Deuteron lifetime in hot and dense nuclear matter near equilibrium

Abstract

We consider deuteron formation in hot and dense nuclear matter close to equilibrium and evaluate the life-time of the deuteron fluctuations within the linear response theory. To this end we derive a generalized linear Boltzmann equation where the collision integral is related to equilibrium correlation functions. In this framework we then utilize finite temperature Green functions to evaluate the collision integrals. The elementary reaction cross section is evaluated within the Faddeev approach that is suitably modified to reflect the properties of the surrounding hot and dense matter.PACS numbers: 21.65.+f,24.60.-k,25.70.-z 21.45.+v I. INTRODUCTIONThe complicated dynamics of heavy-ion collisions provides a great challenge for many-particle theory. In particular at intermediate energies where the elementary ingredients are rather well known -in terms of constituents and their respective interactions -the main problem arises from a sufficient description of the many-particle aspect. To provide single-particle distribution functions such reactions can be simulated on the basis of kinetic equations as, e.g., supplied by the Boltzmann-Uhlenbeck-Uhling (BUU) approach (see, e.g., Refs. [1][2][3][4][5][6]).However, the formation of light clusters such as deuterons, helium, α-particles, etc., is an important phenomenon of heavy-ion collisions at intermediate energies, see, e.g., Ref. [7]. Empirical evidence, including recent experimental data on cluster formation [8,9], indicate that a large fraction of deuterons can be formed in heavy-ion collisions of energies below E/A ≤ 200 MeV. Also, during the expansion of the system the density can drop below the Mott-density of deuteron dissociation [10][11][12].The description of the formation of such bound states (clusters) during the expansion of hot and dense matter is not as well elaborated as the single-particle distribution. The main obstacle is that the formation of bound states requires the notion of few-body reactions within the medium. Even the simplest case, i.e., the abundances of deuterons that are determined by the deuteron formation via N N N → dN (N nucleon, d deuteron) and break-up, dN → N N N , reactions, requires a proper treatment of the effective three-body problem. Previous studies of the kinetics of deuteron production have utilized the impulse approximation to calculate the reaction cross section at energies above 200 MeV [13]. For lower energies, viz. E/A ≤ 200 MeV, the impulse approximation fails badly and a full three-body treatment of the scattering problem is necessary [14]. Furthermore, a consistent treatment of cluster formation in expanding hot and dense matter requires the inclusion of medium effects into the respective elementary reaction cross sections as has been done in the nucleon nucleon (NN)-case and proven to be substantial in BUUsimulations of heavy-ion reactions [6]. Therefore we present an exact treatment of the three-body problem including medium modifications in mean-field approximation.The cluster formation during the expansion ...

Few-body correlations in the QCD phase diagram

“…Within linear response theory for infinite nuclear matter the use of in-medium rates leads to faster time scales for the deuteron life time and the chemical relaxation time as has been shown in detail in Refs. [20,21]. This faster time scales should have consequences for the freeze out of fragments.…”

Few-Body States in Fermi-Systems and Condensation Phenomena

“…In a more elaborated theory one has to consider rescattering of the incoming deuteron with the nucleon(s) of the medium. Summing up all the respective diagrams leads to a generic three-body in-medium scattering matrix, that has been derived in [6,7]. As a consequence the reaction rate depends strongly on the surrounding medium.…”

“…The numerical result for the life-time of the deuteron is shown in Fig. 4, where we in addition compare the use of the isolated to the in-medium break-up cross section at T = 10 MeV and a nuclear density of n = 0.007 fm −3 ≃ n 0 /25 [7,10]. The medium dependent elementary cross section leads to shorter fluctuation times.…”

“…For a numerical solution of the scattering problem we use a separable ansatz for the strong nucleon-nucleon potential [6]. In [6] we have calculated the break up cross section N d → N N N and found considerable dependence of the deuteron fluctuation time on the proper treatment of the medium dependence [7], see also Fig. 4.…”

“…for the formation of deuterons in a heavy-ion reaction, has been given in [6]. As a first application the life time of deuteron fluctuations in nuclear matter was calculated in [7]. In [8] we have given an exploratory calculation of the four-body condensate in strongly coupled fermionic systems.…”