PHQMD

Parton-Hadron-Quantum-Molecular Dynamics

A microscopic N-body transport approach for heavy-ion collisions, cluster formation, and hypernuclei production.

About PHQMD

The Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) transport approach is designed to provide a microscopic description of nuclear cluster and hypernucleus formation, as well as general particle production in heavy-ion reactions at relativistic energies.

PHQMD is a microscopic n-body transport approach that combines baryon propagation from the Quantum Molecular Dynamics (QMD) model with the dynamical properties and interactions of hadronic and partonic degrees of freedom from the established Parton-Hadron-String Dynamics (PHSD) approach.

In contrast to coalescence or statistical models often used for cluster formation, PHQMD forms clusters dynamically through baryon interactions within QMD, allowing the propagation of n-body Wigner density and n-body phase-space correlations, which are essential for cluster formation.

Clusters are identified by the MST (Minimum Spanning Tree) or SACA (Simulated Annealing Cluster Algorithm), which search for the most bound nucleon-cluster configurations. Collisions among hadrons, Quark-Gluon-Plasma formation, and parton dynamics are treated in PHQMD in the same way as in PHSD.

Cluster Production in PHQMD

Clusters can be identified in PHQMD using three different algorithms:

Potential mechanism: The attractive potential between baryons with small relative momentum can form bound nucleon groups. In the MST clusterization algorithm, nucleons i and j are considered bound when |r_i^* - r_j^*| < r_clus, where positions are boosted to the pair center-of-mass frame and r_clus = 4 fm (approximately the range of the attractive NN potential). Additionally, clusters must satisfy negative binding energy, E_B < 0. MST is used as a cluster recognition tool (applied perturbatively), while QMD propagates baryons rather than pre-formed clusters.
Kinetic mechanism: Deuterons are created through catalytic hadronic reactions πNN ↔ πd and NNN ↔ Nd in different isospin channels. Quantum effects are included via excluded volume and projection onto the deuteron wave function in momentum space, which reduces production especially at target/projectile rapidities.
Coalescence mechanism: A proton and neutron form a deuteron if their phase-space distance at freeze-out satisfies |r₁ - r₂| ≤ 3.575 fm and |p₁ - p₂| ≤ 285 MeV/c. In PHQMD this method is used for model studies and comparison purposes.

Publications

How to cite PHQMD and selected related publications.

How to cite PHQMD

Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) - A Novel Microscopic N-Body Transport Approach for Heavy-Ion Collisions, Dynamical Cluster Formation and Hypernuclei Production

J. Aichelin, E. Bratkovskaya, A. Le Fevre, V. Kireyeu, V. Kolesnikov, Y. Leifels, V. Voronyuk, G. Coci · Phys. Rev. C 101 (2020) 044905

DOI arXiv Inspire

Show abstract

Cluster and hypernuclei production in heavy-ion collisions is investigated within the PHQMD transport approach. The model propagates n-body correlations and forms clusters dynamically via QMD interactions, with cluster recognition via MST/SACA. The work shows a good description of bulk observables from SIS to RHIC energies and provides the basis for dedicated cluster and hypernuclei studies.

PHQMD - A Microscopic Transport Approach for Heavy-Ion Collisions and Cluster Formation

J. Aichelin, M. Winn, E. L. Bratkovskaya, A. Le Fevre, Y. Leifels, V. Kireyeu, V. Kolesnikov, V. Voronyuk

Advances in Nuclear Physics: Structure and Reactions, 105-117

DOI Inspire

Dynamical mechanisms for deuteron production at mid-rapidity in relativistic heavy-ion collisions from SIS to RHIC energies

G. Coci, S. Glaessel, V. Kireyeu, J. Aichelin, C. Blume, E. Bratkovskaya, V. Kolesnikov, V. Voronyuk

arXiv Inspire

Cluster formation near midrapidity - can the mechanism be identified experimentally?

V. Kireyeu, G. Coci, S. Glaessel, J. Aichelin, C. Blume, E. Bratkovskaya

arXiv Inspire

Cluster and hyper-cluster production in relativistic heavy-ion collisions within the PHQMD approach

S. Glaessel, V. Kireyeu, V. Voronyuk, J. Aichelin, C. Blume, E. Bratkovskaya, G. Coci, V. Kolesnikov, M. Winn · Phys. Rev. C 105 (2022) 014908

DOI arXiv Inspire

Deuteron production in ultrarelativistic heavy-ion collisions

V. Kireyeu, J. Steinheimer, J. Aichelin, M. Bleicher, E. Bratkovskaya · Phys. Rev. C 105 (2022) 044909

DOI arXiv Inspire

Modelling relativistic heavy-ion collisions with dynamical transport approaches

M. Bleicher and E. Bratkovskaya · Prog. Part. Nucl. Phys. 122 (2022), 103920

DOI Inspire

Midrapidity cluster formation in heavy-ion collisions

E. Bratkovskaya et al. · EPJ Web of Conferences 276, 03005 (2023)

DOI arXiv Inspire

Prospects for the study of strangeness production within PHQMD

V. Kireyeu et al. · Journal of Physics: Conference Series 1690 (2020) 012113

DOI Inspire

Cluster dynamics studied with the phase-space minimum spanning tree approach

V. Kireyeu · Phys. Rev. C 103, 054905 (2021)

DOI arXiv Inspire

Comparison of heavy ion transport simulations: Ag + Ag collisions at Elab = 1.58A GeV

T. Reichert, A. Elz, T. Song, G. Coci, M. Winn, E. Bratkovskaya, J. Aichelin, J. Steinheimer and M. Bleicher · J. Phys. G 49 (2022) 055108

DOI arXiv Inspire

Dynamical cluster and hypernuclei production in heavy-ion collisions

S. Glaessel, V. Kireyeu, V. Voronyuk, J. Aichelin, C. Blume, E. Bratkovskaya, G. Coci, V. Kolesnikov and M. Winn · EPJ Web Conf. 259 (2022), 11003

DOI arXiv Inspire

Monte-Carlo studies of the MPD detector performance for the measurement of hypertritons in heavy-ion collisions at NICA energies

V. I. Kolesnikov, V. A. Kireyeu, A. A. Mudrokh, V. A. Vasendina, A. I. Zinchenko, D. A. Zinchenko, J. Aichelin, and E. Bratkovskaya · Phys. Part. Nucl. Lett. 19 (2022) 46-53

DOI Inspire

Prospects of studying the production of hypernuclei in heavy-ion interactions at the NICA collider at JINR

V. Kireyeu, A. Mudrokh, V. Kolesnikov, A. Zinchenko, V. Vasendina, J. Aichelin and E. Bratkovskaya · PoS PANIC2021 (2022), 220

DOI Inspire

Parton Hadron Quantum Molecular Dynamics (PHQMD) - A Novel Microscopic N-Body Transport Approach For Heavy-Ion Dynamics and Hypernuclei Production

Elena Bratkovskaya, Joerg Aichelin, Arnaud Le Fevre, Viktar Kireyeu, Vadim Kolesnikov, Yvonne Leifels, and Vadim Voronyuk · Springer Proc. Phys. 250 (2020) 197-201

DOI arXiv Inspire

Hadron production in elementary nucleon-nucleon reactions from low to ultra-relativistic energies

V. Kireyeu, I. Grishmanovskii, V. Kolesnikov, V. Voronyuk, E. Bratkovskaya · Eur. Phys. J. A 56 (2020) 223

DOI arXiv Inspire

A new review of excitation functions of hadron production in pp collisions in the NICA energy range

V. Kolesnikov, V. Kireyeu, V. Lenivenko, A. Mudrokh, K. Shtejer, D. Zinchenko, E. Bratkovskaya · Phys. Part. Nucl. Lett. 17 (2020) 142-153

DOI arXiv Inspire

PHQMD Model for the Formation of Nuclear Clusters and Hypernuclei in Heavy Ion Collisions

V. Kireyeu, J. Aichelin, E. Bratkovskaya, A. Le Fevre, V. Lenivenko, V. Kolesnikov, Y. Leifels, V. Voronyuk · Izv. Ross. Akad. Nauk Ser. Fiz. 84 (2020) 1161-1166

DOI arXiv Inspire

Progress in the construction of the NICA accelerator complex

V. I. Kolesnikov et al. · Phys. Scripta 95 (2020) 094001

DOI Inspire

Prospects for Studying Hyperons and Hypernuclei on the NICA Collider

V. I. Kolesnikov, A. I. Zinchenko, V. A. Vasendina · Bull. Russ. Acad. Sci. Phys. 84 (2020) 451-454

DOI PDF Inspire

Perspektivy izucheniya giperonov i giperyader na kollaidere NICA

V. I. Kolesnikov, A. I. Zinchenko, V. A. Vasendina · Izvestiya RAN, Seriya fizicheskaya 84 (2020) 575-579

PDF

Results

Selected PHQMD comparison plots and links to references.

q1: rise and fall of cluster multiplicity — q1: Multiplicity of clusters versus Zbound2.

"Rise and fall" of the multiplicity of clusters with Z in [3, 30] as a function of total bound charge Zbound2.

Paper Experimental data Experimental data

q2: average charge of the largest cluster — q2: Average charge of the largest cluster versus bound charge.

PHQMD results with SACA at different times compared to ALADIN data.

Paper Experimental data

q3: rapidity distribution from FOPI comparison — q3: Scaled rapidity distributions in central Au+Au collisions.

Comparison of PHQMD cluster-identification strategies (MST/SACA) to FOPI observables.

Paper Experimental data

q4: invariant multiplicities for central collisions — q4: Invariant multiplicities for 10% central Au+Au collisions.

p, d, t, 3He, 4He multiplicities at low pT versus rapidity in Ebeam = 11 AGeV.

Paper Experimental data Experimental data

q5: invariant multiplicities for min-bias collisions — q5: Invariant multiplicities for min-bias Au+Au collisions.

PHQMD prediction with hard EoS and MST cluster identification for minimum-bias events.

Paper Experimental data Experimental data

Compilation of experimental cluster data used for PHQMD validation

Experiment	System	Energy	Species	Paper
FOPI	Au+Au	E_lab = 1.5 A.GeV	d, t	10.1016/j.nuclphysa.2010.09.008
E802	Au+Pb	E_lab = 10.6 A.GeV	d	10.1016/j.nuclphysa.2010.09.008
E864	Au+Pb / Au+Pt	E_lab = 10.6 A.GeV	d,t,3He, 4He	PhysRevC.61.064908 PhysRevLett.83.5431 PhysRevC.70.024902
E878 + E886	Au+Au	E_lab = 10.6 A.GeV	d, t, 3He, 4He	10.1103/PhysRevC.58.1155
NA49	Pb+Pb	P_lab = 20, 30, 40, 80, 158 GeV/c	d,t,3He	10.1103/PhysRevC.94.044906
STAR BES	Au+Au	sqrt(sNN) = 7.7, 11.5, 19.6, 27, 39, 62.4, 200 GeV	d	10.1103/PhysRevC.99.064905