n--d breakup reaction and the n--n scattering length. Page: 4 of 8
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THE n - d BREAKUP ACTION AND THE n - n SCATTERING LENGTH
B. F. Gibson and G. J. Stephenson, Jr.
A simple approximation to the Faddeev theory of the n - d
breakup reaction is reviewed in an attempt to emphasize the
difficulty of obtaining a precision measurement of the n - n
scattering length using this reaction mechanism.
It has long been known that the nucleon-nu-
cleon force is not charge independent; i.e., the
neutron-proton singlet force is not the same as
either the neutron-neutron force or the Coulomb
corrected proton-proton force. Henley and
Keliher1 have recently proposed a form of charge
symmetry breaking potential that would imply a
difference between the n-n and Coulomb corrected
p - p scattering lengths of approximately 0.8 fm.
At present, however, the experimental measurement
of the n - n scattering length is not precise
enough to enable one to make any definite state-
ment about charge symmetry breaking in the nucleon-
nucleon force (see Appendix). Therefore, a pre-
cise determination of a is of fundamental in-
terest to physics.
Many attempts have been make to exploit the
n - d breakup reaction
n + d -n + n + p
to determine ann At the recent Few Particle
Conference held at UCLA it was clear that suffi-
cient accuracy in this measurement has not been
attained, since the reported uncertainties in the
neutron-neutron scattering lengths indicated that
the results were accurate to only about t 2 fm .
Proposals submitted to LAMF indicate that further
attempts to measure a by means of the n - d
breakup reaction will be made. Therefore, we wish
to review here a theoretical picture due to the
several people noted below and summarized by
Aitchison3 that provides a good fit to and a sim-
ple understanding of the high energy peak in the
proton spectrum from this reaction. It reproduces
the three-body Faddeev result for low energy, dis-
plays explicitly the dependence of the spectrum on
a , and explains why the impulse approximation
gives a much better fit to the data than does the
It was shown by Popova that, for low values
of the relative neutron-neutron momentum, the ma-
trix element describing the n - d breakup reac-
tion is given to a reasonable approximation by the
sum of the three diagrams:
n n n p
d p d n
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Gibson, B.F. & Stephenson, G.J. Jr. n--d breakup reaction and the n--n scattering length., report, January 1, 1973; [New Mexico]. (digital.library.unt.edu/ark:/67531/metadc1028934/m1/4/: accessed October 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.