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Search for a viable nucleus–nucleus potential in heavy-ion nuclear reactions

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Abstract

We have constructed empirical formulae for the fusion and interaction barriers using a large number of experimental values chosen randomly from the literature available till date. The obtained fusion barriers have been compared with different model predictions based on the proximity, Woods–Saxon and double folding potentials along with several empirical formulas, time-dependent Hartree–Fock theories and experimental results. The comparison allows us to find the best model, which is nothing but the present empirical formula only. Most remarkably, the fusion barrier and radius show excellent consonance with the experimental findings for the reactions meant for the synthesis of superheavy elements also. Furthermore, it is seen that substitution of the predicted fusion barrier and radius in classic Wong formula (Wong, Phys. Rev. Lett. 31:766 (1973) for the total fusion cross-sections agrees very well with the experiments. Similarly, current interaction barrier predictions have also been compared well with a few experimental results available and Bass potential model meant for the interaction barrier predictions. Importantly, the present formulae for the fusion as well as interaction barrier will have practical implications in carrying out physics research near the Coulomb barrier energies. Furthermore, the present fusion barrier and radius provide us with a good nucleus–nucleus potential which is useful for numerous theoretical applications.

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References

  1. B B Back, H Esbensen, C L Jiang and K E Rehm, Rev. Mod. Phys. 86(1), 317 (2014)

    Article  ADS  Google Scholar 

  2. R Bass, Nucl. Phys. A 231(1), 45 (1974)

    Article  ADS  Google Scholar 

  3. R Bass, Rainer, Phys. Lett. B 47(2), 139 (1973)

    Article  ADS  Google Scholar 

  4. B Blocki, J Randrup, W J Światecki and C F Tsang, Ann. Phys. 105(2), 427 (1977)

    Article  ADS  Google Scholar 

  5. G R Satchler and W G Love, Phys. Rep. 55(3), 183 (1979)

    Article  ADS  Google Scholar 

  6. P R Christensen and A Winther, Phys. Lett. B 65(1), 19 (1976)

    Article  ADS  Google Scholar 

  7. W Reisdorf, J. Phys. G 20(9), 1297 (1994)

    Article  ADS  Google Scholar 

  8. A Winther, Nucl. Phys. A 594(2), 203 (1995)

    Article  ADS  Google Scholar 

  9. I Dutt and R K Puri, Phys. Rev. C 81(4), 044615 (2010)

    Article  ADS  Google Scholar 

  10. K Siwek-Wilczyńska and J Wilczyński, Phys. Rev. C 69(2), 024611 (2004)

    Article  ADS  Google Scholar 

  11. N Wang, W Xizhen, Z Li, M Liu and W Scheid, Phys. Rev. C 74(4), 044604 (2006)

    Article  ADS  Google Scholar 

  12. A S Freitas, L Marques, X X Zhang, M A Luzio, P Guillaumon, R P Condori and R Lichtenthäler, Braz. J. Phys. 46(1), 120 (2016).

    Article  ADS  Google Scholar 

  13. S Mitsuoka, H Ikezoe, K Nishio, K Tsuruta, S C Jeong, and Y Watanabe, Phys. Rev. Lett. 99(18), 182701 (2007)

    Article  ADS  Google Scholar 

  14. I Dutt and R K Puri, Phys. Rev. C 81(6), 064609 (2010)

    Article  ADS  Google Scholar 

  15. V I Zagrebaev, Phys. Rev. C 78(4), 047602 (2008)

    Article  ADS  Google Scholar 

  16. P Sharma and T Nandi, Phys. Rev. Lett. 119(20), 203401 (2017)

    Article  ADS  Google Scholar 

  17. T Banerjee, S Nath and S Pal, Phys. Rev. C 91(3), 034619 (2015)

    Article  ADS  Google Scholar 

  18. R Bass, Phys. Rev. Lett. 39(5), 265 (1977)

    Article  ADS  Google Scholar 

  19. N Rowley, G R Satchler and P H Stelson, Phys. Lett. B 254(1), 25 (1991)

    Article  ADS  Google Scholar 

  20. M V Andres, N Rowley and M A Nagarajun, Phys. Lett. B 202(3), 292 (1988)

    Article  ADS  Google Scholar 

  21. H Timmers, J R Leigh, M Dasgupta, D J Hinde, R C Lemmon, J C Mein, C R Morton, J O Newton and N Rowley, Nucl. Phys. A 584(1), 190 (1995)

    Article  ADS  Google Scholar 

  22. K Hagino and N Rowley, Phys. Rev. C 69(5), 054610 (2004)

    Article  ADS  Google Scholar 

  23. Y Le Beyec, M Lefort and M Sarda, Nucl. Phys. A 192(2), 405 (1972)

    Article  ADS  Google Scholar 

  24. J R Birkelund, L E Tubbs, J R Huizenga, J N De and D Sperber, Phys. Rep. 56(3), 107 (1979)

    Article  ADS  Google Scholar 

  25. W J Swikatecki, K Siwek-Wilczyńska, and J Wilczyński, Phys. Rev. C 71(1), 014602 (2005)

    Article  ADS  Google Scholar 

  26. H C Manjunatha, K N Sridhar, N Nagaraja and N Sowmya, Eur. Phys. J. Plus 133(6), 227 (2018)

    Article  Google Scholar 

  27. W D Myers and W J Swiatecki, Phys. Rev. C 62(4), 044610 (2000).

    Article  ADS  Google Scholar 

  28. P Möller, J R Nix, W D Myers and W J Swiatecki, At. Data Nucl. Data Table 59(2), 185 (1995)

    Article  ADS  Google Scholar 

  29. W D Myers and W J Swiatecki, Ark. Fys. 36(4), 343 (1967)

    Google Scholar 

  30. M Liu, N Wang, Z Li, X Wu and E Zhao, Nucl. Phys. A 768(1), 80 (2006)

    Article  ADS  Google Scholar 

  31. J Bartel and K Bencheikh, Eur. Phys. J. A 14(2), 179 (2002)

    Article  ADS  Google Scholar 

  32. V Zanganeh, M Mirzaei and N Wang, Commun. Theor. Phys. 64(2), 177 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  33. R Moustabchir and G Royer, Nucl. Phys. A 683(1–4), 266 (2001)

    Article  ADS  Google Scholar 

  34. G Royer and B Remaud, J. Phys. G 10(8), 1057 (1984)

    Article  ADS  Google Scholar 

  35. G Giardina, F Hanappe, A I Muminov, A K Nasirov and L Stuttgè, Nucl. Phys. A 671(1–4), 165 (2000)

    Article  ADS  Google Scholar 

  36. N V Antonenko, E A Cherepanov, A K Nasirov, V P Permjakov and V V Volkov, Phys. Lett. B 319(4), 425 (1993)

    Article  ADS  Google Scholar 

  37. N V Antonenko, E A Cherepanov, A K Nasirov, V P Permjakov and V V Volkov, Phys. Rev. C 51(5), 2635 (1995)

    Article  ADS  Google Scholar 

  38. W Swiatecki, Phys. Scr. 24(1), 113 (1981)

    Article  ADS  Google Scholar 

  39. K Banerjee et al, Phys. Rev. Lett. 122(23), 232503 (2019)

    Article  ADS  Google Scholar 

  40. F Käppeler, F K Thielemann and M Wiescher, Ann. Rev. Nucl. Part. Sci. 48(1), 175 (1998)

    Article  ADS  Google Scholar 

  41. O K Ganiev and A K Nasirov, J. Phys. G 47(4), 045115 (2020)

    Article  ADS  Google Scholar 

  42. R Bass, Nuclear reactions with heavy ion (Springer, 1980)

    Google Scholar 

  43. R A Broglia and A Winther, Heavy ion reactions: The elementary processes (Addison Wesley Publishing Company, 1991) Vol. 84

    Google Scholar 

  44. A B Migdal, Nucl. Phys. 13(5), 655 (1959)

    Article  Google Scholar 

  45. G Bertsch, J Borysowicz, H McManus and W G Love, Nucl. Phys. A 284(3), 399 (1977)

    Article  ADS  Google Scholar 

  46. N Anantaraman, H Toki and G F Bertsch, Nucl. Phys. A 398(2), 269 (1983)

    Article  ADS  Google Scholar 

  47. H C Manjunatha, N Sowmya, N Manjunatha, P S Damodara Gupta, L Seenappa, K N Sridhar, T Ganesh and T Nandi, Phys. Rev. C 102(6), 064605 (2020)

    Article  ADS  Google Scholar 

  48. H C Manjunatha, L Seenappa, P S Damodara Gupta, N Manjunatha, K N Sridhar, N Sowmya and T Nandi, Phys. Rev. C 103(2), 024311 (2021)

    Article  ADS  Google Scholar 

  49. G Royer and R A Gherghescu, Nucl. Phys. A 699(3–4), 479 (2002)

    Article  ADS  Google Scholar 

  50. D N Poenaru and R A Gherghescu, Phys. Rev. C 94(1), 014309 (2016)

    Article  ADS  Google Scholar 

  51. G Royer, M Prince, X Scannell, I Lele-Cheudjou and A Samb, Nucl. Phys. A 1000, 121811 (2020)

  52. H M Albers et al, Phys. Lett. B 808, 135626 (2020)

    Article  Google Scholar 

  53. R O Akyuz and A Winther, Proc. Enrico Fermi Int. School of Physics 491 (1979)

  54. W Scobel, H H Gutbrod, M Blann and A Mignerey, Phys. Rev. C 14(5), 1808 (1976)

    Article  ADS  Google Scholar 

  55. M M Shaikh et al, J. Phys. G 45(9), 095103 (2018)

    Article  ADS  Google Scholar 

  56. J O Newton, R D Butt, M Dasgupta, D J Hinde, I I Gontchar, C R Morton and K Hagino, Phys. Rev. C 70(2), 024605 (2004)

    Article  ADS  Google Scholar 

  57. N Rowley, A Kabir and R Lindsay, J. Phys. G 15(12), L269 (1989)

    Article  ADS  Google Scholar 

  58. C Y Wong, Phys. Rev. Lett. 31(12), 766 (1973)

    Article  ADS  Google Scholar 

  59. K Hagino and N Takigawa, Prog. Theor. Phys. 128(6), 1061 (2012)

    Article  ADS  Google Scholar 

  60. R Gharaei and G L Zhang, Nucl. Phys. A 990, 294 (2019)

  61. A M Stefanini et al, Phys. Rev. C 76(1), 014610 (2007)

    Article  ADS  Google Scholar 

  62. J W Negele, Rev. Mod. Phys. 54(4), 913 (1982)

    Article  ADS  Google Scholar 

  63. K Washiyama and D Lacroix, Phys. Rev. C 78(2), 024610 (2008)

    Article  ADS  Google Scholar 

  64. C Simenel, Phys. Rev. Lett. 105(19), 192701 (2010)

    Article  ADS  Google Scholar 

  65. C Simenel, R Keser, A S Umar and V E Oberacker, Phys. Rev. C 88(2), 024617 (2013)

    Article  ADS  Google Scholar 

  66. B Yilmaz, S Ayik, D Lacroix and K Washiyama, Phys. Rev. C 83(6), 064615 (2011)

    Article  ADS  Google Scholar 

  67. G Klotz-Engmann et al, Nucl. Phys. A 499(2), 392 (1989)

    Article  ADS  Google Scholar 

  68. W Swiatecki, Prog. Part. Nucl. Phys. 4, 383 (1980)

    Article  ADS  Google Scholar 

  69. R Rafiei, R G Thomas, D J Hinde, M Dasgupta, C R Morton, L R Gasques, M L Brown, M D Rodriguez, Phys. Rev. C 77(2), 024606 (2008)

    Article  ADS  Google Scholar 

  70. A Diaz-Torres and I J Thompson, Phys. Rev. C 65(2), 024606 (2002).

    Article  ADS  Google Scholar 

  71. A Diaz-Torres, D J Hinde, J A Tostevin, M Dasgupta and L R Gasques, Phys. Rev. Lett. 98(15), 152701 (2007)

    Article  ADS  Google Scholar 

  72. R A Broglia, C H Dasso and A Winther, Phys. Lett. B 53(4), 301 (1974).

    Article  ADS  Google Scholar 

  73. P Braun-Munzinger, G M Berkowitz, T M Cormier, C M Jachcinski, J W and Harris, J Barrette and M J LeVine, Phys. Rev. Lett. 38(17), 944 (1977)

  74. L C Vaz, J M Alexander and G R Satchler, Phys. Rep. 69(5), 373 (1981).

    Article  ADS  Google Scholar 

  75. P Sperr, S Vigdor, Y Eisen, W Henning, D G Kovar, T R Ophel and B Zeidman, Phys. Rev. Lett. 36(8), 405 (1976)

    Article  ADS  Google Scholar 

  76. C M Jachcinski, D G Kovar, R R Betts, C N Davids, D F Geesaman, C Olmer, M Paul, S J Sanders and J L Yntema, Phys. Rev. C 24(5), 2070 (1981)

    Article  ADS  Google Scholar 

  77. Y Eisen, I Tserruya, Y Eyal, Y Fraenkel and M Hillman, Nucl. Phys. A 291(2), 459 (1977)

    Article  ADS  Google Scholar 

  78. S Gary and C Volant, Phys. Rev. C 25(4), 1877 (1982)

    Article  ADS  Google Scholar 

  79. G M Berkowitz, P Braun-Munzinger, J S Karp, R H Freifelder, T R Renner and H W Wilschut, Phys. Rev. C 28(2), 667 (1983)

    Article  ADS  Google Scholar 

  80. J O Newton, C R Morton, M Dasgupta, J R Leigh, J C Mein, D J Hinde, H Timmers and K Hagino, Phys. Rev. C 64(6), 064608 (2001)

    Article  ADS  Google Scholar 

  81. E F Aguilera, J J Kolata, P A DeYoung and J J Vega, Phys. Rev. C 33(6), 1961 (1986)

    Article  ADS  Google Scholar 

  82. H H Gutbrod, W G Winn and M Blann, Phys. Rev. Lett. 30(25), 1259 (1973)

    Article  ADS  Google Scholar 

  83. A Mukherjee, M Dasgupta, D J Hinde, K Hagino, J R Leigh, J C Mein, C R Morton, J O Newton and H Timmers, Phys. Rev. C 66(3), 034607 (2002)

    Article  ADS  Google Scholar 

  84. A M Stefanini et al, Phys. Rev. C 73(3), 034606 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  85. H Gauvin, Y Le Beyec and N T Porile, Nucl. Phys. A 223(1), 103 (1974)

    Article  ADS  Google Scholar 

  86. F Scarlassara, S Beghini, G Montagnoli, G F Segato, D Ackermann, L Corradi, C J Lin, A M Stefanini and L F Zheng, Nucl. Phys. A 672(1–4), 99 (2000)

    Article  ADS  Google Scholar 

  87. K Nishio, H Ikezoe, S Mitsuoka and J Lu, Phys. Rev. C 62(1), 014602 (2000)

  88. W Reisdorf et al, Nucl. Phys. A 438(1), 212 (1985)

    Article  ADS  Google Scholar 

  89. H Gauvin, Y Le Beyec, M Lefort and C Deprun, Phys. Rev. Lett. 28(11), 697 (1972)

    Article  ADS  Google Scholar 

  90. V E Viola Jr and T Sikkeland, Phys. Rev. 128(2), 767 (1962)

    Article  ADS  Google Scholar 

  91. D J Hinde, C R Morton, M Dasgupta, J R Leigh, J C Mein and H Timmers, Nucl. Phys. 592(2), 271 (1995)

    Article  Google Scholar 

  92. Y L Beyec, M Lefort and A Vigny, Phys. Rev. C 3(3), 1268 (1971)

    Article  ADS  Google Scholar 

  93. R Bimbot, H Gauvin, Y Le Beyec, M Lefort, N T Porile and B Tamain, Nucl. Phys. A 189(3), 539 (1972)

    Article  ADS  Google Scholar 

  94. M Lefort, C Ngo, J Peter and B Tamain, Nucl. Phys. A 216(1), 166 (1973)

    Article  ADS  Google Scholar 

  95. P Sperr, T H Braid, Y Eisen, D G Kovar, F W Prosser Jr, J P Schiffer, S L Tabor and S Vigdor, Phys. Rev. Lett. 37(6), 321 (1976).

    Article  ADS  Google Scholar 

  96. D Shapira, D DiGregorio, J G Del Campo, R A Dayras, J L C Ford Jr, A H Snell, P H Stelson, R G Stokstad and F Pougheon, Phys. Rev. C 28(3), 1148 (1983)

    Article  ADS  Google Scholar 

  97. P R S Gomes, T J P Penna, E F Chagas, R L Neto, J C Acquadro, P R Pascholati, E Crema, C Tenreiro, N Carlin Filho and M M Coimbra, Nucl. Phys. A 534(2), 429 (1991)

    Article  ADS  Google Scholar 

  98. L T Baby, V Tripathi, J J Das, P Sugathan, N Madhavan, A K Sinha, M C Radhakrishna, P V M Rao, S K Hui and K Hagino, Phys. Rev. C 62(1), 014603 (2000)

    Article  ADS  Google Scholar 

  99. A M Stefanini et al, Nucl. Phys. A 456(3), 509 (1986)

    Article  ADS  Google Scholar 

  100. A A Sonzogni, J D Bierman, M P Kelly, J P Lestone, J F Liang and R Vandenbosch, Phys. Rev. C 57(2), 722 (1998)

    Article  ADS  Google Scholar 

  101. J R Leigh et al, Phys. Rev. C 52(6), 3151 (1995)

    Article  ADS  Google Scholar 

  102. C R Morton, A C Berriman, M Dasgupta, D J Hinde, J O Newton, K Hagino and I J Thompson, Phys. Rev. C 60(4), 044608 (1999)

    Article  ADS  Google Scholar 

  103. A M Vinodkumar, K M Varier, N V S Prasad, D L Sastry, A K Sinha, N Madhavan, P Sugathan, D O Kataria and J J Das, Phys. Rev. C 53(2), 803 (1996)

    Article  ADS  Google Scholar 

  104. A M Stefanini, L Corradi, A M Vinodkumar, Y Feng, F Scarlassara, G Montagnoli, S Beghini and M Bisogno, Phys. Rev. C 62(1), 014601 (2000)

    Article  ADS  Google Scholar 

  105. H Timmers, D Ackermann, S Beghini, L Corradi, J H He, G Montagnoli, F Scarlassara, A M Stefanini and N Rowley, Nucl. Phys. A 633(3), 421 (1998)

    Article  ADS  Google Scholar 

  106. M Beckerman, M Salomaa, A Sperduto, H Enge, J Ball, A DiRienzo, S Gazes, Y Chen, J D Molitoris and M Nai-Feng, Phys. Rev. Lett. 45(18), 1472 (1980)

    Article  ADS  Google Scholar 

  107. M Beckerman, M Salomaa, A Sperduto, J D Molitoris and A DiRienzo, Phys. Rev. C 25(2), 837 (1982)

    Article  ADS  Google Scholar 

  108. S S Ntshangase et al, Phys. Lett. B 651(1), 27 (2007)

    Article  ADS  Google Scholar 

  109. M Trotta, A M Stefanini, L Corradi, A Gadea, F Scarlassara, S Beghini and G Montagnoli, Phys. Rev. C 65(1), 011601 (2001)

    Article  ADS  Google Scholar 

  110. M Klaassen, A Lindström, H Meltofte and T Piersma, Nature 413(6858), 794 (2001)

    Article  ADS  Google Scholar 

  111. D J Hinde, A C Berriman, M Dasgupta, J R Leigh, J C Mein, C R Morton and J O Newton, Phys. Rev. C 60(5), 054602 (1999)

    Article  ADS  Google Scholar 

  112. M Dasgupta, D J Hinde, J R Leigh, R C Lemmon, J C Mein, C R Morton, J O Newton and H Timmers, Lectures on Probability and Second Order Random Fields (1994)

  113. M Dasgupta, D J Hinde, N Rowley and A M Stefanini, Ann. Rev. Nucl. Part. Sci. 48(1), 401 (1998)

    Article  ADS  Google Scholar 

  114. J O Newton, R D Butt, M Dasgupta, D J Hinde, I I Gontchar, C R Morton and K Hagino, Phys. Lett. B 586(3–4), 219 (2004)

    Article  ADS  Google Scholar 

  115. M M Shaikh, S Roy, A Mukherjee, A Goswami, B Dey, S Pal, S Roy, A Shrivastava, S K Pandit and K Mahata, Phys. Rev. C 102(2), 024627 (2020)

    Article  ADS  Google Scholar 

  116. M M Shaikh, S Roy, S Rajbanshi, M K Pradhan, A Mukherjee, P Basu, S Pal, V Nanal, R G Pillay and A Shrivastava, Phys. Rev. C 91(3), 034615 (2015)

    Article  ADS  Google Scholar 

  117. S Mukherjee, B K Nayak, D S Monteiro, J Lubian, P R S Gomes, S Appannababu and R K Choudhury, Phys. Rev. C 80(1), 014607 (2009)

  118. B K Nayak, R K Choudhury, A Saxena, P K Sahu, R G Thomas, D C Biswas, B V John, E T Mirgule, Y K Gupta, M Bhike and H G Rajprakash, Phys. Rev. C 75(5), 054615 (2007)

    Article  ADS  Google Scholar 

  119. G Kaur, B R Behera, A Jhingan, B K Nayak, R Dubey, P Sharma, M Thakur, R Mahajan, N Saneesh, T Banerjee, Khushboo, A Kumar, S Mandal, A Saxena, P Sugathan and N Rowley, Phys. Rev. C 94(3), 034613 (2016)

  120. S Sinha, M R Pahlavani, R Varma, R K Choudhury, B K Nayak and A Saxena, Phys. Rev. C 64(2), 024607 (2001)

    Article  ADS  Google Scholar 

  121. L G Moretto, Nucl. Phys. A 180(2), 337 (1972)

    Article  ADS  Google Scholar 

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Acknowledgements

The authors would like to acknowledge the illuminating discussions with Subir Nath, Ambar Chatterjee, B R Behra and S Kailas.

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Authors and Affiliations

  1. Inter University Accelerator Centre, Aruna Asaf Ali Marg, JNU New Campus, New Delhi, 110 067, India

    T Nandi, D K Swami & S Chakraborty

  2. Rajah Serfoji Government College affiliated to Bharathidasan University, Thiruchirappalli, 620 024, India

    P S Damodara Gupta

  3. Department of Physics, Government First Grade College, Kolar, 563 101, India

    P S Damodara Gupta

  4. Dipartimento di Fisica “Galileo Galilei”, Università di Padova, 35131, Padova, Italy

    Yash Kumar

  5. Department of Physics, Government College for Women, Kolar, 563 101, India

    H C Manjunatha

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  1. T Nandi
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Nandi, T., Swami, D.K., Gupta, P.S.D. et al. Search for a viable nucleus–nucleus potential in heavy-ion nuclear reactions. Pramana - J Phys 96, 84 (2022). https://doi.org/10.1007/s12043-022-02331-0

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