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To describe the projectile-target interaction in heavy-ion collision, this paper improves the traditional optical model and establishes a corresponding optical model for heavy-ion collisions. The program APOMHI was developed accordingly. In heavy-ion collisions, the masses of the projectile and target nuclei are comparable. Therefore, the projectile and target nuclei must be treated equally. The potential field for their relative motion must arise from an equivalent contribution by both nuclei, not solely from the target nucleus. Consequently, the angular momentum coupling scheme must employL-S coupling, not j-j coupling. The projectile spin i and target spin I first couple to form the projectile-target system spin S (which varies between |i- I| and i + I). This system spin S then couples with the orbital angular momentum L of the relative motion to form the total angular momentum J. Thus, the radial wave function UlSJ (r) involves three quantum numbers: l, S, and J, in contrast to the traditional optical model which involves only l and j. Furthermore, since the projectile and target masses are similar, the form of the optical model potential is symmetrized with respect to the projectile and target (see Eqs. (1)-(10) in the Theoretical Basis section). The projectile and target nuclei are still assumed to be spherical, and their excited states are not considered. The projectile may be lighter or heavier than the target, but they cannot be identical particles. Using this optical model program APOMHI, the elastic scattering angular distributions and compound nucleus absorption cross sections for heavy-ion collisions can be calculated. As an example, we consider the series of heavy-ion collision reactions with 18O as the projectile nucleus, a corresponding set of universal optical potential parameters was obtained by fitting experimental data. Comparisons show that the theoretical calculations generally agree well with the available experimental data. Here, we present as examples the results for fusion cross-sections and elastic scattering angular distributions using several representative target nuclei (lighter, comparable in mass, heavier, and heavy compared to the projectile nucleus). Specifically, the fusion cross-section results correspond to targets 9Be, 27Al, 63Cu and 150Sm, while the elastic scattering angular distributions correspond to targets 16O, 24Mg, 58Ni, and 120Sn.
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Keywords:
- Optical model /
- Heavy-ion collision /
- Global /
- Phenomenological
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[1] Feshbach H 1958Ann. Phys. 5 357
[2] Pruitt C D, Escher J E, Rahman R 2023Phys. Rev. C 107 014602
[3] Capote R, Herman M, Obložinský P, Young P G, Goriely S, Belgya T, Ignatyuk A V, Koning A J, Hilaire S, Plujko V A, Avrigeanu M, Bersillon O, Chadwick M B, Fukahori T, Ge Z G, Han Y L, Kailas S, Kopecky J, Maslov V M, Reffo G, Sin M, Soukhovitskii E S, Talou P 2009Nucl. Data Sheets 110 3107
[4] Moumene I, Bonaccorso A 2023Phys. Rev. C 108 044609
[5] Pruitt C D, Escher J E, Rahman R 2023Phys. Rev. C 107 014602
[6] Jeukenne J P, Lejeune A, Mahaux C 1977Phys. Rev. C 16 80
[7] Jeukenne J P, Lejeune A, Mahaux C 1976Phys. Rep. 25 83
[8] Bauge E, Delaroche J P, Girod M 1998Phys. Rev. C 58 1118
[9] Bauge E, Delaroche J P, Girod M 2001Phys. Rev. C 63 024607
[10] Nobre G P A, Palumbo A, Herman M, Brown D, Hoblit S 2015Phys. Rev. C 91 024618
[11] Soukhovitskiĩ E S, Capote R, Quesada J M, Chiba S, Martyanov D S 2016Phys. Rev. C 94 064605
[12] Mahaux C, Sartor R 1991Adv. Nucl. Phys. (Boston, MA:Springer US) pp1-223
[13] Quesada J M, Capote R, Molina A, Lozano M 2003Phys. Rev. C 67 067601
[14] Morillon B, Romain P 2007Phys. Rev. C 76 044601
[15] Mueller J M, Charity R J, Shane R, Sobotka L G, Waldecker S J, Dickhoff W H, Crowell A S, Esterline J H, Fallin B, Howell C R, Westerfeldt C, Youngs M, Crowe B J, Pedroni R S 2011Phys. Rev. C 83 064605
[16] Mahzoon M H, Charity R J, Dickhoff W H, Dussan H, Waldecker S J 2014Phys. Rev. Lett. 112162503
[17] Atkinson M C, Dickhoff W H 2019Phys. Lett. B 798 135027
[18] Zhao X, Sun W, Capote R, Capote R, Soukhovitskiĩ E S, Martyanov D S, Quesada J M 2020 Phys. Rev. C 101 064618
[19] An H, Cai C 2006Phys. Rev. C 73 054605
[20] Han Y, Shi Y, Shen Q 2006Phys. Rev. C 74 044615
[21] Koning A J, Delaroche J P 2003Nucl. Phys. A 713 231
[22] Li X H, Chen L W 2012Nucl. Phys. A 874 62
[23] Liang C T, Li X H, Cai C H 2009J. Phys. G:Nucl. Part. Phys. 36 085104
[24] Li X, Liang C, Cai C 2007Nucl. Phys. A 789 103
[25] Shen Q B 2002Nucl. Sci. Eng. 141 78
[26] Xu Y, Han Y, Hu J, Liang H, Wu Z, Guo H, Cai C 2018Phys. Rev. C 98 024619.
[27] Xu Y, Han Y, Liang H, Wu Z, Guo H, Cai C 2019Phys. Rev. C 99 034618
[28] Xu Y, Han Y, Hu J, Liang H, Wu Z, Guo H, Cai C 2018Phys. Rev. C 97 014615
[29] Xu Y L, Han Y L, Su X W, Sun X J, Liang H Y, Guo H R, Cai C H 2021Chin. Phys. C 45 114103
[30] Cai C H 2024 Personal communication
[31] Raynal J 1994 CEA Saclay report CEA-N-2772
[32] Roth H A, Christiansson J E, Dubois J 1980Nucl. Phys. A 343 148
[33] Anjos R M, Added N, Carlin N, Fante L, Figueira M C S, Matheus R, Szanto E M, Tenreiro C, Szanto A 1994Phys. Rev. C 492018
[34] Rudchik A T, Shyrma Y O, Kemper K W, Rusek K, Koshchy E I, Kliczewski S, B 2011Nucl. Phys. A 8521
[35] Thomas J, Chen Y T, Hinds S, Langanke K, Meredith D, Olson M, Barnes C A 1985Phys. Rev. C 31 1980
[36] Thomas J, Chen Y T, Hinds S, Meredith D, Olson M 1986Phys. Rev. C 331679
[37] Szilner S, Haas F, Basrak Z, Freeman R M, Morsad A, Nicoli M P 2006Nucl. Phys. A 77921
[38] Tabor S L, Geesaman D F, Henning W, Kovar D G, Rehm K E, Prosser F W 1978Phys. Rev. C 17 2136
[39] Bernas M, Pougheon F, Roy-Stephan M, Berg G P A, Berthier B, Le J P 1980Phys. Rev. C 22 1872
[40] Rascher R, Muller W F J, Lieb K P 1979Phys. Rev. C 201028
[41] Eisen Y, Tserruya I, Eyal Y, Fraenkel Z, Hillman M 1977Nucl. Phys. A 291 459
[42] Bozek E, De Castro-Rizzo D M, Cavallaro S, Delaunay B, Delaunay J, Dumont H, D'onofrio A, Saint-Laurent M G, Sperduto L, Terrasi F 1986Nucl. Phys. A 451171
[43] Borges A M, Silva C P, Pereira D, Chamon L C, Rossi E S, 1992Phys. Rev. C 46 2360
[44] Silva C P, Pereira D, Chamon L C, Rossi E S 1997Phys. Rev. C 553155
[45] Rossi E S, Pereira D, Chamon L C, Silva C P, Alvarez M A G, Gas L R 2002Nucl. Phys. A 707 325
[46] Alves J J S, Gomes P R S, Lubian J, Chamon L C, Pereira D, Anjos R M 2005Nucl. Phys. A 748 59
[47] Rehm K E, Koerner H J, Richter M, Rother H P, Schiffer J P, Spieler H 1975Phys. Rev. C 12 1945
[48] Chamon L C, Pereira D, Rossi E S, Silva C P, Razeto G R, Borges A M, Gomes L C, Sala O 1992Phys. Lett. B 275 29
[49] Salem-Vasconcelos S, Takagui E M, Bechara M J, Koide K, Dietzsch O, Baur A 1994Phys. Rev. C 50 927
[50] Jia H M, Lin C J, Xu X X, Zhang H Q, Liu Z H, Yang L, Zhang S T, Bao P F, Sun L J 2012Phys. Rev. C 86 044621
[51] Jha V, Roy B J, Chatterjee A, Machner H 2004Eur. Phys. J. A 19 347
[52] Benjelloun M, Galster W, Vervier J 1993Nucl. Phys. A 560 715
[53] Bohlen H G, Hildenbrand K D, Gobbi A, Kubo K I 1975Z. Phys. A 273211
[54] Robertson B C, Sample J T, Goosman D R, Nagtani K, Jones K W 1971Phys. Rev. C 4 2176
[55] Broda R, Ishihara M, Herskind B, Oeschler H, Ogaza S, Ryde H 1975Nucl. Phys. A 248 356
[56] Hinde D J, Charity R J, Foote G S, Leigh J R, Newton J O, Ogaza S, Chattejee A 1986Nucl. Phys. A 452 550
[57] Charity R J, Leigh J R, Bokhorst J J M, Chatterjee A, Foote G S, Hinde D J, Newton J O, Ogaza S, Ward D 1986Nucl. Phys. A 457 441
[58] Sahu P K, Choudhury R K, Biswas D C, Nayak B K 2001Phys. Rev. C 64 014609
[59] Plicht J, Britt H C, Fowler M M, Fraenkel Z, Gavron A, Wilhelmy J B 1983Phys. Rev. C 28 2022
[60] Laveen P V, Prasad E, Madhavan N, Pal S, Sadhukhan J, Nath S, Gehlot J, Jhingan A, Varier K M, Thomas R G 2015J. Phys. G 42 95105
[61] Yanez R, Loveland W, Barrett J S, Yao L 2013Phys. Rev. C 88 14606
[62] Appannababu S, Mukherjee S, Singh N L, Rath P K, Kumar G K 2009Phys. Rev. C 80 24603
[63] Vulgaris E, Grodzins L, Steadman S G, Ledoux R 1986Phys. Rev. C 33 2017
[64] Rudchik A A, Rudchik A T, Kliczewski S, Koshchyc E I, Ponkratenko O A, 2007Nucl. Phys. A 785293
[65] Heusch B, Beck C, Coffin J P, Engelstein P, Freeman R M, Guillaume G, Haas F, Wagner P 1982Phys. Rev. C 26 542
[66] Beck C, Haas F, Freeman R M, Heusch B, Coffin J P, Guillaume G, Rami F, Wagner P 1985Nucl. Phys. A 442 320
[67] Kovar D G, Geesaman D F, Braid T H, Eisen Y, Henning W, Ophel T R, Paul M, Rehm K E, Sanders S J 1979Phys. Rev. C 20 1305
[68] Sperr P, Braid T H, Eisen Y, Kovar D G, Prosser F W, Schiffer J P, Tabor S L, Vigdor S 1976Phys. Rev. Lett. 37 321
[69] Steinbach T K, Vadas J, Schmidt J, Haycraft C, Hudan S, deSouza R T 2014Phys. Rev. C 90 41603
[70] Eyal Y, Beckerman M, Chechik R, Fraenkel Z, Stocker H 1976Phys. Rev. C 131527
[71] Szilner S, Nicoli M P, Basrak Z, Freeman R M, Haas F, Morsad A 2001Phys. Rev. C 64064614
[72] Al-Abdullah T, Carstoiu F, Gagliardi C A 2014Phys. Rev. C 89 064602
[73] Rudchik A T, Shyrma Y O, Kemper K W, Piasecki E, Romanyshyna G P, Stepanenko Y M, Strojek I, Sakuta S B, Budzanowski A, Głowacka L, Skwirczyńska I, Siudak R, Choiński J, Szczurek A 2011Eur. Phys. J. A 47 1
[74] Deb N K, Kalita K, Rashid H A, Das A, Nath S, Gehlot J, Madhavan N, Biswas R, Sahoo R N, Giri P K, Parihari A, Rai N K, Biswas S, Mahato A, Roy B J 2022Phys. Rev. C 105 054608
[75] Wong C Y 1973Phys. Rev. Lett. 31 766
[76] Wang L, Zhao K, Tian J L 2013Nucl. Phys. Rev. 30 289
[77] Chen J B, Yang Y Y, Wang J S, Wang Q, Jin S L, Ma P, Ma J B, Huang M R, Han J L, Bai Z, Hu Q, Jin L, Li R, Zhao M H 2014Nucl. Phys. Rev. 31 53
[78] Xu Y L, Han Y L, Su X W, Sun X J, Liang H Y, Guo H R, Cai C H 2020Chin. Phys. C 44 124103
[79] Zamrun F M, Hagino K 2008Phys. Rev. C 77 014606
[80] Xu Y L, Han Y L, Liang H Y, Wu Z D, Guo H R, Cai C H 2020Chin. Phys. C 44 034101
[81] Beck C, Keeley N, Diaz-Torres A 2007Phys. Rev. C 75 054605
[82] Pieper S C, Macfarlane M H, Gloeckner D H, Kovar D G, Becchetti F D, Harvey B G, Hendrie D L, Homeyer H, Mahoney J, Pühlhofer F, Oertzen W, Zisman M S 1978Phys. Rev. C 18 180
[83] Al-Ghamdi A H, Ibraheem A A, Hamada S 2022J. Taibah Univ. Sci. 16 1026
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