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Proton-induced nucleon knockout from polarized 3He at 290 MeV
Physics Letters B 275 (1992) 259-263 North-Holland
P H YS IC $ t_ET T ER $ B
Proton-induced nucleon knockout from polarized 3He at 290 MeV A. Rahav a O. H~iusser a,b C.A. Miller b, p.p.j. Delheij b W.P. Alford c, T.E. Chupp d K. Ferguson b, R.S. Henderson b, C.D.P. Levy b, K.P. Jackson b, j. Mildenberger a, B. Morrissette b, M.C. Vetterli b and R.M. Woloshyn b Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 b TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, Canada V6T 2.43 c University of Western Ontario, London, Ontario, Canada N6A 3K7 d Physics Laboratories, Harvard University, Cambridge, MA 02138, USA a
Received 11 November 1991
A novel polarized 3He gas target has been used to measure spin observables for (~, 2p) and (~, pn) nucleon knockout in quasielastic kinematics at 290 MeV. Comparisons with PWIA calculations show the importance of rescanering corrections, especially for neutron knockout and the target-related asymmetry Aon.The A,n (~, 2p ) results agree with the PWlA and qualitatively indicate the effects of spin momentum distributions of protons in 3He as predicted by Faddeev calculations.
Quasifree scattering from nuclei is one o f the most direct methods o f investigating single nucleon motion in the nucleus. Following the early (p, 2p) proton knockout experiments carried out at the 185 MeV synchrocyclotron in U p p s a l a [ 1 ] a large b o d y o f inf o r m a t i o n has been o b t a i n e d on binding energies, m o m e n t u m distributions and widths o f nucleons in individual nuclear shells both from proton [2] and electron [3] induced knockout reactions. In (~, 2p) reactions with polarized protons from spin-zero nuclei analyzing powers are observed which can be explained [2] by an effective polarization o f the knocked-out nucleon that is opposite for j = l + ½ and j = l - ½nucleons. The b e a m - r e l a t e d analyzing powers in proton knockout, e.g. from the ls~/2 inner shell in ~60 [4], are smaller c o m p a r e d to distorted wave impulse a p p r o x i m a t i o n ( D W I A ) calculations. This is an indication o f either a density-dependence o f the n u c l e o n - n u c l e o n interaction in the nuclear m e d i u m a n d / o r o f the i m p o r t a n c e o f multiple scattering effects. Quasielastic scattering from p o l a r i z e d nuclear targets adds a new d i m e n s i o n to the study of nucleon m o t i o n in nuclei. Target-related a s y m m e t r i e s d e p e n d on the spin orientation o f the knocked-out nucleon relative to that o f the target spin, and this can be in-
vestigated versus the nucleon m o m e n t u m . Previously, such information could only be inferred indirectly and incompletely from other observables, e.g. nuclear magnetic m o m e n t s or matrix elements in G a m o w - T e l l e r 13 decay. In this p a p e r we present the first observation o f target-related spin observables in h a d r o n - i n d u c e d nucleon knockout from a polarized nuclear target (A > 2). The experiment has become feasible because o f recent d r a m a t i c i m p r o v e m e n t s [5,6] in producing polarized 3He targets by optical p u m p i n g of Rb and R b - 3 H e spin-exchange collisions. H a d r o n i c and electroweak reactions with polarized 3He are o f great current interest because of the a p p r o x i m a t e alignment o f the spin o f the o d d neutron with that o f the 3He spin predicted by F a d deev calculations o f the 3He wavefunction [7]. Polarized 3He might thus be a target o f choice for determining fundamental properties o f the neutron, e.g. electromagnetic form factors [8,9] and spin structure functions [ 10,1 1 ]. However, the interpretation o f these experiments requires that spin effects arising from the full nucleonic wavefunction be taken into account [8,10] and, furthermore, that rescattering effects in the hadronic final state be investigated and understood. The present paper addresses both the
0370-2693/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
259
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questions of 3He structure and of hadronic rescattering effects. The experiment was carried out with the 290 MeV polarized proton beam from the T R I U M F cyclotron. A full description of the experiment, the data analysis, and the plane-wave impulse a p p r o x i m a t i o n ( P W I A ) calculations used for theoretical comparisons is given elsewhere [ 12 ]. The polarized 3He target setup developed at T R I U M F for target polarization normal to the scattering plane has been described by Larson et al. [6] and is shown schematically in fig. 1. The target used here consisted of an 8 cm long × 1.6 cm inner d i a m e t e r glass cell and was o f relatively low density, containing 3.16 standard atm o f 3He, 100 Tort of N2 quench gas, and a few mg o f Rb metal. An oven m a d e of the p o l y i m i d e VESPEL was at a temperature of 450 K to produce a Rb vapor density of ~ 4 × 10 ~4 cm 3. A b o u t 4 W o f circularly polarized photons of wavelength 2 = 795.7 nm were used to optically p u m p Rb via the DI line. The target assembly was in a vertical magnetic holding field IB o [ = 3 mT. The atomic polarization is transferred from Rb atoms to the 3He nucleus during R b - 3 H e collisions by the F e r m i contact hyperfine interaction. The bulk 3He polarization was reversed and analyzed using the technique o f adiabatic fast passage N M R ( A F P ) . The target cell was characterized by a wall
];
To aiR
Ar IA-t .J
::'/-
~
I,as(W
Fig. 1. Schematic layout of the polarized 3He target. For a detailed description see ref. [6]. 260
30 January 1992
relaxation rate F = (43 h) ~ and by a p u m p - u p rate of~9h '. At the beginning and end o f each ~ 3 h run N M R scans were taken to obtain the representative polarization. The m a x i m u m and average polarizations o f ~ 63% and 54%, respectively, differed because o f variations in laser power. Absolute normalization factors were obtained by comparing the 3He A F P signals with weak proton N M R signals from water-filled cells o f the same dimension. An independent check o f this m e t h o d which is sensitive only to 3He in the b e a m interaction region was obtained recently [ 13 ] from beam-related asymmetries for the 3He(p, ~+ )4He reaction. The a d o p t e d "safe" error for the absolute target polarization, A p , = 0 . 0 5 , is about twice as large as the value indicated by the reproducibility o f the A F P N M R calibrations. The experiment was carried out with the 290 MeV proton beam from the T R I U M F cyclotron at a beam current o f 3-10 nA. Both the 3He(p, 2p) and (p, p n ) reactions were measured simultaneously in a two-arm coincidence setup to determine the directions and m o m e n t a of the scattered proton and the knock-on nucleon. Within the P W I A the nucleon m o m e n t u m in the nucleus before knock-out, q, can then be inferred from f o u r - m o m e n t u m conservation. The leading protons were detected to the left of the beam with the M e d i u m Resolution Spectrometer ( M R S ) at 01=27.5 ° for a range of energy transfers 5 0 < 0 ) = E - E ' < 120 MeV. Knock-on nucleons were detected to the right o f the beam in two arrays o f plastic scintillators positioned about 8 m from the target at angles 02 = 58 ° and 71 °, respectively. Each array with an active area of I m z consisted o f a 0.6 cm thick hodoscope followed by two 15 cm thick scintillator layers. The geometry was chosen to emphasize low mom e n t a o f the struck nucleons, i.e. Iql = 0 - 1 1 0 M e V / c for the 58: array and iql = 7 0 - 1 6 0 M e V / c for the 71 ° array. The 58 ° array was placed at the conjugate angle and thus the mapping o f (0), 02) events onto the I q l axis produces double valued observables versus Iql. The time-of-flight resolution of the proton hodoscope was not sufficient to cleanly resolve the d e u t e r i u m ground state from the d* spin singlet unbound state in the (p, 2p) reaction. For the results presented in the following we have s u m m e d over all events within a missing mass window of about 8 MeV width which encompasses both d and d* final states
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PHYSICS LETTERS B
in (p, 2p). This facilitates comparison with the PWIA calculations [ 12 ] which use the closure approximation for the A = 2 final states. Two sets of horizontal drift chambers between the target and the MRS provided tracking to the target with ~ 1 m m spatial resolution. Events originating from the interaction of the 2 m m wide achromatic beam with the 0.14 m m thick beam entry and exit windows were clearly separated from the 3He events of interest. A special cell filled with 2340 Torr of pure N2 was used to measure separately background from the small amount of N2 in the 3He cell. This background correction reduces the cross section by only about 4% because p-shell spectral functions in N2 are small at small q and because of limited overlap with the 3He missing mass window. The error contribution of the N2 background to the spin observables turned out to be negligible. For polarized beam and target, with both polarizations normal to the scattering plane the spin-dependent cross section can be written as 0 " = 6 0 ( 1 +A,,oP b +AonPt + A n n P b P t )
,
( 1)
where the subscripts (b, t) in A,o, Ao, and A~n refer to the direction of the projectile and target polarization [ 14 ] and Pb and P~ are the known polarizations of beam and target, respectively. Polarizations of the final state particles were not measured and corresponding subscripts have been omitted. Using the four spin combinations for beam and target, a completely determined system o f four equations is obtained. However, because of variations in the beam and target polarizations the data were subdivided and the resulting system of equations was solved by a leastsquares-fitting procedure. After applying corrections for energy loss, spectrometer acceptance, random coincidences, and background from N2 in the target, the differential spin-averaged cross sections oo for (p, 2p) have been used to extract [12] pp(q), the m o m e n t u m density distributions of protons in 3He using the P W I A (see fig. 2). Because of uncertainties in the acceptance of the two-arm setup the data contain an overall arbitrary normalization factor. Data and theoretical predictions using the Faddeev wavefunctions of Afnan and Birrell [ 15 ] are shown separately for the 02 = 58 ° and 71° arrays. The results on the shape Of pp(q) which are similar to those from (e, e ' p ) [16], and
30 January 1992
aHe(p,gp)
290 MeV
103 ~
1
~., 10 z
>
"~
"~ ~ 10'
-
1
10 ° 0
50
100 q (MeV/e)
150
200
Fig. 2. The momentum density distribution pp(q) versus the momentum of the struck proton. The experimental data have been multiplied by a single arbitrary normalization factor. The solid points are for the 58 ° array, the open squares are for the 71 ° array. Corresponding momentum distributions from Faddeev wavefunctions are indicated by solid and dashed lines, respectively.
more extensive at low q than previous (p, 2p) results [17] are consistent with the PWIA. Because of uncertainties in the neutron detection efficiencies of the scintillator arrays we have not attempted an extraction o f p . (q), the momentum density distribution for neutrons in 3He. The spin observables A,,o, Ann and Aon are shown in fig. 3 for both proton knockout (left panels) and neutron knockout (right panels). The errors include contributions from counting statistics and uncertainties in target and beam polarizations. The more conventional [ 2,4 ] beam-related asymmetries A,,o are in good agreement with the PWIA for both reactions as one might have expected for such a light few-nucleon target. At q = 0 A,,o assumes the on-shell free nucleonnucleon ( N N ) values. In contrast to this the "novel" spin observables which involve reversal of the target spin show significant deviations from the PWIA. These deviations are especially large for neutron knockout and Ao,, and least severe for proton knock~ out and A,,,,. Our data sample for the 3He(p, pn) reaction is only about 6% of that for the (p, 2p) reaction as a consequence o f the three times smaller neutron knockout probability and of the low neutron detection efficiencies [ ( 1 0 - 2 0 ) % at E , = 4 0 - 1 1 0 MeV]. Only the 58 ° array gave statistically significant results. No instrumental effect could be found 261
Volume 275, number 3,4 3He(p,2p)
PHYSICS LETTERS B
290 MeV
aHe(p,pn)
02Itttt <
290 MeV
DSS' (q) =
0.4
--
-0 2 ~
02f ~ ,
"
50
""
~
100
" 150
q (MeV/c)
i
200
_0"2[ 0
40
80
120
q (MeV/c)
Fig. 3. Beam-related asymmetries A,0 (top), spin correlation parameters A~, (middle), and target-related asymmetries Ao,, versus the momenta of the struck proton (left) and neutron (right). The data are for two directions of the struck nucleon (solid points: 58 ° array; open points: 71 ° array). The solid and dashed curves represent the corresponding PWIA calculations referred to in the main text.
to explain the quenching o f Ao,, and A,,, in (p, pn ). A new experiment [18] has recently been performed with nearly an order o f magnitude i m p r o v e m e n t in statistical accuracy, and at 220 MeV where A,,,, ( n p ) is a factor of two larger than at 290 MeV. Preliminary analysis has shown [18] that deviations from the P W I A in (p, p n ) are even more d r a m a t i c at the lower energy. The more accurate (p, 2p) data are much closer to the P W I A predictions, both at 290 MeV and 220 MeV [18]. The data for proton knockout show shifts of the Ao, data towards larger values, which are small for the 58 ° array but substantial for the 71 ° array. At nucleon m o m e n t a where data from both arrays overlap the results for the spin correlation parameters A,,,, agree both in shape and magnitude with the PWIA. More sophisticated reaction calculations which take rescattering effects into account will be required to decide whether this agreement is fortuitous, or whether it quantitatively reflects the effects o f spin m o m e n t u m distributions 262
g*~t-,,A(q,S')'gA-LA(q,S)
1 )final states
(2)
-0,2
~0.0
~ (A
0'0 f
0.0
30 January 1992
o f nucleons in the target, measured here for the first time. In this expression gA- ~,A(q, S) is the probability a m p l i t u d e for finding a nucleon in a plane wave state of m o m e n t u m q and spin S, and with the rest o f the nucleus in a state SA_ ~ and invariant mass a/IA_ ~. The P W l A calculations [12] use as input DSS'(q) from the Faddeev wavefunction for 3He [ 15 ] and the invariant NN amplitudes constructed from the SM86 phase shift solution [ 19 ]. F o r proton knockout A,,, is roughly three times more sensitive to D ss' (q) than Ao,. The measured A,,, values are much smaller than those for pp scattering ( A n , ( p p ) ~ 0.82) as would be expected for nearly antiparallel proton spins in 3He. F r o m F a d d e e v calculations, e.g. those o f Afnan and Birrell [ 15], it is expected that at q = 0 more protons have their spin opposite to the 3He spin than parallel to it, whereas protons with q ~ 90 M e V / c should be spin saturated, i.e. D :vs' is i n d e p e n d e n t of S ' . These features are seen in both the P W I A predictions for A , , and in the data. In the absence of calculations which take rescattering effects into account one may speculate why neutron knockout is so much more sensitive to rescattering effects than proton knockout. First, an initial reaction of the incident proton is three times more likely to occur with a proton in 3He, with the neutron subsequently originating from a secondary reaction of the knock-on proton. The target-related spin observable for this process is then characterized by the elementary pp rather than the pn amplitudes. A second difference consists in the fact that the residual final state in proton knockout is to approximately 75% d o m i n a t e d by the deuteron b o u n d state whereas in neutron knockout the residual final state is in a pure d i p r o t o n scattering state. Which o f these two effects is responsible for the present observations can be decided by future high resolution (p, 2p) experiments which separate d and d* final states, and by theoretical calculations which include final state interactions. In s u m m a r y we have shown that spin observables for nucleon knockout from 3He in quasieleastic kinematics may deviate from simple P W I A predictions. These deviations which are largest for neutron knockout and the target-related a s y m m e t r y Ao, are
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PHYSICS LETTERS B
a t t r i b u t e d to rescattering effects r a t h e r t h a n to d e v i a tions f r o m a c c e p t e d F a d d e e v w a v e f u n c t i o n s for 3He. T h e a g r e e m e n t o f Ann d a t a for p r o t o n k n o c k o u t with the P W I A i m p l i e s a first q u a l i t a t i v e o b s e r v a t i o n o f the effects o f n u c l e o n spin m o m e n t u m d i s t r i b u t i o n s in a p o l a r i z e d nucleus (A > 2) a l t h o u g h a q u a n t i t a tive i n t e r p r e t a t i o n will d e p e n d on future explicit calculations o f rescattering effects. F u r t h e r m o r e , o u r results suggest that it m i g h t be w o r t h w h i l e to investigate rescattering effects in i n c l u s i v e quasielastic e l e c t r o n scattering f r o m p o l a r i z e d 3He [9] w h i c h i n v o l v e a wide range o f m o m e n t a for the struck n u c l e o n . Analyses o f these i n c l u s i v e e x p e r i m e n t s w h i c h are a i m e d at e x t r a c t i n g e l e c t r o m a g n e t i c f o r m factors o f the neutron h a v e so far n e g l e c t e d h a d r o n i c final state interaction effects. T h i s w o r k was s u p p o r t e d by grants f r o m the N a t ural Sciences and E n g i n e e r i n g R e s e a r c h C o u n c i l o f Canada.
References [1 ] H. Tyrdn, P. Hillman and Th.A.J. Maris, Nucl. Phys. 7 (1958) 10.
30 January 1992
[2] P. Kitching, W.J. McDonald, Th.A.J. Maris and C.A.Z. Vasconcellos, in: Advances in nuclear physics, eds. J.W. Negele and E.W. Vogt, Vol. 15 (Plenum, New York, 1985 ) p. 43. [ 3] S. Frullani and J. Mougey, in: Advances in nuclear physics, eds. J.W. Negele and E.W. Vogt, Vol. 14 (Plenum, New York, 1984) p. 1. [4] C.A. Miller et al., Colloq. Phys. 51 (1990) C6-595. [5]T.E. Chupp et al., Phys. Rev. C 36 (1987) 2244, and references therein. [ 6 ] B. Larson et al., Phys. Rev. A 44 ( 1991 ) 3108. [ 7 ] J.L. Friar et al., Phys. Rev. C 42 ( 1991 ) 2310. [8 ] B. Blankleider and R.M. Woloshyn, Phys. Rev. C 29 (1984) 538. [9] C.E. Woodward et al., Phys. Rev. Lett. 65 (1990) 698; A.K. Thompson et al., preprint; and private communication. [10] R.M. Woloshyn, Nucl. Phys. A496 (1989) 749. [ 11 ] HERMES proposal for HERA (1990), unpublished; E142 proposal for SLAC (1990), unpublished. [ 12] A. Rahav et al., TRIUMF preprint; and to be published. [ ! 3 ] O. H/~usser, in: Spin and isospin in nuclear reactions, Proc. Telluride Conf., ed. S.W. Wissink (Plenum, New York, 1991 ). [14] G.G. Ohlsen, Rep. Prog. Phys. 35 (1972) 717. [ 15 ] I.R. Afnan and N.D. Birrell, Phys. Rev. C 16 (1977) 823. [ 16] E. Jans et al., Nucl. Phys. A 475 (1987) 687. [ 17] M.B. Epstein et al., Phys. Rev. C 32 (1985) 967. [ 18 ] E.J. Brash et al., TRIUMF experiment E616, to be published. [19] R.A. Arndt and L.D. Roper, Scattering analysis dial-in (SAID) program, unpublished. [ 20 ] O. H~usser, Colloq. Phys. 51 (1990) C6-99.
263
P H YS IC $ t_ET T ER $ B
Proton-induced nucleon knockout from polarized 3He at 290 MeV A. Rahav a O. H~iusser a,b C.A. Miller b, p.p.j. Delheij b W.P. Alford c, T.E. Chupp d K. Ferguson b, R.S. Henderson b, C.D.P. Levy b, K.P. Jackson b, j. Mildenberger a, B. Morrissette b, M.C. Vetterli b and R.M. Woloshyn b Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 b TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, Canada V6T 2.43 c University of Western Ontario, London, Ontario, Canada N6A 3K7 d Physics Laboratories, Harvard University, Cambridge, MA 02138, USA a
Received 11 November 1991
A novel polarized 3He gas target has been used to measure spin observables for (~, 2p) and (~, pn) nucleon knockout in quasielastic kinematics at 290 MeV. Comparisons with PWIA calculations show the importance of rescanering corrections, especially for neutron knockout and the target-related asymmetry Aon.The A,n (~, 2p ) results agree with the PWlA and qualitatively indicate the effects of spin momentum distributions of protons in 3He as predicted by Faddeev calculations.
Quasifree scattering from nuclei is one o f the most direct methods o f investigating single nucleon motion in the nucleus. Following the early (p, 2p) proton knockout experiments carried out at the 185 MeV synchrocyclotron in U p p s a l a [ 1 ] a large b o d y o f inf o r m a t i o n has been o b t a i n e d on binding energies, m o m e n t u m distributions and widths o f nucleons in individual nuclear shells both from proton [2] and electron [3] induced knockout reactions. In (~, 2p) reactions with polarized protons from spin-zero nuclei analyzing powers are observed which can be explained [2] by an effective polarization o f the knocked-out nucleon that is opposite for j = l + ½ and j = l - ½nucleons. The b e a m - r e l a t e d analyzing powers in proton knockout, e.g. from the ls~/2 inner shell in ~60 [4], are smaller c o m p a r e d to distorted wave impulse a p p r o x i m a t i o n ( D W I A ) calculations. This is an indication o f either a density-dependence o f the n u c l e o n - n u c l e o n interaction in the nuclear m e d i u m a n d / o r o f the i m p o r t a n c e o f multiple scattering effects. Quasielastic scattering from p o l a r i z e d nuclear targets adds a new d i m e n s i o n to the study of nucleon m o t i o n in nuclei. Target-related a s y m m e t r i e s d e p e n d on the spin orientation o f the knocked-out nucleon relative to that o f the target spin, and this can be in-
vestigated versus the nucleon m o m e n t u m . Previously, such information could only be inferred indirectly and incompletely from other observables, e.g. nuclear magnetic m o m e n t s or matrix elements in G a m o w - T e l l e r 13 decay. In this p a p e r we present the first observation o f target-related spin observables in h a d r o n - i n d u c e d nucleon knockout from a polarized nuclear target (A > 2). The experiment has become feasible because o f recent d r a m a t i c i m p r o v e m e n t s [5,6] in producing polarized 3He targets by optical p u m p i n g of Rb and R b - 3 H e spin-exchange collisions. H a d r o n i c and electroweak reactions with polarized 3He are o f great current interest because of the a p p r o x i m a t e alignment o f the spin o f the o d d neutron with that o f the 3He spin predicted by F a d deev calculations o f the 3He wavefunction [7]. Polarized 3He might thus be a target o f choice for determining fundamental properties o f the neutron, e.g. electromagnetic form factors [8,9] and spin structure functions [ 10,1 1 ]. However, the interpretation o f these experiments requires that spin effects arising from the full nucleonic wavefunction be taken into account [8,10] and, furthermore, that rescattering effects in the hadronic final state be investigated and understood. The present paper addresses both the
0370-2693/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
259
Volume 275, number 3,4
PHYSICS LETTERS B
questions of 3He structure and of hadronic rescattering effects. The experiment was carried out with the 290 MeV polarized proton beam from the T R I U M F cyclotron. A full description of the experiment, the data analysis, and the plane-wave impulse a p p r o x i m a t i o n ( P W I A ) calculations used for theoretical comparisons is given elsewhere [ 12 ]. The polarized 3He target setup developed at T R I U M F for target polarization normal to the scattering plane has been described by Larson et al. [6] and is shown schematically in fig. 1. The target used here consisted of an 8 cm long × 1.6 cm inner d i a m e t e r glass cell and was o f relatively low density, containing 3.16 standard atm o f 3He, 100 Tort of N2 quench gas, and a few mg o f Rb metal. An oven m a d e of the p o l y i m i d e VESPEL was at a temperature of 450 K to produce a Rb vapor density of ~ 4 × 10 ~4 cm 3. A b o u t 4 W o f circularly polarized photons of wavelength 2 = 795.7 nm were used to optically p u m p Rb via the DI line. The target assembly was in a vertical magnetic holding field IB o [ = 3 mT. The atomic polarization is transferred from Rb atoms to the 3He nucleus during R b - 3 H e collisions by the F e r m i contact hyperfine interaction. The bulk 3He polarization was reversed and analyzed using the technique o f adiabatic fast passage N M R ( A F P ) . The target cell was characterized by a wall
];
To aiR
Ar IA-t .J
::'/-
~
I,as(W
Fig. 1. Schematic layout of the polarized 3He target. For a detailed description see ref. [6]. 260
30 January 1992
relaxation rate F = (43 h) ~ and by a p u m p - u p rate of~9h '. At the beginning and end o f each ~ 3 h run N M R scans were taken to obtain the representative polarization. The m a x i m u m and average polarizations o f ~ 63% and 54%, respectively, differed because o f variations in laser power. Absolute normalization factors were obtained by comparing the 3He A F P signals with weak proton N M R signals from water-filled cells o f the same dimension. An independent check o f this m e t h o d which is sensitive only to 3He in the b e a m interaction region was obtained recently [ 13 ] from beam-related asymmetries for the 3He(p, ~+ )4He reaction. The a d o p t e d "safe" error for the absolute target polarization, A p , = 0 . 0 5 , is about twice as large as the value indicated by the reproducibility o f the A F P N M R calibrations. The experiment was carried out with the 290 MeV proton beam from the T R I U M F cyclotron at a beam current o f 3-10 nA. Both the 3He(p, 2p) and (p, p n ) reactions were measured simultaneously in a two-arm coincidence setup to determine the directions and m o m e n t a of the scattered proton and the knock-on nucleon. Within the P W I A the nucleon m o m e n t u m in the nucleus before knock-out, q, can then be inferred from f o u r - m o m e n t u m conservation. The leading protons were detected to the left of the beam with the M e d i u m Resolution Spectrometer ( M R S ) at 01=27.5 ° for a range of energy transfers 5 0 < 0 ) = E - E ' < 120 MeV. Knock-on nucleons were detected to the right o f the beam in two arrays o f plastic scintillators positioned about 8 m from the target at angles 02 = 58 ° and 71 °, respectively. Each array with an active area of I m z consisted o f a 0.6 cm thick hodoscope followed by two 15 cm thick scintillator layers. The geometry was chosen to emphasize low mom e n t a o f the struck nucleons, i.e. Iql = 0 - 1 1 0 M e V / c for the 58: array and iql = 7 0 - 1 6 0 M e V / c for the 71 ° array. The 58 ° array was placed at the conjugate angle and thus the mapping o f (0), 02) events onto the I q l axis produces double valued observables versus Iql. The time-of-flight resolution of the proton hodoscope was not sufficient to cleanly resolve the d e u t e r i u m ground state from the d* spin singlet unbound state in the (p, 2p) reaction. For the results presented in the following we have s u m m e d over all events within a missing mass window of about 8 MeV width which encompasses both d and d* final states
Volume 275, number 3,4
PHYSICS LETTERS B
in (p, 2p). This facilitates comparison with the PWIA calculations [ 12 ] which use the closure approximation for the A = 2 final states. Two sets of horizontal drift chambers between the target and the MRS provided tracking to the target with ~ 1 m m spatial resolution. Events originating from the interaction of the 2 m m wide achromatic beam with the 0.14 m m thick beam entry and exit windows were clearly separated from the 3He events of interest. A special cell filled with 2340 Torr of pure N2 was used to measure separately background from the small amount of N2 in the 3He cell. This background correction reduces the cross section by only about 4% because p-shell spectral functions in N2 are small at small q and because of limited overlap with the 3He missing mass window. The error contribution of the N2 background to the spin observables turned out to be negligible. For polarized beam and target, with both polarizations normal to the scattering plane the spin-dependent cross section can be written as 0 " = 6 0 ( 1 +A,,oP b +AonPt + A n n P b P t )
,
( 1)
where the subscripts (b, t) in A,o, Ao, and A~n refer to the direction of the projectile and target polarization [ 14 ] and Pb and P~ are the known polarizations of beam and target, respectively. Polarizations of the final state particles were not measured and corresponding subscripts have been omitted. Using the four spin combinations for beam and target, a completely determined system o f four equations is obtained. However, because of variations in the beam and target polarizations the data were subdivided and the resulting system of equations was solved by a leastsquares-fitting procedure. After applying corrections for energy loss, spectrometer acceptance, random coincidences, and background from N2 in the target, the differential spin-averaged cross sections oo for (p, 2p) have been used to extract [12] pp(q), the m o m e n t u m density distributions of protons in 3He using the P W I A (see fig. 2). Because of uncertainties in the acceptance of the two-arm setup the data contain an overall arbitrary normalization factor. Data and theoretical predictions using the Faddeev wavefunctions of Afnan and Birrell [ 15 ] are shown separately for the 02 = 58 ° and 71° arrays. The results on the shape Of pp(q) which are similar to those from (e, e ' p ) [16], and
30 January 1992
aHe(p,gp)
290 MeV
103 ~
1
~., 10 z
>
"~
"~ ~ 10'
-
1
10 ° 0
50
100 q (MeV/e)
150
200
Fig. 2. The momentum density distribution pp(q) versus the momentum of the struck proton. The experimental data have been multiplied by a single arbitrary normalization factor. The solid points are for the 58 ° array, the open squares are for the 71 ° array. Corresponding momentum distributions from Faddeev wavefunctions are indicated by solid and dashed lines, respectively.
more extensive at low q than previous (p, 2p) results [17] are consistent with the PWIA. Because of uncertainties in the neutron detection efficiencies of the scintillator arrays we have not attempted an extraction o f p . (q), the momentum density distribution for neutrons in 3He. The spin observables A,,o, Ann and Aon are shown in fig. 3 for both proton knockout (left panels) and neutron knockout (right panels). The errors include contributions from counting statistics and uncertainties in target and beam polarizations. The more conventional [ 2,4 ] beam-related asymmetries A,,o are in good agreement with the PWIA for both reactions as one might have expected for such a light few-nucleon target. At q = 0 A,,o assumes the on-shell free nucleonnucleon ( N N ) values. In contrast to this the "novel" spin observables which involve reversal of the target spin show significant deviations from the PWIA. These deviations are especially large for neutron knockout and Ao,, and least severe for proton knock~ out and A,,,,. Our data sample for the 3He(p, pn) reaction is only about 6% of that for the (p, 2p) reaction as a consequence o f the three times smaller neutron knockout probability and of the low neutron detection efficiencies [ ( 1 0 - 2 0 ) % at E , = 4 0 - 1 1 0 MeV]. Only the 58 ° array gave statistically significant results. No instrumental effect could be found 261
Volume 275, number 3,4 3He(p,2p)
PHYSICS LETTERS B
290 MeV
aHe(p,pn)
02Itttt <
290 MeV
DSS' (q) =
0.4
--
-0 2 ~
02f ~ ,
"
50
""
~
100
" 150
q (MeV/c)
i
200
_0"2[ 0
40
80
120
q (MeV/c)
Fig. 3. Beam-related asymmetries A,0 (top), spin correlation parameters A~, (middle), and target-related asymmetries Ao,, versus the momenta of the struck proton (left) and neutron (right). The data are for two directions of the struck nucleon (solid points: 58 ° array; open points: 71 ° array). The solid and dashed curves represent the corresponding PWIA calculations referred to in the main text.
to explain the quenching o f Ao,, and A,,, in (p, pn ). A new experiment [18] has recently been performed with nearly an order o f magnitude i m p r o v e m e n t in statistical accuracy, and at 220 MeV where A,,,, ( n p ) is a factor of two larger than at 290 MeV. Preliminary analysis has shown [18] that deviations from the P W I A in (p, p n ) are even more d r a m a t i c at the lower energy. The more accurate (p, 2p) data are much closer to the P W I A predictions, both at 290 MeV and 220 MeV [18]. The data for proton knockout show shifts of the Ao, data towards larger values, which are small for the 58 ° array but substantial for the 71 ° array. At nucleon m o m e n t a where data from both arrays overlap the results for the spin correlation parameters A,,,, agree both in shape and magnitude with the PWIA. More sophisticated reaction calculations which take rescattering effects into account will be required to decide whether this agreement is fortuitous, or whether it quantitatively reflects the effects o f spin m o m e n t u m distributions 262
g*~t-,,A(q,S')'gA-LA(q,S)
1 )final states
(2)
-0,2
~0.0
~ (A
0'0 f
0.0
30 January 1992
o f nucleons in the target, measured here for the first time. In this expression gA- ~,A(q, S) is the probability a m p l i t u d e for finding a nucleon in a plane wave state of m o m e n t u m q and spin S, and with the rest o f the nucleus in a state SA_ ~ and invariant mass a/IA_ ~. The P W l A calculations [12] use as input DSS'(q) from the Faddeev wavefunction for 3He [ 15 ] and the invariant NN amplitudes constructed from the SM86 phase shift solution [ 19 ]. F o r proton knockout A,,, is roughly three times more sensitive to D ss' (q) than Ao,. The measured A,,, values are much smaller than those for pp scattering ( A n , ( p p ) ~ 0.82) as would be expected for nearly antiparallel proton spins in 3He. F r o m F a d d e e v calculations, e.g. those o f Afnan and Birrell [ 15], it is expected that at q = 0 more protons have their spin opposite to the 3He spin than parallel to it, whereas protons with q ~ 90 M e V / c should be spin saturated, i.e. D :vs' is i n d e p e n d e n t of S ' . These features are seen in both the P W I A predictions for A , , and in the data. In the absence of calculations which take rescattering effects into account one may speculate why neutron knockout is so much more sensitive to rescattering effects than proton knockout. First, an initial reaction of the incident proton is three times more likely to occur with a proton in 3He, with the neutron subsequently originating from a secondary reaction of the knock-on proton. The target-related spin observable for this process is then characterized by the elementary pp rather than the pn amplitudes. A second difference consists in the fact that the residual final state in proton knockout is to approximately 75% d o m i n a t e d by the deuteron b o u n d state whereas in neutron knockout the residual final state is in a pure d i p r o t o n scattering state. Which o f these two effects is responsible for the present observations can be decided by future high resolution (p, 2p) experiments which separate d and d* final states, and by theoretical calculations which include final state interactions. In s u m m a r y we have shown that spin observables for nucleon knockout from 3He in quasieleastic kinematics may deviate from simple P W I A predictions. These deviations which are largest for neutron knockout and the target-related a s y m m e t r y Ao, are
Volume 275, number 3,4
PHYSICS LETTERS B
a t t r i b u t e d to rescattering effects r a t h e r t h a n to d e v i a tions f r o m a c c e p t e d F a d d e e v w a v e f u n c t i o n s for 3He. T h e a g r e e m e n t o f Ann d a t a for p r o t o n k n o c k o u t with the P W I A i m p l i e s a first q u a l i t a t i v e o b s e r v a t i o n o f the effects o f n u c l e o n spin m o m e n t u m d i s t r i b u t i o n s in a p o l a r i z e d nucleus (A > 2) a l t h o u g h a q u a n t i t a tive i n t e r p r e t a t i o n will d e p e n d on future explicit calculations o f rescattering effects. F u r t h e r m o r e , o u r results suggest that it m i g h t be w o r t h w h i l e to investigate rescattering effects in i n c l u s i v e quasielastic e l e c t r o n scattering f r o m p o l a r i z e d 3He [9] w h i c h i n v o l v e a wide range o f m o m e n t a for the struck n u c l e o n . Analyses o f these i n c l u s i v e e x p e r i m e n t s w h i c h are a i m e d at e x t r a c t i n g e l e c t r o m a g n e t i c f o r m factors o f the neutron h a v e so far n e g l e c t e d h a d r o n i c final state interaction effects. T h i s w o r k was s u p p o r t e d by grants f r o m the N a t ural Sciences and E n g i n e e r i n g R e s e a r c h C o u n c i l o f Canada.
References [1 ] H. Tyrdn, P. Hillman and Th.A.J. Maris, Nucl. Phys. 7 (1958) 10.
30 January 1992
[2] P. Kitching, W.J. McDonald, Th.A.J. Maris and C.A.Z. Vasconcellos, in: Advances in nuclear physics, eds. J.W. Negele and E.W. Vogt, Vol. 15 (Plenum, New York, 1985 ) p. 43. [ 3] S. Frullani and J. Mougey, in: Advances in nuclear physics, eds. J.W. Negele and E.W. Vogt, Vol. 14 (Plenum, New York, 1984) p. 1. [4] C.A. Miller et al., Colloq. Phys. 51 (1990) C6-595. [5]T.E. Chupp et al., Phys. Rev. C 36 (1987) 2244, and references therein. [ 6 ] B. Larson et al., Phys. Rev. A 44 ( 1991 ) 3108. [ 7 ] J.L. Friar et al., Phys. Rev. C 42 ( 1991 ) 2310. [8 ] B. Blankleider and R.M. Woloshyn, Phys. Rev. C 29 (1984) 538. [9] C.E. Woodward et al., Phys. Rev. Lett. 65 (1990) 698; A.K. Thompson et al., preprint; and private communication. [10] R.M. Woloshyn, Nucl. Phys. A496 (1989) 749. [ 11 ] HERMES proposal for HERA (1990), unpublished; E142 proposal for SLAC (1990), unpublished. [ 12] A. Rahav et al., TRIUMF preprint; and to be published. [ ! 3 ] O. H/~usser, in: Spin and isospin in nuclear reactions, Proc. Telluride Conf., ed. S.W. Wissink (Plenum, New York, 1991 ). [14] G.G. Ohlsen, Rep. Prog. Phys. 35 (1972) 717. [ 15 ] I.R. Afnan and N.D. Birrell, Phys. Rev. C 16 (1977) 823. [ 16] E. Jans et al., Nucl. Phys. A 475 (1987) 687. [ 17] M.B. Epstein et al., Phys. Rev. C 32 (1985) 967. [ 18 ] E.J. Brash et al., TRIUMF experiment E616, to be published. [19] R.A. Arndt and L.D. Roper, Scattering analysis dial-in (SAID) program, unpublished. [ 20 ] O. H~usser, Colloq. Phys. 51 (1990) C6-99.
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