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Proton-proton final state interaction in the 3He (p, pd)p reaction
Volume 28B, number
PHYSICS
3
PROTON-PROTON IN THE
LETTERS
FINAL 3He(p, pd)p
25 November
1968
STATE INTERACTION REACTION *
C. C. CHANG, E. BAR-AVRAHAM, H. H. FORSTER and C. C. KIM University ofSouthern Califoomia and J. R. RICHARDSON, P. TOMAS ** and J. W. VERBA University of California Received
8 October
1968
The final state p-p interaction has been observed by means of a 3He(p. pd)p angular correlation experiment It was found that the probability of formation of the singlet state is most pronounced for an internal energ!, of the two-proton system of %0.4 MeV.
Recently, nucleon-nucleon interactions have been studied by means of nuclear reactions with three particles in the final state [e.g. 11. These experiments lead to information about the singlet, T = 1, states of the Iwo-nucleon systems, and in turn, to the determination of the parameters describing the nucleon-nucleon interactions. Most of these experiments were performed with single counter telescopes. However, in a single-counter experiment, some useful information may be lost due to the fact that it is a kinematically “incomplete” experiment. For this reason it seems desirable to perform a kinematically “complete” experiment. As far as the 3He(p, d)2p reaction is concerned, single-counter experiments have been used to investigate the p-p final state interaction at incident proton energies 11.94 MeV [2], 25.5 MeV [l], 30.2 MeV [3] and 46.0 MeV [3]. However, no correlation experiments have been reported for the p + 3He breakup reaction. The purpose of the experiment described below was to examine the p-p final state interaction by means of the reaction 3He(p,pd)p. A 46.5 MeV proton beam was used for the experiment. Two counter telescopes, each consisting of a AE passing counter and an E stopping counter were used. One of the telescopes was primarily intended to de* This work is supported in part by the U. S. Atomic Energy Commission under contracts AT(04-3)-136 and AT(ll-1) GEN 10 P. A. 18. ** On leave of absence from Institute “R. BoBkoviC. ” Zagreb, Yugoslavia.
tect deuterons, the other protons. From the single-counter experiments [3], it was known that the p-p final state interaction is most pronounced near the high-energy end point of the deuteron spectra. Kinematically this corresponds to lowenergy protons. Therefore it seemed desirable to detect protons with as low an energy as possible. The electronics was set up as follows: the two fast signals from the AE detectors were used as start and stop signals for a time-to-pulseheight converter, which in turn was gated by the output of the AE-E coincidence in the detector arm chosen primarily to detect deuterons. In each arm the signals from the AE and E detectors were summed. The output of the time-to-pulseheight convertor, after passing through a single-channel analyzer, was used to gate the two AE + E summed signals. The experiment was designed to investigate the following properties of the p-p final state interaction: 1) the internal energy of the p-p system corresponding to strong enhancement of the final state interaction; 2) the angular dependence of the p-p final state interaction. The single-counter 3He(p, d)2p experiments at 30.2 and 46.0 MeV [3] showed enhancement in the deuteron spectrum near the high-energy cutoff. This was interpreted as evidence for final state p-p interaction. The angular distribution of this enhancement showed a maximum for f?d(lab) N 5 350. Therefore, in order to further investigate the features of the p-p final state interaction, the deuteron arm was first set at 0d = 40° and BP was varied from 680 to 880 in 5O steps; second, 175
Volume
PHYSICS
28B, number 3
8d was varied from 3o” to 45O in 5o steps, while the proton arm was set along the diproton recoil axis. The results of the angular dependence of the p-p final state interaction will be discussed in a separate article. A typical two-parameter E 1 versus E 2 plot for 81 = od = 350 and 82 = BP = 64.70 is shown in fig. la. Curve I is the kinematic contour for detecting protons at 82 = 84.7O and deuterons at 61 = = 35O; however, it was also possible to detect protons at 35O. The contour for the case in which
d3a dEpdQpd%
(mb/MeV-sr2)
LETTERS
25 November
1968
a proton is detected at 01 and a deuteron at 02 is shown in curve II. In figs. lb and lc the data along contour I are projected onto the two energy axes; thus fig. lb shows the deuteron spectrum obtained in this experiment. It is similar to the deuteron spectrum obtained in the 3He(p, d)2p experiments [3], and shows the same enhancement near the high-energy cutoff. The solid curve corresponds to a plot of the internal energy of the two-proton system, Ez~, as a function of the deuteron energy Ed.
B
‘He (p,pd P El, = 46.5 MeV 8, = 35O e2 = 84.7O
Fig. la. Two dimensional contour plots of EI versus E2; El is the summed energy of the particle detected at 81 = = 350, E2 is that of the coincident particle detected at & = 84.70. Curve I represents the kinematic contour for detecting a deuteron at 8I and a correlated proton at 82; curve II corresponds to a deuteron at 82 and a proton at 81. lb. Projection of curve I onto the deuteron energy axis. The solid curve indicates the internal energy of the twoproton system. The insert shows the detector settings. lc. Projection of curve I onto the proton energy axis. The solid curve indicates the internal energy of the two-proton system.
176
Volume 28B, number 3
PHYSICS
25 November 1968
LETTERS
Fig. lc is a similar projection of the experimental data along contour I onto the proton energy axis. The solid curve labelled Ezp corresponds to a plot of the internal energy of the two-proton system as a function of the proton energy Ep. It is particularly interesting to note that the cross section d30/dEpds2,dSZd shows a minimum at an internal energy Ezp = 0 MeV and two broad maxima for Ezp N 0.4 MeV. It can be concluded from the experimental results: 1) that final state p-p interaction, corresponding to formation of the two-nucleon system in the singlet state contributes significantly to the three-body breakup process of p + 3He at the angular settings chosen for the two detector telescopes, and 2) that in the final state the proton pair is preferably being emitted with an approximate internal energy of 0.4 MeV. The asymmetry in the two peaks in fig. lc is due mainly to the phase space factor; symmetric peaks are obtained when the phase space factor is divided out. It is interesting to note that a calculation of the energy of the p-p singlet, T = 1 state, using low energy p-p scattering parameters, that is up = = - 7.72 fm and Y = 2.72 fm gives a value of E2P = 0.5 MeV. Al similar value for the internal energy of the p-p system has recently been deduced by Blackmore and Warren [4], from a 3He(3He, 2p)4He experiment. Fig. 2 shows a tentative energy diagram of the virtual states of the two-nucleon systems. The T = 1 states in 2H and 2n are calculated with the
3.14 .-__..~ 1.84
0’ Tr,
3.005 n+n
0’
____~,r, 1443 P’P T=O 2
n
Fig. 2. Energy level diagram of the two-nucleon systems. following nucleon-nucleon singlet scattering parameters: anp = - 23.71 fm, Ynp = 2.4 fm; arm = = - 16.1 fm, Ynn = 2.65 fm. The virtual state in 2He is based on the approximate experimental value of 0.4 MeV deduced in this experiment.
References I. Qlaus, Rev. Mod. Phys. 39 (1967) 575, and references quoted therein. T.A.Tombrello and A.D.Bacher, Phys. Letters 17 (1965) 37. C. C. Chang, Ph. D. dissertation, University of Southern California (1968), to be published. E. W.Blackmore and J. B. Warren. Can. J. Phys. 46 (1968) 233.
*****
177
PHYSICS
3
PROTON-PROTON IN THE
LETTERS
FINAL 3He(p, pd)p
25 November
1968
STATE INTERACTION REACTION *
C. C. CHANG, E. BAR-AVRAHAM, H. H. FORSTER and C. C. KIM University ofSouthern Califoomia and J. R. RICHARDSON, P. TOMAS ** and J. W. VERBA University of California Received
8 October
1968
The final state p-p interaction has been observed by means of a 3He(p. pd)p angular correlation experiment It was found that the probability of formation of the singlet state is most pronounced for an internal energ!, of the two-proton system of %0.4 MeV.
Recently, nucleon-nucleon interactions have been studied by means of nuclear reactions with three particles in the final state [e.g. 11. These experiments lead to information about the singlet, T = 1, states of the Iwo-nucleon systems, and in turn, to the determination of the parameters describing the nucleon-nucleon interactions. Most of these experiments were performed with single counter telescopes. However, in a single-counter experiment, some useful information may be lost due to the fact that it is a kinematically “incomplete” experiment. For this reason it seems desirable to perform a kinematically “complete” experiment. As far as the 3He(p, d)2p reaction is concerned, single-counter experiments have been used to investigate the p-p final state interaction at incident proton energies 11.94 MeV [2], 25.5 MeV [l], 30.2 MeV [3] and 46.0 MeV [3]. However, no correlation experiments have been reported for the p + 3He breakup reaction. The purpose of the experiment described below was to examine the p-p final state interaction by means of the reaction 3He(p,pd)p. A 46.5 MeV proton beam was used for the experiment. Two counter telescopes, each consisting of a AE passing counter and an E stopping counter were used. One of the telescopes was primarily intended to de* This work is supported in part by the U. S. Atomic Energy Commission under contracts AT(04-3)-136 and AT(ll-1) GEN 10 P. A. 18. ** On leave of absence from Institute “R. BoBkoviC. ” Zagreb, Yugoslavia.
tect deuterons, the other protons. From the single-counter experiments [3], it was known that the p-p final state interaction is most pronounced near the high-energy end point of the deuteron spectra. Kinematically this corresponds to lowenergy protons. Therefore it seemed desirable to detect protons with as low an energy as possible. The electronics was set up as follows: the two fast signals from the AE detectors were used as start and stop signals for a time-to-pulseheight converter, which in turn was gated by the output of the AE-E coincidence in the detector arm chosen primarily to detect deuterons. In each arm the signals from the AE and E detectors were summed. The output of the time-to-pulseheight convertor, after passing through a single-channel analyzer, was used to gate the two AE + E summed signals. The experiment was designed to investigate the following properties of the p-p final state interaction: 1) the internal energy of the p-p system corresponding to strong enhancement of the final state interaction; 2) the angular dependence of the p-p final state interaction. The single-counter 3He(p, d)2p experiments at 30.2 and 46.0 MeV [3] showed enhancement in the deuteron spectrum near the high-energy cutoff. This was interpreted as evidence for final state p-p interaction. The angular distribution of this enhancement showed a maximum for f?d(lab) N 5 350. Therefore, in order to further investigate the features of the p-p final state interaction, the deuteron arm was first set at 0d = 40° and BP was varied from 680 to 880 in 5O steps; second, 175
Volume
PHYSICS
28B, number 3
8d was varied from 3o” to 45O in 5o steps, while the proton arm was set along the diproton recoil axis. The results of the angular dependence of the p-p final state interaction will be discussed in a separate article. A typical two-parameter E 1 versus E 2 plot for 81 = od = 350 and 82 = BP = 64.70 is shown in fig. la. Curve I is the kinematic contour for detecting protons at 82 = 84.7O and deuterons at 61 = = 35O; however, it was also possible to detect protons at 35O. The contour for the case in which
d3a dEpdQpd%
(mb/MeV-sr2)
LETTERS
25 November
1968
a proton is detected at 01 and a deuteron at 02 is shown in curve II. In figs. lb and lc the data along contour I are projected onto the two energy axes; thus fig. lb shows the deuteron spectrum obtained in this experiment. It is similar to the deuteron spectrum obtained in the 3He(p, d)2p experiments [3], and shows the same enhancement near the high-energy cutoff. The solid curve corresponds to a plot of the internal energy of the two-proton system, Ez~, as a function of the deuteron energy Ed.
B
‘He (p,pd P El, = 46.5 MeV 8, = 35O e2 = 84.7O
Fig. la. Two dimensional contour plots of EI versus E2; El is the summed energy of the particle detected at 81 = = 350, E2 is that of the coincident particle detected at & = 84.70. Curve I represents the kinematic contour for detecting a deuteron at 8I and a correlated proton at 82; curve II corresponds to a deuteron at 82 and a proton at 81. lb. Projection of curve I onto the deuteron energy axis. The solid curve indicates the internal energy of the twoproton system. The insert shows the detector settings. lc. Projection of curve I onto the proton energy axis. The solid curve indicates the internal energy of the two-proton system.
176
Volume 28B, number 3
PHYSICS
25 November 1968
LETTERS
Fig. lc is a similar projection of the experimental data along contour I onto the proton energy axis. The solid curve labelled Ezp corresponds to a plot of the internal energy of the two-proton system as a function of the proton energy Ep. It is particularly interesting to note that the cross section d30/dEpds2,dSZd shows a minimum at an internal energy Ezp = 0 MeV and two broad maxima for Ezp N 0.4 MeV. It can be concluded from the experimental results: 1) that final state p-p interaction, corresponding to formation of the two-nucleon system in the singlet state contributes significantly to the three-body breakup process of p + 3He at the angular settings chosen for the two detector telescopes, and 2) that in the final state the proton pair is preferably being emitted with an approximate internal energy of 0.4 MeV. The asymmetry in the two peaks in fig. lc is due mainly to the phase space factor; symmetric peaks are obtained when the phase space factor is divided out. It is interesting to note that a calculation of the energy of the p-p singlet, T = 1 state, using low energy p-p scattering parameters, that is up = = - 7.72 fm and Y = 2.72 fm gives a value of E2P = 0.5 MeV. Al similar value for the internal energy of the p-p system has recently been deduced by Blackmore and Warren [4], from a 3He(3He, 2p)4He experiment. Fig. 2 shows a tentative energy diagram of the virtual states of the two-nucleon systems. The T = 1 states in 2H and 2n are calculated with the
3.14 .-__..~ 1.84
0’ Tr,
3.005 n+n
0’
____~,r, 1443 P’P T=O 2
n
Fig. 2. Energy level diagram of the two-nucleon systems. following nucleon-nucleon singlet scattering parameters: anp = - 23.71 fm, Ynp = 2.4 fm; arm = = - 16.1 fm, Ynn = 2.65 fm. The virtual state in 2He is based on the approximate experimental value of 0.4 MeV deduced in this experiment.
References I. Qlaus, Rev. Mod. Phys. 39 (1967) 575, and references quoted therein. T.A.Tombrello and A.D.Bacher, Phys. Letters 17 (1965) 37. C. C. Chang, Ph. D. dissertation, University of Southern California (1968), to be published. E. W.Blackmore and J. B. Warren. Can. J. Phys. 46 (1968) 233.
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177