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Production of deuterons in the interaction of fast nucleons with nuclei
Nuclear Phys,cs 34 (1962) 644--647, ~ ) North-Holland Pubhsh,ng Co., Amsterdam Not
to be reproduced by photoprlnt or microfilm without written permasmon from the pubhsher
P R O D U C T I O N OF D E U T E R O N S IN T H E I N T E R A C T I O N OF F A S T N U C L E O N S WITH NUCLEI V. S. B A R A S H E N K O V and V M M & L T S E V
Joint Institute ]or Nuclear Research, Laboratory o] Theoretlcal Physzcs, Dubna, U S S R Recexved 30 December 1961 A b s t r a c t : A large yield of deuterons in p r o t o n - n u c l e u s interactions at energies T ~> 1 GeV m a y be explained b y m e a n s of peripheral interactions of p r i m a r y p r o t o n s w i t h nuclei. I n this case deuterons arise as a result of m e l a s t m nucleon-nucleon interactsons.
It has been shown by several authors that nucleon-nucleus interactions in a very wide energy region, starting from some tens of MeV up to very high energies of the order of several tens and hundreds of GeV are well explained by the mechanism of the intranuclear cascade (see, for example, refs. 1-7), where a detailed bibliography is given). However, at present there are m a n y experimental data which cannot be explained within the framework of such a simple model. In refs. s, ~) it has been found for the first time that in nucleon-nucleus interactions at energies of the order of several hundreds of MeV deuterons are produced with large probability. So, at T = 660 MeV the cross section of production of deuterons on Be, C, 0 nuclei is about 1 % of the cross section of all inelastic processes. In subsequent experiments this phenomenon was detected at higher energies as well 10,11). Estimations showed that such a large cross section of deuteron formation at energies some hundred and thousand times higher than its binding energy cannot be explained even qualitatively within the framework of the simple model of the intranuclear cascade. It has been shown 12) that in the energy region of the order of several hundreds of MeV agreement with experimental data within an order of magnitude can be obtained if one takes into account not only pair interactions of cascade particles inside the nucleus, but interactions with groups of nucleons which arise from the fluctuations in the density of nuclear matter as well. It is necessary for this that the fluctuation take place in a volume whose dimensions do not exceed the size of the nucleon core. It is only in this case that the fluctuation of nuclear matter may be considered as a whole *. * We m e a n b y " c o r e " the central region m a nucleon v.lth the radius r ~ ~/Mc ~ 0 2 fm, where the b u l k of the nuclear m a t t e r of the nucleon is c.'~ncentrat~d 7, x,). I n a later p a p e r 14) the m a x a m u m size of the region of the fluctuation is chosen to be equal to the De Broglie wave length of the p r i m a r y nucleon. However, this is t r u e only for p o i n t particles (or m the low energy region w h e n the wave length ~ is considerably larger t h a n the dimensions of t h e core). I t is n o t the De Broglie wave length ~ b u t the geometrmal dimensions of the partacles which are i m p o r t a n t w h e n we consider interactions of real particles 644
OF
PRODUCTION
645
DEUTERONS
However, with increasing energy the elastic interaction of the primary nucleon with the deuteron assumes more and more pronounced diffractional character. In this case the probability of collisions with a large transfer of m o m e n t u m to the deuteron decreases rapidly. Estimations show t h a t deuteron production owing to the fluctuation in the nuclear matter becomes unessential already at energies T ~ 1 to 2 GeV. At energies higher than several GeV, deuterons can be produced as a result of inelastic NN and nN collisions inside the nucleus x6). However, the estimations show that the greater part of the deuterons produced in this way is absorbed before t h e y have time to leave the nucleus le). Unabsorbed remain only deuterons which were produced in a distant diffuse region of the nucleus where collisions between the primary nucleon and the nucleon of the nucleus are not accompanied by an intranuclear cascade. In this case the momentum transferred to the nucleus is not large and the nucleus remains weakly excited. (d/P)pt
005
004-
003-
0 02
10
15
E MeV
Fig. 1. The ratio dip as a function of s for the interaction of 25 GeV p r o t o n s w i t h p l a t i n u m .
For calculating such collisions we m a y use the shell model of the nucleus. We denote by Nnz ~ and P ~ , the number of neutrons and protons on the level with quantum numbers (n, l, j). Let the coefficient Mn~ characterize a partial contribution from the interaction with a nucleon on this level. Then, the experimentaUy observed ratio of deuterons and protons produced for some nucleus X turns out to be
(d) x= (d)NN ~ (N,a~+P.,j)M.~ ,
(1)
646
V.S. BAEASHENKOVAND V. M MALTSEV
where (d/p)s N is the ratio of numbers of deuterons and protons with equal momenta, produced in inelastic NN collision. The summation is to be extended over all levels of the nucleus X involved in the reaction. The number of the levels is defined b y the excitation energy of nucleus e. This energy is an essential parameter of the theory. The dependence of the ratio (d/p) on the quantity e for the case of interaction of 25 GeV protons with platinum is plotted in fig. 1. The calculation is made for the angle 0 = 16° in the laboratory system, and for the momentum of produced particles of Pa-----Pp = 5.3 GeV/c which corresponds to the experimental conditions lo). The value (d/p)Ns is taken from ref. 15), where it has been calculated b y means of the statistical theory of multiple particle production. The coefficients Mn ~were calculated b y applying Benioff's data 17). In order to obtain agreement with the experimental value (d/p)v t = 0.024 40.003 (ref. 10)), it should be assumed that e ~ 8 MeV, i.e., that the main part of the deuterons is produced in collisions in which only the highest levels of nucleus are excited. A similar result was obtained for the aluminium nucleus. The comparison of experimental data with theory is given in table 1. TABLE 1 The ratios of numbers of deuterons, protons and ~+-mesons produced in P t and A1 Theory (d/p)pt (dlp)Al (d/p)pt : (d/p)Al (d/=+)pt (d/~+)Al
0.03 0.02 1.5 0.008 0.05
Experiment 10) 0.024 =50.003 0.017 =50.002 1.41 :[-0.34 0.080=50 010 0g053 =50.008
As is seen the model of peripheral interactions of protons with nuclei m a y explain the available experimental data. A characteristic feature of this model is that the deuteron yield changes rapidly near magic nuclei. In conclusion we consider our pleasant d u t y to thank D. I. Blokhintsev, I. K. Vsorov, M. G. Meshcheryakov for discussions and valuable critical remarks. References 1) N. Metropolis, R. Bivins, M. Storm, A. Turkevich, I M Miller and G. Friedlander, Phys. Rev.
110 (1958) 185 2) N. Metropolis, R. Bwins, M. Storm, I. M. Miller, G. Friedlander and A. Turkevich, Phys. :Rev. 110 (1958) 204 3) V M. Maltsev and Yu. D. Prokhoskin, J E T P 39 (1960) 1625 4) V. S. Barashenkov, V A. Bellakov, V. V Glagolev, N Dalkhazhav, Yao Tsyng Se, L. F. Klrillova, R. M Lebedev, V. M. Maltsev, P. K Markov, M. G. Shairanova, K. D Tolstoy, E. N. Tsyganov and Wang Shou Feng, Nuclear Physics 14 (1960) 522
PRODUCTION OF DEUTERONS 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17)
647
V. S Barashenkov, V. M. Maltsev and E. K Mihul, Nuclear Physics 24 (1961) 642 T. P. Lazareva and P A Usik, Proc Int. Conf. on Cosmic Rays, Moscow, 1 (1959) 71 V. S. Barashenkov, Fortschr. der Phys. 9 (1961) 29 G. A. Leksin, J E T P 32 (1957) 445 L. S. Azhgirh, I. K Vzorov, V. P. Zrelov, M G Meshcheryakov, B S. Neganov and A. F. Shabudin, J E T P 33 (1957) 1185 V. T. Cocconi, T. Fazzini, G. Fidecaro, M. Legros, N. H. Lipman and A. W. Merrison, Phys. Rev. Lett 5 (1960) 19 I Oostens, Preprint Saclay, 1961 D I. Blokhintsev, J E T P 33 (1957) 1295 D. I. Blokhintsev, V S. Barashenkov and B. M Barbashov, Usp Flz Nauk 68 (1959) 417 A. A. Rukhadze, J E T P 34 (1958) 1014 R. Hagedorn, Phys. Rev. Lett. B (1960) 276 I. yon Behr and R Hagedorn, P r e p r m t CERN, 1961 P. A. Benioff, Phys. Rev 119 (1960) 324
to be reproduced by photoprlnt or microfilm without written permasmon from the pubhsher
P R O D U C T I O N OF D E U T E R O N S IN T H E I N T E R A C T I O N OF F A S T N U C L E O N S WITH NUCLEI V. S. B A R A S H E N K O V and V M M & L T S E V
Joint Institute ]or Nuclear Research, Laboratory o] Theoretlcal Physzcs, Dubna, U S S R Recexved 30 December 1961 A b s t r a c t : A large yield of deuterons in p r o t o n - n u c l e u s interactions at energies T ~> 1 GeV m a y be explained b y m e a n s of peripheral interactions of p r i m a r y p r o t o n s w i t h nuclei. I n this case deuterons arise as a result of m e l a s t m nucleon-nucleon interactsons.
It has been shown by several authors that nucleon-nucleus interactions in a very wide energy region, starting from some tens of MeV up to very high energies of the order of several tens and hundreds of GeV are well explained by the mechanism of the intranuclear cascade (see, for example, refs. 1-7), where a detailed bibliography is given). However, at present there are m a n y experimental data which cannot be explained within the framework of such a simple model. In refs. s, ~) it has been found for the first time that in nucleon-nucleus interactions at energies of the order of several hundreds of MeV deuterons are produced with large probability. So, at T = 660 MeV the cross section of production of deuterons on Be, C, 0 nuclei is about 1 % of the cross section of all inelastic processes. In subsequent experiments this phenomenon was detected at higher energies as well 10,11). Estimations showed that such a large cross section of deuteron formation at energies some hundred and thousand times higher than its binding energy cannot be explained even qualitatively within the framework of the simple model of the intranuclear cascade. It has been shown 12) that in the energy region of the order of several hundreds of MeV agreement with experimental data within an order of magnitude can be obtained if one takes into account not only pair interactions of cascade particles inside the nucleus, but interactions with groups of nucleons which arise from the fluctuations in the density of nuclear matter as well. It is necessary for this that the fluctuation take place in a volume whose dimensions do not exceed the size of the nucleon core. It is only in this case that the fluctuation of nuclear matter may be considered as a whole *. * We m e a n b y " c o r e " the central region m a nucleon v.lth the radius r ~ ~/Mc ~ 0 2 fm, where the b u l k of the nuclear m a t t e r of the nucleon is c.'~ncentrat~d 7, x,). I n a later p a p e r 14) the m a x a m u m size of the region of the fluctuation is chosen to be equal to the De Broglie wave length of the p r i m a r y nucleon. However, this is t r u e only for p o i n t particles (or m the low energy region w h e n the wave length ~ is considerably larger t h a n the dimensions of t h e core). I t is n o t the De Broglie wave length ~ b u t the geometrmal dimensions of the partacles which are i m p o r t a n t w h e n we consider interactions of real particles 644
OF
PRODUCTION
645
DEUTERONS
However, with increasing energy the elastic interaction of the primary nucleon with the deuteron assumes more and more pronounced diffractional character. In this case the probability of collisions with a large transfer of m o m e n t u m to the deuteron decreases rapidly. Estimations show t h a t deuteron production owing to the fluctuation in the nuclear matter becomes unessential already at energies T ~ 1 to 2 GeV. At energies higher than several GeV, deuterons can be produced as a result of inelastic NN and nN collisions inside the nucleus x6). However, the estimations show that the greater part of the deuterons produced in this way is absorbed before t h e y have time to leave the nucleus le). Unabsorbed remain only deuterons which were produced in a distant diffuse region of the nucleus where collisions between the primary nucleon and the nucleon of the nucleus are not accompanied by an intranuclear cascade. In this case the momentum transferred to the nucleus is not large and the nucleus remains weakly excited. (d/P)pt
005
004-
003-
0 02
10
15
E MeV
Fig. 1. The ratio dip as a function of s for the interaction of 25 GeV p r o t o n s w i t h p l a t i n u m .
For calculating such collisions we m a y use the shell model of the nucleus. We denote by Nnz ~ and P ~ , the number of neutrons and protons on the level with quantum numbers (n, l, j). Let the coefficient Mn~ characterize a partial contribution from the interaction with a nucleon on this level. Then, the experimentaUy observed ratio of deuterons and protons produced for some nucleus X turns out to be
(d) x= (d)NN ~ (N,a~+P.,j)M.~ ,
(1)
646
V.S. BAEASHENKOVAND V. M MALTSEV
where (d/p)s N is the ratio of numbers of deuterons and protons with equal momenta, produced in inelastic NN collision. The summation is to be extended over all levels of the nucleus X involved in the reaction. The number of the levels is defined b y the excitation energy of nucleus e. This energy is an essential parameter of the theory. The dependence of the ratio (d/p) on the quantity e for the case of interaction of 25 GeV protons with platinum is plotted in fig. 1. The calculation is made for the angle 0 = 16° in the laboratory system, and for the momentum of produced particles of Pa-----Pp = 5.3 GeV/c which corresponds to the experimental conditions lo). The value (d/p)Ns is taken from ref. 15), where it has been calculated b y means of the statistical theory of multiple particle production. The coefficients Mn ~were calculated b y applying Benioff's data 17). In order to obtain agreement with the experimental value (d/p)v t = 0.024 40.003 (ref. 10)), it should be assumed that e ~ 8 MeV, i.e., that the main part of the deuterons is produced in collisions in which only the highest levels of nucleus are excited. A similar result was obtained for the aluminium nucleus. The comparison of experimental data with theory is given in table 1. TABLE 1 The ratios of numbers of deuterons, protons and ~+-mesons produced in P t and A1 Theory (d/p)pt (dlp)Al (d/p)pt : (d/p)Al (d/=+)pt (d/~+)Al
0.03 0.02 1.5 0.008 0.05
Experiment 10) 0.024 =50.003 0.017 =50.002 1.41 :[-0.34 0.080=50 010 0g053 =50.008
As is seen the model of peripheral interactions of protons with nuclei m a y explain the available experimental data. A characteristic feature of this model is that the deuteron yield changes rapidly near magic nuclei. In conclusion we consider our pleasant d u t y to thank D. I. Blokhintsev, I. K. Vsorov, M. G. Meshcheryakov for discussions and valuable critical remarks. References 1) N. Metropolis, R. Bivins, M. Storm, A. Turkevich, I M Miller and G. Friedlander, Phys. Rev.
110 (1958) 185 2) N. Metropolis, R. Bwins, M. Storm, I. M. Miller, G. Friedlander and A. Turkevich, Phys. :Rev. 110 (1958) 204 3) V M. Maltsev and Yu. D. Prokhoskin, J E T P 39 (1960) 1625 4) V. S. Barashenkov, V A. Bellakov, V. V Glagolev, N Dalkhazhav, Yao Tsyng Se, L. F. Klrillova, R. M Lebedev, V. M. Maltsev, P. K Markov, M. G. Shairanova, K. D Tolstoy, E. N. Tsyganov and Wang Shou Feng, Nuclear Physics 14 (1960) 522
PRODUCTION OF DEUTERONS 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17)
647
V. S Barashenkov, V. M. Maltsev and E. K Mihul, Nuclear Physics 24 (1961) 642 T. P. Lazareva and P A Usik, Proc Int. Conf. on Cosmic Rays, Moscow, 1 (1959) 71 V. S. Barashenkov, Fortschr. der Phys. 9 (1961) 29 G. A. Leksin, J E T P 32 (1957) 445 L. S. Azhgirh, I. K Vzorov, V. P. Zrelov, M G Meshcheryakov, B S. Neganov and A. F. Shabudin, J E T P 33 (1957) 1185 V. T. Cocconi, T. Fazzini, G. Fidecaro, M. Legros, N. H. Lipman and A. W. Merrison, Phys. Rev. Lett 5 (1960) 19 I Oostens, Preprint Saclay, 1961 D I. Blokhintsev, J E T P 33 (1957) 1295 D. I. Blokhintsev, V S. Barashenkov and B. M Barbashov, Usp Flz Nauk 68 (1959) 417 A. A. Rukhadze, J E T P 34 (1958) 1014 R. Hagedorn, Phys. Rev. Lett. B (1960) 276 I. yon Behr and R Hagedorn, P r e p r m t CERN, 1961 P. A. Benioff, Phys. Rev 119 (1960) 324