The sup 11 Li neutron halo radius from pion double charge exchange Page: 3 of 6
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the radial wave functions in the two cases causes the DCX cross-section to be
quite sensitive to size of the neutron halo.
At a pion energy of Tir=164 MeV, the DCX reaction is dominated by two se-
quential single charge exchanges. We have performed calculations of the DCX re-
action using finite range distorted waves and a closure approximation for the inter-
mediate states. The calculational technique has already been described elsewhere5.
The nuclear structure input was expressed in term of shell model two-body density
matrix elements derived from a p-shell calculation6. In a p-shell model "Li,,.*. is
described as a single p;)/2 proton with the neutrons forming a closed shell. The
magnetic moment is then just the Schmidt p:j/2 value, 3.79 /in, which is in rea-
sonable agreement with the measured value of 3.667/jn. The wave function for
"Bj.,., obtained by diagonalizing the Cohen-Kurath (8-16)2BME effective inter-
action, reproduces the ground state magnetic and quadrupole moments reasonably
well.
In calculating the DCX reaction the nils radius of the last two neutrons in "hi
(/?2n) was varied in order to determine the value giving the best representation of
the data4. This was done by adjusting the size of the Woods-Saxon well used to
obtain the single particle wave functions, while keeping the binding energy of the
11 Li neutrons fixed at 200 keV. The nils radius of the two protons on which the
reaction proceeds was held fixed at 2.65 fm, a value suggested by the difference in
charge radius between "D and ”Li. The 11 B protons were bound by 11 MeV.
As the volume in which the exchanged neutrons are Lo be found increases the
cross section deceases sinte the reaction only has significant strength when the
overlap of the wave function of the final neutrons with the initial protons is large.
In the limit as the radius of the two final neutrons becomes very large, it is the
initial wave function alone which controls the volume over which the reaction takes
place. When this limiting situation is reached the shape of the transition density
no longer changes and the cross section scales as the inverse volume squared or
as l/H'J,,. The results of the calculation are shown in Figure 1 for a range of rms
radii covering those that have been suggested in the literature. We note that a
radius of 12 fm, as suggested by Anne of a/.‘\ would imply a cross section 3 orders
of magnitude smaller than that observed.
Wo estimated tin* uncertainty in the calculated cross sections from systematic
studies of nuclear structure and DCX for nuclei in this mass region. 'The us- ol
p-shell wave runciions may be too restrictive, particularly in the case of the "Li
nucleus where di-neutron clustering is important. The description of a di-neutron
cluster state in a harmonic oscillator shell model basis would require a large multi
/lu.’ calculation. The inclusion of states of very high excitation is necessary in order
to give a realistic description of the relative motion wave function. While the
problem is mitigated by our use of Woods-Saxon single-particle wave functions,
and by the fact that our p-shell neutrons aic strongly correlated7, additional
correlations can he introduced by increasing the model basis to allow sd shell or
higher excitations, and these have been shown to give up to a factor of two in
the DC' X cross seel ion:: between isobaric analog stales. In the present non analog
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Hayes, A.C. The sup 11 Li neutron halo radius from pion double charge exchange, article, January 1, 1991; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1071793/m1/3/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.