A CONTINUOUS MEDIUM MODEL OF ATOMIC NUCLEI

HU JI-MIN

Chinese Physics C> 1981, Vol. 5> Issue(2) : 244-254

A CONTINUOUS MEDIUM MODEL OF ATOMIC NUCLEI

HU JI-MIN

Peking University

Abstract
HTML
Reference
Related

PDF

Abstract：
In this model, the nucleus is consiered as a continuous medium with variable nucleon densities, ρ_p and ρ_n. The energy of the system is expressed by the formula:

where ρ_o=t/(4πa³)[1+exp((r-R)/a)]^-1 is a reference density which is assumed to be the average density of an ideal nucleus with N=Z and without coulomb interactions. The binding energy and the density distributions of a nucleus were determined from the condition δE=0.The parameters were determined by fitting the nuclear masses and the general behavior of unclear charge distributions. Their preliminary values are: a=0.528 fm, t=0.3, a₁=16.1027 MeV, a₃=26.583 MeV, a₄=15.19 MeV, a₆=14.62 MeY, a₂=1/2 a₂, a₅=1/2 a₆. With this set of parameters, together with Myers and Swiatecki's formulae for shell corrcctions and pairing energies, the experimental nuclear masses can be reproduced wi thin 5 MeV and the nuclear mean wqare root radius within a few percent. These constants probably could further be improved by fitting other nuclear properties.With this new mass formula, the empirical mass difference between mirror nuclei can be reproduced within 4% (for A≥20). This is a substantial improvement over the liquid drop model. A theory of nuclear giant multipole resonance was developed by this model. Preliminary calculation on the giant dipole resonance yields rather promising results.

References

[1]

A.玻尔,B. R.莫特逊,《原子核结构》,卷1,第二章第一节,1969科学出版社出版.[2] A. de Shalit, H. Feshbach, "Theoretical Nuclear Phyeice Vol.Nuclear truature",p. 188,1974, John Wiley and Sone, Inc. New York.[3] M. A. Preston. R. H. Bhaduri:"Structure of the Nucleus", p. 99. 1975, Addition-Wesley Pub.Co. Inc, Reading, Massachusetts.[4] W. J. Swiatecki in “Nuclear,Reactions Induced by Heavy Ions ", p. 729, 1970. North Holland Pub. Co.Amsterdam-Lonndon.[5] W. D. MYere and W. J. Swiatecki, Ann. Phys., (N. Y.) 55(1969), 395[6] W. D. Myers, "Droplet Model of Atamic Nuclei", 1977, IFI/Plenum Data Company.[7] W. D. Mvere and W. J. Swiatecki, in Proe. of the Lysekil Sympoaium (1966), Ark. Fys., 36(1967),343.[8] 参见D.A. Bromley in Proe. of the Int. Conf.on Nuclear Physics, Munich 1973, 2, 35, North Holland Pub. Co.Amstordam-London.[9] H. A. Brueekner et al., Phya. Rev., C4(1971), 732及所引文献.[10] H. Stock, Nucl. Phys., A237 (1975 ) , 365[1l」见文献[1].voi. 1,英文版152页.[12] R U. Barrett, D. F. Jackson, "Nuclear Sizea and Structure",第6章,1977, Clarendon Presa. 0xford.[13] J. W. Negele et al., Comments Nucl. Phys., 8(19T9), 135.[14]曾谨言,物理学报,14(1975), 151.Nucl. Phys., A334(1980), 470.[15] V. S. Shirley, C. M. Lederer, 'Nuclear Wallet Carde". U. S. Nuclear Data Network 1979.[l6]见文献[1] Vol. 2, p. 666--671.[17] B. L. Berman, S. C. Fultz, Rev, Mod, phys., 47(1975), 713

[1]	YE Wei . Possible Dependence of Dissipation Strength on Angular Momentum. Chinese Physics C, 2006, 30(8): 759-760.
[2]	LIU Chang-Long , LU Yi-Ying , YIN LI . Effects of Additional Vacancy-Like Defects Produced by Ion Impealations on Boron Thermal Diffusion in Silicon. Chinese Physics C, 2005, 29(11): 1107-1111.
[3]	HU Xi-Duo , SHAO Ming-Zhu , LUO Shi-Yu , LIU Yong-Sheng , ZHU De-Hai . Average Field Idea and Single Particle Model for 2 Dimension Crystallization Beams(Ⅱ). Chinese Physics C, 2004, 28(2): 196-199.
[4]	Guo Hua . In-medium QMC Model Parameters and Quark Condensation in Nuclear Matter. Chinese Physics C, 1999, 23(5): 459-468.
[5]	Li Yangguo . Antiproton -Nucleus Charge Exchange Reaction and Inelastic Scattering. Chinese Physics C, 1996, 20(11): 1021-1027.
[6]	ZHU Xiang , SHEN Wen-Qing , HU Xiao-Qing , ZHU Yong-Tai , WANG Bing . A SIMPLE MODEL ANALYSIS OF THE INCOMPLETE DIC REACTION. Chinese Physics C, 1990, 14(9): 835-841.
[7]	WU Zhong-Li . ANALYSIS OF THE MOMENTUM DISTRIBUTION WIDTH OF THE PREOJECTILE-LIKE-FRAGMENT FROM HEAVY ION COLLISIONS. Chinese Physics C, 1989, 13(8): 752-754.
[8]	WANG Man , LI Jin , CUI Xiang-Zong , XIA Xiao-Mi , LAI Yuan-Fen , YAO Xiao-Guang . PROTOTYPE OF END CAP SHOWER COUNTERAND ITS BEAM TEST. Chinese Physics C, 1987, 11(3): 321-326.
[9]	Sa Ben-hao , Zhang Xi-zhen , Li Zhu-xia , Shi Yi-jin . A PRIMARY RESEARCH OF THE PHONON RENORMALIZATION OF NUCLEAR FIELD THEORY. Chinese Physics C, 1980, 4(3): 398-400.
[10]	WU SHI-SHU . ON NUCLEAR SINGLE-PARTICLE POTENTIALS（Ⅲ）SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIAL U_αβ=M_αβ（ε_β）. Chinese Physics C, 1979, 3(4): 469-483.

Access

Get Citation

HU JI-MIN. A CONTINUOUS MEDIUM MODEL OF ATOMIC NUCLEI[J]. Chinese Physics C, 1981, 5(2): 244-254.

HU JI-MIN. A CONTINUOUS MEDIUM MODEL OF ATOMIC NUCLEI[J]. Chinese Physics C, 1981, 5(2): 244-254. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1980-09-16
Revised: 1900-01-01

Article Metric

Article Views(2136)
PDF Downloads(312)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

A CONTINUOUS MEDIUM MODEL OF ATOMIC NUCLEI

HU JI-MIN

Peking University

Received Date: 1980-09-16
Accepted Date: 1900-01-01
Available Online: 1981-04-05

Abstract: In this model, the nucleus is consiered as a continuous medium with variable nucleon densities, ρ_p and ρ_n. The energy of the system is expressed by the formula:

where ρ_o=t/(4πa³)[1+exp((r-R)/a)]^-1 is a reference density which is assumed to be the average density of an ideal nucleus with N=Z and without coulomb interactions. The binding energy and the density distributions of a nucleus were determined from the condition δE=0.The parameters were determined by fitting the nuclear masses and the general behavior of unclear charge distributions. Their preliminary values are: a=0.528 fm, t=0.3, a₁=16.1027 MeV, a₃=26.583 MeV, a₄=15.19 MeV, a₆=14.62 MeY, a₂=1/2 a₂, a₅=1/2 a₆. With this set of parameters, together with Myers and Swiatecki's formulae for shell corrcctions and pairing energies, the experimental nuclear masses can be reproduced wi thin 5 MeV and the nuclear mean wqare root radius within a few percent. These constants probably could further be improved by fitting other nuclear properties.With this new mass formula, the empirical mass difference between mirror nuclei can be reproduced within 4% (for A≥20). This is a substantial improvement over the liquid drop model. A theory of nuclear giant multipole resonance was developed by this model. Preliminary calculation on the giant dipole resonance yields rather promising results.