Journal of Physical Studies 25(1), Article 1101 [12 pages] (2021) DOI: https://doi.org/10.30970/jps.25.1101 ELECTRIC FORM FACTORS OF NUCLEONS AND CHARGE DEUTERON FORM FACTOR V. I. Zhaba  Uzhgorod National University, Department of Theoretical Physics, 54, Voloshyn St., Uzhgorod, UA-88000, Ukraine, e-mail: viktorzh@meta.ua Received 30 April 2020; accepted 29 October 2020; published online 16 February 2021

The study reviews basic approximation dependences for the isoscalar electric form factors of the proton $G_{\rm Ep}$ and the neutron $G_{\rm EN}$. The peculiarities of their obtaining and subsequent application for approximation by experimental data are analyzed. The basic experimental data of nucleon electric form factors are described. Using the approximation dependences of this review, corresponding parameters were obtained for the electric form factors of the nucleons $G_{\rm Ep}$ and $G_{\rm EN}$. In most cases, they generally describe the experimental data fairly well. The best parameterizations for describing experimental data of the electric proton form factor $G_{\rm Ep}$ are polynomials and polynomial ratios. Experimental measurements of the electric neutron form factor $G_{\rm EN}$ are best described by the Galster parameterization. The quality of the approximation for the electric nucleon form factors is controlled by determining the charge radius of proton $r_{\rm Ep}$ and neutron $r_{\rm EN}$. According to the approximation dependences of the electric nucleon form factors and the deuteron wave functions in the coordinate representation for Reid93 and CD-Bonn potentials and DDM model, the deuteron charge form factor $G_{\rm C}(p)$ is calculated. The theoretical values of the form factor $G_{\rm C}(p)$ are compared with the experimental data of the leading collaborations and reviews. Depending on the choice of electric nucleon form factors, the secondary maximum for the deuteron charge form factor $G_{\rm C}(p)$ is located for Reid93 potential in the momentum range at $p=5.60$-5.80 fm$^{-1}$, for CD-Bonn potential at $p=6.00$-6.40 fm$^{-1}$ and for model DDM at $p=5.45$-5.65 fm$^{-1}$. The zero position is located at the momentum $p_{0}=4.60$ fm$^{-1}$ for Reid93 potential, $p_{0}=5.05$ fm$^{-1}$ for CD-Bonn potential and $p_{0}=4.45$ fm$^{-1}$ for DDM model. The numerical values of the root-mean-square charge $r_{\rm ch}$ and the structural $r_{\rm str}$ deuteron radius are in good agreement with the results of experimental and other theoretical data. Using the obtained parameters of approximation dependences for isoscalar nucleon electric form factors and known magnetic nucleon form factors, in further studies we can calculate the structure functions $A(p)$, $B(p)$, the components of tensor and vector deuteron polarizations $t_{ij}(p)$, and tensor analyzing power $A_{yy}$ and other polarization observables.

Key words: nucleon, deuteron, form factor, radius, wave function, approximation

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1. D. K. Hasell et al., Annu. Rev. Nucl. Part. Sci. 61, 409 (2011);
   Crossref
2. R. Gilman, F. Gross, J. Phys. G. 28, R37 (2002);
   Crossref
3. V. P. Ladygin et al., Eur. Phys. J. A 8, 409 (2000);
   Crossref
4. M. P. Rekalo, E. Tomasi-Gustafsson, Phys. Rev. C 54, 3125 (1996);
   Crossref
5. G. I. Gakh, A. G. Gakh, E. Tomasi-Gustafsson, Phys. Rev. C 90, 064901 (2014);
   Crossref
6. G. I. Gakh, M. I. Konchatnij, N. P. Merenkov, J. Exp. Theor. Phys. 115, 212 (2012);
   Crossref
7. D. Abbott et al., Eur. Phys. J. A 7, 421 (2000);
   Crossref
8. E. Tomasi-Gustafsson, G. I. Gakh, C. Adamuscin, Phys. Rev. C 73, 045204 (2006);
   Crossref
9. T. Gutsche, V. E. Lyubovitskij, I. Schmidt, Phys. Rev. D 94, 116006 (2016);
   Crossref
10. L. E. Marcucci et al., J. Phys. G 43, 023002 (2016);
    Crossref
11. В. І. Жаба, Вісн. Львів. ун-ту. Сер. фіз. 56, 43 (2019);
    Crossref
12. V. G. J. Stoks et al., Phys. Rev. C 49, 2950 (1994);
    Crossref
13. J. J. de Swart et al., Few-Body Syst. Suppl. 8, 438 (1995);
    Crossref
14. R. Machleidt, Phys. Rev. C 63, 024001 (2001);
    Crossref
15. M. N. Platonova, V. I. Kukulin, Phys. Atom. Nucl. 73, 86 (2010);
    Crossref
16. M. Gourdin, Nuovo Cim. 28, 533 (1963);
    Crossref
17. D. Benaksas, D. Drickey, D. Frerejacque, Phys. Rev. 148, 1327 (1966);
    Crossref
18. I. The et al., Phys. Rev. Lett. 67, 173 (1991);
    Crossref
19. M. Garcon et al., Phys. Rev. C 49, 2516 (1994);
    Crossref
20. D. Abbott et al., Phys. Rev. Lett. 84, 5053 (2000);
    Crossref
21. M. Bouwhuis et al., Phys. Rev. Lett. 82, 3755 (1999);
    Crossref
22. D. M. Nikolenko et al., Phys. Rev. Lett. 90, 072501 (2003);
    Crossref
23. D. M. Nikolenko et al., Phys. Atom. Nucl. 73, 1322 (2010);
    Crossref
24. С. А. Зеваков и др., препринт ИЯФ 2006-024 (2006).
25. M. Kohl, Nucl. Phys. A 805, 361c (2008);
    Crossref
26. C. Zhang et al., Phys. Rev. Lett. 107, 252501 (2011);
    Crossref
27. B. Boden et al., Z. Phys. C: Part. Fields 49, 175 (1991);
    Crossref
28. V. Punjabi et al., Eur. Phys. J. A 51, 79 (2015);
    Crossref
29. A. Bekzhanov, S. Bondarenko, V. Burov, Nucl. Phys. B (Proc. Suppl.) 245, 65 (2013);
    Crossref
30. A. V. Bekzhanov, S. G. Bondarenko, V. V. Burov, J. Exp. Theor. Phys. Lett. 99, 613 (2014);
    Crossref
31. M.I. Haftel, L. Mathelitsch, H.F.K. Zingl, Phys. Rev. C 22, 1285 (1980);
    Crossref
32. V.V. Burov et al., Europhys. Lett. 24, 443 (1993);
    Crossref
33. C. Adamuscin et al., Nucl. Phys. Proc. Suppl. 245, 69 (2013);
    Crossref
34. T-S. Cheng, L. S. Kisslinger, Nucl. Phys. A 457, 602 (1986);
    Crossref
35. M. Garcon, J.W. van Orden, Adv. Nucl. Phys. 26, 293 (2001);
    Crossref
36. S. Galster et al., Nucl. Phys. B 32, 221 (1971);
    Crossref
37. F. Iachello, A.D. Jackson, A. Lande, Phys. Lett. B\textbf{ 43}, 191 (1973);
    Crossref
38. M. Gari, W. Krumpelmann, Z. Phys. A 322, 689 (1985);
    Crossref
39. J. J. Kelly, Phys. Rev. C 70, 068202 (2004);
    Crossref
40. P. E. Bosted, Phys. Rev. C 51, 409 (1995);
    Crossref
41. R. Bradford et al., Nucl. Phys. B (Proc. Suppl.) 159, 127 (2006);
    Crossref
42. J. Friedrich, Th. Walcher, Eur. Phys. J. A 17, 607 (2003);
    Crossref
43. S. I. Bilen'kaya, Yu. M. Kazarinov, L. I. Lapidus, Sov. Phys. J. Exp. Theor. Phys. 34, 1192 (1972).
44. W. M. Alberico et al., Phys. Rev. C 79, 065204 (2009);
    Crossref
45. E. Geis et al., Phys. Rev. Lett. 101, 042501 (2008);
    Crossref
46. W. Bertozzi et al., Phys. Lett. B 41, 408 (1972);
    Crossref
47. P. Lehmann et al., Phys. Rev. 126, 1183 (1962);
    Crossref
48. B. Dudelzak et al., Nuovo Cim. 28, 18 (1963);
    Crossref
49. L. N. Hand et al., Rev. Mod. Phys. 35, 335 (1963);
    Crossref
50. W. Albrecht et al., Phys. Rev. Lett. 17, 1192 (1966);
    Crossref
51. T. Janssens et al., Phys. Rev. 142, 922 (1966);
    Crossref
52. W. Albrecht et al., Phys. Rev. Lett. 18, 1014 (1967);
    Crossref
53. J. Litt et al., Phys. Lett. 31B, 40 (1970);
    Crossref
54. Ch. Berger et al., Phys. Lett. 35B, 87 (1971);
    Crossref
55. L. E. Price et al., Phys. Rev. D 4, 45 (1971);
    Crossref
56. W. Bartel et al., Nucl. Phys. B 58, 429 (1973);
    Crossref
57. K. M. Hanson et al., Phys. Rev. D 8, 753 (1973);
    Crossref
58. P. N. Kirk et al., Phys. Rev. D 8, 63 (1973);
    Crossref
59. J. J. Murphy et al., Phys. Rev. C 9, 2125 (1974);
    Crossref
60. F. Borkowski et al., Nucl. Phys. B 93, 461 (1975);
    Crossref
61. G. Hohler et al., Nucl. Phys. B 114, 505 (1976);
    Crossref
62. G. G. Simon et al., Nucl. Phys. A 333, 381 (1980);
    Crossref
63. P. E. Bosted et al., Phys. Rev. Lett. 68, 3841 (1992);
    Crossref
64. L. Andivahis et al., Phys. Rev. D 50, 5491 (1994);
    Crossref
65. R. C. Walker et al., Phys. Rev. D 49, 5671 (1994);
    Crossref
66. M. E. Christy et al., Phys. Rev. C 70, 015206 (2004);
    Crossref
67. I. A. Qattan et al., Phys. Rev. Lett. 94, 142301 (2005);
    Crossref
68. J. C. Bernauer et al., Phys. Rev. Lett. 105, 242001 (2010);
    Crossref
69. J. C. Bernauer, Ph.D. thesis, Johannes Gutenberg University Mainz (2010).
70. M. Mihovilovic et al., Phys. Lett. B 771, 194 (2017);
    Crossref
71. E. B. Hughes et al., Phys. Rev. 139, B458 (1965);
    Crossref
72. J. R. Dunning et al., Phys. Rev. 141, 1286 (1966);
    Crossref
73. P. Stein et al., Phys. Rev. Lett. 16, 592 (1966);
    Crossref
74. S. Platchkov et al., Nucl. Phys. A 510, 740 (1990);
    Crossref
75. C. E. Jones-Woodward et al., Phys. Rev. C 44, R571 (1991);
    Crossref
76. A. K. Thompson et al., Phys. Rev. Lett. 68, 2901 (1992);
    Crossref
77. A. Lung et al., Phys. Rev. Lett. 70, 718 (1993);
    Crossref
78. T. Eden et al., Phys. Rev. C 50, R1749 (1994);
    Crossref
79. M. Meyerhoff et al., Phys. Lett. B 327, 201 (1994);
    Crossref
80. E. E. W. Bruins et al., Phys. Rev. Lett. 75, 21 (1995);
    Crossref
81. J. Becker et al., Eur. Phys. J. A 6, 329 (1999);
    Crossref
82. C. Herberg et al., Eur. Phys. J. A 5, 131 (1999);
    Crossref
83. M. Ostrick et al., Phys. Rev. Lett. 83, 276 (1999);
    Crossref
84. I. Passchier et al., Phys. Rev. Lett. 82, 4988 (1999);
    Crossref
85. D. Rohe et al., Phys. Rev. Lett. 83, 4257 (1999);
    Crossref
86. J. Golak et al., Phys. Rev. C 63, 034006 (2001);
    Crossref
87. H. Zhu et al., Phys. Rev. Lett. 87, 081801 (2001);
    Crossref
88. J. Bermuth et al., Phys. Lett. B 564, 199 (2003);
    Crossref
89. R. Madey et al., Phys. Rev. Lett. 91, 122002 (2003);
    Crossref
90. G. Warren et al., Phys. Rev. Lett. 92, 042301 (2004);
    Crossref
91. G. I. Glazier et al., Eur. Phys. J. A 24, 101 (2005);
    Crossref
92. B. Plaster et al., Phys. Rev. C 73, 025205 (2006);
    Crossref
93. S. Riordan et al., Phys. Rev. Lett. 105, 262302 (2010);
    Crossref
94. B. S. Schlimme, Pros Sci. QNP2012 57, 097 (2012);
    Crossref
95. T. Gutsche, V. E. Lyubovitskij, I. Schmidt, Phys. Rev. D 97, 054011 (2018);
    Crossref
96. C. Patrignani et al., Chin. Phys. C 40, 100001 (2016);
    Crossref
97. F. Cap, W. Gröbner, Nuovo Cim. 1, 1211 (1955);
    Crossref
98. V. I. Zhaba, J. Phys. Stud. 20, 3101 (2016);
    Crossref
99. W. Plessas V. Christian, R.F. Wagenbrunn, Few-Body Syst. Suppl. 9, 429 (1995);
    Crossref
100. А. Ф. Крутов, Теор. физ. 3, 5 (2002).
101. N. A. Khokhlov, A. A. Vakulyuk, Phys. Atom. Nucl. 78, 92 (2015);
     Crossref
102. H. Arenhovel, F. Ritz, T. Wilbois, Phys. Rev. C 61, 034002 (2000);
     Crossref
103. A. J. Buchmann, H. Henning, P.U. Sauer, Few-Body Systems 21, 149 (1996);
     Crossref
104. B. Rezaei, A. Dashtimoghadam, J. Theor. Appl. Phys. 8, 203 (2014);
     Crossref
105. V. А. Babenko, N. М. Petrov, Phys. Atom. Nucl. 71, 1730 (2008);
     Crossref
106. I. Sick, D. Trautmann, Phys. Lett. B 375, 16 (1996);
     Crossref
107. I. Sick, D. Trautmann, Nucl. Phys. A 637, 559 (1998);
     Crossref
108. T. Herrmann, R. Rosenfelder, Eur. Phys. J A 2, 29 (1998);
     Crossref
109. M. Kalinowski, Phys. Rev. A 99, 030501(R) (2019);
     Crossref
110. A. A. Filin et al., Phys. Rev. Lett. 124, 082501 (2020);
     Crossref
111. D. R. Phillips, J. Phys. G: Nucl. Part. Phys. 34, 365 (2007);
     Crossref