This is a new version of the DFMSPH (DFMSPH14) code published earlier. The new version is designed to obtain the nucleus–nucleus potential between two spherical nuclei by using the double folding model (DFM). In particular, the code enables to find the Coulomb barrier. Using the new version one can employ two types of the nucleon–nucleon interaction: the M3Y and Migdal interactions. The main functionalities of the original code (the nucleus–nucleus potential as a function of the distance between the centers of mass of colliding nuclei and the Coulomb barrier characteristics) have been extended: in the new version the curvature and skewness of the barrier (in addition to its height and radius) are evaluated. Program Title: DFMSPH19 Program Files doi: http://dx.doi.org/10.17632/n6bsf4zxcz.2 Licensing provisions: CC0 1.0 Programming language: C Journal reference of previous version: Comp. Phys. Comm. 206 (2016) 97-102 Does the new version supersede the previous version? Yes Reason for new version: Both M3Y and Migdal effective NN -forces are used in the literature by different groups of researchers but never within the same numerical scheme. Nature of problem: The code calculates in a semi-microscopic way the bare interaction potential between two spherical colliding nuclei. The potential is evaluated as a function of the center of mass distance. The height, radius, curvature, and skewness of the Coulomb barrier are evaluated. Dependence of the barrier parameters upon the type and/or characteristics of the effective nucleon–nucleon (NN) forces (like e.g. M3Y or Migdal type, the range of the exchange part of the nuclear term) as well as upon the parameters of the density distributions can be studied. Solution method: The nucleus–nucleus potential is evaluated using the double folding model with the Coulomb and the effective M3Y/Migdal NN interactions. For the direct parts of the Coulomb and nuclear terms, the Fourier transform method is used. In order to calculate the exchange part of the nucleus–nucleus potential based on the M3Y interactions, the density matrix expansion method is applied. Summary of revisions: 1. Additional features of DFMSPH19 (a) The DFM nucleus–nucleus potential based on the effective Migdal nucleon–nucleon forces In the DFMSPH and DFMSPH14 [1–3], only the M3Y effective NN -forces were used as the basis for the double folding model (DFM) nucleus–nucleus interaction potential. In the new version, DFMSPH19, the user still has the same option, but there is an extra possibility to use the Migdal effective NN -forces [4]. The nucleus–nucleus potential based on the Migdal forces is widely utilized in the literature (see, e.g. [5,6] and references therein). In this case, the nucleus–nucleus potential as a function of the distance R between the centers of mass of colliding projectile ("P") and target ("T") nuclei reads (1) U n M I G R = ∫ d r → P ∫ d r → T ρ P n r → P v n n s ρ T n r → T + ρ P p r → P v p p s ρ T p r → T + + ρ P n r → P v n p s ρ T p r → T + ρ P p r → P v p n s ρ T n r → T . The components of nucleon–nucleon interaction depend upon the proton ("p") and neutron ("n") densities of the interacting nuclei: v n n r → P , r → T = a + 2 g − a ρ P n r → P + ρ T n r → T ρ P n 0 + ρ T n 0 δ s → , (2) v p p r → P , r → T = a + 2 g − a ρ P p r → P + ρ T p r → T ρ P p 0 + ρ T p 0 δ s → , v n p r → P , r → T = φ + 2 γ − φ ρ P n r → P + ρ T p r → T ρ P n 0 + ρ T p 0 δ s → , v p n r → P , r → T = φ + 2 γ − φ ρ P p r → P + ρ T n r → T ρ P p 0 + ρ T n 0 δ s → . Here vector s → = R → + r → T − r → P corresponds to the distance between two specified interacting points of the projectile and target nuclei (the radius vectors of these points are r → P and r → T , respectively). The coefficients in Eq. (2) read: a = C f e x + f e x ′ , g = C f i n + f i n ′ , φ = C f e x − f e x ′ , γ = C f i n − f i n ′ . The values of the constants are: C = 300 MeV fm 3 , f i n = 0. 09 , f i n ′ = 0. 42 , f e x = − 2. 59 , f e x ′ = 0. 54. This potential is defined by the amplitude of the interaction of nucleons (i) from the peripheral parts of the density distributions, f e x ± f e x ′ (i.e. at ρ P r → P + ρ T r → T ≪ ρ P 0 + ρ T 0 ); (ii) from the peripheral part and from the inner part of the density distributions f i n ± f i n ′ (i.e. at ρ P r P → ≪ ρ P 0 , ρ T r T → ≲ ρ T 0 and ρ P r P → ≲ ρ P 0 , ρ T r T → ≪ ρ T 0 ); and (iii) from the inner parts of the density distributions 2 f i n ± f i n ′ − (f e x ± f e x ′ ) (i.e. at ρ P r P → ≲ ρ P 0 , ρ T r T → ≲ ρ T 0 ). The nucleus–nucleus potentials based on the M3Y-forces, U n M 3 Y , and on the Migdal forces, U n M I G , for the reaction 16 O+ 92 Zr are compared in Fig. 1. In this calculation the Hartree–Fock SKX nucleon densities from [7] are used. Comparing this figure with the similar ones published earlier (Fig. 3 of Ref. [8]) we conclude that our modified code produces correct results. The value of nuclear density at the given point r P (r T) is found using the input file () by means of the cubic interpolation which works rather accurately. However, in the case of the finite-range exchange term of the M3Y interaction, due to inevitable numerical errors in the derivatives entering the effective Fermi momentum k F (see Eq. (9) in Ref. [2]), the value of k F 2 sometimes becomes negative. Therefore, in the present code we keep only zero-order term calculating k F as it is made in Ref. [9]: (3) k F (r →) = 1. 5 π 2 ρ A (r →) 1 ∕ 3 The quality of this approximation is illustrated by Fig. 1 of Ref. [9]. (b) Finding the curvature and skewness of the Coulomb barrier In the present version, we add a new function FUN_Hom() which is designed to evaluate the curvature and skewness of the Coulomb barrier. For this aim the total DFM nucleus–nucleus potential is approximated by the third-order polynomial as follows: (4) U a p p R = U B + C 2 B R − R B 2 + C 3 B R − R B 3. Here U B (R B) is the height (radius) of the barrier. The stiffness C 2 B and skewness C 3 B are found by least square method for the iC2b points to the left and to the right from the barrier. The value of iC2b parameter is defined by the user in file. The value (5) ℏ ω B = C 2 B m r e d 1 ∕ 2 is calculated in this function as well. Here m r e d is the reduced mass of the reagents. The values of C 2 B (C2b), C 3 B (C3b), and ℏ ω B (Hom) are printed in the main output file . 2. The program The code consists now of 6 files and one header file. It reads the data from 5 input files and prints the results into two (for Migdal NN -forces) or 3 (for M3Y NN -forces) output files. The details of the changes in each source file as well as the description of the input and output files are presented in the file . The input and output files corresponding to two test runs are included in the program files archive. References: [1] I.I. Gontchar, D.J. Hinde, M. Dasgupta, J.O. Newton, Phys. Rev. C 69 (2004) 024610 [2] I.I. Gontchar, M.V. Chushnyakova, Comput. Phys. Commun. 181 (2010) 168–182 [3] I.I. Gontchar, M.V. Chushnyakova, Comput. Phys. Commun. 206 (2016) 97–102 [4] A.B. Migdal, Theory of Finite Fermi Systems and Application to Atomic Nuclei, Interscience, New York, 1967 [5] V. Zagrebaev, A. Karpov, Y. Aritomo, M. Naumenko, W. Greiner, Phys. Part. Nucl. 38 (2007) 469–491 [6] R.A. Kuzyakin, V. V. Sargsyan, G.G. Adamian, N. V. Antonenko, E.E. Saperstein, S. V. Tolokonnikov, Phys. Rev. C 85 (2012) 034612 [7] M. V. Chushnyakova, R. Bhattacharya, I.I. Gontchar, Phys. Rev. C. 90 (2014) 017603 [8] I.I. Gontchar, M. V. Chushnyakova, J. Phys. G Nucl. Part. Phys. 43 (2016) 045111 [9] I.I. Gontchar, M. V. Chushnyakova, Comput. Phys. Commun. 222 (2018) 414–417 [ABSTRACT FROM AUTHOR]