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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
ORNUP-1oon
(To be published in the Proceedings of the International Conference on
Polarization Phenomena of Nucleons, Karlsruhe, Germany, September 6-10, 1965)
Conf. 650928-5
N-D Scattering - Vector Polarization of Recoil Deuterons from
a. Polarized Neutron Beam*
H. B. Willard, S. T. Thornton, and C. M. Jones
Oak Ridge National Laboratory
Oak Ridge, Tennessee, USA
The scattering of low energy neutrons by deuterons has long been
plagued with the ambiguity of two different possible sets of interaction
parameters (scattering lengths) as well as the very formidable theoretical
difficulties inherent in three-body calculations. Measurement of the
"zero" energy coherent and incoherent scattering cross sections leads to
the following sets of scattering lengths:-

Set I
Set II
0.89 + 0.23 fm
6.32 $ 0.09 fm
8.13 $ 0.23 fm
2.70 0.09 fm
DELEASED FOR ANNOUNCEMENT
IN NUCLEAR SCIENCE ABSTRACTS
where an, the doublet scattering length, corresponds to channel spin 1/2
and als the quartet scattering length, corresponds to channel spin 3/2.
Theoretical calculations based upon the known nucleon-nucleon inter-
action now seem to support the conclusion that the n-D interaction is
predominantly quartet (i.e. Set I). However, to date there has been no
direct experimental confirmation of these results.
One could envision resolving this question by the conceptually
simple experiment of scattering polarized thermal neutrons from a polarized
deuterium target. Such measurements should be straightforward once the
Research sponsored by the U.S. Atomic Energy Commission under contract
with the Union Carbide Corporation.
Oak Ridge Graduate Fellow from the University of Tennessee, U.S. Atomic
Energy Commission Fellowship administered by the Oak Ridge Institute of
Nuclear Studies.
-2
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considerably difficult techniques associated with producing polarized
targets have been carried out.
We propose an alternative solution to the problem which necessitates
a triple scattering experiment. In the first "scattering" a beam of polar-
ized neutrons is produced by a suitable nuclear reaction. These polarized
neutrons then undergo a second scattering by an unpolarized deuterium
target. The polarization states of the recoil deuterons are then analyzed
in a third scattering (or nuclear reaction).
Polarizations resulting from scattering a beam of polarized neutrons
from an unpolarized deuterijim target have been calculated by the general
tensor moment technique of Simon and Welton. Assuming only s-wave inter-
actions we find that:
B
lRozle + 8(ROZPO4 + ROZPO4? + 101 Ro4!
Tijë + 2]R, 12
and
and
TA
via
- Rolle - 2(R2R64 + Röz Ro4) + 5|R0417
Ro212 + 2/80412
taf
where
Po is the incident neutron vector polarization
TRA TRE TRA
is the scattered neutron vector polarization
is the recoil deuteron vector polarization
Ros is the s-wave doublet reaction matrix
Rol is the s-wave quartet reaction matrix.
The reaction matrices are related to their corresponding s-Wave scattering
- 3 -
lengths and phase shifts by the usual relations:
R = 2iełº sin 8, and a = - 4 tan 8.
In this s-wave approximation the scattered neutron and recoil
deuteron vector polarizations are independent of the scattering or recoil
angles (as they should be) and are parallel or
ti-parallel to the in-
cident neutron polarization vector. Furthermore the second rank tensor
moments of the deuteron polarization are all zero.
These happy conclu-
sions allow the experimentalist to choose large solid angles for observing
the polarization states.
The magnitudes of B and F; were then calculated as a function of
the doublet and quartet scattering lengths for an incident beam of com-
pletely polarized "zero" energy neutrons. Sets I and II give nearly the
same values for the scattered neutron polarizati
respectively. However, the recoil deuteron vector polarization differs
not only in magnitude but also in sign for the two sets. Set I corresponds
to Po = + 50% and Set II to P = - 33%. It is thus clear that measurement
of the recoil deuteron vector polarization provides a very sensitive
means for experimental resolution of this longstanding ambiguity.
In order to perform such experiments it is more convenient if the
recoil deuterons have sufficient energy to induce nuclear reactions that
may serve to analyze the polarization. The Li' (p,n)Be reaction provides
a source of 300-400 keV neutrons polarized* to greater than 50%. At these
higher neutron energies the values of PM and Ps can be estimated from the
phase shifts. However, the contribution from p-wave interactions? must
also be included and therefore the product polarizations become a function
of the scattering (recoil) angle. Fortunately, the interference of p-wave
MER
TF.
and s-wave scattering is small and in particular goes to zero at 90° in
the center-of-mass system. Assuming the incident neutron beam is
polarized perpendicular to the scattering plane, the deuterons recoiling
at 90° will have vector polarizations of + 42% for Set I or - 23% for
Set II.
Vector polarized deuterons of a few hundred keV energy can be
analyzed with high efficiency by the D(d,p)r reaction.
Assuming good
geometry, the maximum observable left-right asymmetry in the triple scat-
tering experiment we have outlined would be 1.28 for Set I and 0.88 for
Set II. When finite solid angles and energy spreads are considered these
asymmetries will be reduced, but we estimate that counting rates of better
than 1 per minute are feasible with geometries sufficiently good to uniquely
resolve this question.
5
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References
1. Calculated from data tabulated in BNL-325, Second Edition, Supplement
2, May 1964. See also W. Bartolini, R. E. Donaldson, and L. Passell,
Bull. Am. Phys. Soc. 8 (1963) 477 for the coherent scattering cross
section.
2. L. M. Delves, J. N. Lyness, J. M. Blatt, Phys. Rev. Letters 12 (1964)
542; R. Aaron, R. D. Amado, and Y. Y. Yam, Phys. Rev. Letters 13
(1964) 574, 702E.
3. A. Simon and T. A. Welton, Phys. Rev. 90 (1953) 1036; A. Simon, Phys.
Rev. 92 (1933) 1050; T. A. Welton, Fast Neutron Physics, Vol. II
(1963) ed. J. B. Marion and J. L. Fowler (Wiley - Interscience
Publishers, Inc., New York) 1317 ff.
4. A. J. Elwyn and R. O. Lane, Nuclear Phys. 31 (1962) 78.
5. A. J. Elwyn, R. O. Lane, and A. Langsdorf, Jr., Phys. Rev. 128
(1962) 779.
6. H. A. Christ and L. Brown, private communication.
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DATE FILMED
11/ 8 /65