Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Expressions for the number of J=0 pairs in even-even Ti isotopes   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 in terms of the probability amplitude D(Jp Jn) that the
protons couple to Jp and the neutrons to Jn. 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, 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,
e.g., 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=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, as well as the QQ interaction. We
are also able to obtain simplified formulae for the number of J=0 pairs for the
I=0 states in {46}Ti and {48}Ti by noting that the unique state with isospin
|Tz|+2 is orthogonal to all the states with isospin |Tz|.

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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: math
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th