Quantum mechanical localization effects for Bose-Einstein correlations

Abstract

For a set of N identical massive boson wavepackets with optimal initial quantum mechanical localization, we calculate the Hanbury-Brown/Twiss (HBT) two-particle correlation function. Our result provides an algorithm for calculating one-particle spectra and two-particle correlations from an arbitrary phase space occupation (qi, pi, ti)i=1,N as e.g. returned by event generators. It is a microscopic derivation of the result of the coherent state formalism, providing explicit finite multiplicity corrections. Both the one-and two-particle spectra depend explicitly on the initial wavepacket width σ which parametrizes the quantum mechanical wavepacket localization. They provide upper and lower bounds which suggest that a realistic value for σ has the order of the Compton wavelength.

Coulomb final state interactions for Gaussian wave packets

“…To sum up: as long as the Gaussian wave packet width σ is included consistently in the definition of the source size, both the plane wave calculations 1,2,3,7,8,10,21,22,23 and the Gaussian wave packet formalism 16,17,18,19 lead to qualitatively and quantitatively equivalent results. While the present study proved this only for Gaussian source models, we expect it to be true quite generally since we know that 11 the relation (15) between the effective emission function and the Wigner density of single particle wave packets holds for arbitrary model distributions and that 15 two-particle momentum correlations are mostly sensitive to the Gaussian characteristics of the source in space-time.…”

“…This integral can be simplified to a 4-dimensional expression similar to (18). The limits∆ → ∞ andR → ∞ of the first term C dir (q) are obtained from (16/17) by replacing −η → η.…”

“…Unlike-sign pion correlations. -Our starting point is a set of Gaussian one-particle wave packets 16,17,18,19 …”

Testing the space-time structure of event generators

“…The "quantum" interpretation [16,15,14,5] of the event generator output starts from the observation that, for a given event, i.e. a single term in the sum of (4), the simultaneous sharp definition of the particle momenta and positions at emission violates the uncertainty relation.…”

“…Since in practice, however, one has to work with finite numbers of events, one may wish to ensure consistency with the uncertainty principle on the single-event level. This is achieved [15][16][17] by associating the centers of single-particle wave packets with the set of generated phase-space points {{(ř i ,p i ,ť i )} i∈ [1,Nm] } m∈ [1,Nev] :…”