Using two specific models and a model-independent formalism, we show that in addition to the usual quadratic "side, " "out, " and "longitudinal" terms, a previously neglected "out-longitudinal" cross term arises naturally in the exponent of the two-particle correlator. Since its effects can be easily observed, such a term should be included in any experimental fits to correlation data. We also suggest a method of organizing correlation data using rapidity rather than longitudinal momentum differences, since in the former every relevant quantity is longitudinally boost invariant.PACS numbers: 25.75.+rThe experimentally measured Hanbury-Brown -Twiss (HBT) correlation between two identical particles emitted in a high energy collision defines a six-dimensional function of the momenta p~a nd p2 [1]. A popular way of presenting these is in terms "size parameters" derived from a Gaussian fit to the data of the form [2 -5]

Using a quadratic saddle-point approximation, we show how information about a particle-emitting source can be extracted from gaussian fits to twoparticle correlation data. Although the formalism is completely general, extraction of the relevant parameters is much simpler for sources within an interesting class of azimuthally symmetric models. After discussing the standard fitting procedure, we introduce a new gaussian fitting procedure which is an azimuthally symmetric generalization of the Yano-Koonin formalism for spherically symmetric sources. This new fitting procedure has the advantage that in addition to being able to measure source parameters in a fixed frame or the longitudinally co-moving system, it can also measure these parameters in the local rest frame of the source.

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We clarify the relationship between the current formalism developed by Gyulassy, Kaufmann and Wilson and the Wigner function formulation suggested by Pratt for the 2-particle correlator in Hanbury-Brown Twiss interferometry. When applied to a hydrodynamical description of the source with a sharp freeze-out hypersurface, our results remove a slight error in the prescription given by Makhlin and Sinyukov which has led to confusion in the literature.It is widely accepted that if the nuclear matter created in ultra-relativistic heavyion collisions attains a high enough energy density, it will undergo a phase transition into a quark-gluon plasma. For this reason, it is of great interest to determine the energy densities actually attained in these collisions. The total interaction energy of a given reaction can be directly measured by particle calorimeters and spectrometers.Although there is no analogous direct measurement for the size of the reaction region, Hanbury-Brown Twiss interferometry [1] provides an indirect measurement in termsof the correlations between produced particles.Ten years ago, Pratt [2] used the covariant current formulation of Gyulassy, Kaufmann and Wilson [3] to show that the correlations between two particles could be expressed in terms of one-particle pseudo-Wigner functions. Although Pratt's derivation was non-relativistic, it provided a valuable link between the experimental data and many semi-classical event generators whose output came in the form of one-particle * Work supported by BMFT, DFG, and GSI

Let S be a numerical monoid (i.e. an additive submonoid of ℕ0) with minimal generating set 〈n1,…,nt〉. For m ∈ S, if [Formula: see text], then [Formula: see text] is called a factorization length of m. We denote by [Formula: see text] (where mi < mi+1 for each 1 ≤ i < k) the set of all possible factorization lengths of m. The Delta set of m is defined by Δ(m) = {mi+1 - mi|1 ≤ i < k} and the Delta set of S by Δ(S) = ∪m∈SΔ(m). In this paper, we address some basic questions concerning the structure of the set Δ(S). In Sec. 2, we find upper and lower bounds on Δ(S) by finding such bounds on the Delta set of any monoid S where the associated reduced monoid S red is finitely generated. We prove in Sec. 3 that if S = 〈n, n + k, n + 2k,…,n + bk〉, then Δ(S) = {k}. In Sec. 4 we offer some specific constructions which yield for any k and v in ℕ a numerical monoid S with Δ(S) = {k, 2k,…,vk}. Moreover, we show that Delta sets of numerical monoids may contain natural "gaps" by arguing that Δ(〈n, n + 1, n2 - n - 1〉) = {1,2,…,n - 2, 2n - 5}.

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We construct an algorithm which computes the catenary and tame degree of a numerical monoid. As an example we explicitly calculate the catenary and tame degree of numerical monoids generated by arithmetical sequences in terms of their first element, the number of elements in the sequence and the di¤erence between two consecutive elements of the sequence.

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