrated that there exist systematic deviations from the predictions of Butler's theory, and some doubt always arises as to the validity of the theory in the particular cases concerned. A basic check of what has been stated above, both with regard to the hypotheses of the configuration of protons as expected on the basis of the shell model and the validity of Butler's theory, can be made by measuring the angular distribution of the deuterons emitted in the reaction. According to the above theory, this distribution is in fact determined by the orbit of the shell model on which the proton in the nucleus lies. With this in mind, we have begun the measurement of the angular distribution of deuterons of maximum energy emitted by the elements examined in the above quoted work. The present work reports the results obtained for Fe 54.
2. Experimental Apparatus The experimental apparatus is the same one used in the previous work 4). The deuterons are detected by means of a telescopic unit of proportional counters and a scintillator in coincidence. By measuring the energy loss in a proportional counter the separation of particles of different mass is achieved. Therefore, the measurements are not affected by the protons emitted in the (n, p) reaction on the same nucleus. The energy resolution of the system is 5 %. The measurements are carried out taking the pulse energy spectrum at 10 angles between 7 ° and 120 °, with an average angular opening varying from 10 ° to 15 °. In the spectra thus obtained, the peak corresponding to the deuterons of maximum energy is experimentally identified (fig. 1) and the number of deuterons contained in the peak is calculated. The result of the angular distribution so obtained is shown in fig. 2.
3. Discussion The ground state of Mn 5~ has spin ~, as foreseen by the shell model, and the first excited level at 0.38 MeV has unknown spin value 5). We m a y note at once that the energy resolution of our measurement is not such as to enabel us to discriminate between these two levels and therefore both levels could contribute to the measured peaks. In the pick-up theory, the transition obey the angular momentum conservation law expressed by the formula:
(J~n+Jtln+ S)max~ l ~ (Jln+J~ln+ S)mln. where Jln and Jnn are the angular momenta of the initial and final states, S is the proton spin, and l is the transferred angular momentum.
THE (n, d) REACTION ON Fe64
473
Number orj pulses per channel 9 = 15 °
7060X
50XX X
40-
X
30xx
x
x x
X
20-
x x
x x~
10-
x x)~
2'0
3'0
4'0
5'0
xx
x
6'0
Channels
Fig. 1. E n e r g y s p e c t r u m of d e u t e r o n s f r o m t h e Fe 6¢(n, d )Mn 6s reaction a t 15 °. The p e a k of d e u t e r o n s oI m a x i m u m energy is p r o m i n e n t .
mb str
54
Fe (..d)
4-
26
n
2B
3 ~
/,,, /
2-
i
j'
1-
i ,,'--~
/ o
.
.
.
.
.
.
":,-.-,-'
+
+
. . . .
(3° 10° 20 o 30°40 ° 50° 600 70 o BOo 90 ° 100e110° 120°
- -
0 C.M.
Fig. 2. A n g u l a r d i s t r i b u t i o n s of d e u t e r o n s of m a x i m u m energy f r o m the Fei4(n, d)Mn 8a reaction. P o i n t s are e x p e r i m e n t a l results. B a r s on each p o i n t s h o w t h e statistical errors. The d o t t e d curve is calculated b y Satchler using a distorted w a v e - B o r n a p p r o x i m a t i o n and a s s u m i n g transferred a n g u l a r m o m e n t u m I = 3. The curve d r a w n in fullis obtained t a k i n g 68 % of l = I t r a n s i t i o n plus 32 % of 1 : 3.
474
G. B A S S A N I
et al.
Due to this limitation, the l = 3 value is the only one p e r m i t t e d for the transition to the Mn 53 g r o u n d state, because Jtn = 0 and Jnn 7 The angular distribution proposed b y Butler's t h e o r y for the transition to the g r o u n d state is a curve with a m a x i m u m at 40 ° and therefore in complete disagreement with the e x p e r i m e n t a l results. Satchler 6) has r e c e n t l y calculated the angular distribution e x p e c t e d on the basis of the d i s t o r t e d wave Born a p p r o x i m a t i o n for a reaction v e r y similar to the one studied b y us, viz. the FeS~(n, d)Mn 55 reaction. Using these calculations, we find for the transition with l = 3, the d o t t e d curve shown in fig. 2, which presents a m a x i m u m at 32 °. The curve is arbitrarily normalized. Comparing the part of the angular distribution at small angles with the curve calculated for other values of l, one finds t h a t the m a x i m u m at ~ 1 5 ° coincides r a t h e r well with the calculations for a transition with a transferred angular m o m e n t u m l = 1. In fact, taking 68 °/o of the 1 = 1 transition, and 32 °/o of the l = 3 transition, we obtain the full curve of fig. 2. T h e agreement of this curve with the e x p e r i m e n t a l points seems to verify the presence of the l = 1 transition. Considering now the restrictions given b y the angular m o m e n t u m conservation laws, one can see t h a t the only possibility of having an l = 1 transition is t h a t the J value of the final nucleus is 3. So, given the g r o u n d state spin of 7, we m u s t a t t r i b u t e the value { to the first excited level at 0.38 MeV. T h e r e seems to be no other possibility for explaining the presence of the value l = 1, if we w a n t to ~:~p the hypothesis of a pure pick-up mechanism. As for the possibility tb~* the first excited level has J = { the following m a y be observed: examining .'~e level spectra of nuclei with the p r o t o n and n e u t r o n configuration similaI to the one of Mn 53, we find t h a t the first excited level above the { g r o u n d state has in some cases J = { and in others J - 2 . 3 Therefore, the assignment does not seem to be unlikely at all. It m a y be n o t e d t h a t even a small part of the p l configuration mixing is easily detectable, because a transition with l = 1, is, in absolute value, an order of m a g n i t u d e higher t h a n the one with l = 3. Finally, following this m e a s u r e m e n t , we should re-examine some of the conclusions drawn from the a b o v e - q u o t e d work, in which the transition probabilities were discussed for deuterons of m a x i m u m e n e r g y in the case of nuclei from Sc .5 to Ni 6° made on the simple l = 3 hypothesis. It is quite clear from the present m e a s u r e m e n t t h a t the presence of the transition with l -7- 1 changes the value of the specroscopic factor calculated on the basis of the hypothesis t h a t the transition has p u r e l y l ----- 3. B u t this fact does not substantially alter the agreement between the theoretical predictions and the e x p e r i m e n t a l results, since t h a t agreement was qualita--
2"
THE (n, d) REACTION ON Fes4
475
tive within a factor of 2, and therefore remains such; it shows, however, t h a t the study of the angular distribution of deuterons emitted in these reactions would be necessary in order to obtain more detailed information concerning the nuclear structure of the residual nuclei. References 1) 2) 3) 4) 5)
L. Colli, F. Cvelbar, S. Micheletti a n d M. Pignanelli, N u o v o Cim. 13 (1969) 868 L. Colli, F. Cvelbar, S. Micheletti a n d M. Pignanelli, N u o v o Cim. 14 (1959) 1220 L. Colli, M. G. Marcazzan, F. Merzari, P. G. Sona a n d F. Tonolini, N u o v o Cim. 16 (1960) 991 L. Colli, I. Iori, S. Micheletti a n d M. Pignanelli, N u o v o Cim. 20 (1961) 94 L a n d o l t - B 6 r n s t e i n , N u m e r i c a l d a t a a n d f u n d a m e n t a l relationship in science a n d t e c h n o l o g y , n e w series, G r o u p I, Vol. I (Springer-Verlag, Berlin, 1961) 6) R. Satchler, p r i v a t e c o m m u n i c a t i o n