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The D(p,2p)n reaction at 51.8 MeV
Volume
40B, number
5
PHYSICS
THE D(p,2p)n
LETTERS
REACTION
I August
1972
AT 5 1.8 MeV
J. SANADA and S. SEKI Tokyo Unzveraty of Educahon,
Otsuka, Tokyo, Japan
and S ORYU Scrence Unwersrty of Tokyo, Noda, Chrba, Japan Received
16 June 1972
The results of the deuteron breakup by protons, measured m coplanar symmetric geometry at forward were compared with calculations based on the three-body Faddeev formahsm and other theories
Recently it has become clear that relatively simple calculations of the proton-proton bremsstrahlung, such as the soft-photon theory and a calculatron using the half-off-shell phase shifts, which show excellent agreement with experrmental results at large angles and near 50 MeV, fail remarkably at forward angles [ 1, 21. In a srmilar sense we have been interested in the cross section for deuteron breakup by protons at forward angles, where the ratio of the final to the mitral relative momentum is expected to be small, and any effect off the energy shell may be found. We present here the results of a measurement on the D(p,2p)n reaction at 5 1.8 MeV and comparisons with existing theories, particularly wrth calculations based on the three-body Faddeev formahsm. The measurement was made for coplanar symmetric geometry with 0 1 = -02 = 8.5” and 12.5”. The experimental arragement was the same as m the measurement of proton-proton bremsstrahlung [l] , except that the target gas was replaced by deuterium or a mixture of deuterium and hydrogen of known ratio. The two protons in the final state were detected in coincidence by a pan of counter telescopes. The energy sharing spectra were recorded on a twodimensional 64X64 drsplay. The angular resolutions wereAi3=+1.9” andA@=+l.O”. The measured values of d3a/daZlda2dE1 are shown in fig. 1 by dots, with error bars which indicate the total errors, whrch are almost entrrely due to counting statistics. In fig. 2, the values of d%/da;2,dQ;2,dE, at E, = E2 are grven versus the angle in the coplanar symmetric geometry. Dots are the present results averaged over a 5 MeV interval
angles,
around the point El = E,. The pomt at 30”-30” was obtamed by Slaus et al. at 46 MeV [3], the point at 42.5”-42.5” by Durand et al. at 49.4 MeV [4], the points at 43”-43” by Margaziotrs et al. at 45 MeV [5] and by Brarthwarte et al. at 46 MeV [6]. One of the authors has developed the Faddeev equation with the inclusion of the Coulomb force [7] . The energy sharing spectra neat 43O-43” and 50 MeV were calculated with two-body on-energy-shell
E =51 8MeV
El
(MN)
Fig. 1. Energy sharmg spectra at 8.5”-8.5” and 12 5”-12.5”. Dots mdlcate measured values The full lmes mdlcate the results of calculation based on the Faddeev formahsm with the two-body off-energy-shell amphtude.
Volume
40B, number
5
PHYSICS
ref3
0
o ret 6 A ref 5
i (sharp
IO
20
30
\ \‘MS,A
,),
---MIA
cut-off
40
I ;
(smooth cut-off)
SO
60
70
60
( degrees)
en=-8,
Fig 2. Angular dependence of d30/dn IdQdE, at El = Ez m coplanar symmetric geometry Symbols mdlcate expertmental results Lmes mdlcate theoretrcal results
amplitude and two-body off-energy-shell amphtude, respectively. The latter case showed better agreement with the experimental results [3,6, 81. The calculatrons mentioned above have been extended into the forward region and the region of larger angles. The dot-dashed and the full line in fig. 2 show the results of the angular dependence upon the two-body on-energy-shell amplitude and the twobody off-energy-shell amplitude, respectively. Both predictions reproduce, on the whole, the existing data over a wide angular range. This time, too, the result wrth the two-body off-energy-shell amplitude shows
+ Got;
c$dGot$Go
Frg 3. Diagrams D(p,Zp) reaction
td
Go t;
(b)
(a) which have important at 50 MeV. Notation ref. (71.
contrlbutlons m the is the same as that m
LETTERS
I August
1972
better overall fit. At forward angles these calculated values fall wrthm the experimental error and cannot be distinguished one from the other due to the poor counting statistics. However, it becomes clear that the difference between them amounts to more than 30% at 20” -20” and near 60”-60”) where further measurements are desrrable. It IS worth noting that m our calculatron the r&scattering term corresponding to the diagram of fig. 3(b) has an important contribution, as does the simple quasifree scattering term of fig. 3(a) over a wide angular range. The rescattering term, which mvolves the singlet neutron-proton amplitude t$ in place of the triplet amplitude td of fig. 3(b), has a minor effect, Forward cross sections at 5 1.8 MeV predtcted by the simple impulse approxrmatron (S-IA) [ 9] , the modified SIA with a sharp cut-off m the ground state deuteron wave function [5, lo] and the modified SIA with a smooth cut-off [ 1 l] are also mteresting. The results are shown in fig. 2, mcludmg the SIA (thick dahsed line), the modified SIA with a sharp cut-off at the radius R=4 fm (thin dashed lme), and the modified SIA wrth a smooth cut-off of 0 = 0.5 fm-l m the Hulthen wave function (dotted he). Cut-off parameters of the modified versions were chosen so that the calculated cross section at the point E, ‘=E2 fitted the experimental value at 43”43” of ref. [6]. The characteristics whrch have been observed m the width of the energy sharing spectrum [ 1 l] are reflected as well on the angular dependence from the peak of the quasifree scattering to the region off the quasifree scattering. The modified SIA with smooth cut-off proves to be a very satisfactory phenomenological approach for the forward region also. For this approxzmation, data at angles larger than 50°-50” are desirable for comparison. The energy sharing spectra calculated by use of the Faddeev formalism with the two-body off-energy-shell amplitude are given in fig. 1 by the full line, and are compatible with the experimental results. The authors are grateful to Prof. N. Ryu and members of Hiroshima University, and Dr. K. Kuriyama and members of Tokyo University of Education, who cooperated in takmg data. They also wish to thank Mr. S. Shioyama for the valuable suggestion on the computer programmmg, and Prof. D.C. Worth for reading the manuscript. 547
Volume
40B, number
5
PHYSICS
References [l] J. Sanada et al., Phys. Lett. 39B (1972) 509 [2] J.H. McCmre, private communication, Phys. Lett. to be pubhshed. (31 1. Slaus et al., Phys. Lett. 23 (1966) 358. [4] J L. Durand, J. Arvieux, A Fiore and C. Perrm, Phys. Rev. C4 (1971) 1957. 1.51 D.J. Margaziotts et al., Phys. Rev. C2 (1970) 2050.
54X
LETTERS
7 August
1972
[6] W.J Braithwaite et al , m Three-Body Problem m Nuclear and Particle Physics (North-Holland, Amsterdam, 1970) p. 407 [7] S Oryo, Prog. Theor. Phys 44 (1970) 1208,and 45 (1971) 386. [8] R J Griffith and K.M Knight, Nucl Phys. 54 (1964) 56 [9] A S. Kuckes, R. Wilson and P.F. Cooper, Ann of Phys. 15 (1961) 193 [lo] G. Paic, J.C Young and Margaziotts, Phys Lett. 32B (1970) 437. [ll] J.A McIntyre et al, Phys. Rev CS (1972) 1796.
40B, number
5
PHYSICS
THE D(p,2p)n
LETTERS
REACTION
I August
1972
AT 5 1.8 MeV
J. SANADA and S. SEKI Tokyo Unzveraty of Educahon,
Otsuka, Tokyo, Japan
and S ORYU Scrence Unwersrty of Tokyo, Noda, Chrba, Japan Received
16 June 1972
The results of the deuteron breakup by protons, measured m coplanar symmetric geometry at forward were compared with calculations based on the three-body Faddeev formahsm and other theories
Recently it has become clear that relatively simple calculations of the proton-proton bremsstrahlung, such as the soft-photon theory and a calculatron using the half-off-shell phase shifts, which show excellent agreement with experrmental results at large angles and near 50 MeV, fail remarkably at forward angles [ 1, 21. In a srmilar sense we have been interested in the cross section for deuteron breakup by protons at forward angles, where the ratio of the final to the mitral relative momentum is expected to be small, and any effect off the energy shell may be found. We present here the results of a measurement on the D(p,2p)n reaction at 5 1.8 MeV and comparisons with existing theories, particularly wrth calculations based on the three-body Faddeev formahsm. The measurement was made for coplanar symmetric geometry with 0 1 = -02 = 8.5” and 12.5”. The experimental arragement was the same as m the measurement of proton-proton bremsstrahlung [l] , except that the target gas was replaced by deuterium or a mixture of deuterium and hydrogen of known ratio. The two protons in the final state were detected in coincidence by a pan of counter telescopes. The energy sharing spectra were recorded on a twodimensional 64X64 drsplay. The angular resolutions wereAi3=+1.9” andA@=+l.O”. The measured values of d3a/daZlda2dE1 are shown in fig. 1 by dots, with error bars which indicate the total errors, whrch are almost entrrely due to counting statistics. In fig. 2, the values of d%/da;2,dQ;2,dE, at E, = E2 are grven versus the angle in the coplanar symmetric geometry. Dots are the present results averaged over a 5 MeV interval
angles,
around the point El = E,. The pomt at 30”-30” was obtamed by Slaus et al. at 46 MeV [3], the point at 42.5”-42.5” by Durand et al. at 49.4 MeV [4], the points at 43”-43” by Margaziotrs et al. at 45 MeV [5] and by Brarthwarte et al. at 46 MeV [6]. One of the authors has developed the Faddeev equation with the inclusion of the Coulomb force [7] . The energy sharing spectra neat 43O-43” and 50 MeV were calculated with two-body on-energy-shell
E =51 8MeV
El
(MN)
Fig. 1. Energy sharmg spectra at 8.5”-8.5” and 12 5”-12.5”. Dots mdlcate measured values The full lmes mdlcate the results of calculation based on the Faddeev formahsm with the two-body off-energy-shell amphtude.
Volume
40B, number
5
PHYSICS
ref3
0
o ret 6 A ref 5
i (sharp
IO
20
30
\ \‘MS,A
,),
---MIA
cut-off
40
I ;
(smooth cut-off)
SO
60
70
60
( degrees)
en=-8,
Fig 2. Angular dependence of d30/dn IdQdE, at El = Ez m coplanar symmetric geometry Symbols mdlcate expertmental results Lmes mdlcate theoretrcal results
amplitude and two-body off-energy-shell amphtude, respectively. The latter case showed better agreement with the experimental results [3,6, 81. The calculatrons mentioned above have been extended into the forward region and the region of larger angles. The dot-dashed and the full line in fig. 2 show the results of the angular dependence upon the two-body on-energy-shell amplitude and the twobody off-energy-shell amplitude, respectively. Both predictions reproduce, on the whole, the existing data over a wide angular range. This time, too, the result wrth the two-body off-energy-shell amplitude shows
+ Got;
c$dGot$Go
Frg 3. Diagrams D(p,Zp) reaction
td
Go t;
(b)
(a) which have important at 50 MeV. Notation ref. (71.
contrlbutlons m the is the same as that m
LETTERS
I August
1972
better overall fit. At forward angles these calculated values fall wrthm the experimental error and cannot be distinguished one from the other due to the poor counting statistics. However, it becomes clear that the difference between them amounts to more than 30% at 20” -20” and near 60”-60”) where further measurements are desrrable. It IS worth noting that m our calculatron the r&scattering term corresponding to the diagram of fig. 3(b) has an important contribution, as does the simple quasifree scattering term of fig. 3(a) over a wide angular range. The rescattering term, which mvolves the singlet neutron-proton amplitude t$ in place of the triplet amplitude td of fig. 3(b), has a minor effect, Forward cross sections at 5 1.8 MeV predtcted by the simple impulse approxrmatron (S-IA) [ 9] , the modified SIA with a sharp cut-off m the ground state deuteron wave function [5, lo] and the modified SIA with a smooth cut-off [ 1 l] are also mteresting. The results are shown in fig. 2, mcludmg the SIA (thick dahsed line), the modified SIA with a sharp cut-off at the radius R=4 fm (thin dashed lme), and the modified SIA wrth a smooth cut-off of 0 = 0.5 fm-l m the Hulthen wave function (dotted he). Cut-off parameters of the modified versions were chosen so that the calculated cross section at the point E, ‘=E2 fitted the experimental value at 43”43” of ref. [6]. The characteristics whrch have been observed m the width of the energy sharing spectrum [ 1 l] are reflected as well on the angular dependence from the peak of the quasifree scattering to the region off the quasifree scattering. The modified SIA with smooth cut-off proves to be a very satisfactory phenomenological approach for the forward region also. For this approxzmation, data at angles larger than 50°-50” are desirable for comparison. The energy sharing spectra calculated by use of the Faddeev formalism with the two-body off-energy-shell amplitude are given in fig. 1 by the full line, and are compatible with the experimental results. The authors are grateful to Prof. N. Ryu and members of Hiroshima University, and Dr. K. Kuriyama and members of Tokyo University of Education, who cooperated in takmg data. They also wish to thank Mr. S. Shioyama for the valuable suggestion on the computer programmmg, and Prof. D.C. Worth for reading the manuscript. 547
Volume
40B, number
5
PHYSICS
References [l] J. Sanada et al., Phys. Lett. 39B (1972) 509 [2] J.H. McCmre, private communication, Phys. Lett. to be pubhshed. (31 1. Slaus et al., Phys. Lett. 23 (1966) 358. [4] J L. Durand, J. Arvieux, A Fiore and C. Perrm, Phys. Rev. C4 (1971) 1957. 1.51 D.J. Margaziotts et al., Phys. Rev. C2 (1970) 2050.
54X
LETTERS
7 August
1972
[6] W.J Braithwaite et al , m Three-Body Problem m Nuclear and Particle Physics (North-Holland, Amsterdam, 1970) p. 407 [7] S Oryo, Prog. Theor. Phys 44 (1970) 1208,and 45 (1971) 386. [8] R J Griffith and K.M Knight, Nucl Phys. 54 (1964) 56 [9] A S. Kuckes, R. Wilson and P.F. Cooper, Ann of Phys. 15 (1961) 193 [lo] G. Paic, J.C Young and Margaziotts, Phys Lett. 32B (1970) 437. [ll] J.A McIntyre et al, Phys. Rev CS (1972) 1796.