  Baryons with one or more heavy quarks have been shown, in the context of a
nonrelativistic description, to exhibit mass inequalities under permutations of
their quarks, when spin averages are taken. These inequalities sometimes are
invalidated when spin-dependent forces are taken into account. A notable
instance is the inequality $2E(Mmm) > E(MMm) + E(mmm)$, where $m = m_u = m_d$,
satisfied for $M = m_b$ or $M = m_c$ but not for $M = m_s$, unless care is
taken to remove effects of spin-spin interactions. Thus in the quark-level
analog of nuclear fusion, the reactions $\Lambda_b \Lambda_b \to \Xi_{bb}N$ and
$\Lambda_c \Lambda_c \to \Xi_{cc}^{++}n$ are exothermic, releasing respectively
138 and 12 MeV, while $\Lambda \Lambda \to \Xi N$ is endothermic, requiring an
input of between 23 and 29 MeV. Here we explore such mass inequalities in the
context of an approach, previously shown to predict masses successfully, in
which contributions consist of additive constituent-quark masses, spin-spin
interactions, and additional binding terms for pairs each member of which is at
least as heavy as a strange quark.
