- Email: [email protected]
On the mechanism of the reactions (π, πN) on light nuclei
Volume
30B, number
ON
THE
PHYSICS
1
MECHANISM
OF
THE
LETTERS
1 September
REACTIONS
(n,
nN)
ON
L,IGHT
1969
NUCLEI
V. M. KOLYBASOV and N. Ya. SMORODINSKAYA Institute for Experimental
and Theoretical Received
It is shown that the available
curve
Fig. 1. a) Pole graph for the reaction 12C(?r, rN)LLC. b) Triangle graph corresponding to the impulse mation for the reaction 13C(7r. 71’) 12C*.
to be either dominant or compar-
?I+ + 12C -
(1)
was shown (see ref. 1) to have a peak close to the maximum corresponding the the N33 isobar in the elastic n-n-scattering cross section. The width of the peak appears to be 1.5 times larger than the isobar width. Therefore it was suggested [2] that the reaction (1) is quasi-elastic, i.e. the pole graph (see fig. la) dominates. The calculated excitation curve and the absolute value of the cross section were in qualitative agreement with the experiment. The discrepency remaining in the low incident energy region was proposed [3] to be due to the rescattering of the isobar on the residual nucleus. However, as was shown in ref. 2, the accuracy of the theoretical absolute value of the cross section is not good and the available experimental data were insufficient for unambigious identification of the reaction mechanism. Indeed, the recent data [4] on the a--nucleus interactions in isobar energy region have shown that the ratio of the reaction (1) cross section to the summed cross section of the reactions
approxi-
USSR
on light nuclei in the N33 isobar
knock out contribution
of the reaction
7r- + 12c -7rn-+n+llC
Moscow.
15 July 1969
data on the (n, aN) and (a. ad) reactions
energy region give evidence for the quasi-elastic able with the contribution of other mechanisms.
The excitation
Physics.
i7+ + n + llC
and Tf+ + i2c - 7ro + p + llc is approximately 1 in contradiction with the quasi-elastic mechanism. If the reactions x-n - v-n, r’n - n+n and n+n - sop proceeded only via isospin 3/2 state the pole approximation would give [ul /(u2 + a3)] = 3. Taking into account the isospin l/2 state together with the internuclear motion of nucleons changes the result [5]. We have made an exact calculation of the above-mentioned ratio. It equals to 2.2 - 2.4 at 180 MeV and 2.4 - 2.6 at the energy 220 MeV which corresponds to the maximum of the theoretical excitation curve. *) We give here some intervals for the ratio, firstly, because of errors in the low-energy x-p and n+p cross sections and, secondly, because this ratio depends on the nuclear from factor of the decay 12C - 1% + n. The same calculation gives the following values for the reduced neutron width of 11~ (with formation of llC in its ground state): e2 = = 0.44*0.08 for the channel radius R = 3 fm and e2 = 0.55*0.10 for R = 4 fm. The same quantity from the reaction 12C(p, d)llC is 0.34 [2,6], 0.33 [?‘I, 0.24 [8] and from the reaction l2C(p, 2p)llB it is 0.37 [9]. The comparison of these values shows that other mechanisms may contribute considerably. Let us note that the above-mentioned isobar rescattering graph gives for the ratio of the rand r+ cross sections a value 3 and cannot, therefore, improve the situation. (This ratio follows from the isotopic invariance and takes *) The effect of internuclear motion of nucleons seems to be overestimated in ref. 5 for there were used incorrect a-p data.
11
Volume
30B, number 1
PHYSICS
for any mechanism if the initial nucleus isospin T is zero and there are a T, = 0 nucleus and an isobar in the final state. ) In order to explain such a discrepancy, the authors of paper [4] suggested that a considerable number of events consist of inelastic n-meson scattering with formation of highly excited states of l2C or l2N which decay into IIC and a nucleon. The analogous mechanism was independently proposed in [lo] to explain anisotropy in the angular distribution of the residual nuclei from the reaction 12C(n-, n-p)llB at 1GeV. There are three essential facts: 1) the cross section of llC formation predicted by such mechanism is less for r- mesons than for 7r+mesons in contradiction to the quasi-elastic knock-out; 2) if the T = 1 states of l2C are excited, the isotopic relations give [ 01 /(u2 + u3)] = l/3 (the amplitude includes a product of the isotopic Clebsch-Gordan doefficients in the vertices 71+ 12C- n’ + 12C*(12N*) and 12C*(12N*) - llC + n(p)), from where al : a2 : 03 = 1: 1: 2 ; 3) actually this ratio is somewhat larger as the T = 0 states of I2C are also excited and then a3 = 0, 01 = 02. We have estimated the shape of the excitation curve considering inelastic r- meson scattering in the impulse approximation (i.e. the graph of fig. lb was taken into account). To explain the experimental ratio of 710to IT+-meson cross sections it should be proposed that the pole mechanism and the inelastic a-meson scattering give approximately the same contribution to the cross section. The shape of the summed excitation curve for this case is shown in fig. 2a by the solid line. The pole calculation is presented by the dotted line in the same figure. The cross section corresponding to the graph of fig. lb was estimated to be really 15+ 30 mb. (The p, p’) data [ 111 were used under the assumption of the same mechanism). It should be noted, however, that the estimation is rather rough. In paper [4] there are also data on the reactions (77-,a-p) and (n+, ati) with gBe. They are shown in fig. 2b together with the results of the pole approximation. Here the maximum of the (n+, s+p) curve was fitted to the experiment, the (n-, n-p) curve being drawn without free parameters. One can see that the pole mechanism explains the ratio of the n- to n+ cross sections quite well and gives a better agreement between the experimental and theoretical points than for 12C. An impression appears that the additional mechanism, which is essential for 12C, gives for some reasons a small contribution in the case of ‘Be.
LETTERS
l September
1969
place
12
b(mgj
to40-
a-
I
+
/
a
n \ k.
do-
:
\
;
I J
Fig. 2. The excitation curves for the reactions: a) -12C @-,n-n)llC. b) gBe6r-.n-o)8Li and gBe6r+.*‘a)8Li. The dotted c&es are calculated in pole approximation. The solid curves correspond to the equal contribution from the quasi-elastic knock-out and inelastic scattering (a, n’). The experimental data are from [1,4].
If we take the channel radius for gBe - pTaLi to be 4 fm, then the mentioned data give 6 = 0.54hO.05, where Q2 is the sum of the gBe proton widths corresponding to formation of aLi in the ground and several low-excited states. Though the theoretical curves in fig. 2 are in rather good agreement with the experiment, the experimental errors do not allow us to exclude the essential contribution from the isobar rescattering mechanism [3]. The upper limit for the isobar scattering length on aLi iscu, C 0.14fm. Let us note that the isobar scattering length on 11~ has appeared to be 0.2 fm [3]. However, the latter quantity will strongly decrease if the supposition is right on the considerable contribution of the inelastic n--meson scattering to the reaction 12C(7r-, a-n)llC. Except the one-nucleon knock-out ;f;er;,wf{ also investigated in [a] the reactions 0 N with two-nucleon knock-out and their cross sections appeared to be large. The simplest mechanism is the quasi-elastic- deuteron knock-out which is like the well-investigated (p,pd) pro-
Volume
30B, number
PHYSICS
1
LETTERS
1 September
1969
It follows from the above results that the available data do not contradict the suggestion that the pole graph sometimes contributes dominantly and sometimes is of the same order as the contribution of the other mechanisms. To make this problem clear we need more detailed experiments where all independent kinematical variables in different regions, are measured. We are indebted to Professor I. S. Shapiro for the discussion of the results and to Dr. Allardyce for sending us the experimental data. References 1. P. L. Reeder and S. S. Markovitz,
240 EF (rvev) Fig. 3. The excitation curves for the reaction I*0(7r. nd)16N. The solid curve is calculated in pole approximation. The experimental data are from [4].
2. 3. 4.
cess [12]. The excitation curve calculated in pole approximation is shown in fig. 3. The summed deuteron reduced width corresponding to the formation of l6 N in the ground and several low-excited states is e2 = 0.68+~0.11for R = 4 fm. Certainly the character of this process is nuclear and there can contribute other mechanisms, in particular the one-nucleon knock-out followed by the evaporation of another nucleon although the equality of r+ and v- cross sections at 160 and 240 MeV does not give evidence for this mechanism because the I80 nucleus is not mirror-like. Let us note, however, that the reaction (n+, 2p) can hardly give here a large contribution as supposed in [13]. The point is that the ad elastic cross section is an order larger than the cross section of the reaction a++d-+2p and there seem to be no reasons which could strongly change this relation for internuclear deuterons.
5. 6.
7. 8. 9. 10. 11. 12.
13. 14.
Phys. Rev. 133 (1964)B639. V.M.Kolybasov, Yad. Fiz. 2 (1965) 144. O.D.Dalkarov. Phys. Letters 26B (1968) 610. D. J.Chivers, E.M.Rimmer. B. W.Allardyce et al., Nucl. Phgs. Al26 (1969) 129; Preprint 33/68. Nuclear Physics Laboratory. Oxford University. V.M.Kolybasov, Phys.Letters 27B (1968) 3. D.Bachelier, M.Bernas, C.Detraz et al., Direct Interactions and Nuclear Reactions Mechanisms (Gordon and Breach Publ.. 1963) p. 1141. K. Matsuda. Direct Interactions and Nuclear Reactions Mechanisms (Gordon and Breach Publ., 1963) p. 499. M. H. Macfarlane and J. B. French. Rev. Mod. Phys. 32 (1960) 567. V. M. Kolybasov and N. Ya. Smorodinskaya. Nucl. Phys.. to be published. A.O.Aganyants. Yu.Bayukov. V. N.Deza et al.. Nucl , Phys. (in print). D. Hasselgren. P. V.Renberg. 0. Sundberg et al., Nucl. Phys. 69 (1965) 81. L. S.Azhgirei, I. K. Vzorov et al.. JETP 33 (1957) 1185; R. J.Sutter, J. L. Friedes, H. Palevsky et al.. Phys. Rev. Letters 19 (1967) 1189; V. M. Kolybasov and N. Ya. Smorodinskaya, JETP Letters 8 (1968) 335. T.Bressani. G.Charpak, J.Favier et al.. Nucl. Phys. B9 (1969) 427. I. S. Shapiro and V. M. Kolybasov. Preprint ITEP No. 591 (1968).
*****
13
30B, number
ON
THE
PHYSICS
1
MECHANISM
OF
THE
LETTERS
1 September
REACTIONS
(n,
nN)
ON
L,IGHT
1969
NUCLEI
V. M. KOLYBASOV and N. Ya. SMORODINSKAYA Institute for Experimental
and Theoretical Received
It is shown that the available
curve
Fig. 1. a) Pole graph for the reaction 12C(?r, rN)LLC. b) Triangle graph corresponding to the impulse mation for the reaction 13C(7r. 71’) 12C*.
to be either dominant or compar-
?I+ + 12C -
(1)
was shown (see ref. 1) to have a peak close to the maximum corresponding the the N33 isobar in the elastic n-n-scattering cross section. The width of the peak appears to be 1.5 times larger than the isobar width. Therefore it was suggested [2] that the reaction (1) is quasi-elastic, i.e. the pole graph (see fig. la) dominates. The calculated excitation curve and the absolute value of the cross section were in qualitative agreement with the experiment. The discrepency remaining in the low incident energy region was proposed [3] to be due to the rescattering of the isobar on the residual nucleus. However, as was shown in ref. 2, the accuracy of the theoretical absolute value of the cross section is not good and the available experimental data were insufficient for unambigious identification of the reaction mechanism. Indeed, the recent data [4] on the a--nucleus interactions in isobar energy region have shown that the ratio of the reaction (1) cross section to the summed cross section of the reactions
approxi-
USSR
on light nuclei in the N33 isobar
knock out contribution
of the reaction
7r- + 12c -7rn-+n+llC
Moscow.
15 July 1969
data on the (n, aN) and (a. ad) reactions
energy region give evidence for the quasi-elastic able with the contribution of other mechanisms.
The excitation
Physics.
i7+ + n + llC
and Tf+ + i2c - 7ro + p + llc is approximately 1 in contradiction with the quasi-elastic mechanism. If the reactions x-n - v-n, r’n - n+n and n+n - sop proceeded only via isospin 3/2 state the pole approximation would give [ul /(u2 + a3)] = 3. Taking into account the isospin l/2 state together with the internuclear motion of nucleons changes the result [5]. We have made an exact calculation of the above-mentioned ratio. It equals to 2.2 - 2.4 at 180 MeV and 2.4 - 2.6 at the energy 220 MeV which corresponds to the maximum of the theoretical excitation curve. *) We give here some intervals for the ratio, firstly, because of errors in the low-energy x-p and n+p cross sections and, secondly, because this ratio depends on the nuclear from factor of the decay 12C - 1% + n. The same calculation gives the following values for the reduced neutron width of 11~ (with formation of llC in its ground state): e2 = = 0.44*0.08 for the channel radius R = 3 fm and e2 = 0.55*0.10 for R = 4 fm. The same quantity from the reaction 12C(p, d)llC is 0.34 [2,6], 0.33 [?‘I, 0.24 [8] and from the reaction l2C(p, 2p)llB it is 0.37 [9]. The comparison of these values shows that other mechanisms may contribute considerably. Let us note that the above-mentioned isobar rescattering graph gives for the ratio of the rand r+ cross sections a value 3 and cannot, therefore, improve the situation. (This ratio follows from the isotopic invariance and takes *) The effect of internuclear motion of nucleons seems to be overestimated in ref. 5 for there were used incorrect a-p data.
11
Volume
30B, number 1
PHYSICS
for any mechanism if the initial nucleus isospin T is zero and there are a T, = 0 nucleus and an isobar in the final state. ) In order to explain such a discrepancy, the authors of paper [4] suggested that a considerable number of events consist of inelastic n-meson scattering with formation of highly excited states of l2C or l2N which decay into IIC and a nucleon. The analogous mechanism was independently proposed in [lo] to explain anisotropy in the angular distribution of the residual nuclei from the reaction 12C(n-, n-p)llB at 1GeV. There are three essential facts: 1) the cross section of llC formation predicted by such mechanism is less for r- mesons than for 7r+mesons in contradiction to the quasi-elastic knock-out; 2) if the T = 1 states of l2C are excited, the isotopic relations give [ 01 /(u2 + u3)] = l/3 (the amplitude includes a product of the isotopic Clebsch-Gordan doefficients in the vertices 71+ 12C- n’ + 12C*(12N*) and 12C*(12N*) - llC + n(p)), from where al : a2 : 03 = 1: 1: 2 ; 3) actually this ratio is somewhat larger as the T = 0 states of I2C are also excited and then a3 = 0, 01 = 02. We have estimated the shape of the excitation curve considering inelastic r- meson scattering in the impulse approximation (i.e. the graph of fig. lb was taken into account). To explain the experimental ratio of 710to IT+-meson cross sections it should be proposed that the pole mechanism and the inelastic a-meson scattering give approximately the same contribution to the cross section. The shape of the summed excitation curve for this case is shown in fig. 2a by the solid line. The pole calculation is presented by the dotted line in the same figure. The cross section corresponding to the graph of fig. lb was estimated to be really 15+ 30 mb. (The p, p’) data [ 111 were used under the assumption of the same mechanism). It should be noted, however, that the estimation is rather rough. In paper [4] there are also data on the reactions (77-,a-p) and (n+, ati) with gBe. They are shown in fig. 2b together with the results of the pole approximation. Here the maximum of the (n+, s+p) curve was fitted to the experiment, the (n-, n-p) curve being drawn without free parameters. One can see that the pole mechanism explains the ratio of the n- to n+ cross sections quite well and gives a better agreement between the experimental and theoretical points than for 12C. An impression appears that the additional mechanism, which is essential for 12C, gives for some reasons a small contribution in the case of ‘Be.
LETTERS
l September
1969
place
12
b(mgj
to40-
a-
I
+
/
a
n \ k.
do-
:
\
;
I J
Fig. 2. The excitation curves for the reactions: a) -12C @-,n-n)llC. b) gBe6r-.n-o)8Li and gBe6r+.*‘a)8Li. The dotted c&es are calculated in pole approximation. The solid curves correspond to the equal contribution from the quasi-elastic knock-out and inelastic scattering (a, n’). The experimental data are from [1,4].
If we take the channel radius for gBe - pTaLi to be 4 fm, then the mentioned data give 6 = 0.54hO.05, where Q2 is the sum of the gBe proton widths corresponding to formation of aLi in the ground and several low-excited states. Though the theoretical curves in fig. 2 are in rather good agreement with the experiment, the experimental errors do not allow us to exclude the essential contribution from the isobar rescattering mechanism [3]. The upper limit for the isobar scattering length on aLi iscu, C 0.14fm. Let us note that the isobar scattering length on 11~ has appeared to be 0.2 fm [3]. However, the latter quantity will strongly decrease if the supposition is right on the considerable contribution of the inelastic n--meson scattering to the reaction 12C(7r-, a-n)llC. Except the one-nucleon knock-out ;f;er;,wf{ also investigated in [a] the reactions 0 N with two-nucleon knock-out and their cross sections appeared to be large. The simplest mechanism is the quasi-elastic- deuteron knock-out which is like the well-investigated (p,pd) pro-
Volume
30B, number
PHYSICS
1
LETTERS
1 September
1969
It follows from the above results that the available data do not contradict the suggestion that the pole graph sometimes contributes dominantly and sometimes is of the same order as the contribution of the other mechanisms. To make this problem clear we need more detailed experiments where all independent kinematical variables in different regions, are measured. We are indebted to Professor I. S. Shapiro for the discussion of the results and to Dr. Allardyce for sending us the experimental data. References 1. P. L. Reeder and S. S. Markovitz,
240 EF (rvev) Fig. 3. The excitation curves for the reaction I*0(7r. nd)16N. The solid curve is calculated in pole approximation. The experimental data are from [4].
2. 3. 4.
cess [12]. The excitation curve calculated in pole approximation is shown in fig. 3. The summed deuteron reduced width corresponding to the formation of l6 N in the ground and several low-excited states is e2 = 0.68+~0.11for R = 4 fm. Certainly the character of this process is nuclear and there can contribute other mechanisms, in particular the one-nucleon knock-out followed by the evaporation of another nucleon although the equality of r+ and v- cross sections at 160 and 240 MeV does not give evidence for this mechanism because the I80 nucleus is not mirror-like. Let us note, however, that the reaction (n+, 2p) can hardly give here a large contribution as supposed in [13]. The point is that the ad elastic cross section is an order larger than the cross section of the reaction a++d-+2p and there seem to be no reasons which could strongly change this relation for internuclear deuterons.
5. 6.
7. 8. 9. 10. 11. 12.
13. 14.
Phys. Rev. 133 (1964)B639. V.M.Kolybasov, Yad. Fiz. 2 (1965) 144. O.D.Dalkarov. Phys. Letters 26B (1968) 610. D. J.Chivers, E.M.Rimmer. B. W.Allardyce et al., Nucl. Phgs. Al26 (1969) 129; Preprint 33/68. Nuclear Physics Laboratory. Oxford University. V.M.Kolybasov, Phys.Letters 27B (1968) 3. D.Bachelier, M.Bernas, C.Detraz et al., Direct Interactions and Nuclear Reactions Mechanisms (Gordon and Breach Publ.. 1963) p. 1141. K. Matsuda. Direct Interactions and Nuclear Reactions Mechanisms (Gordon and Breach Publ., 1963) p. 499. M. H. Macfarlane and J. B. French. Rev. Mod. Phys. 32 (1960) 567. V. M. Kolybasov and N. Ya. Smorodinskaya. Nucl. Phys.. to be published. A.O.Aganyants. Yu.Bayukov. V. N.Deza et al.. Nucl , Phys. (in print). D. Hasselgren. P. V.Renberg. 0. Sundberg et al., Nucl. Phys. 69 (1965) 81. L. S.Azhgirei, I. K. Vzorov et al.. JETP 33 (1957) 1185; R. J.Sutter, J. L. Friedes, H. Palevsky et al.. Phys. Rev. Letters 19 (1967) 1189; V. M. Kolybasov and N. Ya. Smorodinskaya, JETP Letters 8 (1968) 335. T.Bressani. G.Charpak, J.Favier et al.. Nucl. Phys. B9 (1969) 427. I. S. Shapiro and V. M. Kolybasov. Preprint ITEP No. 591 (1968).
*****
13