re-measurement of the neutron-tritium scattering length

4
Volume 165B, number 1,2,3 PHYSICS LETTERS 19 December 1985 RE-MEASUREMENT OF THE NEUTRON-TRITIUM SCATI'ERING LENGTH H. RAUCH, D. TUPPINGER, H. W~)LWITSCH Atominstitut der Osterreichischen Universiti~ten, Vienna, Austria and T. WROBLEWSKI 1 lnstitut Laue- Langevin, Grenoble, France and Institut ]'ur Experimentalphysik, UniversitiJt Dortmund, Dortmund, Fed. Rep. Germany Received 17 June 1985 By making use of a new skew symmetric neutron interferometer and a new tritium container, a more accurate measurement of the coherent neutron-tritium scattering length has been performed. The value obtained for the bound scattering length is bc = 4.792+0.027 fm, which is related to a free scattering length of a c = 3.59+0.02 fm. The combination with the known free scattering cross section yields new values for the singlet and triplet scattering lengths: a s = 4.98 __. 0.29 fm, a t = 3.13 + 0.11 fm. In the investigation of the low-energy four-nucleon problem the system neutron-tritium is of special in- terest. No assumptions have to be made how to sub- tract the Coulomb effect as in the case of proton- tritium or proton-3He scattering. Furthermore, in contrast to neutron-3He, the Pauli principle causes a strong repulsive interaction. So the related singlet (as) and triplet (at) scattering lengths are fairly weakly de- pendent on the potential shape, which serves as a cru- cial test of various few-body models. Experimentally, the singlet and triplet scattering lengths can be gained indirectly by the combination of two independent measurements of the coherent scattering length (as), the total free scattering cross section (as) or the incoherent cross section (ai) ac= ~ as + ~ at , Os = n(lasl2 + 31atl2), oi = ] rr(at - as) 2 . (1) At present, only measurements of the former two quantities are available, because the incoherent cross section is small and difficult to measure. 1 Present address: DESY, Notkestrasse 85, D-2000 Hamburg, Fed. Rep. Germany. 0370-2693/85/$ 0330 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) In 1981 we measured the coherent neutron-tritium scattering length by a neutron interferometric method and obtained a value ofa e = 3.82 -+ 0.07 fm [1]. However, the error bar of this value dominates the errors for the singlet and triplet scattering lengths, ob- tained by the combination with a rec-~at value for the total free cross section (o s = 1.70 -+ 0.03b [2,3]). Therefore we repeated the measurement at the neu- tron interferometer facility S18 at the high-flux reac- tor at Grenoble with a more advanced arrangement. The improvement of the experimental set-up is mainly based on the use of a new skew symmetrically cut interferometer crystal, which produces parallel partial beams. In contrast to the previous tritium ex- periment of our group the container is constructed so, that no partial beam penetrates the container near a welding seam. Therefore this arrangement is much less sensitive to misadjustments at the necessary refer- ence measurements without tritium gas. In addition, the parallel partial beams allow a more effective utili- sation of the available amount of tritium gas. As in ref. [1] a measuring procedure with constant phase shift has been chosen as shown in fig. 1. Commonly the phase shift of a neutron beam with wave length ~, caused by a material with thickness D, 39

Upload: h-rauch

Post on 02-Sep-2016

225 views

Category:

Documents


5 download

TRANSCRIPT

Page 1: Re-measurement of the neutron-tritium scattering length

Volume 165B, number 1,2,3 PHYSICS LETTERS 19 December 1985

R E - M E A S U R E M E N T O F T H E N E U T R O N - T R I T I U M S C A T I ' E R I N G L E N G T H

H. R A U C H , D. T U P P I N G E R , H. W ~ ) L W I T S C H

Atominstitut der Osterreichischen Universiti~ten, Vienna, Austria

and

T. W R O B L E W S K I 1

lnstitut Laue- Langevin, Grenoble, France and Institut ]'ur Experimentalphysik, UniversitiJt Dortmund, Dortmund, Fed. Rep. Germany

Received 17 June 1985

By mak ing use of a new skew symmet r ic neu t ron in ter ferometer and a new t r i t ium container , a more accurate measuremen t of the coherent n e u t r o n - t r i t i u m scat ter ing length has been performed. The value ob ta ined for the bound scat ter ing length is b c = 4 .792+0 .027 fm, which is re la ted to a free scat ter ing length of a c = 3 .59+0 .02 fm. The combina t i on wi th the k n o w n free scat ter ing cross sect ion yields new values for the singlet and t r iplet sca t ter ing lengths: a s = 4.98 __. 0.29 fm, a t = 3.13 + 0.11 fm.

In the investigation of the low-energy four-nucleon problem the system neut ron- t r i t ium is of special in- terest. No assumptions have to be made how to sub- tract the Coulomb effect as in the case of p r o t o n - tritium or p r o t o n - 3 H e scattering. Furthermore, in contrast to neu t ron-3He , the Pauli principle causes a strong repulsive interaction. So the related singlet (as) and triplet (at) scattering lengths are fairly weakly de- pendent on the potential shape, which serves as a cru- cial test o f various few-body models.

Experimentally, the singlet and triplet scattering lengths can be gained indirectly by the combination of two independent measurements of the coherent scattering length (as), the total free scattering cross section (as) or the incoherent cross section (ai)

ac= ~ as + ~ at ,

Os = n(lasl2 + 31atl2), oi = ] rr(at - as) 2 . (1)

At present, only measurements of the former two quantities are available, because the incoherent cross section is small and difficult to measure.

1 Present address: DESY, Notkes t rasse 85, D-2000 Hamburg ,

Fed. Rep. Ge rmany .

0370-2693/85/$ 0 3 3 0 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

In 1981 we measured the coherent neut ron- t r i t ium scattering length by a neutron interferometric method and obtained a value o f a e = 3.82 -+ 0.07 fm [1]. However, the error bar of this value dominates the errors for the singlet and triplet scattering lengths, ob- tained by the combination with a rec-~at value for the total free cross section (o s = 1.70 -+ 0 .03b [2,3]). Therefore we repeated the measurement at the neu- tron interferometer facility S18 at the high-flux reac- tor at Grenoble with a more advanced arrangement.

The improvement of the experimental set-up is mainly based on the use of a new skew symmetrically cut interferometer crystal, which produces parallel partial beams. In contrast to the previous tritium ex- periment of our group the container is constructed so, that no partial beam penetrates the container near a welding seam. Therefore this arrangement is much less sensitive to misadjustments at the necessary refer- ence measurements without tritium gas. In addition, the parallel partial beams allow a more effective utili- sation of the available amount of tritium gas. As in ref. [1] a measuring procedure with constant phase shift has been chosen as shown in fig. 1.

Commonly the phase shift of a neutron beam with wave length ~, caused by a material with thickness D,

39

Page 2: Re-measurement of the neutron-tritium scattering length

Volume 165B, number 1,2,3 P H Y S I C S L E T T E R S

auxilliary phase ,

shifter ~ ~/ P

Pos I Pos 2 Pos. 3

Fig. I. Arrangement of the new tritium container within the skew symmetric neutron interferometer.

4" E ,;500

~ooo

35OO

19 December 1985

.

I i i i i i i i i

particle density N and composed of nuclei with a bound coherent scattering length b e is given by

X = (n - 1)kD = - X N b e D . (2)

The walls o f the tritium container (D = 4 mm) made of non-magnetic steel (AFNOR-Z-2-CND- 17-13) cause the dominant contribution to the phase shift of one partial beam. This is compensated by the dummy ves- sel containing air under normal conditions, which acts as a reference phase shifter. So in all three positions of the tritium container, the phase difference be- tween the two partial waves is governed by the gas within the vessels.

The relative phase shift is deduced from the inter- ference pattern, produced by rotating an auxiliary aluminium phase shifter (×A1)" For each position j the intensity is modulated according to

t

h = hj + Bj cos (XAI + AX i + x}nt) , (3)

where Ai, B~ and ~n t are internal parameters of the interferometer set-up including the sample container; AX i is the difference of the phase shift between both beams caused by the gaswithin the container. In order to eliminate the influence of the tritium container, reference measurements (//)0 must be performed with the tritium vessel evacuated.

Up to the order o f interference m, the phase shift of the tritium results as

X ° + 2rrm XT = X12 -- X102 + 27rm = X32 - 32

with Xi /= AXi -- AX] . (4)

Typical results of the intensity modulations of trit- ;ium and reference measurements are shown in fig. 2. The tritium gas (~-,22 bar, 700 Ci) was on loan from the Centre d'Etudes de Bruyeres-le-Chatel, France.

40

* PO$. I • Pos. 2

~ 45oo

1 0.4 (15 a 6

ADAI ( r a m )

Fig, 2. Typical intensity modulation for the three measuring positions without (above) and with tritium (below).

Its composition at the time of the experiment was (in at%): T = 98.9+ 0 .1 ;D = 0.36 -+ 0 .02;H = 0.31 -+ 0.02, 3He = 0.415 + 0.01; N = 0.023 -+ 0.01; rest < 0.01. The particle density N = (1.0602 -+ 0.0022) × 1021 cm -3 has been deduced via pressure and tem- perature measurements using the known virial coeffi- cients of H 2 and D 2 [4]. During the reference meas- urements which started four days after the tritium runs had been finished, the tritium vessel was evacuat- ed to < 5 X 10 -2 torr. By a careful adjustment o f the container it was assured that the contribution o f the container to the phase differences remained constant at both cycles. The order o f interference (m = - 4 ) has been determined from the previously known b e values [1,5]. The phase shift of the tritium gas (×T = --23.62 -+ 0.13) was extracted from ten runs. Taking into account the mean neutron wave length (h0 = 1.858 + 0.003 A) and the inner width o f the tritium vessel (D = 25.08 + 0.03 mm), a bound coherent scat- tering length

b e = 4.7916 -+0.027 f m (5)

Page 3: Re-measurement of the neutron-tritium scattering length

Volume 165B, number 1,2,3 PHYSICS LETTERS 19 December 1985

is obtained, which is related to the free coherent scat- tering length (a¢ = beA/(A + 1), A: tritium neutron mass ratio)

a c = 3.59 -+ 0.02 fm. (6)

The combination with the free scattering cross sec- tion [2,3] yields two sets for the singlet and triplet scattering length:

Set I:

a s = 4 . 9 8 + - 0 . 2 9 f m , a t = 3 . 1 3 + 0 . 1 1 f m .

Set II:

a s = 2.10 + 0.31 fm, a t = 4.05 +0.09 fm .

The results are plotted in a modified (a s, at) plane in fig. 3 together with some theoretical values (refs. [ 1 ,2,5-14]) . By theoretical considerations [6] the first data set for a s and a t is favoured. The new value o f the coherent scattering length lies within the error bars of the experimental value from Donaldson et al. [5], but outside the error bar of our previous mea- surement [1]. This indicates that some systematic er- rors were involved in one o f our experiments. The re- cent measurement has profited from the experience of the previous one and the new measuring method using parallel beams avoids some possible misalign- ments. Therefore, it is justified to recommend the new value for further use. All errors reported by the various authors are statistical. Assuming the three available values being statistically independent and

4.5

- . ~.0

~'3.5

3.0

,oJ Donoldson et at.[5]

Ül • •

2 4 8 tnis .,or*

0 s ( f r o )

Fig. 3. Plot of the experimental and theoretical results in an (as, at) plane.

taking the weighted mean yields a e = 3.61 -+ 0.02 fm which is practically equivalent to our value. The error bar is reduced once more and the contribution to the errors of the a s and a t values is comparable to that from the free cross section.

The theoretical values in fig. 3 are mainly based on Faddeev-Yakubovsky calculations, using various separable nucleon-nucleon potentials o f the central exchange type. Some other values originate from mod- ified two-body calculations [12] and from an R-matrix analysis [13].

Both, our favoured data set and the most recent theoretical calculations [ 13,14], indicate a singlet scattering length distinctly larger than the triplet scat- tering length. In the case of neutron tritium scatter- ing the ratio at/a s provides a direct indication of the relative strengths of the singlet and triplet interac- tions. By this measurement it is restricted to a value between 0.57 and 0.69. This can be understood quali- tatively by a stronger attraction to the proton in the S = 1 state compared to the S = 0 state.

This project has been supported financially by the "Fends zur F6rderung der Wissenschaftlichen Forschung in Osterrech" (project 4230), by the "Bundesministerium ffir Wissenschaft und Forschung" (project "Tritium in MetaUen") and by the Institute Laue-Langevin in Grenoble. We are grateful to Mr. B. Hircq and Mr. A. Strazielle from the Commissariat l'Energie (Centre de Bruy6res-le-Chatel, France) for the loan of the tritium gas and for its analysis and to Mr. H. Salle for organizing the security precautions and to Mr. G. Le Lan, Mr. J. Mary and Mr. G. Schmid for their help during the experiment and ILLS. Hammerschmied transferred his experience from the previous measurement, which is gratefully acknow- ledged too.

References

[1] S. Hammerschmied, H. Ranch, H. Clerc and U. Kisehko, Z. Phys. A302 (1981) 323.

[2] J.D. SeagFave, B.L. Berman and T.W. Phillips, Phys. Lett. 91B (1980) 200.

[3] T.W. Phillips, B.L. Berman and }.D. Seagzave, Phys. Rev. C22 (1980) 384.

[4] K. Seh~er and G. Beggerow, Eigenschaften der Materie in ihren Aggregatzusfftnden, Teil 1 (1971).

[5] R.E. Donaldson, W. Bartolini and H. Otsuki, Phys. Rev. C5 (1972) 1952.

41

Page 4: Re-measurement of the neutron-tritium scattering length

Volume 165B, number 1,2,3 PHYSICS LETTERS 19 December 1985

[6] V.F. Karchenko and V.P. Levashev, Nucl. Phys. A343 (1980) 249.

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

[8] J.A. Tjon, Phys. Lett. 63B (1976) 391. [9] R. Pemc and W. Sandhas, in: Few-body systems and

nuclear forces I, eds. H. Zingl, M. Haftel and H. Zankel, Lecture Notes in Physics, Vol. 82 (Springer, Berlin, 1978) p. 263.

[10] J.A. Tjon, in: Few-body systems and nuclear forces II, eds. H. Zing[, M. Haftel and H. Zankel, Lecture Notes in Physics, Vol. 87 (Springer, Berlin, 1978) p. 320.

[11] V.P. Levashev, Soy. J. Nud. Phys. 38 (1983) 336. [12] P. Szydlik and C. Wemtz, Phys. Roy. 138 (1965) 866. [13] G.M. Hale and D.C. Dodder, Proc. 9th Intern. Conf. on

Few-body problems (Oregon, 1980), Vol. I, pp. 11-17. [14] V.P. Levashev, Proe. 10th Intern. Conf. on Few-body

problems (Karlsruhe, August, 1983).

42