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Role of nucleon clusters in deep photo-disintegration of light nuclei
L
2.1
Nuclear Phys4cs 27 (1961) 337---343 ; @ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint -r microfilm without written permission from the publisher
L
NUCLEON CLUSTERS I EE OTOS T G ATI N LIGHT NUCLEI
V. V. BALASHOV and V. N. FETISOV Nuclear Research Institute of the Moscow State University, Moscow, USSR Received 18 January 1961 Abstract: The paper elucidates the general properties of the manifestation of nucleon clusters in photo-nuclear reactions and gives a theoretical interpretation, in good agreement with experiment, of the reaction Cia (y, pt) 2m . The paper discusses the use of deep photodisintegration for investigating the internal nuclear shells .
Under deep photodisintegration is understood the decay of a nucleus due to a y-quantum, with the emission of compound particles, tritons, a-particles, etc . as well as the ejection of strongly bound nucleons from the internal shells of the nucleus, leading to the production of highly excited states of the residual nucleus. These effects have received very little experimental attention so far. Yet they are extremely interesting in particular, there is abundant qualitative evidence 1) pointing to the existence of clusters of nucleons in nuclei leading to a number of singularities in the cross sections, angular distributions and spectra of photo-nuclear reaction products. It was shown in ref . 2) (concerned with the calculation of the reduced widths of light nuclei for nucleon clusters) that the mo.A essential features of nucleon association in a nucleus are described satisfactorily by the shell model. The present paper is concerned with the application of the methods proposed in ref . 2) for studying deep photodisintegration of light nuclei. The analysis is based on the experimental work of Maikov 3) in which the author gave the most systematic treatment (though not very rich in statistics) to the reaction C12+y --> p+H3+He4+He4. According to ref. 3), the main maximum of the cross section of reaction (1) lies at the y-quantum energy E .- 43 MeV and the second maximum is in evidence in the region E = 60 to 65 MeV (See fig. 1) . In analyzing his experimental data, the author 3) concludes that the reaction (1) has two stages . The absorption of the y-quantum by the C12 nucleus leads to the ejection of a proton which carries away most of the quantum energy (direct photoeffect) . The resulting highly excited state of the B11 nucleus 337
338
V. V. BALASHOV AXV V. N. FETISOV
disintegrates, with the emission of a triton, into the lower levels of the Bee nucleus (the ground state 0-}- and the first excited state 2+ at E* - 2.9 MeV) . The direct photoeffect on C12, during which the V-quantum transfers nearly all its energy to the emitted particle may in principle occur with the ejection of a nucleon from 1p as wcP as from the is shell. Yet the ejection of a proton from the lp shell of C12 1eads to a weak excitation of the B11 nucleus when no further decay with triton emission is energetically possible. Now, the ejection of the s proton corresponds to a far higher excitation of the BI' nucleus. It is rather difficult to calculate the excitation energy of this state. Rough theoretical estimates given for the ®16 nucleus 4) show that in our case we should expect the value of the excitation energy of the B].1 nucleus to be in the neighbourhood of 20 MeV. In the present paper the calculation is performed for different energy values of the excitation of BI' taken from the experiment 3) in which they are determined under the assumption of the following decayscheme C12 + ,y --> p+Bll* Bell -}- Hei. In the calculation of the first stage of eq. (1) _C12 (y, p) 1311* , we take the wave function of the s state of the harmonic oscillator with Am = 16 MeV as a function of the initial state . The function of the final state is selected in the form of a plane wave . In doing this we take no account of the interaction of the proton with the B11 nucleus in the final state. It is known $) that taking account of this interaction can essentially change the magnitude of the cross section in the giant resonance region. Yet in our energy region, far removed from the giant resonance, this influeni;e is probably not large. The use of the oscillator function of the initial state is also a rough assumption . Calculations show that the use of a rectangular well function instead of an oscillator function changes the cross section appreciably. This, however, little affects the position of the cross section maximum and consequently cannot alter the qualitative conclusions . The Hamiltonian of radiation-nucleus interaction is taken in the form 27rAc 2 e{k -ri e$ ~
8®
where ® is the photon momentum and is the polarization vector. The calculated curve of the cross section of the reaction C12 (y, p) B11* with the ejection of an s proton is represented in fig. 1. It is clear from fig. 1 that it is possible to obtain good agreement with experiment for the position of the first maximum by varying EBgl within the limits indicated in ref. 3 for the given reaction )
339
NUCLEON CLUSTERS
scheme. The assumption on the ejection of an s proton is confirmed by comparing the calculated and measured angular proton distributions (see fig. 2) . The second stage of (1) presupposes the decay of Bll into H3 and Bell. The calculation of the widths is given in the framework of the theory evolved in ref. 2).
0 .4
0.3
0.2
30
40
50
50
so
70
90 Er[Muv]
Fig. 1. Comparison of theoretical cross sections Ci$ (y, p) Bli* «ith experiments) for different values of E*gil .
0
20
40
50
80
100
120
140 150
180. e
Fig. 2. Proton angular distribution . Dots designate the experimental values 11 ).
The excited state of B11 may disintegrate not only with the emission of a triton, but also according to the scheme which would. correspond to the reaction p+He4 4-Li7.
(`1) Table 1 represents the calculated ratio of the probabilities of the decay o the excited state of t311 through the channels Be8 + He$ a nd Li7 + He4 for C12+y ->
340
V. V., BALASHOV AND V. N . FETISOV
different excitation energies and channel radii, from which it is clear that the decay probability for the channel Bes+He3 is on the average 20 times as large as for the channel Li7 +He4 (as for (4), this reaction probably materializes through a mechanism different from the decay of B11* into a+Li7) . TABLE 1
Ratio of the decay probabilities of excited state for the canals Bee + HS and Lil-}-Hes EBL i R(fm) 4.0 4.5
15 MeV
19 MeV
12 .9
21 .6
15.0
5.0
25 .0
22 .3
38 .8
21 MeV
l
22 .4 29 .2 39 .0
Speaking formally, the one-nucleon decay of $11 described by the configuration Js3 ps i is allowed for the configuration only with the production of the state (s3 p7>, but this process is impossible from energy considerations . Actually, the shell state (s3p8 j contains about 10 % of "spurious" states corresponding to the excited motion of the nuclear centre of gravity as a whole . Taking account of these effects can give a small nucleon width of the decay of the B11 state of the order of a triton width. TABLE 2
Ratio of the probabilities oil the decay of Bll* for the canal Bee+H$ into different levels of the Bee nucleus EB~a
R(fm) 4.0 4.5 5.0
15 MeV
19 MeV
21 MeV
140 .0
2.4
1.9
53 .0
2.2
1.9
8.0
2.3
1.9
Table 2 represents the ratio of the decay probabilities of B,1].* through the channel Be8+H3 into different levels of the Be8 nucleus. The ratio I'(0+) lr(2+) decreases with the growth of the excitation energy of B11. This ratio is in satisfactory agreement for EBu = 19 MeV. Fig. 3 represents the curve of the cross section of reaction (1) calculated at EB, = 19 MeV. It is clear from fig. 3 that the position of the first maximum agrees well with the calculation. The present calculation does not aim at obtaining the absolute cross section value. On the other hand, fig. 3 compares the experimental crosE section of
34 1
NUCLEON CLUSTERS
the reaction C12 (;,r, pt) 2m with the calculated cross section of the formation of the B11 nucleus, including other than triton decays . On the other hand, in the calculation of the formation we neglected, as has peen pointed out above, the interaction in the final state and confined olu-selves to the use of the oscillator function . The above mechanism for the consecutive emission of. a proton and a triton in reaction (1) does not explain the presence of the second maximum in the cross section . The -reaction (y, np) at high energies is known to materialize through the two-nucleon absorption of a y-quantum . While considering the reaction (y, pt) it is natural to assume the presence of a similar` mechanism of "quasi-alpha particle" absorption, in which the y-quantum djmba OA
0.3
o.2
30
40
50
60
70
so
go
Er[MoV]
Fig. 3. Relation between the mechanism of the consecutive emission of a proton and a triton in the reaction Cx$ (y, pT) Bee and the "quasi-alpha-particle" absorption mechanism.
breaks up the alpha-cluster as it penetrates the nucleus. The technique evolved in ref. 2) makes it possible -o obtain what is known as the "effective number of alpha particles" in C12 corresponding to different states of Bes. For 0+, 2+ and 4+ levels of Be8, these numbers are 067, 0.84 and 0.86 respectively . Having identified the photodisintegration cross section of the a-cluster and the experimental photodisintegration cross section a) and performed a rough calculation of the kinematics of the discharge of the three particles Nvith this absorption of the y-quantum, we obtain an addiltiortai contribution to the cross section of reaction (1) in the range from 60 to 70 MeV (see fig. 3) . The above analysis of the reaction 012 (y, pt) Bell shows trat the method proposed in ref. 2) for evaluating nuclev~t association in tâe framewirk of the shell model can be succ.assfally applied for explaining the peculiarities of the cross sectioj, angular distribution and energy spectra of deep photodisintegration products of light nuclei .
342
V . V . BALASUOV AND V . N . FETYSOV
Bearing in mind the approximate character of our investigation as well as the low accuracy of the experimental data used, we do not seek to obtain full agreement with experiment in the present paper. Rather our purpose is to establish a general pattern of nucleon clusters in photonuclear reactions and give a point of reference for further investigation of the effects involved . The above analysis of the re~.ction CY2 (y, pt) 2a leads us to the following conclusions. There are two possibilities of the manifestation of the clusters in the deep photodisintegration reactions of light nuclei 1) Compound particles (a-particles, tritons etc.) originate in the decay of the nuclear excited states arising in the absorption of a 7-quantum . These decays can be observed in the region of the giant resonance region (wherever this is possible energetically and is not prohibited by the conventional rules) as well as at energies above the giant resonance, which usually corresponds to the ejection of a nucleon out of the inner shells of the nucleus. The decay probabilities of these states in transitions to different states of the residual nucleus can be calculated by the shell model. 2) At a y-quantum energy of the order of 60 to 70 MeV there may be a peculiar "quasi-alpha particle" mechanism of absorption of y-quanta, leading to the simultaneous emission of a proton any. a trit>:)n from the nucleus -- a mechanism similar to the well-knoim "quasi-deuteron" mechanism of absorption at high y-quantum energies . In conclusion we shall emphasize the important role of photo-nuclear reactions for investigating the interna shells of the nucleus. It is common knowledge that the hole excitations are invF stigated mainly in the "pick-up reactions" (p, d), (d, t), etc. Yet the ejection of nucleons from the internal closed shells is effective only for nuclei containing a very small number of external nucleons. As soon as the number of the nucleons over the closed shells increases there arises a peculiar screening of the internal nucleons, which strongly suppresses the "pick-up cross section" . This screening makes the investigator go far beyond the limits of - the energies usually used in nuclear physics while investigating these hole excitations in particle reactions. The respective investigations undertaken by Tyrdn et al . 7 ) in irradiating light nuclei by 450 MeV protons are well knawn. The deep photodisintegration reactions suggest another possibility for investigating the above states . A. y-quantum penetrates the nucleus freely and. ejects a nucleon from the internal closed shells . In this process, it is probablv difficult to ic, late experimentally the respective group of particles from the total spectrum of the reactions (y, n) and (y, p) . The fact is that in the most interesting cases, when the number of nucleons i) . the closed shells is large, the nucleons ejected from the external non-closed shells account for an over-
NUCLEON CLUSTERS
34 3
whelming portion of the (y, n) and (y, p) spectrum. The transiti:)ris with ejection of nucleons out of the closed shells can be isolated through the analysis of secondary processes (of a type considered above in the reaction C12 (y, pt) 2x of the decay of Bll with the emission of a triton) . In this connection it should. be noted that the excitation energy of - -..he B" nucleus formed during the ejection of an s nucleon frorn C12 is equal, according to the above analysis, to - 19 MeV and corresponds to the coupling energy of the s nucleon in C 12 E ,. 35 MeV. This agrees with the respective value given by Tyr6n et al. 7 ). q
The authors express their gratitude to Prof. Komar as well to as I. N. Gorbunov and V. N . Maikov for stimulating discussions . efere ces 1) N. V. Chuvilo and V. G. Shevchenko, Nuclear reactions at low and medium energies (Moscow, 1958) 2) V. V. Balashov et al., JETP 37 (1959) 1385 3) V. N. Maikov, Nuclear reactions at low and medium energies, Thesis, P. N. Lebedev Physical Institute, Moscow, 1959 4) G. E. Tauber and T. Y. Wu, Phys . Rev. 105 (1957) 1772 5) D. H. Wilkinson, Physica 22 (1956) 1039 6) A. N. Gorbunov and V. M . Spiridonov, Nuclear reactions at low and medium energies (Moscov,r,
1958) 7) Tyrdn, report Second All-Union Conf . nuclear reactions at low and medium energies, Moscow, 1960
2.1
Nuclear Phys4cs 27 (1961) 337---343 ; @ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint -r microfilm without written permission from the publisher
L
NUCLEON CLUSTERS I EE OTOS T G ATI N LIGHT NUCLEI
V. V. BALASHOV and V. N. FETISOV Nuclear Research Institute of the Moscow State University, Moscow, USSR Received 18 January 1961 Abstract: The paper elucidates the general properties of the manifestation of nucleon clusters in photo-nuclear reactions and gives a theoretical interpretation, in good agreement with experiment, of the reaction Cia (y, pt) 2m . The paper discusses the use of deep photodisintegration for investigating the internal nuclear shells .
Under deep photodisintegration is understood the decay of a nucleus due to a y-quantum, with the emission of compound particles, tritons, a-particles, etc . as well as the ejection of strongly bound nucleons from the internal shells of the nucleus, leading to the production of highly excited states of the residual nucleus. These effects have received very little experimental attention so far. Yet they are extremely interesting in particular, there is abundant qualitative evidence 1) pointing to the existence of clusters of nucleons in nuclei leading to a number of singularities in the cross sections, angular distributions and spectra of photo-nuclear reaction products. It was shown in ref . 2) (concerned with the calculation of the reduced widths of light nuclei for nucleon clusters) that the mo.A essential features of nucleon association in a nucleus are described satisfactorily by the shell model. The present paper is concerned with the application of the methods proposed in ref . 2) for studying deep photodisintegration of light nuclei. The analysis is based on the experimental work of Maikov 3) in which the author gave the most systematic treatment (though not very rich in statistics) to the reaction C12+y --> p+H3+He4+He4. According to ref. 3), the main maximum of the cross section of reaction (1) lies at the y-quantum energy E .- 43 MeV and the second maximum is in evidence in the region E = 60 to 65 MeV (See fig. 1) . In analyzing his experimental data, the author 3) concludes that the reaction (1) has two stages . The absorption of the y-quantum by the C12 nucleus leads to the ejection of a proton which carries away most of the quantum energy (direct photoeffect) . The resulting highly excited state of the B11 nucleus 337
338
V. V. BALASHOV AXV V. N. FETISOV
disintegrates, with the emission of a triton, into the lower levels of the Bee nucleus (the ground state 0-}- and the first excited state 2+ at E* - 2.9 MeV) . The direct photoeffect on C12, during which the V-quantum transfers nearly all its energy to the emitted particle may in principle occur with the ejection of a nucleon from 1p as wcP as from the is shell. Yet the ejection of a proton from the lp shell of C12 1eads to a weak excitation of the B11 nucleus when no further decay with triton emission is energetically possible. Now, the ejection of the s proton corresponds to a far higher excitation of the BI' nucleus. It is rather difficult to calculate the excitation energy of this state. Rough theoretical estimates given for the ®16 nucleus 4) show that in our case we should expect the value of the excitation energy of the B].1 nucleus to be in the neighbourhood of 20 MeV. In the present paper the calculation is performed for different energy values of the excitation of BI' taken from the experiment 3) in which they are determined under the assumption of the following decayscheme C12 + ,y --> p+Bll* Bell -}- Hei. In the calculation of the first stage of eq. (1) _C12 (y, p) 1311* , we take the wave function of the s state of the harmonic oscillator with Am = 16 MeV as a function of the initial state . The function of the final state is selected in the form of a plane wave . In doing this we take no account of the interaction of the proton with the B11 nucleus in the final state. It is known $) that taking account of this interaction can essentially change the magnitude of the cross section in the giant resonance region. Yet in our energy region, far removed from the giant resonance, this influeni;e is probably not large. The use of the oscillator function of the initial state is also a rough assumption . Calculations show that the use of a rectangular well function instead of an oscillator function changes the cross section appreciably. This, however, little affects the position of the cross section maximum and consequently cannot alter the qualitative conclusions . The Hamiltonian of radiation-nucleus interaction is taken in the form 27rAc 2 e{k -ri e$ ~
8®
where ® is the photon momentum and is the polarization vector. The calculated curve of the cross section of the reaction C12 (y, p) B11* with the ejection of an s proton is represented in fig. 1. It is clear from fig. 1 that it is possible to obtain good agreement with experiment for the position of the first maximum by varying EBgl within the limits indicated in ref. 3 for the given reaction )
339
NUCLEON CLUSTERS
scheme. The assumption on the ejection of an s proton is confirmed by comparing the calculated and measured angular proton distributions (see fig. 2) . The second stage of (1) presupposes the decay of Bll into H3 and Bell. The calculation of the widths is given in the framework of the theory evolved in ref. 2).
0 .4
0.3
0.2
30
40
50
50
so
70
90 Er[Muv]
Fig. 1. Comparison of theoretical cross sections Ci$ (y, p) Bli* «ith experiments) for different values of E*gil .
0
20
40
50
80
100
120
140 150
180. e
Fig. 2. Proton angular distribution . Dots designate the experimental values 11 ).
The excited state of B11 may disintegrate not only with the emission of a triton, but also according to the scheme which would. correspond to the reaction p+He4 4-Li7.
(`1) Table 1 represents the calculated ratio of the probabilities of the decay o the excited state of t311 through the channels Be8 + He$ a nd Li7 + He4 for C12+y ->
340
V. V., BALASHOV AND V. N . FETISOV
different excitation energies and channel radii, from which it is clear that the decay probability for the channel Bes+He3 is on the average 20 times as large as for the channel Li7 +He4 (as for (4), this reaction probably materializes through a mechanism different from the decay of B11* into a+Li7) . TABLE 1
Ratio of the decay probabilities of excited state for the canals Bee + HS and Lil-}-Hes EBL i R(fm) 4.0 4.5
15 MeV
19 MeV
12 .9
21 .6
15.0
5.0
25 .0
22 .3
38 .8
21 MeV
l
22 .4 29 .2 39 .0
Speaking formally, the one-nucleon decay of $11 described by the configuration Js3 ps i is allowed for the configuration only with the production of the state (s3 p7>, but this process is impossible from energy considerations . Actually, the shell state (s3p8 j contains about 10 % of "spurious" states corresponding to the excited motion of the nuclear centre of gravity as a whole . Taking account of these effects can give a small nucleon width of the decay of the B11 state of the order of a triton width. TABLE 2
Ratio of the probabilities oil the decay of Bll* for the canal Bee+H$ into different levels of the Bee nucleus EB~a
R(fm) 4.0 4.5 5.0
15 MeV
19 MeV
21 MeV
140 .0
2.4
1.9
53 .0
2.2
1.9
8.0
2.3
1.9
Table 2 represents the ratio of the decay probabilities of B,1].* through the channel Be8+H3 into different levels of the Be8 nucleus. The ratio I'(0+) lr(2+) decreases with the growth of the excitation energy of B11. This ratio is in satisfactory agreement for EBu = 19 MeV. Fig. 3 represents the curve of the cross section of reaction (1) calculated at EB, = 19 MeV. It is clear from fig. 3 that the position of the first maximum agrees well with the calculation. The present calculation does not aim at obtaining the absolute cross section value. On the other hand, fig. 3 compares the experimental crosE section of
34 1
NUCLEON CLUSTERS
the reaction C12 (;,r, pt) 2m with the calculated cross section of the formation of the B11 nucleus, including other than triton decays . On the other hand, in the calculation of the formation we neglected, as has peen pointed out above, the interaction in the final state and confined olu-selves to the use of the oscillator function . The above mechanism for the consecutive emission of. a proton and a triton in reaction (1) does not explain the presence of the second maximum in the cross section . The -reaction (y, np) at high energies is known to materialize through the two-nucleon absorption of a y-quantum . While considering the reaction (y, pt) it is natural to assume the presence of a similar` mechanism of "quasi-alpha particle" absorption, in which the y-quantum djmba OA
0.3
o.2
30
40
50
60
70
so
go
Er[MoV]
Fig. 3. Relation between the mechanism of the consecutive emission of a proton and a triton in the reaction Cx$ (y, pT) Bee and the "quasi-alpha-particle" absorption mechanism.
breaks up the alpha-cluster as it penetrates the nucleus. The technique evolved in ref. 2) makes it possible -o obtain what is known as the "effective number of alpha particles" in C12 corresponding to different states of Bes. For 0+, 2+ and 4+ levels of Be8, these numbers are 067, 0.84 and 0.86 respectively . Having identified the photodisintegration cross section of the a-cluster and the experimental photodisintegration cross section a) and performed a rough calculation of the kinematics of the discharge of the three particles Nvith this absorption of the y-quantum, we obtain an addiltiortai contribution to the cross section of reaction (1) in the range from 60 to 70 MeV (see fig. 3) . The above analysis of the reaction 012 (y, pt) Bell shows trat the method proposed in ref. 2) for evaluating nuclev~t association in tâe framewirk of the shell model can be succ.assfally applied for explaining the peculiarities of the cross sectioj, angular distribution and energy spectra of deep photodisintegration products of light nuclei .
342
V . V . BALASUOV AND V . N . FETYSOV
Bearing in mind the approximate character of our investigation as well as the low accuracy of the experimental data used, we do not seek to obtain full agreement with experiment in the present paper. Rather our purpose is to establish a general pattern of nucleon clusters in photonuclear reactions and give a point of reference for further investigation of the effects involved . The above analysis of the re~.ction CY2 (y, pt) 2a leads us to the following conclusions. There are two possibilities of the manifestation of the clusters in the deep photodisintegration reactions of light nuclei 1) Compound particles (a-particles, tritons etc.) originate in the decay of the nuclear excited states arising in the absorption of a 7-quantum . These decays can be observed in the region of the giant resonance region (wherever this is possible energetically and is not prohibited by the conventional rules) as well as at energies above the giant resonance, which usually corresponds to the ejection of a nucleon out of the inner shells of the nucleus. The decay probabilities of these states in transitions to different states of the residual nucleus can be calculated by the shell model. 2) At a y-quantum energy of the order of 60 to 70 MeV there may be a peculiar "quasi-alpha particle" mechanism of absorption of y-quanta, leading to the simultaneous emission of a proton any. a trit>:)n from the nucleus -- a mechanism similar to the well-knoim "quasi-deuteron" mechanism of absorption at high y-quantum energies . In conclusion we shall emphasize the important role of photo-nuclear reactions for investigating the interna shells of the nucleus. It is common knowledge that the hole excitations are invF stigated mainly in the "pick-up reactions" (p, d), (d, t), etc. Yet the ejection of nucleons from the internal closed shells is effective only for nuclei containing a very small number of external nucleons. As soon as the number of the nucleons over the closed shells increases there arises a peculiar screening of the internal nucleons, which strongly suppresses the "pick-up cross section" . This screening makes the investigator go far beyond the limits of - the energies usually used in nuclear physics while investigating these hole excitations in particle reactions. The respective investigations undertaken by Tyrdn et al . 7 ) in irradiating light nuclei by 450 MeV protons are well knawn. The deep photodisintegration reactions suggest another possibility for investigating the above states . A. y-quantum penetrates the nucleus freely and. ejects a nucleon from the internal closed shells . In this process, it is probablv difficult to ic, late experimentally the respective group of particles from the total spectrum of the reactions (y, n) and (y, p) . The fact is that in the most interesting cases, when the number of nucleons i) . the closed shells is large, the nucleons ejected from the external non-closed shells account for an over-
NUCLEON CLUSTERS
34 3
whelming portion of the (y, n) and (y, p) spectrum. The transiti:)ris with ejection of nucleons out of the closed shells can be isolated through the analysis of secondary processes (of a type considered above in the reaction C12 (y, pt) 2x of the decay of Bll with the emission of a triton) . In this connection it should. be noted that the excitation energy of - -..he B" nucleus formed during the ejection of an s nucleon frorn C12 is equal, according to the above analysis, to - 19 MeV and corresponds to the coupling energy of the s nucleon in C 12 E ,. 35 MeV. This agrees with the respective value given by Tyr6n et al. 7 ). q
The authors express their gratitude to Prof. Komar as well to as I. N. Gorbunov and V. N . Maikov for stimulating discussions . efere ces 1) N. V. Chuvilo and V. G. Shevchenko, Nuclear reactions at low and medium energies (Moscow, 1958) 2) V. V. Balashov et al., JETP 37 (1959) 1385 3) V. N. Maikov, Nuclear reactions at low and medium energies, Thesis, P. N. Lebedev Physical Institute, Moscow, 1959 4) G. E. Tauber and T. Y. Wu, Phys . Rev. 105 (1957) 1772 5) D. H. Wilkinson, Physica 22 (1956) 1039 6) A. N. Gorbunov and V. M . Spiridonov, Nuclear reactions at low and medium energies (Moscov,r,
1958) 7) Tyrdn, report Second All-Union Conf . nuclear reactions at low and medium energies, Moscow, 1960