Seibt, E.

Weddigen, C.

Weigele, K.

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August 1968Institut für Experimentelle KernphysikDouble Scattering of 51 MeV Deuterons on CarbonE. Seibt, Ch. Weddigen, K. WeigeleKFI~ 1006August 1968KERNFORSCHUNGSZENTRUM KARLSRUHEKFK 1006Institut für Experimentelle KernphysikDouble Scattering of 51 MeV Deuterons on CarbonE. Seibt, Ch. Weddigen und K. WeigeleGesellschaft für Kernforschung m.b.H KarlsruheAbstract:Double scattering of 51 MeV deuterons on carbon shows strongvectör polarization effects. Tensor polarization effects arefound to be small. Optical model predictions by SATCHLER couldbe confirmed qualitatively. Quantitatively, there are significantdiscrepancies.This report has been published in Phys.Letters 27 B (1968)567 in part.- 1 -Double scattering experiments with deuterons are less nPfuerousthan those with spin=1/2 particles. Due to additional tensorpolarization effects intensities must be determined not onlyat azimuthangles 0 = 0 and n, but at n/2 (and or 3n/2) also.Thisrequires axial symmetry of the secondary beam with re-11spect to the intensity and to the beam dilergence, which isdifficult to achieve with the necessary precision.The interpretation of deuteron double scattering experiments[1] in thelow energy region is difficult because o~ possiblecompound nucleus contributions. The two early double scatter-ing experiments [2] at high energies suffer from a lack ofenergy resolution~ The present double scattering experimentperformed at the Karlsruhe isochronous cyclotron uses ener-gies where compound nucleus contributions should be smalland where separation of elastic from inelastic scattering isstill possible with plastic scintillators. No deuteron pola-rization data for this enerß7 region are available so fareIn order to get information on the spin dependent terms ofthe optical model we performed double scattering experimentsfor deuteron scattering on carbon with a primary deuteronenergy of 51.5 MeV. The experimental setup [3] uses a firstscattering chamber, a quadrupole triplet focusses the scattereddeuterons into another scattering chamber. This chamber can15e rota ted around the axis of symmetry of the secondary beam.A circular diaphragm in front of the second target providesaxial symmetry in intensity on the second scatterer. Axialsymmetry in divergence is monitored by two counters positioneddirectly in the secondary beam and fixed to the rotating scat-tering chamber. The parameters A and B of azimuthai asymmetry,defined by N.fV 1 + Acos0 + Bcos20, are taken for two symmetri-cally located counter telescopes as weIl as for the monitorsmentioned above. The asymmetries in the telescopes were foundtodepend linearlyon the asymmetries in the monitors. Linearinterpolation of the 'telescope asymmetries to zero monitorasymmetries results in the experimental azimuthai asymmetry- 2 -due to spin dependent components of the nuclear interaction.Theexperimental setup was tested with double scattering of100 MeV ~-particles. The resultant effective deviations fromideal symmetry were found to be EA = 0.015 ~ 0.014° for Aand EB = 0.010 ~ 0.0090 for B. The corresponding systematicerrors to be expected for deuteron scattering areA dlncr cuA,B = dQ ~A,B, (1 )where dis the differential scattering cross section and 0the. polar angle for the second scattering.Measurements extended over several months. An overall X2test yielding X2 = 271.4 for 274 degrees of freedom shows theconsistency of the results.The asymmetry parameters A and B depend on the deuteron ener-gies E1 and E2 and on the polar scattering angles Q1 and Q2in the GM-system for the first end the second scattering,respectively. The first scattering acts as apolarizer, thesecond one as an analyzer. Using the notation of LAKIN [4],the asymmetry parameters A and Bare given byA =2«iT11 )1 (iT11 )2 - (T21 )1 (T21 )2)1 + (T20 )1 (T20)2, (2)B =2(T22)1 (T22)21 + (T20)1 (T20 )2•Rere, the tensor components Tjk with subscript 1 and 2 descri-be the spin orientation in the laboratory system created bythe first scattering and by the time reversed second scatter-ing for unpolarized incident particles, respectively.- 3 -During each experiment for a fixed primary angle Q1 the azi-muthai asymmetries A and Bare measured as a function of 02.In two eXl>eriments, significant polarization effects were ob-served.For the first experiment, 01 was chosen near a pronounced in-terference minimum in the differential cross section (Fig. 1).The resulting azimuthai asymmetries as a function cf 02 areshown in Fig. 2. At G2~Q1' a positive value of A was ob-tained. For this secondary angle, B is zero within statistics.A negative maximum in A was found at Q2 = 57.6°.Fer the primaryangle of the first experiment the polarizationwas expected to vary rapidly with angle and energy. This wasnot the case with the angular region of the observed negativeminimum. Hence, a second experiment at G1 = 57.60 was perform-ed (Fig. 3). Under this primary angle, a pronouneed maximum inA appears at Q2 =430 • As to B, the largest deviation fromzero (-0.030 :!: 0.008) is found in a region of maximum slopedlnC1/dQ at about 230 • Here, aeeording to (1), instrumentalaSYmmetries reach ~B = - 0.015 ~ 0.014. So, within statisties,ourresults in B are not ineonsistent with a vanishing differ-enee between the experimental points and the expected instru-mental asymmetries.The tensor comp_onents T-,,- in (2) for elastie seatterinrr ofJK: • - . .....51.5 MeV deuterons on carbon have been caleulated by SATCHLER[5]. He analyzed the differential cross section data measuredby SCHMIDT-ROHR et ale [6] and BR1tCKl1ANU et ale (7) using anoptieal potential [8] with a Saxon-Wood-type real central term,a Thomas-type imaginary eentral term, and areal Thomas-typeLS term. A search routine applied to the data for scatteringangles bet'\>leen 15 and 1600 yielded the model parameters. Someof the resultant optieal model parameter sets are given inTable I. A good fit was obtained even without any spin dependantterm. All these parameter sets give nearly the same fit shownin Fig. 1.- 4 -The azimuthaI asymmetries Apredicted by the correspondingpotentials in Table I are shown in Figs. 2 and 3 also. On-ly for potential 1 the energy dependence of polarizationhas been taken into account (curves 1e). A comparison withour results shows qualitative agreement in A. However, asignificant difference in magnitude is observed for 01 = 57.6°and 02 = 43°. This discrepancy coincides with a small devi-ation cf the fit from the experimental differential crosssection in Fig. 1.For a first interpretation of our results we neglect theenergy dependence of the expansion coefficient Tjk in (2).As to B,theexperimental values for 02~ 01 = 22.8 and57.6° give statistical upper limits for T22 with IT221<O.07in both cases. This upper limit is not inconsistent withthe resul ts of SCH\.fANDT and HAEBERLI [9], who have shown theneed for a tensor term in the optical potential to describeelastic scattering of polarized deuterons below 12 MeV .. Themaximum value for °< 600 predicted by the potentials ofTable I is T22 = - 0.005 (pot. 2 at 220 ).Neglecting tensor componentsT2k also, according to (2) theabsolute value of iT11 can be calculated for 01 = G2 = 57.6°.This yields ascale factor of +2.41 to be applied to the Ascale of Fig. 3. Thus, one obtains iT11 as a function of Q2.The sign of the scale factor was chosen in order to get con-sistence with the calculated iT11 values in angular regions,where agreement between predicted asymmetries and experimentwas .faund. Under these assumpt'ions ans obtains 8" maximum ans ..lyzing power (iT11 )2=-O.448 ± 0.050 (Basle convention) at02 = 430 for E2 = 41 MeV. This is 75% of the absolute maxi-mum value compatible with vanishing tensor components T2k•Underthese conditions, carbon seems to be a good analyzerfor deuteron vector polarization with an extrapolated differ-ential cross section of about40 mb/sterad.- 5 -Taking into account the calculated energy dependence of iT11for ° = 57.60 the scale factor ment ioned above would become+1.64. In this case one gets a mean value of Vs=7.3 .:!: 0.8 MeV.for the LS term. This value was obtained by comparing the ex-pected asymmetries for potential 1 and 3 (Table I) with theexperimental value of A at 01 = 02 = 57.60 • The indicatederror contains statistics, uncertainty in the radial depen-dence of the LS term, and the uncertainty in T2k•Absolute calibration and energy dependence of iT11 areunderinvestigation.We would like tothankthe cyclotron group for their effortsto obtain an intense external beam from the Karlsruhe cyclo-tron. We especially appreciate the most valu,able theoreticalsupport by Professor R. Satchler.- 6 -References:[1] L.V. Gustova, Yu. A. Nemilov, and L.A. Pobedonostsev -JETP 44(1963)44-Yu. A. Nemilov and L.A. Pobedonostsev - JETP 45(1963)76E.M. Bernstein, G.C. Ohlsen, V.S. Starkovich, and W.G. Simon -Phys.Rev.Letters 18(1967)966N.I. Zaiks, Yu.V. Kibkalo, A.V. Mokhnach, O.F. Nemets,P.L. Shmarin, and A.:M. Yasnogorodsky - Jadernja Fizika7(1968)754[2] J. Baldwin, O. Chamberlain, E. Segre, R. Tripp, C. Wiegand,and T. Ypsilantis - Phys.Rev. 103(1956)1502J. Button end R. Mermod -Phys.Rev. 118(1960)1333[3] E. Seibt, Ch. Weddigen, and K. Weigele - to be published[4] W. Lakin - Phys.Rev. 98(1955)139[5] R. Satchler - private communication[6] U. Schmidt-Rohr - private communication[7] H. Brückmann - private communication[8] R. Satchler - Nucl. Physics 85(1966)273[9] P. Schwandt and W. Haeberli - Nucl.Physics A110(1968)585- 7 -Captions ofFigures:Figure 1:Figure 2:Figure 3:Table I:Differential cross section for elastic deuteronscattering on carbon at 51. 5 MeV. Experimental da-ta [6] and optical model fit [5].Parameters A and B for the azimuthaI asymmetry,def'ined by N-1 + Acos0 + Bcos20, as a f'unctionof the polar angle Q2 for the second scattering andfor Q1 = 22.8°. The curves are optical model pre-dictions deduced from the corresponding potentialsin Table I.°As figure 2, but for Q1 = 57.6 •Optical model parameter sets obtained by SATCHLER [5]to fit the differential cross section [6], [7] forelastic deuteron scattering on carbon at 51.5 MeV,in thenotation of [8]. Z2 relates to 66 degrees offreedom.Pot.No. V r o ao 4Wd r' .... a' Vs r s as O"R %21 86.0 1.024 0.766 33.0 1.343 0.757 4.16 r o ao 790 472 n n .. n u 11".., f'\ I:.I V.,/3 91 .. 8 0.965 0 .. 807 34- .. 3 1.374 0.732 6.76 r o ao 787 5482.9 1.059 0.740 32.3 1.297 0.802 0 800 55-8-0>0CO(J)~C'J~Lnu11CD-clLJ.-0N(.0~U~-0.-..---0(J)'--"NL.......::JU0Cl'-'t--tL0.2A0.1- 9 -dC12Cfc12d8 1CM =22,8°E1=51 MeV E2=47.5MeVFigure 2A0.1-0,1- 10 -dC12 erC12 d6 1CM =57.6°E1=51MeV E2=41MeV0.~51 I ·1- O.051'----~'=-----L_--L_----L-_~I_I20 40 8 2CM 60°Figure 3

Double-scattering of 51 MeV deuterons on carbon

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Double-scattering of 51 MeV deuterons on carbon

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