### Abstract

This is a new version of the DFMSPH code designed to obtain the nucleus-nucleus potential by using the double folding model (DFM) and in particular to find the Coulomb barrier. The new version uses the charge, proton, and neutron density distributions provided by the user. Also we added an option for fitting the DFM potential by the Gross-Kalinowski profile. The main functionalities of the original code (e.g. the nucleus-nucleus potential as a function of the distance between the centers of mass of colliding nuclei, the Coulomb barrier characteristics, etc.) have not been modified. New version program summary: Program title: DFMSPH14. Catalog identifier: AEFH_v2_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. Licensing provisions: GNU General Public License, version 3. No. of lines in distributed program, including test data, etc.: 7211. No. of bytes in distributed program, including test data, etc.: 114404. Distribution format: tar.gz. Programming language: C. Computer: PC and Mac. Operation system: Windows XP and higher, MacOS, Unix/Linux. Memory required to execute with typical data: below 10 Mbyte. Classification: 17.9. Catalog identifier of previous version: AEFH_v1_0. Journal reference of previous version: Comp. Phys. Comm. 181 (2010) 168. Does the new version supersede the previous version?: Yes. Nature of physical problem: The code calculates in a semimicroscopic way the bare interaction potential between two colliding spherical nuclei as a function of the center of mass distance. The height and the position of the Coulomb barrier are found. The calculated potential is approximated by an analytical profile (Woods-Saxon or Gross-Kalinowski) near the barrier. Dependence of the barrier parameters upon the characteristics of the effective NN forces (like, e.g. the range of the exchange part of the nuclear term) can be investigated. Method of solution: The nucleus-nucleus potential is calculated using the double folding model with the Coulomb and the effective M3Y NN interactions. For the direct parts of the Coulomb and the nuclear terms, the Fourier transform method is used. In order to calculate the exchange parts, the density matrix expansion method is applied. Typical running time: less than 1 minute. Reason for new version: Many users asked us how to implement their own density distributions in the DFMSPH. Now this option has been added. Also we found that the calculated Double-Folding Potential (DFP) is approximated more accurately by the Gross-Kalinowski (GK) profile. This option has been also added. Summary of revisions: 1. Additional features of DFMSPH14 (a) Projectile and target densities as input files In the DFMSPH, there was a limited number of profiles for the charge, proton, and neutron density distributions among which the user could choose. In the new version, DFMSPH14, the user must provide two input files < inp_rhoP.c. > and < inp_rhoT.c. >. In these files the charge (RHO_q), proton (RHO_Z), neutron (RHO_N), and nucleon (RHO_A) density distributions are defined for the projectile (P) and target (T) nuclei as functions of the distance from the nucleus center (r). The technical explanation of these files might be found in subsection 2.9. (b) New analytical profile for fitting the calculated potential Now the nuclear term of the double folding potential Un(R) might be fitted by the Gross-Kalinowski profile in addition to the Woods-Saxon (WS) profile. The Gross-Kalinowski (GK) profile V(R)reads [1] (1)V(R)=-ln(1+exp(-δRaGK))[A0GK+A1GKδR+A2GKδR2],(2)δR=R-rGK(AP1/3+AT1/3). The quality of the GK or WS fits is represented by a relative error (3)χ2=1N∑i=1N(Un(Ri)-V(Ri)Un(Ri)+V(Ri))2 (two variables chi2WSmin and chi2GKmin correspond to these errors). The distances Ri span the values fRBfin(dot operator)RB<Ri<fRBstart(dot operator)RB around the fusion barrier radius RB. The step of Ri variation, δRfit, is defined by the variable deliR: (4)δRfit=RCCstep(dot operator)deliR. The values of deliR, fRBstart, and fRBfin are defined by the user in the file <inp_dfmsph14.c. >. The recommended values for the GK-profile are: deliR=5, fRBstart = 1.2, and fRBfin = 0.8. The recommended values for the WS-profile are: deliR = 5, fRBstart = 1.1, and fRBfin = 0.9. The range and the step of the variation of the Gross-Kalinowski parameters are defined by the user in the file <inp_dfmsph14.c. >. The recommended values are following: 20<A0GKMeV-1<40,δA0GK=0.5MeV ;0<A1GKMeV-1fm<5,δA1GK=0.5MeVfm-1;0<A2GKMeV-1fm2<5,δA2GK=0.5MeVfm-2;0.5<aGKfm-1<0.8,δaGK=0.02fm ;1.2<rGKfm-1<1.4,δrGK=0.02fm The fits are performed provided the variables chi2WS and/or chi2GK in the file <inp_dfmsph14.c. > are positive. The values of the parameters rGK, aGK, A0GK, A1GK, A2GK corresponding to the minimum value of the χ2 as well as this value itself are printed in the main output file <out_dfmsph14.c. >.The GK approximation fits the DFP more accurately in a wider range of R than the WS profile does. This is useful, in particular, for performing the dynamical modeling of the fusion process (see details in [2]). Fig. 1 shows to what extent the GK approximation (thin solid curve) is better than the conventional WS (thick solid curve) one. Note, that the use of wider range of R for the WS fitting results in poor agreement with DFP (the latter is shown by symbols in Fig. 1). We take this opportunity to correct several misprints in [3]. Eq. (21) should read (5)UnD(R)=2πg(EP)∫0kmaxdkk2j0(kR)vD(k)C(ÃPAÃTA+αhDPhDT-γzDPzDT). Eq. (24) should read (6)zDP(T)(k)=4π∫0rmaxρP(T)A(r)ρP(T)A(r)j0(kr)r2dr. Display Omitted. 2. The program The code consists now of 6 files and one header file. It reads the data from three input files and prints the results into three output files. Below the list of the files with short comments concerning the revisions is presented. 2.1. File <dfmsph_. mai.c> This file has been changed.double BARR(double RCMini, double RCMfin, double RCMstep) - unchanged;. void WS_DFP() - has been changed. Now the range of the center of mass distance, in which the approximation of the DFP is performed, is defined by the user (the variables fRBstart and fRBfin in <inp_dfmsph14.c. > are responsible for that, see subsections 1b, 2.8).void GK_DFP() - a new function which fits the nuclear term of the double folding potential by the Gross-Kalinowski profile (1), (2). 2.2. File <dfmsph_. fun.c> This file has been changed.double CubeInterpD2gDx2(double x, double *ydim, double *gdim) - a new function calculating the second derivative of the polynomial function (spline) g with respect to the variable y at the point x.double CubeInterpDgDx(double x, double *ydim, double *gdim) - a new function calculating the first derivative of the polynomial function (spline) g with respect to the variable y at the point x.double CubeInterp(double x, double *ydim, double *gdim) - a new function interpolating the discrete function gdim defined at the nodes ydim by a polynomial function (spline) g and calculating the value g(x).long CheckIndex(long down, long index, long up) - unchanged.double j0BRay(double x) - unchanged.double Dj0BRayDx(double x) - unchanged.double D2j0BRayDx2(double x) - unchanged.void GAUSS() - unchanged.int Number() - unchanged.double diffsimple(double stepp, dou

Original language | English |
---|---|

Journal | Computer Physics Communications |

DOIs | |

Publication status | Accepted/In press - 15 Mar 2016 |

### Fingerprint

### Keywords

- Coulomb barrier
- Density dependent NN forces
- Double folding model
- M3Y-interaction
- Nucleus-nucleus collision

### ASJC Scopus subject areas

- Hardware and Architecture
- Physics and Astronomy(all)

### Cite this

*Computer Physics Communications*. https://doi.org/10.1016/j.cpc.2016.04.012

**DFMSPH14 : A C-code for the double folding interaction potential of two spherical nuclei.** / Gontchar, I. I.; Chushnyakova, M. V.

Research output: Contribution to journal › Article

*Computer Physics Communications*. https://doi.org/10.1016/j.cpc.2016.04.012

}

TY - JOUR

T1 - DFMSPH14

T2 - A C-code for the double folding interaction potential of two spherical nuclei

AU - Gontchar, I. I.

AU - Chushnyakova, M. V.

PY - 2016/3/15

Y1 - 2016/3/15

N2 - This is a new version of the DFMSPH code designed to obtain the nucleus-nucleus potential by using the double folding model (DFM) and in particular to find the Coulomb barrier. The new version uses the charge, proton, and neutron density distributions provided by the user. Also we added an option for fitting the DFM potential by the Gross-Kalinowski profile. The main functionalities of the original code (e.g. the nucleus-nucleus potential as a function of the distance between the centers of mass of colliding nuclei, the Coulomb barrier characteristics, etc.) have not been modified. New version program summary: Program title: DFMSPH14. Catalog identifier: AEFH_v2_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. Licensing provisions: GNU General Public License, version 3. No. of lines in distributed program, including test data, etc.: 7211. No. of bytes in distributed program, including test data, etc.: 114404. Distribution format: tar.gz. Programming language: C. Computer: PC and Mac. Operation system: Windows XP and higher, MacOS, Unix/Linux. Memory required to execute with typical data: below 10 Mbyte. Classification: 17.9. Catalog identifier of previous version: AEFH_v1_0. Journal reference of previous version: Comp. Phys. Comm. 181 (2010) 168. Does the new version supersede the previous version?: Yes. Nature of physical problem: The code calculates in a semimicroscopic way the bare interaction potential between two colliding spherical nuclei as a function of the center of mass distance. The height and the position of the Coulomb barrier are found. The calculated potential is approximated by an analytical profile (Woods-Saxon or Gross-Kalinowski) near the barrier. Dependence of the barrier parameters upon the characteristics of the effective NN forces (like, e.g. the range of the exchange part of the nuclear term) can be investigated. Method of solution: The nucleus-nucleus potential is calculated using the double folding model with the Coulomb and the effective M3Y NN interactions. For the direct parts of the Coulomb and the nuclear terms, the Fourier transform method is used. In order to calculate the exchange parts, the density matrix expansion method is applied. Typical running time: less than 1 minute. Reason for new version: Many users asked us how to implement their own density distributions in the DFMSPH. Now this option has been added. Also we found that the calculated Double-Folding Potential (DFP) is approximated more accurately by the Gross-Kalinowski (GK) profile. This option has been also added. Summary of revisions: 1. Additional features of DFMSPH14 (a) Projectile and target densities as input files In the DFMSPH, there was a limited number of profiles for the charge, proton, and neutron density distributions among which the user could choose. In the new version, DFMSPH14, the user must provide two input files < inp_rhoP.c. > and < inp_rhoT.c. >. In these files the charge (RHO_q), proton (RHO_Z), neutron (RHO_N), and nucleon (RHO_A) density distributions are defined for the projectile (P) and target (T) nuclei as functions of the distance from the nucleus center (r). The technical explanation of these files might be found in subsection 2.9. (b) New analytical profile for fitting the calculated potential Now the nuclear term of the double folding potential Un(R) might be fitted by the Gross-Kalinowski profile in addition to the Woods-Saxon (WS) profile. The Gross-Kalinowski (GK) profile V(R)reads [1] (1)V(R)=-ln(1+exp(-δRaGK))[A0GK+A1GKδR+A2GKδR2],(2)δR=R-rGK(AP1/3+AT1/3). The quality of the GK or WS fits is represented by a relative error (3)χ2=1N∑i=1N(Un(Ri)-V(Ri)Un(Ri)+V(Ri))2 (two variables chi2WSmin and chi2GKmin correspond to these errors). The distances Ri span the values fRBfin(dot operator)RB<Ri. The recommended values for the GK-profile are: deliR=5, fRBstart = 1.2, and fRBfin = 0.8. The recommended values for the WS-profile are: deliR = 5, fRBstart = 1.1, and fRBfin = 0.9. The range and the step of the variation of the Gross-Kalinowski parameters are defined by the user in the file . The recommended values are following: 20<A0GKMeV-1<40,δA0GK=0.5MeV ;0<A1GKMeV-1fm<5,δA1GK=0.5MeVfm-1;0<A2GKMeV-1fm2<5,δA2GK=0.5MeVfm-2;0.5 are positive. The values of the parameters rGK, aGK, A0GK, A1GK, A2GK corresponding to the minimum value of the χ2 as well as this value itself are printed in the main output file .The GK approximation fits the DFP more accurately in a wider range of R than the WS profile does. This is useful, in particular, for performing the dynamical modeling of the fusion process (see details in [2]). Fig. 1 shows to what extent the GK approximation (thin solid curve) is better than the conventional WS (thick solid curve) one. Note, that the use of wider range of R for the WS fitting results in poor agreement with DFP (the latter is shown by symbols in Fig. 1). We take this opportunity to correct several misprints in [3]. Eq. (21) should read (5)UnD(R)=2πg(EP)∫0kmaxdkk2j0(kR)vD(k)C(ÃPAÃTA+αhDPhDT-γzDPzDT). Eq. (24) should read (6)zDP(T)(k)=4π∫0rmaxρP(T)A(r)ρP(T)A(r)j0(kr)r2dr. Display Omitted. 2. The program The code consists now of 6 files and one header file. It reads the data from three input files and prints the results into three output files. Below the list of the files with short comments concerning the revisions is presented. 2.1. File This file has been changed.double BARR(double RCMini, double RCMfin, double RCMstep) - unchanged;. void WS_DFP() - has been changed. Now the range of the center of mass distance, in which the approximation of the DFP is performed, is defined by the user (the variables fRBstart and fRBfin in are responsible for that, see subsections 1b, 2.8).void GK_DFP() - a new function which fits the nuclear term of the double folding potential by the Gross-Kalinowski profile (1), (2). 2.2. File This file has been changed.double CubeInterpD2gDx2(double x, double *ydim, double *gdim) - a new function calculating the second derivative of the polynomial function (spline) g with respect to the variable y at the point x.double CubeInterpDgDx(double x, double *ydim, double *gdim) - a new function calculating the first derivative of the polynomial function (spline) g with respect to the variable y at the point x.double CubeInterp(double x, double *ydim, double *gdim) - a new function interpolating the discrete function gdim defined at the nodes ydim by a polynomial function (spline) g and calculating the value g(x).long CheckIndex(long down, long index, long up) - unchanged.double j0BRay(double x) - unchanged.double Dj0BRayDx(double x) - unchanged.double D2j0BRayDx2(double x) - unchanged.void GAUSS() - unchanged.int Number() - unchanged.double diffsimple(double stepp, dou

AB - This is a new version of the DFMSPH code designed to obtain the nucleus-nucleus potential by using the double folding model (DFM) and in particular to find the Coulomb barrier. The new version uses the charge, proton, and neutron density distributions provided by the user. Also we added an option for fitting the DFM potential by the Gross-Kalinowski profile. The main functionalities of the original code (e.g. the nucleus-nucleus potential as a function of the distance between the centers of mass of colliding nuclei, the Coulomb barrier characteristics, etc.) have not been modified. New version program summary: Program title: DFMSPH14. Catalog identifier: AEFH_v2_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. Licensing provisions: GNU General Public License, version 3. No. of lines in distributed program, including test data, etc.: 7211. No. of bytes in distributed program, including test data, etc.: 114404. Distribution format: tar.gz. Programming language: C. Computer: PC and Mac. Operation system: Windows XP and higher, MacOS, Unix/Linux. Memory required to execute with typical data: below 10 Mbyte. Classification: 17.9. Catalog identifier of previous version: AEFH_v1_0. Journal reference of previous version: Comp. Phys. Comm. 181 (2010) 168. Does the new version supersede the previous version?: Yes. Nature of physical problem: The code calculates in a semimicroscopic way the bare interaction potential between two colliding spherical nuclei as a function of the center of mass distance. The height and the position of the Coulomb barrier are found. The calculated potential is approximated by an analytical profile (Woods-Saxon or Gross-Kalinowski) near the barrier. Dependence of the barrier parameters upon the characteristics of the effective NN forces (like, e.g. the range of the exchange part of the nuclear term) can be investigated. Method of solution: The nucleus-nucleus potential is calculated using the double folding model with the Coulomb and the effective M3Y NN interactions. For the direct parts of the Coulomb and the nuclear terms, the Fourier transform method is used. In order to calculate the exchange parts, the density matrix expansion method is applied. Typical running time: less than 1 minute. Reason for new version: Many users asked us how to implement their own density distributions in the DFMSPH. Now this option has been added. Also we found that the calculated Double-Folding Potential (DFP) is approximated more accurately by the Gross-Kalinowski (GK) profile. This option has been also added. Summary of revisions: 1. Additional features of DFMSPH14 (a) Projectile and target densities as input files In the DFMSPH, there was a limited number of profiles for the charge, proton, and neutron density distributions among which the user could choose. In the new version, DFMSPH14, the user must provide two input files < inp_rhoP.c. > and < inp_rhoT.c. >. In these files the charge (RHO_q), proton (RHO_Z), neutron (RHO_N), and nucleon (RHO_A) density distributions are defined for the projectile (P) and target (T) nuclei as functions of the distance from the nucleus center (r). The technical explanation of these files might be found in subsection 2.9. (b) New analytical profile for fitting the calculated potential Now the nuclear term of the double folding potential Un(R) might be fitted by the Gross-Kalinowski profile in addition to the Woods-Saxon (WS) profile. The Gross-Kalinowski (GK) profile V(R)reads [1] (1)V(R)=-ln(1+exp(-δRaGK))[A0GK+A1GKδR+A2GKδR2],(2)δR=R-rGK(AP1/3+AT1/3). The quality of the GK or WS fits is represented by a relative error (3)χ2=1N∑i=1N(Un(Ri)-V(Ri)Un(Ri)+V(Ri))2 (two variables chi2WSmin and chi2GKmin correspond to these errors). The distances Ri span the values fRBfin(dot operator)RB<Ri. The recommended values for the GK-profile are: deliR=5, fRBstart = 1.2, and fRBfin = 0.8. The recommended values for the WS-profile are: deliR = 5, fRBstart = 1.1, and fRBfin = 0.9. The range and the step of the variation of the Gross-Kalinowski parameters are defined by the user in the file . The recommended values are following: 20<A0GKMeV-1<40,δA0GK=0.5MeV ;0<A1GKMeV-1fm<5,δA1GK=0.5MeVfm-1;0<A2GKMeV-1fm2<5,δA2GK=0.5MeVfm-2;0.5 are positive. The values of the parameters rGK, aGK, A0GK, A1GK, A2GK corresponding to the minimum value of the χ2 as well as this value itself are printed in the main output file .The GK approximation fits the DFP more accurately in a wider range of R than the WS profile does. This is useful, in particular, for performing the dynamical modeling of the fusion process (see details in [2]). Fig. 1 shows to what extent the GK approximation (thin solid curve) is better than the conventional WS (thick solid curve) one. Note, that the use of wider range of R for the WS fitting results in poor agreement with DFP (the latter is shown by symbols in Fig. 1). We take this opportunity to correct several misprints in [3]. Eq. (21) should read (5)UnD(R)=2πg(EP)∫0kmaxdkk2j0(kR)vD(k)C(ÃPAÃTA+αhDPhDT-γzDPzDT). Eq. (24) should read (6)zDP(T)(k)=4π∫0rmaxρP(T)A(r)ρP(T)A(r)j0(kr)r2dr. Display Omitted. 2. The program The code consists now of 6 files and one header file. It reads the data from three input files and prints the results into three output files. Below the list of the files with short comments concerning the revisions is presented. 2.1. File This file has been changed.double BARR(double RCMini, double RCMfin, double RCMstep) - unchanged;. void WS_DFP() - has been changed. Now the range of the center of mass distance, in which the approximation of the DFP is performed, is defined by the user (the variables fRBstart and fRBfin in are responsible for that, see subsections 1b, 2.8).void GK_DFP() - a new function which fits the nuclear term of the double folding potential by the Gross-Kalinowski profile (1), (2). 2.2. File This file has been changed.double CubeInterpD2gDx2(double x, double *ydim, double *gdim) - a new function calculating the second derivative of the polynomial function (spline) g with respect to the variable y at the point x.double CubeInterpDgDx(double x, double *ydim, double *gdim) - a new function calculating the first derivative of the polynomial function (spline) g with respect to the variable y at the point x.double CubeInterp(double x, double *ydim, double *gdim) - a new function interpolating the discrete function gdim defined at the nodes ydim by a polynomial function (spline) g and calculating the value g(x).long CheckIndex(long down, long index, long up) - unchanged.double j0BRay(double x) - unchanged.double Dj0BRayDx(double x) - unchanged.double D2j0BRayDx2(double x) - unchanged.void GAUSS() - unchanged.int Number() - unchanged.double diffsimple(double stepp, dou

KW - Coulomb barrier

KW - Density dependent NN forces

KW - Double folding model

KW - M3Y-interaction

KW - Nucleus-nucleus collision

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U2 - 10.1016/j.cpc.2016.04.012

DO - 10.1016/j.cpc.2016.04.012

M3 - Article

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

ER -