Proton-proton final state interaction in the p + 3He reaction

Nuclear Physics At36 Not to be reproduced

(1969) 337-352; by photoprint

PROTON-PROTON

@

North-Holland

Publishing

Co., Amsterdam

or microfilm without written permission from the publisher

FINAL

STATE INTERACTION

IN THE p-k3He REACTION + C. C. CHANG, E. BAR-AVRAHAM, University

H. H. FORSTER and C. C. KIM

of Southern

Califbrnia

and P. TOMAS tt and J. W. VERBA University

of California,

Los Angeles

Received 18 July 1969 The proton-proton final state interaction was studied using the 3He+p -+ d+p tp reaction both in single counter, kinematically “incomplete” (E,, = 30.2 and 46.0 MeV) and angular correlation, kinematically “complete” (E,, = 46.5 MeV) experiments. In the single counter experiment the angular dependence of the final state interaction was determined between &, = 10” and&.,, = 50”. A Watson-Migdal calculation was used to fit the experimental deuteron spectra near the high-energy cutoff, the calculated distributions obtained for a choice of reasonable parameters were found to be wider at the peak than the experimental data indicated. The angular correlation experiments were performed at counter settings at which the contributions from p-p final state interaction were expected to be relatively large; these particular experiments indicated: (i) that p-p final state interaction contributes significantly to the threebody process and, (ii) that the proton pair is preferentially emitted with an internal energy of E,, w 0.4 MeV. A Watson-Migdal calculation applied to the angular correlation experiments gave good agreement with the experimental results. An explanation for the difference in fitting single counter or angular correlation experiments is given.

Abstract:

NUCLEAR

REACTIONS 3He(p, d)2p, jHe(p, pd)p, E = 30,46 MeV; measured o(E; Ed, &), a(& t$, &) o(& %, &I); deduced proton pairs internal energy E,, w 0.4 MeV. Enriched target.

1. Introduction

The study of nuclear reactions leading to three particles in the final state has shown ‘) that if two of the three particles are strongly interacting, the spectrum of the third particle will deviate considerably from the expected phase space distribution. In particular, in reactions such as ‘H(n, p)nn [ref. ‘)I and 2H(p, n)pp [ref. “)I the spectrum of the observed particle shows (at small angles) strong peaking near the kinematic energy limit, indicating a ‘Se final state interaction of the two unobserved nucleons. Thus, reactions of this type should lead to information about the singlet, T = 1 states of the two-nucleon systems. t This work was supportedin part by the U. S. Atomic Energy Commission under contracts AT(O4-3)136 and AT(ll-I) GEN 10 P.A. 18. tt On leave of absence from Institute “R. BoSkoviC”, Zagreb, Yugoslavia. 337

C. C. CHANG

338

et d.

In the present experiment, the p-p interaction was studied by means of the 3He+p --) d + p + p reaction both in kinematically “incomplete” and “complete” experiments. In the former, deuteron spectra from the reaction were investigated at different angular counter settings. However, in a single counter experiment some useful information may be lost. For this reason, it seemed desirable to perform, in addition, a kinematically “complete” experiment, in which deuterons and one of the outgoing protons were detected in coincidence. A suitable theoretical description of final state interactions has to make allowance for Coulomb effects and for the interactions among the three particles. However, in the 3He(p, d)2p reaction the deuteron in the final state does not interact strongly with the two protons; hence it is reasonable to neglect this interaction in a theoretical treatment of the final state interaction. Theoretical treatments of final state interactions have been presented by Watson 4), Migdal ‘), and several other authors 6-8). For the analysis of the data in this set of experiments, the approximations introduced by Watson and Migdal were used. It was previously found that the Watson-Migdal theory of final state interactions gave good fits to experimental data in reactions such as 3He(d, t)pp [refs. 9*1O)] and 4He(p, t)pp [refs. “)I, while in others, as for instance *H(p, n)pp [ref. “)I, 2H(3He, t)pp [ref. ‘“)I, and 3He(p, d)pp [refs. I*, ’ “)I, the calculated energy spectra were too broad near the kinematic energy cutoff in comparison with the experimental results. The reason for this is not well understood. And it seemed interesting, therefore, to compare the experimental and theoretical distributions for the 3He + p + d + p + p reaction both for the single counter and the coincidence experiments. 2. Experimental

procedure

The experiment was carried out at the USC 30 MeV proton linear accelerator and at the UCLA 50 MeV sector focused cyclotron. The 3He gas target (x 99.99 “/‘, WATER

s AE E TEC

Fig.

1. Schematic

diagram

of the scattering

- a--S ENERGY CbLlEJ3ATIoN - COUMATORS - AE-OETECTWS - E-DETECTORS - THERMOELECTRIC COOLERS

chamber.

Fig. 2.

Block diagram of the electronics

used in the angular correlation

cxpcriment.

1000

900 P+ CD2

Ep=46.5

000

MeV

6, = 47.16” C12=60°

700

300

200

100

TIM

(CHANNEL

NUMBER)

Fig. 3. A typical time spectrum of the time-to-pulse-height converter. The small peaks correspond to coincidences between events from different beam bursts.

340

c.

C. CnANG

et al.

isotopically pure) was contained inside a small 10.2 cm diameter aluminum scattering chamber with a 13 pm polyimide foil window, placed in turn at the center of a 30.5 cm evacuated scattering chamber, which housed the solid state detector system. Details of the gas handling system and the scattering chamber have been described elsewhere 14). A schematic diagram of the chamber is given in fig. 1. The detector system was slightly different in the single counter experiment and in the angular correlation experiment. In the former, the counter telescope consisted of a 490 pm thick totally depleted surface barrier Si detector mounted inside the evacuated chamber and a 5 cm diameter x 1.3 cm thick NaI(T1) detector placed outside the chamber. Signals from the AE and E detectors were put into coincidence and gated the Victoreen Scripp two dimensional analyser or the SDS 925 computer operated in a two-dimensional mode. In the angular correlation experiment, two counter telescopes, each consisting of a AE passing counter and an E stopping counter were used. In this case, both the surface barrier AE and the Li-drifted E detectors were in vacuum. The electronic system used has been described elsewhere 1,4), with one exception: since the effect of final state interaction is most pronounced for high-energy deuterons and, correspondingly, for low-energy protons, it was desired to detect as low-energy protons as possible. Therefore, one of the detector telescopes was designed to detect low-energy protons. In this detector telescope an ORTEC 109A preamplifier was used in conjunction with a cross-over technique to provide a stopping signal for a time to pulse height converter (TPHC); the starting signal was provided by the fast output of the AE detector in the other (deuteron) arm. The TPHC itself was gated by the AE-E coincidences in the deuteron arm. (See fig. 2). Due’to energy losses in the gas and the window of the inner chamber, the low-energy cutoff for protons in the proton arm was x 1 MeV. The output of the TPHC was sent to a single-channel analyzer, set so that the time resolution was z 30 nsec. This reduced the accidental coincidences considerably, as can be seen from figs. 3 and 7. In each arm the signals from the AE and E detectors were summed; in order to adjust the summing circuit, a “‘Th alpha source was inserted between the AE and E detectors. In this experiment particle identification was achieved in the angular correlation experiment by obtaining both the AE versus E plot for the telescope detecting primarily deuterons, and the E, versus E2 dependence. Combining these results with a kinematic calculation enables one to recognize different kinematic contours, (that is, p-p, p-d and d-p) for the three-body breakup reactions. 3. Experimental results 3.1. SINGLE COUNTER

If the two interacting particles are emitted with small relative momentum and if the “non-interacting particle” is to be detected, the enhancement due to final state interaction should best be seen at forward angles. For this reason, the differential cross

p+ 3He

REACTION

341

sections d20/dEddQ,, were determined in small angular intervals at laboratory angles ranging from 10” to 50”. Two typical spectra obtained at small laboratory angles for Ep = 30.2 MeV and Ep = 46.0 MeV are shown in figs. 4 and 5. As can be seen from the figures, the deuteron spectra near the high energy cutoff show strong enhancement. The experimental spectra deviated considerably from those obtained by phase space calculations, indicated in figs. 4 and 5 by solid curves.

%e(p,d)2p

20.0-

E, = 30.2 MeV

It

15.0;I

II I

z f T b

“0 ; I”D

10.0.

5.0-

I f., 15

20 DEUTERON ENERGY

, , , ,

25 ( MeV I

Fig. 4. Deuteron energy spectrum for Ep = 30.2 MeV at Cl,,,,= IO”. The solid curve is the calculated phase space distribution.

At both energies, the peaking near the cutoff varies rapidly as the angle of observation is increased; it reaches a minimum at ,!&,, x 22.9 and a maximum at % 35”, as can be seen from the spectra reproduced in fig. 6. In order to determine s q&titatively the angular dependence of the final state interaction, it would be necessary to extract daJdE, from d2a/dE,dsl,. However, there seems to be no

342

c. C. CK4WG et al.

unique method of proceeding with the integration; one has the choice of replacing the peak by a symmetric distribution and integrating over it, or to choose arbitrarily a range of relative energies between the two protons and calculate the number of deuterons emitted corresponding to this energy range at each angular setting. In this experiment, this latter method was chosen. Fig. 7 shows the angular distributions for both the 30.2 MeV and the 46.0 MeV data obtained for a range of relative proton I”..*“.‘r““i~“’

It 7ie c p,d) 4.0 -

E, = 46.0 B,,,=

2P MeV

w

Fig. 5. De&zron energy spectrum for Ep = 46.0 MeV at &,z, = 13”. The solid curve is the cafcufated phase space disttibution.

energies from Ezp = 0 to i&, = 4.0 MeV. For the sake of comparison, the 46.0 MeV data were also integrated from E-+ = 0 to l&, = 8.0 MeV. As can be seen from fig. 7 the shape of the angular djstr~but~on was not affected by this change in the limits of integration.

p + ‘He

3.2.ANGULAR

343

REACTION

CORRELATION

In order to further investigate the features of the p-p final state interaction, it seemed desirable to detect a deuteron and one of the two interacting protons in coincidence, since this permits one to explore the momentum space which favors the final state interaction.

IO

ZI,f c _

s _ 2-

I_

PW-

“3 -

(c)

8,=

15’

ii”

t $ t

s-

Fig. 6.Deuteron energy spectra for ED = 30.2MeV at different deuteron angles for the 3He(p. d)2p reaction.

The single counter experiment had shown that the final state interaction was considerable at QLabx 35” (fig. 7). For this reason, the angular correlation experiment

344

C. C. CHANG

et al.

was performed as follows: First, the deuteron detector was set at Qd = 40” and 9, was varied from 68” to 88” in 5” steps; second, Q,, was varied from 30” to 45” in 5” steps, while the proton detector was each time set along the corresponding diproton recoil axis. Fig. 8(a) shows a two-parameter E, versus E2 distribution for g1 = 35” and QZ = 84.7”. Curve I corresponds to the kinematic contour for detecting deuterons at 91 = 35” and coincident protons at Q2 = 84.7”; however, it was also kinematically possible to detect protons at a1 = 35” and deuterons at Q2 = 84.7”; the kinematic contour corresponding to these events is represented by curve II.

102-

)

I

1

,

*

,

‘Ha(p,d) Angular

5-

9

,

I

,

I

I

I

2p Distribution

IO’--z c z -5

_ 5-

d bC:

-

I ,D’p,

IO"--

I 5.

I I I I I IO 20 30 %,,S Deg

I

I 40

I

50

6C

1

Fig. 7. Angular distributions for the JHe@, d)2p reaction at EP = 30.2 MeV and 46.0 MeV. Curves A, B, and C are obtained by integrating over a deuteron energy interval corresponding to a) Ezp= 04

MeV (A and B); b) Ezp = O-8 MeV at ED = 46.0 MeV (C).

Fig. 8(b) and 8(c) represent the projections of events along contour I onto the two energy axes; the solid curves are the calculated relative energies Ezp of the twoproton system, plotted as functions of Ed and Ep, respectively; the insert in fig. 8(b) shows the angular settings of the two detectors. A three-parameter spectrum is displayed in fig. 9 in which the differential cross sections at Qd = 40” are plotted as a function of the deuteron energy and different proton angles.

p + 3He REACTION

oo+xx

x

4+ ii-+

xxx x x x xy x

+x

xx+om ++: xxx +x+x

x

-

P

s

r I#.7

x

x

??

x

--0 x

:

I.

..

l,

--

**..

n

. .._

f

p + ‘He

347

REACTION

4. Analysis and discussion According to the theory of final state interactions formulated energy dependence of the cross section can be written as:

by Watson

4), the

where 6, is the elastic S-wave phase shift, (it is assumed that only S-wave scattering is important), k is the small relative momentum of the two particles, and p is a phase space factor. In the case of p-p final state interaction, eq. (I) becomes: CP ._~. da z -.[-(I/a)+~r,k2-Pr~k4-_(r])/R]2+C2k2 where a is the scattering

length,

rO the effective range,

(2) C the Coulomb

penetration

1

Fig. 10. The theoretical fits to the experimental energy spectra for EP = 46.0 MeV using the WatsonMigdal formalism (solid curves). Dashed curves are the results with the interaction between deuteron and p-p system taken into account.

348

C. C. CHANG

factor, R the characteristic

et cd.

Coulomb length, P a shape dependent factor, and

h(s) = ??2 f n=l

n(n2+

l

-In v-0.57722. rj2)

The solid curves in fig. 10 show the calculated shapes of the spectra at E,, = 46.0 MeV and Qd = 13” and 15” respectively. The parameters used are the usual lowI

60

50

ez=e30*

3He hpd)p

45 40

Ep=46.5 MeV

35

e,=40° - Watson-Migdal

30 55 !

50-

1

6 = 68.0’

4.5 -

3.5 3025-

15

20

25

15

20 OEUTERON

25 ENERGY

15

20

25

IMeW

Fig. 11. The theoretical fits using Watson-Migdal formalism to the results of the angular correlation experiment projected onto the deuteron energy axis.

30

350

C. C. CHANG

et d.

energy p-p scattering parameters. The results at other angles and at EP = 30.2 MeV are very similar. In all cases, the calculated spectra are broader at the peak than the experimentally obtained ones. This has sometimes been attributed to the fact that the reaction mechanism had not been taken into account and that no correction had been made for any interaction of the outgoing deuteron in the 3He(p, d)2p reaction with the two-proton system. An inclusion of the correction for this latter effect I’) in eq. (2) resulted in the dashed curves in fig. 10. The agreement with the spectra is better; however, on the basis of the angular correlation experiment, a different explanation seems to suggest itself. The experimental results reproduced in part in figs. 8 and 9 had shown that d30/dE,dQ,d0, had a maximum for a small relative p-p energy EZp and that on the other hand, d30/dEPdQ,dS2, had two broad maxima for Ezp z 0.4 MeV. This seems to imply that in the final state the proton pair is preferably being emitted with an internal energy of EZp w 0.4 MeV or, in other words, that the probability of formation of the singlet p-p system is most pronounced for an internal energy of the p-p system of z 0.4 MeV. If the Watson-Migdal formalism is used to calculate the shapes of the triple cross sections at different detector settings, the solid curves in figs. 11 and 12 result. In other words, in the angular correlation experiment, the experimental results are very well reproduced by the Watson-Migdal theory. A possible explanation of the difference in the applicability to single counter or angular correlation experiments might lie in the following: Let us assume a sequential reaction which proceeds according to the following mechanism: a+A + b+C

(3) I+ d+e.

Then the decay products d and e will be found within a certain angular region determined by the detection angle of b, the internal energy of the system (d+e), the energy of the incident particle and the Q-value of the reaction. In the case of p + 3He, based on kinematic considerations alone and for an internal energy of the p-p system of z 0.4 MeV, there will be an angular region which will contribute significantly to the experimental spectrum while contributions from outside this angular range will be small. A diagram showing the acceptable cone for Qd = 40” is shown in fig. 13. In the angular correlation experiments the proton counter was always placed within the acceptable cone and the Watson-Migdal theory predicted distributions which agreed with the experimental results. On the other hand, in single counter experiments the calculations included contributions from outside the accessible region, hence overestimated the cross sections. It is clear from fig. 12 that beside the final state interaction other processes contribute significantly to the cross sections. The effect of these contributions becomes particularly obvious as 9, is decreased. It has been known from other experiments ’ “) that even at a proton energy of Ep = 30 MeV a quasi-elastic p-d scattering process

351

p + 3He REACTION

contributes considerably to the breakup of 3He. A simple calculation of the effect at various angles is shown in fig. 14, which indicates that the relative contributions due to quasi-el~tic p-d scattering decrease as the proton angle is increased from 9, = 68” to 9, = 88”; and that the general shape of the spectra can be reproduced if this effect is taken into account. ‘He fp,d) 2p Ep = 46.5 MeV

BEAM DIRECTION _..._--__-----------_*

II-______

-L 5P j!b-

-R vP

: :

,

:

:

:

Fig. 13. A diagram showing the kinematically acceptable Cone of the recoiling two-proton system for 6, = 40” and Ez,,= 400 keV.

uasi-Elastic

Scolfering

20

0 6

8

IO

12

14

16

I8

20

PROTON

Fig. 14. A simple calculation

22

6 ENERGY

8

IO

12

14

I6

18

20

22

24

(Mev)

of the p-d quasi-elastic scattering contribution reaction using the method of ref. 14).

to the 3He(p, pd)p

352

c. c. cmwo

et al.

The authors wish to express their sincere thanks and appreciation to Professor J. Reginald Richardson for his support and continued interest in this work, to Mr. B. Poarch for his help in the construction of the scattering chamber and to the technicians of the USC Linear Accelerator and the UCLA Cyclotron Laboratory for the effective operation of the machines during the experiments.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)

K. Ilakovac, L. G. Kuo, M. Petravic, I. Slam and P. Tomal, Phys. Rev. Lett. 6 (1961) 356 E. Bar-Avraham, R. Fox, Y. Porath, G. Adam and G. Frieder, Nucl. Phys. Bl (1967) 49 C. J. Batty, R. S. Gilmore and G. H. Stafford, Phys. Lett. 16 (1965) 137 K. M. Watson, Phys. Rev. 88 (1952) 1163 A. B. Migdal, ZhETF 28 (1955) 3; JETP (Sov. Phys.) 1 (1955) 2 G. C. Phillips, T. A. Griffy and L. C. Biedenham, Nucl. Phys. 21 (1960) 327 R. J. N. Phillips, Nucl. Phys. 31 (1962) 643 R. J. N. Phillips, Nucl. Phys. 53 (1964) 650 H. E. Conzett, E. Shield, R. J. Slobodrian and S. Yamabe, Phys. Rev. Lett. 13 (1964) 625 B. J. Morton, E. E. Gross, J. J. Malanity and A. Zucker, Phys. Rev. Lett. 18 (1967) 1007 M. Bernas, J. K. Lee, D. Bachelier, I. Brissaud, C. Detraz, P. Radvanyi and M. Roy, Phys. Lett. 25B (1967) 260 12) T. A. Tombrello and A. D. Bather, Phys. Lett. 17 (1965) 37 13) C. C. Chang, Ph. D. dissertation, University of Southern California (1968) 14) E. Bar-Avraham, C. C. Chang, H. H. Forster, C. C. Kim and J. W. Verba, to be published