This paper presents studies of Bose-Einstein correlations (BEC) in proton-proton collisions at a centre-of-mass energy of 13 TeV, using data from the ATLAS detector at the CERN Large Hadron Collider. Data were collected in a special low-luminosity configuration with a minimum-bias trigger and a high-multiplicity track trigger, accumulating integrated luminosities of 151 $\mu$b$^{-1}$ and 8.4 nb$^{-1}$ respectively. The BEC are measured for pairs of like-sign charged particles, each with $|\eta|$ < 2.5, for two kinematic ranges: the first with particle $p_T$ > 100 MeV and the second with particle $p_T$ > 500 MeV. The BEC parameters, characterizing the source radius and particle correlation strength, are investigated as functions of charged-particle multiplicity (up to 300) and average transverse momentum of the pair (up to 1.5 GeV). The double-differential dependence on charged-particle multiplicity and average transverse momentum of the pair is also studied. The BEC radius is found to be independent of the charged-particle multiplicity for high charged-particle multiplicity (above 100), confirming a previous observation at lower energy. This saturation occurs independent of the transverse momentum of the pair.
We have studied the inclusive production of the hadrons π ± , K ± , p, p , Λ, Λ , ρ and ⋉ in the central region at the ISR s = 53 GeV , in both pp and p p collisions. Differences are observed only for K ± , p, and p production. We then study also correlations between low- p T pp and p p pairs in the two types of collisions, separating the contribution from baryon pair production and from the incident particles (stopping protons). We observe a positive correlation between two stopping protons; between the production of two pairs, and between a stopping proton and a pair production, there are negative correlations.