DOI: 10.58132/tpsabb
title: Three-body physics of ultracold gases: theory of weakly bound quantum states in strongly interacting systems

description: Database contains three directories, each containing a list of subdirectories with ~1500 *.dat files (UTF-8). Database contains README files and one .opju file.Database is related to the research under the NCN 2023/49/N/ST2/03439 grant and it was generated using a program 'ThreeBodyMCJ' and 'CalcRmatrix' both compiled in fortran and partially developed by the author of this database.I) TBP_BaLiLiDirectory contents:1) data*AI* are directories containing three-body recombination rates of the 7Li-7Li-138Ba+ system calculated for a range of collision energies.Naming convention:P'n'-ScaLAA='x'-ScaLAI='y'_P'm'_xNP450_yNP150_CPUs6_RfSVD30.0d0_RSteps1001_Ein'I'_Ef'F'_'N'_NumChs50_fort.3000.datwhere:'n' - number of s-wave bound states for the 7Li2 interaction (L-J potential, C6, C8, C10 coefficients taken from: Yan, et. al, Phys. Rev. A 54, 2824 (1996))'m' - number of s-wave bound states for the (138Ba-7Li)^+ interaction (C4,C6 coefficients calculated using transition matrix elements taken from: www1.udel.edu/atom/index.html)'x' - atom-atom (7Li2) input scattering length in [rvdW] units'y' - atom-ion (138Ba-7Li)^+ input scatteing length in [rs] units, where rs = (2*RedMass*C4)^0.5/2'I' - initial collision energy in [Hartree] units'F' - final collision energy in [Hartree] units'N' - number of calculated pointsThe remaining parameters are numerical. They include e.g. the number of spline function used in the adiabatic basis set, position of calculation change from the SVD (single variable discretization) method to direct calculation of P,Q-matrices, number of CPUs used in the calculation of three-body potentials, number of calculated continuum channels, and a measure of the of hyperradial points used in the calculation of the three-body potentials etc.2) data*NoAI* are directories containing recombination rates of the 7Li-7Li-138Ba system with analogous naming convention to p. '1)'The structure of files is as follows:a_Li2 | a_Ba-Li | E_coll | L3^Tot | L3_1 | ... | L3_f  ,where a_Li2 is the Li-Li scattering length, a_Ba-Li is the Barium-Lithium scattering length (ion or neutral), E_coll is the collision energy, L3^Tot is the total recombination rate, L3_i are the partial recombination rates for each of the molecular channels -- all in atomic units.3) U_AI & U_NoAI - directories contain the adiabatic 3-body potentials of the Ba-Li-Li system (charged and neutral) with similar naming convention as the three-body-recombination ratesThe structure of files is as follows:R | U(R)_1 | ... | U(R)_f  ,where R is the hyperradius in atomic units, U(R)_i is the i-th channel4) 3bodyContains .opju file with a data of energies of 2-body bound states of the (Ba-Li-Li)^+ system. The and also contains the energies of a 3-body bound 'halo' state, obtained using the SVD (single variable discretization) method and diagonalizing the K-matrix to obtain the phase change of the total 3-body wavefunction w.r.t. the energy. The energies were calculated for a range of atom-ion scattering lengths.5) W_AI & W_NoAI - exemplary adiabatic potentials obtained by calculating the non-adiabatic P,Q matrices directly, without using the SVD method.II) TBP_BBBThe directory contains data which allows for calculations of Efimov spectra for a system of three identical bosons interacting via the van-der-Waals potential (~1/r^6) modeled via the Lennard-Jones potential: -16/r^6*(1-lambda^6/r^6), where r is the interatomic distance, and lambda is the postion of the L-J zero. All values are calculated in van-der-Waals units (length - [rvdW], mass - 1, energy - [EvdW]). This also implicates the mathematical form of the two-body potential function. The interaction model consists of two two-body channels (open and closed) with a gaussian coupling:alphaS*exp(-(r-beta)^2/2/gamma^2). Channels are separated by a threshold value of du*B, where du = 0.008 [EvdW/G] and calcultions are performed at resonance values of the magnetic field (which differ depending on the shape of coupling).1) Directories aBg'a'_P'n'_v'b'_U contain the adiabatic three-body potentials U(R),where'a' - 2-body background scattering length in [rvdW]'n' - number of s-wave bound states of the two-body open-channel'b' - the vibrational quantum number + 1 of the closed-channel bound stateFile names are as follows:Bfield='B0'_alpha'aa'_gamma'g'_betaP1min_fort.100.dat'B0' - the on-resonance value of teh magnetic field [G]'aa' - coupling strength in [EvdW]'g' - coupling width in [rvdW]name 'P1min' indicates the coupling is centered at the minimum of the closed channel.The structure of files is as follows:R | U(R)_1 | ... | U(R)_f  ,where R is the hyperradius in atomic units, U(R)_i is the i-th channelThe lambda values for the - open channels in [rvdW] units:P1* - 0.602806782761612P2* - 0.465470137047458 P3* - 0.392804382811181 P4* - 0.346119015107560- closed channels [rvdW]:P1_v1 - 0.450P2_v1 - 0.397 P3_v1 - 0.350P3_v2 - 0.294P4_v1 - 0.300P4_v2 - 0.270P4_v3 - 0.2502) Directories TimeDelay_aBg'a'-P'n'_v'b' contain the functions of the phase of the total three-body wavefunction (sum of eigenvalues of the K-matrix) ver. energy, which allows to calculate the energies and widths of the trimer states (taking the first derivative w.r.t. energy).The directory name can contain the information about the initial and final values of the energy (Ein, Efin) in [EvdW] units.The file name convention is analogous to p. '1)'. Additional information in file names relates to numerical parameters.The structure of files is as follows:E [EvdW] | 0.000 | \Phi^Tot | \Phi_1 | ... | \Phi_f ,where E is the energy in [EvdW] units, \Phi^Tot is the sum of eigenvalues of the K-matrix, and \Phi_i is the i-th eigenvalue of the K-matrix.III) TBP_BBB_Efimov_spectraThe directory contains data of Efimov spectra for a system of three identical bosons interacting via the van-der-Waals potential (~1/r^6) modeled via the Lennard-Jones potential as described in file "II)".The file contains files named:a) "Efimov_spectrum_PnPm.dat"b) "Efimov_spectrum_PnPm_AttractiveForce_sresV.dat", wheren = number of s-wave bound states of the two-body open-channelm = number of s-wave bound states of the two-body closed-channelV = value of the s_res parameter for the underlying Feshbach resonanceThe structure of files is as followsa) s_res | "Around[ En , Gam ]", whereEn = energy of the Efimov state,Gam = lifetime of the Efimov state,b) R0 | "Around[ En , Gam ]"R0 = position of an added, attractive three-body force in the form of a gaussian function = A*Exp[-(R - )/c], where R is the hyperradius, c - width of the gaussian set at 0.25 r_vdW (van der Waals length units), A - ampltiude of the gaussian set at 1.0 E_vdW (van der Waals energy units), R0 - center of the gaussian function in r_vdW units.This test allows to check whether the amplitude of the Efimov state is at long- or short-range which allows to describe the non-universal properties of the state at s_res &lt; 1.