Fetscher, W.

Sattler, K.

Schmeing, N.C.

Seibt, E.

Staudt, R.

Weddingen, Ch.

Weigele, K.

English

Schmeing, N. C.

KITopen

Januar 1971Institut für Experimentelle KernphysikKFK 1357Differential Cross Section and Vector Polarization for theElastic Scattering of 41 to 51 MeV Deuterons on CarbonW. Fetscher, K. Sattler, N. C. Schmeing, E. Seibt, R. Staudt,Ch. Weddigen, K. WeigeleJanuar 1971KERNFORSCHUNGS ZENTRUM KARLSRUHEInstitut für Experimentelle KernphysikKFK 1357Differential Cross Section and Vector Polarization for the+Elastic Scattering of 41 to 51 MeV Deuterons on CarbonW. Fetscher, K. Sattler, N.C. Schmeing, E. Seibt, R. Staudt,Ch. Weddigen, and K. WeigeleGesellschaft für Kernforschung m.b.H. Karlsruhe+ Presented and submitted in part to "Third InternationalSymposium on Polarization Phenomena in Nuclear Reactionsl!,Madison, Wisconsin, 1970AbstractDifferential cross section and vector polarization forthe elastic scattering of 41, 46 and 51 MeV-deuteronson 12C were obtained from single and double scatteringexperiments at the Karlsruhe isochronous cyclotron.Tensor polarization effects were found to be small.The experimental data are compared with the results ofoptical model calculations. Best fits to the polarizat-ion data are obtained with volume spin-orbit-terms forthe deuteron optical potential.Der differentielle Wirkungsquerschnitt und die Vektorpo-larisation wurden für die elastische Streuung von 41, 46und 51 MeV Deuteronen an 12C durch Einfach- und Doppel-streuexperimente am Karlsruher Isochronzyklotron ermittelt.Tensorpolarisationseffekte erwiesen sich als vernachlässig-bar. Die experimentellen Werte werden mit Ergebnissen vonOptischen Potential-Rechnungen verglichen. Volum-Spin-Bahn-Terme im Optischen Potential für die Deuteronen geben diePolarisationswerte am besten wieder.The elastic scattering cross section 6f deuterons oncarbon was measured at energies of 41, 46 and 51 MeV. Thevector polarization was obtained from double scatteringexperiments.Both kinds of experiments were performed on the Karls-ruhe fixed energy cyclotron using the same experimentalset~upl) (fig. 1). It consists of a first scattering chamberand a movable arm bearing a quadrupole triplet and a secondrotating scattering chamber. For cross section measurementsthe movable arm is positioned at 0° and the first target isreplaced by a circular aperture of down to 1 mm diam. Ener-gies were degraded by Be and Al foils.The up-down asymmetry C gives a test for spurious asymmetries.We obtained an average value C = - 0.84 ± 1.65 x 10- 3 with x2 =61.1 for 36 degrees of freedom. From this a root mean squarevalue of ± 7.7 x 10- 3 for spurious asymmetries can be deduced.The cos2~ term B which contains tensor pOlarizations wasalso found to be smal14) (fig.2). The average value B =- 4.22 ± 1.38 x 10- 3 with x2 = 61~6 for 36 degrees of freedomleads to a root mean square asymmetry of :!: 7.2 x 10- 3 in B dueto tensor pOlarization coefficients 5) T22. We assurne tensorpOlarization coefficients T20 and T21 to have an influence ofthe same order of magnitude.If we neglect these small tensor polarization effects, onegets a right-Ieft asymmetry- 2 -and the vector pOlarization quantities 5) for the scatteringfrom the two targets can be extracted from a calibration ex-periment. This we did at the energy pairs (51,46), (46,41)and (51,41) MeV (fig. 3). The sign of iT11 was deduced fromoptical model calculations.Our differential cross section measurements extended ex-perimental data 6,7) for 51 MeV to smaller and larger angles.We degraded the primary beam energy for additional measure-ments at 46 and 41 MeV. The experimental results for bothcross sections and vector polarizations are shown in fig. 4.Numerical values with relative and absolute errors for diffe-rential cross section and vector pOlarizations are given intables I and 11.We thank G.R. Satchler for fitting the cross section at51 MeV using the search code "Hunter" 8) for optical modelcalculations. With a surface spin orbit term 4.2 MeV deepSatchler predicted polarizations (dashed curves in fig. 4).Using a code of B.A. Robson's we did not find much improve-ment when we varied the parameters of the surface ls term.Particularly the minimum in iT11 near 440 could not be fitt-ed. Hence we considered what effects might be relevant at51 MeV as opposed to lower energies.Since at higher energies deuterons see more of the innerpart of the nucleus 9) and spin orbit forces become largerdue to higher angular momenta, the Thomas form of the ls po-tential may no longer be justified 10). Retaining Satchler'scentral terms we tried a volume ls potential with a factorof 5.5 MeV. In addition we introduced a small surface ab-sorptive ls potential 0.1 MeV deep which is proportional tothe imaginary central term. Its sign was chosen so that forj=l+l one gets more interaction with the nuc1eus. The effectsof these changes are: The vo1ume ls potential indeed lowersthe 44 0 m1n1mum ana ~ne ls absorption gives a minimum in thecross section near 1500 •- 3 -Very recently J. Raynal 11) fitted the cross section andpolarization data for 51 MeV using his search code nMagali n12)with a Thomas-form ls potential. Weighting the pelarizationdata by a factor of 20 and starting from different parametersets, Raynal gets ambiguities in the central potential terms(Raynal I and V in fig. 5). Independently of these ambiguitieshe obtains negative radii for the surface ls potential, whichis equivalent to an exponential volume ls potential.The fits to the cross section at 51 MeV based on searchcodes (curves 1 and 3 in fig. 6) are better than the resultof the present calculations (curve 2) as was to be expected.Fig. 7 shows the corresponding fits to the deuteron pola-rization and compares the optical potentials used. For carbonthe Thomas form (potential 1) gives a volume ls potentialalso, but it seems not to be voluminous enough.We expect that further pOlarization experiments at higherenergies could test whether volume ls potentials are physical-ly meaningful.We thank Dr. J. Raynal for sending us results ef opticalmodel calculations prior to publication. We are indebted toDr. G. Schatz and his staff for the supply of the cyclotronbeam.- 4 -References:1) E. Seibt and Ch. Weddigen, to be published in Nucl.Instr. and Meth.4) E. Seibt, Ch. Weddigen, and K. Weigele, Phys. Lett. 29B(1968) 5675) W. Lakin, Phys. Rev. 98 (1954) 1396) U. Schmidt-Rohr et al., Nucl. Phys. A111 (1968) 13337) H. Brückmann et al., private communication (1968)8) R. H. BasseI, R.M. Drisko, and G. R. Satchler, ORNL-32409) B. Tatischeff and I. Brissaud, to be published10) F. G. Perey, Second Polarization Symp., Karlsruhe (1965) 19111) J. Raynal, private communication12) J. Raynal, Technical Report DPh-T/69-42, Saclay (1969)- 5 -Table I: Differential Cross Section with relative andabsolute errors for the elastic Scattering of41, 46, and 51 MeV-deuterons on 12 c.ecM/deg d<1>l mbdQ srEd = 41 MeVeCMI deg d<1> 1mbdQ srd<1> 1mbdQ sr11. 7112.8814.0515.2116.3817.5518.7119.8821.0522.2123.3724.5225.6826.8528.0029.1630.331.532.633.834.937.239.541.81.75xl031. 421.11 28.49xl06.144.302.791. 75 19.37xl04.431. 445.47x10o6.11 11.40x102.613.774.815.896.666.856.796.195.043.8144.146.348.650.853.155.357.559.862.064.266.468.57.0772.975.077.179.381.483.585.687.689.791.893.895.812.88x102.151. 791. 531. 441. 551. 491. 361. 341.211.038.41xl0o6.616.044.813.823.232.732.302.052.191.931. 831. 511. 4996.897.899.8101. 8103.8105.8107.7109.7111. 6113.5115.5117.4119.3123.9128.5133.0137.5141.9146.3150.6152.3154.9159.1163.5167.5o1. 31x101.291.15 -19.99xl08.366.705.835.164.273.102.582.001.621. 06 -28.08xl07.576.785.564.363.763.983.904.926.287.95Relative Error: < 10 % Absolute Error: < 20 %Ed = 46 MeV11. 7112.8814.0515.2116.3817.5518.7121.0522.2123.3723.9424.521.80x1031. 371.06 2- 7. 70xl05.053.352.07 15.72xl0~2.421.131.091. 3644.146.348.650.853.155.357.559.862.064.266.468.52.80xl012.091. 741.631. 501. 421. 321.181.06 08.83x107.095.6395.897.999.9101. 8103.8105.8107.8109.7111.6113.6115.5119.3-17.65x106.685.304.313.563.112.702.171. 721. 331.13 27.40xl0-- 6 -Table I, Ed = 46 MeV continuedecM/deg 3.11mbdO srd~ 1mbdO sr ecM/deg d~/mbdO sr123.9128.5133.0141. 9146.3150.6154.9159.1163.5167.525.68 2.3026.85 3.9928.00 5.2029.16 6.7330.3 7.5231.5 8.0932.6 8.2333.8 8.3234.9 7.9437.2 6.6439.5 5.2241.8 3.77Relative Error: < 7 %70.772.975.077.179.381. 483.585.687.689.791.893.84.503.572.862.301.971. 801. 511.401. 201.08 19.53x10-9.17Absolute Error: < 15 %5.123.983.392.261. 891. 751. 601. 782.182.63+33.7+34.8+37.1+39.440.7+41. 7+43.9+45.1+46.246.3+47.3+48.4+49.6+50.7+51. 8+52.9+54.0+55.2+57.457.6+59.6+61. 8+64.0+66.2+68.4+70.5+72.7+74.8+76.9+79.179.3+81.2+83.35 % 6)a l . , +++85.4+87.4+89.589.7+91.6+93.6+95.6+97.6+99.799.9++102.7++104.7++106.6++109.6109.7++111.5++114.4117.2++119.1119.3++121.0++123.8123.9++128.4128.5133.0137.5141.9146.3150.6154.9159.14.69 6.48xl035.86 4.957.02 4.518.20 3.139.37 2.7310.54 2.2111. 79 1. 7112.88 1.34 214.05 9.41x1015.21 6.76+15.80 5.5316.38 4.37+16.97 3.6217.55 2.74+18.01 2.1418.71 1. 64+19.17 1.19 419.88 8.87xl0+20.33 5.8521.05 4.49+21.49 3.0722.21 2.39+22.77 2.10 1+23.81 2.73x10+25.08 3.88+26.24 5.47+27.40 6.96+28.55 8.0329.10 8.64+29.59 8.78+30.2 9.28+31.4 9.47+32.5 9.16Relative Error: <+ Schmidt-Rohr etEd = 51 MeV8.417.836.334.584.173.532.312.071. 881.971. 771. 721.631.601.491.451.411. 301.171.16 09.96x107.956.535.133.922.912.371.841.611. 381. 411.191.04Absolute Error: 7<)10 %Brückmann et ale-19.17xl07.866.86 -16.89xl05.694.743.883.262.542.561. 791. 451.15 29.74x10-9.157.255.624.303.853.493.132.782.762.062.041. 591.291.059.20x10- 38.509.10 21. l1x10-- 7 -Table 11: Vector polarization iT11 for the elastic Scatter-ing of 41, 46 and 51 MeV-deuterons on 12C (Basel-Convention) .Ed = 41 MeV8cM/ de g iT11 8cM/ de g iT l l15.2 -0.047 + 0.012 34.9 -0.112 + 0.01817.4 -0.057 + 0.010 37.8 -0.136 + 0.02021.1 -0.082 0.015 40.6 -0.173 - 0.027+ +22.7 -0.132 + 0.019 42.9 -0.199 + 0.02524.6 -0.122 0.024 44.4 -0.178 - 0.023+ +26.4 -0.061 + 0.021 48.6 -0.102 + 0.01829.1 -0.061 + 0.022 53.0 +0.008 + 0.01332.0 -0.079 ± 0.015 57.5 +0.095 + 0.018Ed = 46 MeV15.2 -0.007 + 0.032 34.9 -0.115 + 0.04119.0 -0.067 + 0.031 36.4 -0.157 + 0.03821.0 -0.128 + 0.035 38.7 -0.159 + 0.02822.9 -0.148 + 0.039 41.8 -0.182 + 0.04824.3 -0.148 + 0.050 44.1 -0.239 + 0.04425.7 -0.048 + 0.039 46.3 -0.116 + 0.04427.4 +0.023 - 0.038 49.2 +0.012 0.042+ +29.2 -0.050 + 0.033 52.0 +0.149 + 0.05432.0 -0.096 + 0.046 55.3 +0.134 + 0.04157.5 +0.176 + 0.033Ed = 51 MeV19.9 -0.143 + 0.035 38.7 -0.147 + 0.02021.6 -0.202 + 0.028 43.2 -0.165 + 0.02423.4 -0.101 + 0.036 46.1 +0.006 + 0.02126.3 +0.009 + 0.023 49.9 +0.136 + 0.02228.1 +0.046 ± 0.030 54.2 +0.318 + 0.03533.2 -0.080 ± 0.027 57.5 +0.324 + 0.03836.3 -0.130 ± 0.026 62.9 +0.328 + 0.040_ 8_Figure Captions:Fig. 1:Fig. 2:Fig.3 :Fig. 4:Fig. 5:Experimental set-up used for cross section measure-ments (top) and double scattering experiments (bottom).Q,L, = quadrupole lenses, S = movable scintillationscreens, T = targets, C = counter telescopes (combi-nations of surface barrier and scintillation counters),M = monitors (scintillation counters), FK = Faraday-cup, SK = scattering chambers.The cos~-term A and the cos2~-term B for double scat-tering of 51 MeV deuterons on carbon as a function ofthe secondary scattering angle 62CM· E1,2 = energiesat the two targets.Calibration experiments for deducing the vector po-larization quantities (iT11)n from the right-leftasymmetries An. The sign of iT11 is deduced fromcalculations.Differential cross section and vector pOlarizationiT11 (Basel convention) at 51, 46, and 41 MeV.Dashed lines: Satchler prediction from a sear.chon differential cross section at 51 MeV alone;solid lines: present calculations~Definition and values (in MeV and f) of the opticalpotential parameters for fits shown in this paper.Set 1 was obtained by a search on the differentialcross section at 51 MeV alone with apreset valueof V S. The parameter sets of Raynal's are resultssoof a search on differential cross section and vectorpolarization at 51 MeV with different starting para-meter sets; for positive radii these potentials dif-fer in the ls terms only by about 20 %.Fig. 6:Fig. 7:- 9 -Optical model fits to the differential crosssection at 51 MeV. The numbers of the curvesrefer to the parameter sets in fig. 5.Radial dependence of the optical potentialsand corresponding fits to the vector polari-zation iT11 at 51 MeV. The numbers of the dia-grams and curves refer to the parameter setsin fig. 5. The lower part of the potential dia-grams gives the real volume and absorptive sur-face parts of the central potential. The upperpart represents the spin orbit potential divid-ed by -(ls). Note the difference in potentialscales.SK 2L3 L4C2T2 ClI IL._.Ir-"I I01 02 03 Q4I I1mL3 L4 52TlSKlFig. 1SK2I.....oI- 11 -DOUBLE SCATTERING OF DEUTERONSONCARBONN- 1+ Acos ; + Bcos 2 t/J0.08A0.04 t t+Ol-----~------l~-----+-----I-0.04°lC.M.=39°E 1 =51 MeVE 2 =46MeV0.02BO~--~-~-+--+-"'-+~~F-+-"""-"--*'"f- 0.02 [ __Io.-_I..-..-_L-.-_± Ij100 e2C.M. 500Fig. 2- 12 -CALIBRA TION EXPERIMENTIAi =20T1i)1 OT11h I46 MeV51 MeVBe41 MeVAl51 MeVFig. 310 2MfI I I I1.2l iT1112C(d,d)12CddRI ,.....~'-• this experiment l 010 I- _ J ;.JIIYJt:J -~~~ ... Schmidt - Rohr et al.• Brückmann et al.-.27 t J \.\ J~ITJ1k--!- • UI "UI:~~' ~~ .:~,\ -=1 .2ob- *"'-- - - .r: JI-'\..N10-11- ti f 41MeV y~ .,~ _.\-1 -.2, \I " 46 MeV" . .)....... . '"+100 -- ~'\\·'1 .2. \10-21 I iI.,- ., . \r LI 'X\,\I. 'l -.210-330° 60° 90° 120° 150° 180° 10°Fig. 4 0°SeMOPTIC:AL POTENTIAL, 51 MeV-Deuterons on CARBONVer) = Vc - Vo f o - 4iWo ~r f O - ~in:c)2 Vsos ~ ~r f so + VsoV f o + 4iWso ~r f o] (1 s)f - 1 .k - 1 + exp ( (r - rkAl/3)/ak)f-l.~Vo r o a Wo r o ao VsoS r so aso0-1 Satchler 86,0 1.024 0.766 8.25 1. 343 0.757 4.16 1.024 0.766...2 present 86.0 1.024 0.766 8.25 1. 343 0.757calculation - - -3 Raynal V 75.5 1.166 0.760 10.58 1.111 0.857 307.50 -2.264 1. 575Raynal I 105.8 0.867 0.891 8.80 1. 311 0.810 125.89 -1. 310 1.454Vs oV Wso5.5 0.01Fig. 5- 15 -A Schmidt - Rohr et al.e Brückmann et al.12C(d J d) 12 CEd =51 MeV•V1100.11200 1800Fig. 60.4 r I ,. I IiT ll12 C (d, d ) 12 CE d = 511MeV01 SATCHLER2 PRESENTCALCUlATI 0 N-.....3 RAYN,AL V - 0.4600 0'1I I400 eCM1 I 2 I 35 MevI,,--- I ------r-- ~-'Z ;:::== I ---750 MevI"J./ '\"J./ ----,RAYNAl I5fIIFig. 7

Differential Cross Section and Vector Polarization for the elastic scattering of 41 to 51 MeV Deuterons on Carbon

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Differential Cross Section and Vector Polarization for the elastic scattering of 41 to 51 MeV Deuterons on Carbon

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