A CHECK ON INDIVIDUAL TERMS OF THE NUCLEAR MASS FORMULA

ZENG JIN-YAN; LIN CHUN-ZHENG; YANG FU-JIA

Chinese Physics C> 1981, Vol. 5> Issue(2) : 232-243

A CHECK ON INDIVIDUAL TERMS OF THE NUCLEAR MASS FORMULA

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Abstract：
The usual way to check whether a nuclear mass formula is good or not is to compare the calculated mass with experimental value. In this paper some concepts are summaried which check one or two terms in the mass formula separately: (ⅰ) P/P ratio-pairing energy; (ⅱ) Janecke ratio-symmetry energy; (ⅲ) A-dependence of giant resonance energy-symmetry energy; (ⅳ) IMME (isobaric multiplets mass equation)-Coulomb energy; (ⅴ) Difference of Coulomb energies-Coulomb energy; (ⅵ) β-stability lineCoulomb energy and symmetry energy; (ⅶ) Fissibility-Coulomb energy and surface energy. The following nuclear mass formulae are compared with each other: (A) Revised Weizsacker formula; (B) Danos-Gillet formula; (C) Myers-Swiatecki formula; (D) our formula. The main results are the following: (ⅰ) P/P'=1 for (A), (B) or (C);=3/4 for (D), which is in agreement with the experiment. (ⅱ) From the Janecke ratio, the form T(T+1) for the symmetry energy is better than T(T+4) or T². (ⅲ) By the symmetry term T²/A^a, with a=0.90, the A-depeneence of giant resonance can be explained extremely well. (ⅳ) IMME, M(A, T_z)=a+bT_z²+cT_z²+dT z³. Only for (D), d≠0. (ⅴ) △E_o=E_o (Z+I)—E_c (Z), For (A) and (B), △E_cA^1/3/(Z⁺(1/2))=const.; for (C), △E_cA^1/3/(Z+(1/2)) (1—1.689)/A^2/3=const.; for (D), △E_c Z₂^/3=const., which is in good agreement with the experiment. (ⅵ) For the β-stability line, if we compare the calculated Z_A with the experimental value Z_A and calculate the root mean square devidtions, then for (A), RMS=0.450; (B)=0.589; (C)=0.438; (D)=0.429.

References

[1]

C. E. Weizeacker, Z. Physik, 96(1935), 431.[2]H.A. Bethe and R. E. Bacher, Rev. Mod. Phys., 7(1936), 165.[3]E. Fermi,Physics, (Univ, of Chicago Press. 1950).[4]A. E. S. Green, Nuclear Physics, (1955), chap. 9.[5]J. Wing, and P. Fong, Phys. Rev., 136B(1964), 923.[6]J. Wing, A Comparision of Nusleidic Mass Equations with Ezperimental Data, Argonne National Laboratory Report, ANL-6814 (1964).[7]J. Wing, Nucl. Phys., A120(1968), 369.[8]J. Wing, Systematic Comparision of Semiepirical Nucleidic Mass Equations, in Proc. 3rd Int.Conf, on Atomic Masses, Winnipeg (1967).[9]W. D. Ilwera and W. J. Swiatecki. Nucl. Phys.. 81(1968). 1:Annals of Physics 55(1969). 369:Annals of Physics, 84(1974), 186.[10]M.Danoe and P. Gillet, Proc. Int, Conf. on Nuclear Structure, Tokyo, (1977), p. 60.[1l]O. Y. Tseng(曾谨言),T. S. ChenQ(程植生)and F. C. Yang(杨福家),Nucl. Phys., A334(1980), 470.[12]J. Janecke, Nucl. Phys., 73(1965), 57.[13]C. Y. Tseng(曾谨言)and F. C. Yang(杨福家),NBI-80-5 ;或Proc. Int, Cof. on Nuclear Physics, Aug. 24-30, 1980, Berkeley, California, p. 753[14] E. P. Wigner, Proc, of the Robert A. Welch Foundation Conference on Chemical Research, ed. by W.D. Milikan, (1957).[15] W. Beneneon and E. Kashy, Rev. Mod. Phys., 51(1979), 527[16] W. Benenson and E, gashy, Atomic Maesee and Fundamental Constants, Vol. 5, ed. by J. H Saudere and A. H. Wapetra (1976),[17] J. Cerny et al., Phys. Rev. Lett., 13(1964), 726.[18] R. G. H, Robarteon, W. 8. Chien and D. R. Gooeman Rev. Lett.,34(1915), 33.(19] A. G. Ledebnhr et al.,私人通讯(1980 ).[20] J. Aysto et al., Phys. Lett,, 42(1979), 43.[21] D. M. Molts et e1., Phys. Rev. Lett., 42(1979), 43.[22] W. J. Courtney and J. D. Fox, Atomic Data and Nuclear Data Tables, 15(1975), 141.[23]曾谨言,物理学报,24(1975), 151.[24] M. A. Preston and R. K. Bhaduri, Structure of the Nucleus, (1975).[25] J. W. Dewdney, Nucl. Phys., 43(1963), 303.[26] A. Michaudon, Advances in Nuclear Physics, 6(1973), 1.[27] S. Cohen and W. J. Swiatecki, Annals of Physics,19(1962), 67; 22(1963), 406.[28] B. B. Back et al., in Physics and Chemistry of Fission (1973), Vol. 1, p.3; p.25.[29] R. Vandenbosch and J. R. Huizenga, Nuelear Fission (1973), Academic Press.

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ZENG JIN-YAN, LIN CHUN-ZHENG and YANG FU-JIA. A CHECK ON INDIVIDUAL TERMS OF THE NUCLEAR MASS FORMULA[J]. Chinese Physics C, 1981, 5(2): 232-243.

ZENG JIN-YAN, LIN CHUN-ZHENG and YANG FU-JIA. A CHECK ON INDIVIDUAL TERMS OF THE NUCLEAR MASS FORMULA[J]. Chinese Physics C, 1981, 5(2): 232-243. shu

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Received: 1980-07-29
Revised: 1900-01-01

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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

A CHECK ON INDIVIDUAL TERMS OF THE NUCLEAR MASS FORMULA

Received Date: 1980-07-29

Accepted Date: 1900-01-01

Available Online: 1981-04-05

Abstract: The usual way to check whether a nuclear mass formula is good or not is to compare the calculated mass with experimental value. In this paper some concepts are summaried which check one or two terms in the mass formula separately: (ⅰ) P/P ratio-pairing energy; (ⅱ) Janecke ratio-symmetry energy; (ⅲ) A-dependence of giant resonance energy-symmetry energy; (ⅳ) IMME (isobaric multiplets mass equation)-Coulomb energy; (ⅴ) Difference of Coulomb energies-Coulomb energy; (ⅵ) β-stability lineCoulomb energy and symmetry energy; (ⅶ) Fissibility-Coulomb energy and surface energy. The following nuclear mass formulae are compared with each other: (A) Revised Weizsacker formula; (B) Danos-Gillet formula; (C) Myers-Swiatecki formula; (D) our formula. The main results are the following: (ⅰ) P/P'=1 for (A), (B) or (C);=3/4 for (D), which is in agreement with the experiment. (ⅱ) From the Janecke ratio, the form T(T+1) for the symmetry energy is better than T(T+4) or T². (ⅲ) By the symmetry term T²/A^a, with a=0.90, the A-depeneence of giant resonance can be explained extremely well. (ⅳ) IMME, M(A, T_z)=a+bT_z²+cT_z²+dT z³. Only for (D), d≠0. (ⅴ) △E_o=E_o (Z+I)—E_c (Z), For (A) and (B), △E_cA^1/3/(Z⁺(1/2))=const.; for (C), △E_cA^1/3/(Z+(1/2)) (1—1.689)/A^2/3=const.; for (D), △E_c Z₂^/3=const., which is in good agreement with the experiment. (ⅵ) For the β-stability line, if we compare the calculated Z_A with the experimental value Z_A and calculate the root mean square devidtions, then for (A), RMS=0.450; (B)=0.589; (C)=0.438; (D)=0.429.

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