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Contribution of rectangular graphs in the reaction 14N(3He, P5)16O∗ (E∗ = 8.88 MeV )
Volume 41B, number 1
PHYSICS LETTERS
4 September 1972
C O N T R I B U T I O N O F R E C T A N G U L A R G R A P H S IN T H E R E A C T I O N 14N(3He, P5)160 * (E* = 8.88 MeV) J.F. ALLARD and M. AMIEL
lnstitu t d'Etudes Nucl#aires,Algiers, Algeria Received 19 June 1972 A possible evidence of the manifestation of rectangular graphs is presented in the reaction 14N(aHe, Ps)160 * (E* = 8.88 MeV) in a region where such mechanisms were not expected. The angular distribution for the reaction 10Be(t, p)12B(g.s.) cannot be correctly reproduced by means of the classical theory of double stripping but fits very well the one obtained by means of rectangular graphs [ 1]. Arguments are given concerning the fact that this graph appears for a target located in the middle of the Ip shell. Other distributions obtained with the same mechanism for the reaction 9Be(3He, n)11C and 9Be(P, P')9Be agree with the experimental data [2]. It would be interesting to see if such mechanisms may appear also for nuclei located out of the middle of the lp shell. For the nucleus 14N the angular distribution of the reaction 14N(3He, P5)160 * (E* = 8.88 MeV) at 4.5 MeV does not give a good agreement with the one obtained by means of the classical theory [3]. The experimental distribution does not decrease sharply forwards, in contrast with the theoretical one which may be written: exp(-KZ/4T 2) (aj~(kr o) +[3]i(kro))
.
Furthermore Coulombian corrections do not improve the fit at small angles [4]. The rectangular graphs which may contribute to this reaction are shown in fig. 1. We shall keep only 150(g.s.) and 15N(g.s.) as intermediate states for the direct and the crossed graph, these states being strongly connected to 14N and 160* (E* = 8.88 MeV) which is mainly a (lp½) -1 (ld~) 1 state of 160 [5]. We notice that for the crossed graph the first stripping is strongly disfav.oured energetically and we shall neglect this graph. For the direct graph the differential cross section may be written: 18MD,IMHe,NMp ,FKpkD kHeO20'o2SS'(nrt) 3 2 2 6 (2JN+1)KHeh/2, (iklR)h212 (ikFR) MDj)M~,NR
do d~
x
z(-)
-~2k2/.~,/p, N = e D ;
2
D(A, ~,, A , A, ),, A , p) A (A, A', ~) A (A, A', X) Pp (cos 0) K
¢t2k2e/2MD,p = erie.
3.He
d
p
3He
1/*N
150
160*
1~N
d
p
15N
160*
Fig. 1. 29
Volume 41B, number 1
PHYSICS LETTERS
4 September 1972
Sd
o16°TI~(~b1~) 0.5 0.4 0.3 0.2 0.1 I
I
60
I
I
80
i
I
I
120
O(CM)
K
Fie. 3.
Fig. 2. I is the intermediate nucleolus and F the final nucleus, A(A, A', X)is the spatial overlapping integral defined in [I ], K is the angular momenta coupling term which is represented (fig. 2) in the graphical coupling theory representation [6]. Taking R = 5 fro, 0 2 ( l p ) = 0.04 and 02(ld~) = 0.07 [7], the mean theoretical cross section from 0 ° to 60 ° is equal to 0.8 mb compared to the experimental value of 0.5 mb. So the two cross sections have the same order of magnitude. Furthermore the theoretical and experimental distributions decrease slightly at small angles and then sharply up to 90 ° . The agreement with the experiment is rather good in spite of the lack o f adjustable parameters. Then an important contribution o f rectangular graphs may occur for this reaction which involves a target heavier than those considered previously.
References [ 1 ] 1. Bang, N.S. Zelenskaya, E.Zh. Magzumov and V.G. Neudachin, Soy. J. Nucl. Phys. 4 (1967) 688; J. Bang and S. Wollesen, Phys. Letters 33B (1970) 395. [2] E. Zh. Magzumov, V.G. Neudachin and M.S. Belkin, Soy. J. Nucl. Phys. 11 (1970) 331; E. Zh. Magzumov and V.G. Neudatchin, Phys. Letters 31B (1970) 106. [3l S. Gorodetzky, G. Bassompierre, C. St Pierre, A. Gallmann and P. Wagner, Nucl. Phys. 43 0963) 92. [4] G. Bassompierre, Thesis, Facultd des Sciences Strasbourg. [5] V. Gillet and N. Vinh Mau, Nucl. Phys. 54 (1964) 321. [6] A. Yutsis, I. Levinson and V. Vanagas, Mathematical apparatus of the theory of angular momentum (Israel program for scientific translation) Jerusalem 1962; E. El Baz, Trait~ment graphique de l'algebre des moments angulaires (Masson 1969). [7] M.H. Macfarlane and J.B. French, Rev. Mod. Phys. 32 0960) 567.
30
PHYSICS LETTERS
4 September 1972
C O N T R I B U T I O N O F R E C T A N G U L A R G R A P H S IN T H E R E A C T I O N 14N(3He, P5)160 * (E* = 8.88 MeV) J.F. ALLARD and M. AMIEL
lnstitu t d'Etudes Nucl#aires,Algiers, Algeria Received 19 June 1972 A possible evidence of the manifestation of rectangular graphs is presented in the reaction 14N(aHe, Ps)160 * (E* = 8.88 MeV) in a region where such mechanisms were not expected. The angular distribution for the reaction 10Be(t, p)12B(g.s.) cannot be correctly reproduced by means of the classical theory of double stripping but fits very well the one obtained by means of rectangular graphs [ 1]. Arguments are given concerning the fact that this graph appears for a target located in the middle of the Ip shell. Other distributions obtained with the same mechanism for the reaction 9Be(3He, n)11C and 9Be(P, P')9Be agree with the experimental data [2]. It would be interesting to see if such mechanisms may appear also for nuclei located out of the middle of the lp shell. For the nucleus 14N the angular distribution of the reaction 14N(3He, P5)160 * (E* = 8.88 MeV) at 4.5 MeV does not give a good agreement with the one obtained by means of the classical theory [3]. The experimental distribution does not decrease sharply forwards, in contrast with the theoretical one which may be written: exp(-KZ/4T 2) (aj~(kr o) +[3]i(kro))
.
Furthermore Coulombian corrections do not improve the fit at small angles [4]. The rectangular graphs which may contribute to this reaction are shown in fig. 1. We shall keep only 150(g.s.) and 15N(g.s.) as intermediate states for the direct and the crossed graph, these states being strongly connected to 14N and 160* (E* = 8.88 MeV) which is mainly a (lp½) -1 (ld~) 1 state of 160 [5]. We notice that for the crossed graph the first stripping is strongly disfav.oured energetically and we shall neglect this graph. For the direct graph the differential cross section may be written: 18MD,IMHe,NMp ,FKpkD kHeO20'o2SS'(nrt) 3 2 2 6 (2JN+1)KHeh/2, (iklR)h212 (ikFR) MDj)M~,NR
do d~
x
z(-)
-~2k2/.~,/p, N = e D ;
2
D(A, ~,, A , A, ),, A , p) A (A, A', ~) A (A, A', X) Pp (cos 0) K
¢t2k2e/2MD,p = erie.
3.He
d
p
3He
1/*N
150
160*
1~N
d
p
15N
160*
Fig. 1. 29
Volume 41B, number 1
PHYSICS LETTERS
4 September 1972
Sd
o16°TI~(~b1~) 0.5 0.4 0.3 0.2 0.1 I
I
60
I
I
80
i
I
I
120
O(CM)
K
Fie. 3.
Fig. 2. I is the intermediate nucleolus and F the final nucleus, A(A, A', X)is the spatial overlapping integral defined in [I ], K is the angular momenta coupling term which is represented (fig. 2) in the graphical coupling theory representation [6]. Taking R = 5 fro, 0 2 ( l p ) = 0.04 and 02(ld~) = 0.07 [7], the mean theoretical cross section from 0 ° to 60 ° is equal to 0.8 mb compared to the experimental value of 0.5 mb. So the two cross sections have the same order of magnitude. Furthermore the theoretical and experimental distributions decrease slightly at small angles and then sharply up to 90 ° . The agreement with the experiment is rather good in spite of the lack o f adjustable parameters. Then an important contribution o f rectangular graphs may occur for this reaction which involves a target heavier than those considered previously.
References [ 1 ] 1. Bang, N.S. Zelenskaya, E.Zh. Magzumov and V.G. Neudachin, Soy. J. Nucl. Phys. 4 (1967) 688; J. Bang and S. Wollesen, Phys. Letters 33B (1970) 395. [2] E. Zh. Magzumov, V.G. Neudachin and M.S. Belkin, Soy. J. Nucl. Phys. 11 (1970) 331; E. Zh. Magzumov and V.G. Neudatchin, Phys. Letters 31B (1970) 106. [3l S. Gorodetzky, G. Bassompierre, C. St Pierre, A. Gallmann and P. Wagner, Nucl. Phys. 43 0963) 92. [4] G. Bassompierre, Thesis, Facultd des Sciences Strasbourg. [5] V. Gillet and N. Vinh Mau, Nucl. Phys. 54 (1964) 321. [6] A. Yutsis, I. Levinson and V. Vanagas, Mathematical apparatus of the theory of angular momentum (Israel program for scientific translation) Jerusalem 1962; E. El Baz, Trait~ment graphique de l'algebre des moments angulaires (Masson 1969). [7] M.H. Macfarlane and J.B. French, Rev. Mod. Phys. 32 0960) 567.
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