Two-particle Bose–Einstein momentum correlation functions are studied for charged-hadron pairs in lead-lead collisions at a center-of-mass energy per nucleon pair of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msqrt><a:msub><a:mi>s</a:mi><a:mi>NN</a:mi></a:msub></a:msqrt><a:mo>=</a:mo><a:mn>5.02</a:mn><a:mspace width="4pt"/><a:mi>TeV</a:mi></a:mrow></a:math>. The data sample, containing <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>4.27</c:mn><c:mo>×</c:mo><c:msup><c:mn>10</c:mn><c:mn>9</c:mn></c:msup></c:mrow></c:math> minimum bias events corresponding to an integrated luminosity of 0.607 <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msup><d:mtext>nb</d:mtext><d:mrow><d:mo>−</d:mo><d:mn>1</d:mn></d:mrow></d:msup></d:math>, was collected by the CMS experiment in 2018. The experimental results are discussed in terms of a Lévy-type source distribution. The parameters of this distribution are extracted as functions of particle pair average transverse mass and collision centrality. These parameters include the Lévy index or shape parameter <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>α</e:mi></e:math>, the Lévy scale parameter <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>R</f:mi></f:math>, and the correlation strength parameter <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi>λ</g:mi></g:math>. The source shape, characterized by <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mi>α</h:mi></h:math>, is found to be neither Cauchy nor Gaussian, implying the need for a full Lévy analysis. Similarly to what was previously found for systems characterized by Gaussian source radii, a hydrodynamical scaling is observed for the Lévy <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mi>R</i:mi></i:math> parameter. The <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mi>λ</j:mi></j:math> parameter is studied in terms of the core-halo model. ©2024 CERN, for the CMS Collaboration 2024 CERN