Market Definition

We explain the “hypothetical monopolist test” that has become the standard methodology for identifying relevant antitrust markets in merger cases, and discuss two approaches to implementing the test. We then focus on the implementation of the test when firms offer multiple products or services, either inside or outside the candidate market, and discuss the “hypothetical cartel test” introduced in the 2010 U.S. Merger Guidelines

Tensor Forces and the Ground-State Structure of Nuclei

Two-nucleon momentum distributions are calculated for the ground states of nuclei with mass number $A\leq 8$, using variational Monte Carlo wave functions derived from a realistic Hamiltonian with two- and three-nucleon potentials. The momentum distribution of $np$ pairs is found to be much larger than that of $pp$ pairs for values of the relative momentum in the range (300--600) MeV/c and vanishing total momentum. This order of magnitude difference is seen in all nuclei considered and has a universal character originating from the tensor components present in any realistic nucleon-nucleon potential. The correlations induced by the tensor force strongly influence the structure of $np$ pairs, which are predominantly in deuteron-like states, while they are ineffective for $pp$ pairs, which are mostly in $^1$S$_0$ states. These features should be easily observable in two-nucleon knock-out processes, such as $A(e,e^\prime np)$ and $A(e,e^\prime pp)$.Comment: 4 pages including 3 figure

Dependence of two-nucleon momentum densities on total pair momentum

Two-nucleon momentum distributions are calculated for the ground states of 3He and 4He as a function of the nucleons' relative and total momenta. We use variational Monte Carlo wave functions derived from a realistic Hamiltonian with two- and three-nucleon potentials. The momentum distribution of pp pairs is found to be much smaller than that of pn pairs for values of the relative momentum in the range (300--500) MeV/c and vanishing total momentum. However, as the total momentum increases to 400 MeV/c, the ratio of pp to pn pairs in this relative momentum range grows and approaches the limit 1/2 for 3He and 1/4 for 4He, corresponding to the ratio of pp to pn pairs in these nuclei. This behavior should be easily observable in two-nucleon knock-out processes, such as A(e,e'pN).Comment: 3 pages, 3 figure