Transcript
Page 1: Measurement of the coherent neutron scattering length of 3He by neutron interferometry

Volume 71, number 2 PHYSICS LETTERS 21 November 1977

M E A S U R E M E N T O F T H E C O H E R E N T N E U T R O N S C A T T E R I N G L E N G T H O F 3 He BY

N E U T R O N I N T E R F E R O M E T R Y *

H. KAISER, H. RAUCH Atominstitut der Osterreichischen Universita'ten, A-1020 Wien, Austria

W. BAUSPIESS Institut fiir Physik, Universitlit, D-46 Dortmund, Germany, and

lnstitut Laue Langevin, BP 156 Centre de tri, Grenoble Cedex, France

and

U. BONSE Institu t fiir Physik, Universitlit, D-46 Dortmund, Germany

Received 13 September 1977

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.

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 = ¼(3a t + as) and a i = ¼x/~(a t - as) , respectively, and the related cross

* 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).

sections. In the table the results of an effective range theory and a Breit-Wigner estimation of Sears and Khanna [2] are also shown.

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 o fa s and a t with these values only gives rather inaccurate values and there-

fore a precision measurement of a c was started. 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

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Page 2: Measurement of the coherent neutron scattering length of 3He by neutron interferometry

Volume 71B, number 2 PHYSICS LETTERS

Table 1 Summary of theoretical and experimental data on the neutron _3 He system

21 November 1977

Theory

eff. range [2] Breit-Wigner [ 2 ]

Experiment

Faddeev-Y. [11 (ac, o) [4] (ac, oi1%)[ 5 ] *

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

8.8 -+ 0.5 8.0 -+ 0.3 2.8 -+ 0.7 3.05 -+ 0.07

-2.6 -+0.3 -2.15-+0.10 0.84 -+ 0.25 0.58 -+ 0.10

4.29 -+ 0.04 * 2.32 +- 0.04 * 3.16 -+ 0.20 [4]

* Present work.

be wri t ten in the form [7,8]

I 0 = (.4 - B) [C + (1 - C) e x p ( - 2 ; t t ) ] +

+ B [{exp(-2~t t ) + 1 }/2

+ e x p ( - 2 ; t t / 2 ) cos 27r(ff/D - E)],

in which expression the different absorpt ion for the inter-

fering and the non-interfer ing part o f the beams is ac-

counted f o r ; A , B, D, E denote the mean intensi ty, the

ampli tude o f the interfering part, the X-pressure and

the zero phase o f the in te r fe rometer wi thou t absorp-

t ion; C denotes the probabi l i ty for the neu t ron being

20 I ~ He pre ..... e,~ Iz / ~ \ |o

\ - II II #

t

2j5 20 40 PRESSURE [BRR]

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.

in beam II, ~?t = N ( ° a + o) gives the total cross section

which is mainly de termined by absorpt ion; Oa(X = 1.8 A)

= 5327 b; t is the path length within the container and

~" the tempera ture reduced pressure. The mos t impor-

tant quant i ty is the X-pressure D = Px = 211 VM/tLbcX ) where V M is the molar vo lume of He and L the

Avogadro number .

Characteristic results obtained with the in terferom-

eter set-up [9] at the high flux reactor at Grenoble are

shown in fig. 1. An opt imal fit procedure according to

eq. (1) y ie lded a X-pressure o f p x = 19.32 + 0.10 bar

and together wi th the pressure/densi ty relat ion for a

real gas [10], which makes a correct ion of about 2%,

we get b c = +5.73, 0.05 fm or a c = 4.29 + 0.04 fro,

(fro) " ~

I 10 .'"." "" ~ ~ ' ~ eft.range ctppr. [2]

E21 =

4 . . . . . . . . . / . . ' . \ " ~ t h i s work)

I : : ~ I Irl L 2 4 6 8 10

a s (fm)

Fig. 2. Graphical evaluation of as and a t from existing experi- mental results and a comparison to theoretical estimates.

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Page 3: Measurement of the coherent neutron scattering length of 3He by neutron interferometry

Volume 71B, number 2 PHYSICS LETTERS 21 November 1977

respectively. The details o f the measurements and o f

the fit procedure are described elsewhere [8]. The high accuracy of the a c value allows a new de-

te rminat ion o f a s and a t by a combina t ion with the

o-value [4] or wi th the o i / e e ratio [5] which is in agree- ment wi th theoret ical arguments too. (The error bars

for o i /o c are es t imated according to the exper imenta l points o f ref. [5]). The results are shown graphically

in fig. 2 and the most consistent values are summarized

in table 1. The main error cont r ibut ions now arise f rom

the o or ai/cr c values. For a fur ther use we r ecommend

the data set obta ined f rom the (ac, ei/Oc) combina t ion .

The best agreement o f the exper imenta l data wi th theo-

retical predict ions exists for the results of Kharchenko

and Levachev [ 1 ].

References

[2] V.F. Sears and F.C. Khanna, Phys. Lett. 56B (1975) 1. [3] T.A. Kitchens, T. Oversluizen and L. Passel, Phys. Rev.

Lett. 32 (1974) 791. [4] V.P. Alfimenkov, G.G. Akopian, J. Wierzbicki,

A.M. Govorov and L.B. Pikelner, Sov. J. Nucl. Phys. 25 (1977) 1145.

[5] K. Skgld, C.A. Pelizzari, R. Kleb and G.E. Ostrowski, Phys. Rev. Lett. 37 (1976) 842.

[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.

[7] D. Petraschek and H. Rauch, AIAU-report 76401, Atominstitut Vienna (1976).

[8] H. Kaiser et al., Z. Phys. (in preparation). [9] W. Bauspiess, U. Bonse and H. Rauch, Proc. Conf. Neutr.

Scatt., Gatlinburg, Tenn. (1976) Vol. II, p. 1094; H. Rauch et al., Int. Conf. Interaction Neutr. Nuclei, Lowell, Mass. (1976) Vol. II, p. 1027.

[10] J. Otto, "pV-Werte von Gasen ...." in Taschenbuch fiir Chemiker und Physiker, ed. E. Lax, Bd. I (Springer, Berlin 1967) p. 840.

[1] V.F. Kharchenko and V.P. Levashev, Phys. Lett. 60B (1976) 317.

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