This work describes a few-body dynamics method based on the Faddeev integral equations in momentum space for determining the total cross sections of fusion and breakup reactions with two- and three-body final channels in the continuum, employing a cluster representation of the colliding nuclei. Total cross sections were obtained for the reactions $^3\text{He}(T,D)^4\text{He}$ , $^3\text{He}(T,np)^4\text{He}$ , $^3\text{He}(T,nD)^3\text{He}$ , $^3\text{He}(^3\text{He},2p)^4\text{He}$ , $^3\text{He}(^3\text{He},pD)^3\text{He}$ , $^7\text{Li}(^3\text{He},\phantom{0}^4\text{He})^6\text{Li}$ , $^7\text{Li}(^3\text{He},D^4\text{He})^4\text{He}$ , and $^7\text{Li}(^3\text{He},T^3\text{He})^4\text{He}$ , in which both the projectile and the target nucleus were treated in a cluster representation. The work also implements a two-potential method to determine the Coulomb $t-$ matrix and to account for Coulomb effects in short-range dynamics in momentum space. Calculations of the initial-state Coulomb interaction were performed; furthermore, an estimate was obtained for the magnitude of the off-shell effect of the Coulomb $t-$ matrix, as well as the magnitude of the atomic electron anti-screening effect on the Coulomb interaction of the colliding nuclei. The calculated contribution of the cluster mechanism to the total cross section of the considered fusion reactions in the kinetic energy range $T\in[1~\text{keV},20~\text{MeV}]$ is in good agreement with known experimental data.This work describes a few-body dynamics method based on the Faddeev integral equations in momentum space for determining the total cross sections of fusion and breakup reactions with two- and three-body final channels in the continuum, employing a cluster representation of the colliding nuclei. Total cross sections were obtained for the reactions $^3\text{He}(T,D)^4\text{He}$, $^3\text{He}(T,np)^4\text{He}$, $^3\text{He}(T,nD)^3\text{He}$, $^3\text{He}(^3\text{He},2p)^4\text{He}$, $^3\text{He}(^3\text{He},pD)^3\text{He}$, $^7\text{Li}(^3\text{He},\phantom{0}^4\text{He})^6\text{Li}$, $^7\text{Li}(^3\text{He},D^4\text{He})^4\text{He}$, and $^7\text{Li}(^3\text{He},T^3\text{He})^4\text{He}$, in which both the projectile and the target nucleus were treated in a cluster representation. The work also implements a two-potential method to determine the Coulomb $t-$matrix and to account for Coulomb effects in short-range dynamics in momentum space. Calculations of the initial-state Coulomb interaction were performed; furthermore, an estimate was obtained for the magnitude of the off-shell effect of the Coulomb $t-$matrix, as well as the magnitude of the atomic electron anti-screening effect on the Coulomb interaction of the colliding nuclei. The calculated contribution of the cluster mechanism to the total cross section of the considered fusion reactions in the kinetic energy range $T\in[1~\text{keV},20~\text{MeV}]$ is in good agreement with known experimental data.

nucl-thCross-listedarXiv:2604.22537Apr 27, 2026

Theoretical studies of few-body problems

Uttam Kumar Chowdhury

Jan 1, 20120 citations

First-principles path-integral renormalization-group method for Coulombic many-body systems

Masashi Kojo, Kikuji Hirose

An approach for obtaining the ground state of Coulombic many-body systems is presented. This approach is based on the path-integral renormalization-group method with nonorthogonal Slater determinants, is free of the negative sign problem, and can handle higher dimensional systems with consideration of the correlation effect. Furthermore, it can be easily extended to the multicomponent quantum systems that contain more than two kinds of quantum particles. According to our results obtained with the present approach, it achieves the same accuracy as the variational Monte Carlo method with a few Slater determinants and enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation.An approach for obtaining the ground state of Coulombic many-body systems is presented. This approach is based on the path-integral renormalization-group method with nonorthogonal Slater determinants, is free of the negative sign problem, and can handle higher dimensional systems with consideration of the correlation effect. Furthermore, it can be easily extended to the multicomponent quantum systems that contain more than two kinds of quantum particles. According to our results obtained with the present approach, it achieves the same accuracy as the variational Monte Carlo method with a few Slater determinants and enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation.

Physical Review AOct 23, 20094 citations

^3\text{He}(T,D)^4\text{He}

^3\text{He}(T,np)^4\text{He}

^3\text{He}(T,nD)^3\text{He}

^3\text{He}(^3\text{He},2p)^4\text{He}

^3\text{He}(^3\text{He},pD)^3\text{He}

^7\text{Li}(^3\text{He},\phantom{0}^4\text{He})^6\text{Li}

^7\text{Li}(^3\text{He},D^4\text{He})^4\text{He}

, and

^7\text{Li}(^3\text{He},T^3\text{He})^4\text{He}

, in which both the projectile and the target nucleus were treated in a cluster representation. The work also implements a two-potential method to determine the Coulomb

t-

matrix and to account for Coulomb effects in short-range dynamics in momentum space. Calculations of the initial-state Coulomb interaction were performed; furthermore, an estimate was obtained for the magnitude of the off-shell effect of the Coulomb

t-

matrix, as well as the magnitude of the atomic electron anti-screening effect on the Coulomb interaction of the colliding nuclei. The calculated contribution of the cluster mechanism to the total cross section of the considered fusion reactions in the kinetic energy range

T\in[1~\text{keV},20~\text{MeV}]

is in good agreement with known experimental data.