Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting pairs in $^{44}$Ti with various interactions   We count the number of pairs in the single $j-$shell model of $^{44}$Ti for
various interactions. For a state of total angular momentum $I$, the wave
function can be written as $\Psi=\sum_{J_P J_N} D(J_P J_N)
[(j^2)_{J_P}(j^2)_{J_N}]_I$, where $D(J_P J_N)$ is the probability amplitude
that the protons couple to $J_P$ and the neutrons to $J_N$. For I=0 there are
three states with ($I=0, T=0$) and one with ($I=0, T=2$). The latter is the
double analog of $^{44}$Ca. In that case (T=2), the magnitude of $D(JJ)$ is the
same as that of a corresponding two particle fractional parentage coefficient.
In counting the number of pairs with an even angular momentum $J_A$ we find a
new relationship obtained by diagonalizing a unitary nine-j symbol. We are also
able to get results for the 'no-interaction' case for T=0 states, for which it
is found that there are less ($J=1, T=0$) pairs than on the average. Relative
to this 'no-interaction case' we find for the most realistic interaction used
that there is an enhancement of pairs with angular momentum $J_A=0,2,1$ and 7,
and a depletion for the others. Also considered are interactions in which only
the ($J=0, T=1$) pair state is at lower energy, only the ($J=1, T=0$) pair
state is lowered and where both are equally lowered.

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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat