# Measurement of the coherent neutron scattering length of 3He by neutron interferometry

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<ul><li><p>Volume 71, number 2 PHYSICS LETTERS 21 November 1977 </p><p>MEASUREMENT OF THE COHERENT NEUTRON SCATTERING LENGTH OF 3 He BY </p><p>NEUTRON INTERFEROMETRY* </p><p>H. KAISER, H. RAUCH Atominstitut der Osterreichischen Universita'ten, A-1020 Wien, Austria </p><p>W. BAUSPIESS Institut fiir Physik, Universitlit, D-46 Dortmund, Germany, and </p><p>lnstitut Laue Langevin, BP 156 Centre de tri, Grenoble Cedex, France </p><p>and </p><p>U. BONSE Institu t fiir Physik, Universitlit, D-46 Dortmund, Germany </p><p>Received 13 September 1977 </p><p>A precise determination of the coherent scattering length of 3He with a neutron interferometer yields a value a c = 4.29 -+ 0.04 fin. A comparison with various theoretical predictions is made and its relation to the few-body prob- lem is discussed. A combination with other experimental results yield as most probable values for the free singlet- and triplet scattering length a s = 8.0 -+ 0.3 fm and a t = 3.05 +- 0.07 fin, respectively. </p><p>Recent theoretical methods for the calculation of the few-body problem allow a more fundamental treatment of the four-body problem too. Whereas usually the calculation of the binding energy focused the interest, the consideration of the neutron scatter- ing lengths for the neutron-3H and the neutron-3He system yield a more complete test of various theore- tical models. A detailed analysis using the Faddeev- Yacubovsky equations has been carried out by Khachenko and Levashev [1 ] with a charge independent, separable and central potential. For the neutron-3He system both isospin values (T = 0, 1) are possible and for the total spin state S -- 0 a strong effective attrac- tion exists with a marked dependence on the details of the nuclear forces. The results for the singlet (as) and the triplet (at) scattering lengths are included in table 1. These quantities determine the coherent and the incoherent scattering lengths, a c = (3a t + as) and a i = x/~(a t - as) , respectively, and the related cross </p><p>* Work partially supported by "Fonds zur Forderung der wisschenschaftlichen Forschung" (project 3185) and by "Bundesministerium ffir Forschung und Technologie" (KNF-FV-4 DO 1 T). </p><p>sections. In the table the results of an effective range theory and a Breit-Wigner estimation of Sears and Khanna [2] are also shown. </p><p>An experimental determination of a s and a t re- quires the combination of at least two experimentally available quantities like ac, the coherent (Oc) , the in- coherent (oi) or the total scattering cross section (a). The value for the coherent scattering length was meas- ured by Kitchens et al. [3] as a c = 4.57 -+ 0.45, the scattering cross section by Alfimenkov et al. [4] as o = 3.16 + 0.20 and the ratio oi/cr c = 0.250 + 0.024 by Sk61d et al. [5]. An evaluation ofa s and a t with these values only gives rather inaccurate values and there- fore a precision measurement of a c was started. </p><p>A neutron interferometer [6] was used for the de- termination of a c. The phase shift between the two coherent beams of the interferometer produced by the 3He gas with variable pressure depends on the in- dex of refraction (n = 1 - X2Nbc/27r) and therefore on the bound coherent scattering length b c = a c (A + 1)/14 (X -- 1.897 + 0.006 A is the neutron wave length, N the density and A the 3He/n mass ratio). Because 3He is a highly absorbing substance, the in- tensity oscillation behind the interferometer has to </p><p>321 </p></li><li><p>Volume 71B, number 2 PHYSICS LETTERS </p><p>Table 1 Summary of theoretical and experimental data on the neutron _3 He system </p><p>21 November 1977 </p><p>Theory </p><p>eff. range [2] Breit-Wigner [ 2 ] </p><p>Experiment </p><p>Faddeev-Y. [11 (ac, o) [4] (ac, oi1%)[ 5 ] * </p><p>a s (fm 6.07 7.4 7.54 a t (fm) 4.1 3.7 3.07 a i (fm) -0.82 -1.6 -1.93 o i (b) 0.08 0.34 0.47 a c (fm) 4.6 4.62 4.18 o c (b) 2.65 2.68 2.19 o (b) 2.73 3.02 2.66 </p><p>8.8 -+ 0.5 8.0 -+ 0.3 2.8 -+ 0.7 3.05 -+ 0.07 </p><p>-2.6 -+0.3 -2.15-+0.10 0.84 -+ 0.25 0.58 -+ 0.10 </p><p>4.29 -+ 0.04 * 2.32 +- 0.04 * 3.16 -+ 0.20 [4] </p><p>* Present work. </p><p>be written in the form [7,8] </p><p>I 0 = (.4 - B) [C + (1 - C) exp(-2; t t ) ] + </p><p>+ B [{exp(-2~tt ) + 1 }/2 </p><p>+ exp( -2 ; t t /2 ) cos 27r(ff/D - E)], </p><p>in which expression the different absorption for the inter- fering and the non-interfering part of the beams is ac- counted fo r ;A , B, D, E denote the mean intensity, the amplitude of the interfering part, the X-pressure and the zero phase of the interferometer without absorp- tion; C denotes the probabil ity for the neutron being </p><p>20 I~ He pre ..... e,~ Iz / ~ \ |o </p><p>\ - II II # </p><p>t </p><p>2j5 20 40 PRESSURE [BRR] </p><p>Fig. 1. Typical experimental results for the intensities I O and I H behind the interferometer as a function of the SHe pressure, an optimal fit curve according to eq. (1) and a sketch of the experimental arrangement. </p><p>in beam II, ~?t = N(a + o) gives the total cross section which is mainly determined by absorption; Oa(X = 1.8 A) = 5327 b; t is the path length within the container and ~" the temperature reduced pressure. The most impor- </p><p>tant quantity is the X-pressure D = Px = 211 VM/tLbcX ) where V M is the molar volume of He and L the Avogadro number. </p><p>Characteristic results obtained with the interferom- eter set-up [9] at the high flux reactor at Grenoble are shown in fig. 1. An optimal fit procedure according to eq. (1) yielded a X-pressure o fpx = 19.32 + 0.10 bar and together with the pressure/density relation for a real gas [10], which makes a correction of about 2%, we get b c = +5.73, 0.05 fm or a c = 4.29 + 0.04 fro, </p><p>(fro) " ~ </p><p>I 10 .'"." "" ~ ~ ' ~ eft.range ctppr. [2] </p><p>E21 = </p><p>4 . . . . . . . . . / . . ' . \ "~th is work) </p><p>I : :~ I Irl L 2 4 6 8 10 </p><p>a s (fm) </p><p>Fig. 2. Graphical evaluation of as and a t from existing experi- mental results and a comparison to theoretical estimates. </p><p>322 </p></li><li><p>Volume 71B, number 2 PHYSICS LETTERS 21 November 1977 </p><p>respectively. The details of the measurements and of the fit procedure are described elsewhere [8]. </p><p>The high accuracy of the a c value allows a new de- termination of a s and a t by a combinat ion with the o-value [4] or with the oi /e e ratio [5] which is in agree- ment with theoretical arguments too. (The error bars for oi/o c are estimated according to the experimental points of ref. [5]). The results are shown graphically in fig. 2 and the most consistent values are summarized in table 1. The main error contributions now arise from the o or ai/cr c values. For a further use we recommend the data set obtained from the (ac, ei/Oc) combination. The best agreement of the experimental data with theo- retical predictions exists for the results of Kharchenko and Levachev [ 1 ]. </p><p>References </p><p>[2] V.F. Sears and F.C. Khanna, Phys. Lett. 56B (1975) 1. [3] T.A. Kitchens, T. Oversluizen and L. Passel, Phys. Rev. </p><p>Lett. 32 (1974) 791. [4] V.P. Alfimenkov, G.G. Akopian, J. Wierzbicki, </p><p>A.M. Govorov and L.B. Pikelner, Sov. J. Nucl. Phys. 25 (1977) 1145. </p><p>[5] K. Skgld, C.A. Pelizzari, R. Kleb and G.E. Ostrowski, Phys. Rev. Lett. 37 (1976) 842. </p><p>[6] H. Rauch, W. Treimer and U. Bonse, Phys. Lett. 47A (1974) 369; W. Bauspiess, U. Bonse, H. Rauch and W. Treimer, Z. Phys. 271 (1974) 177. </p><p>[7] D. Petraschek and H. Rauch, AIAU-report 76401, Atominstitut Vienna (1976). </p><p>[8] H. Kaiser et al., Z. Phys. (in preparation). [9] W. Bauspiess, U. Bonse and H. Rauch, Proc. Conf. Neutr. </p><p>Scatt., Gatlinburg, Tenn. (1976) Vol. II, p. 1094; H. Rauch et al., Int. Conf. Interaction Neutr. Nuclei, Lowell, Mass. (1976) Vol. II, p. 1027. </p><p>[10] J. Otto, "pV-Werte von Gasen ...." in Taschenbuch fiir Chemiker und Physiker, ed. E. Lax, Bd. I (Springer, Berlin 1967) p. 840. </p><p>[1] V.F. Kharchenko and V.P. Levashev, Phys. Lett. 60B (1976) 317. </p><p>323 </p></li></ul>

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