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TransferDownload »This full account of the partition of India and the transfer of power from England begins with the outbreak of war in 1939 and ends with the transfer itself in 1947. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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11 May 1995
PHYSICS
LETTERS
B
Physics Letters B 350 (1995) 178-183
Measurement of polarization transfer KOand tensor analyzing power TAO in the backward elastic dp scattering V. Punjabi b, R. Abegg g, S. Belostotsky e, M. Boivin d, A. Boudard f, E. Cheung a, V. Ladygin ‘, J. Oha, L. PenchevC, N. PiskunovC, CF. Perdrisat a, I. SitnikC, E.A. Strokovsky ‘, E. Tomasi-Gustafsson d, V. Vikhrove, J. Yonnet d, A. Zghiche d a College of William and Mary, Williamsburg. USA b Norfolk State University, Norfolk, VA, USA c
Laboratoryfor High Energy, JINR, Dubna, Russia d Laboratoire National Sahwne, Saclay, France e Institute for Nuclear Physics, Gatchina, Russia f DAPNIA, Saclay, France g TRIUME Vancouver Canada
Received 3 January 1995; revised manuscript received 28 February 1995 Editor: J.P. Schiffer
Abstract The polarization transfer K~ and the tensor analyzing power TZOfor the ’ H( 2, p) d reaction have been measured up to an internal momentum of k = 0.58 GeV/c. Comparison of the same observables obtained in recent studies for ’ H(&p)X reaction, as a function of k, show different behavior. However the data from these two reactions are almost identical when compared in & versus ~~ correlation plots. We discuss similarities and differences observed in the two reactions.
The deuteron continues to be the object of intense experimental and theoretical work, with the goal of characterizing its structure at sub-nucleonic distances. Because it is the simplest nucleus in nature, these investigations of the deuteron should provide the litmus test of our understanding of the transition from the traditional nuclear picture of “nucleons and mesons” to the more fundamental “quarks and gluons” picture. As the Impulse Approximation (IA) is the first tool available to extract nuclear structure information from medium or high energy scattering data, tests of the validity of this approximation in the domain in which it is used are important. Yet only few detailed studies of the range of application of the IA for hadronic
0370-2693/95/$09.50 @ 1995 Elsevier Science B.V. All rights reserved SSDI 0370-2693( 95)00344-4
reactions are known. Here we present new polarization data [ 1] for backward elastic dp scattering and compare them with previously published data for the 0” inclusive breakup of 2.1 GeV deuteron on hydrogen by Punjabi et al. [2] and Cheung et al. [3]. The one nucleon exchange (ONE) graph for backward elastic scattering and the IA graph for inclusive deuteron breakup shown in Fig. 1 indicate that these two processes are closely related; however higher order processes including multiple scattering, meson exchange and production, will affect the two reactions differently because one is elastic and excludes pions in the final state, and the other is inclusive. Kobuskin [ 41 was first to show that these
V. Punjabi et al./Physics Letters B 350 (1995) 178-183
1
Tzo = JZ
&&w-w2 u2 + w2
t-----l: Fig. 1. Feynman diagrams for backward elastic scattering in the ONE approximation at the top, and for inclusive breakup in the IA at the bottom.
reactions are indeed related; he was able to reproduce both inclusive breakup [5] and backward elastic dp [ 61 cross section data with a single empirical momentum density, the common variable being an internal momentum. That the backward elastic dp and inclusive breakup reactions are closely related is obvious on the basis of phase space also. The maximum proton energy, or kinematical limit, of deuteron breakup on hydrogen (also called the breakup threshold) corresponds to zero relative energy between the outgoing neutron and proton; backward elastic scattering occurs just beyond the breakup kinematical limit, when the neutron and proton fuse together to form a deuteron. Hence forward inclusive breakup becomes progressively “backward elastic” as one nears the kinematical limit; the d 4 np transition at threshold is mostly to the ‘So continuum state (also called d*) but no cross section enhancement has ever been observed in backward elastic pd (for a search of this enhancement see for example by Bennett et al. [ 71). No enhancement was observed in the present experiment either. Vasan [ 81 was the first to show that in ONE the tensor analyzing power, Tzc, for backward elastic scattering is directly related to the deuteron S and D momentum space wave function components, u and w. A similar argument led Wtlkin [ 91 to derive in IA an identical formula for deuteron breakup. One can show that for the polarization transfer, ~0, again for purely vector polarized deuterons, there is a simple connection to u and w, and that the formula for backward elastic and for 0” inclusive breakup are the same; these relations are as follows:
,
(1)
1
$-w2_
Ko =
179
-Jiuw
u2 + w2
(2)
If one eliminates u and w from the two expressions above, one obtains the equation of a circle, as was shown recently by Kuehn et al. [ lo] : (T20+-
K;=i
2 2>)
+
For 0” inclusive breakup, detecting forward protons with momentum larger than half the beam momentum, selects processes in which this proton is a “spectator” of the reaction in the IA sense. The spectator assumption is supported by the approximate target and energy independence of invariant cross section (ICS), T2n and KO in A( d,p) X at 0”. The corresponding data are in Ableev et al. [5], Anderson et al. [ 1 I] and [ 21 for ICS; for T2c they are in [2] and Ableev et al. [ 121, and for KO in [ 31, Nomofilov et al. [ 131 and Kuehn et al. [ 141. Demonstration of energy independence requires use of an internal momentum variable. We will use the Infinite Momentum Frame (IMF) variable k, first introduced by Weinberg [ 151, for both reactions:
(4) where EP + PII ff=G
(5)
where Ep and PII are energy and longitudinal momentum of the proton and Ed and pd are beam deuteron energy and momentum; m is the mass of the nucleon. Although the Feynman diagrams in Fig. 1, are similar for the two reactions, the experimental kinematical conditions are different. In inclusive breakup the initial deuteron momentum Pd is constant, the detected proton momentum is varied from pd/2 to the kinematical limit, corresponding to k = 0 and maximum k, respectively. In backward elastic scattering the 2-body constrain forces one to change the initial deuteron momentum for each k-value; k = 0 requires & = 0, and is not measurable. Both similarities and differences between the two reactions justify the expectation that a
180
V. Punjabi et al. /Physics
comparison of corresponding observables will provide a sensitive test of the reaction mechanism. Together, these two reaction offer a unique opportunity to map the deuteron wave function to large internal momenta, and therefore small distances. The polarization transfer ratio, ~0, for the dp backward elastic scattering has been measured for the first time. These data were obtained at the synchrotron SATURNE using its vector polarized deuteron beam. The transfer ratio is KO = P,/Pd, where P, is the vector polarization of the final proton and Pd that of the initial deuteron. In the same experiment we have also re-measured the tensor analyzing power Tza using the tensor polarized deuteron beam; Tza was measured earlier, in 1982, by Arvieux et al. [ 161. The T20 and KO data for this experiment were obtained at deuteron energies between 0.3 and 2.34 GeV. The polarized deuteron beam was directed onto a liquid hydrogen target of either 10 cm or 4 cm thickness. Measurements with empty target were made at several energies to estimate the contribution from the walls of the target; the relative rates with an empty target were negligibly small. The high energy protons were detected in the magnetic spectrometer SPES IV at a constant laboratory angle of 1.7”; the corresponding center-of-mass scattering angle vary from 175.0” at 2.34 GeV to 176.4’ at 0.3 GeV. Four collimator apertures were available; 10 mm, 15 mm, 34 mm diameter and 55 x 55 mm’. The deuteron beam intensity varied from 2.0 x 10” to 1.8 x IO”. The beam intensity, target thickness and collimator were selected at each beam energy to optimize the count rates. In the configuration used, SPES IV has a twelve scintillator hodoscope in the intermediate focal plane and a thirteen scintillator hodoscope in the final focal plane with a 16 m time-of-flight basis which can be used for particle identification, Further details on the spectrometer can be found in Grorud et al. [ 171. At each deuteron beam energy the proton was selected by SPES IV, and its polarization was measured in the polarimeter POMME located near the final focal plane of SPES IV. This polarimeter contained six multi-wire proportional chambers, each providing an X and a Y coordinate. A carbon target of 3 1.2 cm thickness located between the third and the fourth chamber served as polarization analyzer. The chambers provide position information with a resolution of 1.6 mm (FWHM) in front, and 3.2 mm (FWHM) in
Letters B 350 (1995) 178-183
the back of the analyzer. More detailed information about POMME can be found in Bonin et al. [ 181. POMME was calibrated for the first time in 1988 at energies between 0.2 and 1.2 GeV as described in [ 181. It was calibrated at higher proton energies in 1990 at 1.6 and 1.8 GeV, and again in 1992 at 1.05, 1.35, 2.0, 2.24 and 2.4 GeV. All higher energy calibrations have been fitted between 0.8 and 2.4 GeV [ 191; these calibrations are used here to extract the polarization transfer ratio KO for Td 2 1 GeV. Below 1 GeV the 16-parameter fit of McNaughton et al [ 201 was used. The tensor and vector polarizations of the deuteron beam were measured in a low energy polarimeter located in the injector line, as described by Arvieux et al. [ 2 I] where it was also shown that the deuteron beam does not depolarize during acceleration in SATURNE up to 2.3 GeV. The beam polarization was measured every 24 hours during the experiment; the typical values were P, = 0.910 f 0.006 (f0.026) and P, = 0.620 f 0.006 (f0.020)) where the first uncertainty is statistical, the second is systematic and due mostly to the uncertainty in absolute calibration of the low energy polarimeter [ 2 11. Both for the T2e and the KO measurements, elastic events were selected by applying software cuts in the reconstructed missing mass and in the scattering angle at the target. The missing mass resolution was typically 1.O x 10m3 GeV ( la). In addition, checks were made at 1.2 and 1.6 GeV beam energy by detecting the deuteron instead of the proton; the T2a results were statistically compatible. In general the deuteron detection leads to larger statistical uncertainties because of the unfavorable center-of-mass to lab Jacobian, and the large energy losses in the target. The results for T2a and KO are tabulated in Table 1; the uncertainties for T2o are statistical only. For KO we give the statistical and the systematic errors, the latter from the analyzing power calibration. In addition there is a 3% relative systematic uncertainty for TAO,and a 4% relative uncertainty for KO due to the beam polarization uncertainties. In Fig. 2 we show Tzc versus the internal momentum k for backward elastic scattering (closed circles, this work) and inclusive breakup (open circles) from [ 21. It can be seen that for elastic data, T2a goes through a first minimum near k = 0.25 GeV/c. The IA curve shown in the figure has a similar minimum at this k value; this first structure is thus the result of the interference of the S- and D-
V. Punjabi et al. / Physics Letters B 350 (1995) 178-183
Table 1 T2u and ~0 results of this experiment
(GeV)
k (GeV/c)
0.300 0.400 0.500 0.550 0.600 0.700 0.800 0.900 1.000 1.100 1.200 1.300 I.400 1.500 1.600 1.800 2.100 2.338
0.194 0.226 0.254 0.267 0.280 0.304 0.327 0.348 0.363 0.388 0.406 0.424 0.441 0.458 0.474 0.498 0.549 0.582
Td
Tm
dTz0
-0.482 -0.700 -0.841 -0.833 -0.836 -0.699 -0.585 -0.538 -0.494 -0.507 -0.576 -0.557 -0.537 -0.563 -0.479 -0.383 -0.258 -0.235
stat.
duo syst.
0.018 0.016 0.030
0.018 0.014 0.006
-0.173 -0.327 -0.283
0.03 1 0.028 0.029
0.004 0.007 0.006
-0.389 -0.358 -0.440 -0.484 -0.407 -0.544 -0.446 -0.437 -0.342 -0.227
0.026 0.038 0.025 0.042 0.042 0.034 0.049 0.027 0.034 0.074
0.006 0.007 0.008 0.010 0.010 0.016 0.013 0.01 I 0.009 0.008
dKo
KO
0.023 0.015 0.022 0.014 0.015 0.014 0.014 0.011 0.008 0.008 0.011 0.015 0.014 0.013 0.019 0.012 0.018 0.016
0.910 0.702 0.287
0.0
R b -0.5
-1.0
I
0.0
0.1
I
I
I
0.2
k in
1,
0.3
I
0.4
I
I
0.5
0.6
GeV/c
Fig. 2. Tm versus k; (0) for backward elastic dp and (9) for inclusive breakup. Solid curve is IA using Paris deuteron wave function; straight line is asymptotic prediction [24].
I-
-1.2
0.0
’ 0.1
0.2
k in Pig. 3.
KO
versus k. Symbols
0.3
0.4
0.5
0.6
GeV/c and curves as in Fig. 2.
state in the deuteron. This structure has been observed earlier in [ 161, as was the second structure near k = 0.40 GeV/c; the latter is in the baryonic excitation region and is not understood so far. To explain the second minimum, Boudard and Dillig [ 221, and Nakamura and Satta [ 231 added the one-pion exchange diagram to ONE. Neither calculation succeeded to reproduce the second minimum in T2a. Although the value of T2a in [ 161 are systematically more negative than in the present experiment, both experiments are in general agreement. It is also observed in Fig. 2 that the behavior of TZOis very different for the two reactions past k = 0.25 GeV/c. Shown as a solid line at -0.3 is an asymptotic limit predicted by Kobushkin [ 247 in a QCD-motivated model. The results for KO are shown in Fig. 3 versus k for both reactions ’ . The backward elastic data show the same general trend as the inclusive data up to k = 0.3 GeV/c, and both do not differ greatly from IA shown as a solid curve. Again an asymptotic prediction at 1.06 is shown as a straight line [ 241. Together, the T2a and the KO data show that k is also a good scaling variable for polarization observables in these ’ The inclusive dam is from a reanalysis twice as many momentum bins.
of the data of
[ 3 1, with
K Punjabi et al. /Physics
182
0.5
0.0
WE
-0.5 1 -1.0
-1.5 1a -2.0
1
-1.5
I
I
I
I
I
-1.0
-0.5
0.0
0.5
1.0
1.5
Ice Fig. 4. q prediction,
versus Tan; symbols from Eq. (3).
Letters B 350 (1995) 178-183
relation plot over the whole kinematic range covered, even though their individual behavior (especially T2a as seen in Fig. 2) are very different. However the inclusive breakup data do not follow the IA circle past k = 0.15 GeV/c (the lowest k-value for the backward elastic is 0.19 GeV/c) : the systematic deviation from the IA is due to either final state interaction, or to the presence of additional components in the deuteron wave function; in the latter case relation (3) is not valid. The almost identical correlation for the two reactions suggests that an intrinsic property of the deuteron structure remains visible up to k = OS-O.6 GeV/c or M 0.4 fm. Full exploitation of this finding will have to await additional experimental characterization as well as theoretical work.
as in Fig. 2. The circle is the IA
two reactions. As demonstrated in Eq. (3), the IA predicts that the KO-T~Ocorrelation forms a circle of radius 3/&, for inclusive breakup and backward elastic scattering. The data for both reactions are shown in a KO-TZJ correlation plot in Fig. 4 2 . Each measurement is simply represented by a point corresponding to one KO-T~O pair, without reference to any kinematical condition (like beam energy and (or) proton energy). The data points shown in Fig. 4 are not on the IA circle, yet they reveal the existence of an almost identical correlation for both reactions, supporting the premise that these reactions are closely related. To conclude, we have discussed the results of the T.0 and KO data for both backward elastic and inclusive breakup, over a range of internal momenta reaching 0.58 GeVfc. For backward scattering, T20 does not agree with the ONE prediction anywhere but KO follows ONE up to 0.3 GeV/c. A different picture emerges for inclusive scattering: here T2o follows the IA prediction up to 0.15 GeVlc, and KO up to 0.3 GeVf c. Above 0.3 GeVf c the data for both reactions show a significant and different deviation from ONE or IA; this behavior is of course expected as the distances probed here are 5 0.7 fm, i.e. smaller than the nucleon size. The striking feature of these data is that they give the same signature in the KO-T& cor2 The inclusive Tao data shown was obtained from the data of 12 I for the k-values of the ~0 data by interpolation.
We are grateful to the staff at SATURNE, Saclay for providing excellent conditions for this experiment and for technical help from IPN, Orsay. This work has been supported in part by the US National Science Foundation (PHY91-I 1942)) the US Dept. of Energy (DE-FG05-89ER40525), by Russian Foundation for Fundamental Research (93-02-3961) and by Moscow Inter-regional Electronic Bourse (MEB). We are also pleased to acknowledge the help of Dr. M. Jones and are thankful for useful discussions with Prof. A. Kobushkin. References [ I] V. Punjabi et al., in: 14th international IUPAP conference on
(21 [3] [4] ]S] [6] [7] [8] [ 91
[ IO]
[ 1I ] [ 121
Few Body Problems in Physics (Williamsburg, June 1994). ed. by E Gross (1994) p. 161. V. Punjabi et al., Phys. Rev. C 39 (1989) 608. E. Cheung et al., Phys. Len. B 284 (1992) 210; Ph.D. thesis, College of William and Mary ( 1994), unpublished. A.P Kobushkin, J. Phys. G: Nucl. Phys. 12 (1986) 487. V.G. Ableev et al., Nucl. Phys. A 393 (1983) 491; JINR Rapid Comm. 1[ 521-92 (1992) 10. P Berthet et al., J. Phys. G: Nucl. Phys. 8 (1982) Llll. G.W. Bennett et al., Phys. Rev. Lett. 19 (1967) 387. S.S. Vasan, Phys. Rev. D 8 (1973) 4092. C. Wilkin. Proc. Joumees d’etudes Satume (Roscoff, May 1979). ed. by M. Bordy, p. 47. B. Kuehn, CF. Perdrisat and E.A. Strokovsky, in: International Symposium “Dubna Deuteron-93” (Dubna, September 1993), unpublished; JINR, Dubna preprint El95-7 ( 1995). L. Anderson et al., Phys. Rev. C 28 (1983) 1224. V.G. Ableev et al., Pis’ma Zh. Eksp. Theor. Fiz. 49 ( 1988) 558; JINR Rapid. Comm. 4[43]-90 (1990) 5.
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[20] M.W. McNaughton et al., Nucl. Instr. and Meth. A 241 (1985) 435. [21] J. Arvieux et al., Nucl. [email protected] and Meth. A 273 (1988) 48. [22] A. Boudard and M. Dillig, Phys. Rev. C 31 (1985) 302. [23] A. Nakamura and L. Satta, Nucl. Phys. A 445 (1985) 706. [24] AR Kobushkin, J. Phys. G: Nucl. Part. Phys. 19 (1993) 1993.