Thomas-Fermi approach to nuclear mass formula: (III). Force fitting and construction of mass table

doi:10.1016/0375-9474(91)90418-6

Nuclear Physics A

Volume 528, Issue 1, 3 June 1991, Pages 1-47

https://doi.org/10.1016/0375-9474(91)90418-6 Get rights and content

Abstract

The ETFSI method, developed in two earlier papers, is here used to construct a complete mass table. Since the method allows for interpolation both in the (N, Z) plane and with respect to deformations, without losing the characteristic shell-model fluctuations, it is some 2000 times faster than the HF-BCS method for a given force. The present table is calculated using a preliminary Skyrme-type force with δ-function pairing, fitted to a restricted data set of 491 spherical nuclei. The resulting rms error for all 1492 measured nuclei, spherical and deformed, with A ⩾ 36 is ε_rms = 0.868 MeV, achieved with just 9 parameters. The main experimental trends in ground-state deformations are well followed. The symmetry coefficient of nuclear matter corresponding to our force is 27.5 MeV. Ways of rapidly improving the fit are indicated.

References (59)

A.K. Dutta et al.
Nucl. Phys.
(1986)
F. Tondeur et al.
Nucl. Phys.
(1987)
B. Grammaticos et al.
Ann of Phys.
(1979)
B. Grammaticos et al.
Ann of Phys.
(1980)
P. Möller et al.
At. Data Nucl. Data Tables
(1988)
P. Möller et al.
Nucl. Phys.
(1981)
W.D. Myers et al.
Ann. of Phys.
(1969)
A.K. Dutta et al.
Nucl. Phys.
(1986)
M. Brack et al.
Phys. Reports
(1985)
M. Barranco et al.
Nucl. Phys.
(1981)

V. Bernard et al.

Nucl. Phys.

(1980)

F. Tondeur et al.

Nucl. Phys.

(1984)

F. Tondeur

Nucl. Phys

(1985)

M. Brack et al.

Nucl. Phys.

(1981)

Y.H. Chu et al.

Phys. Lett.

(1977)

M.N. Butler et al.

Nucl. Phys.

(1984)

M. Beiner et al.

Nucl. Phys.

(1975)

F. Tondeur

Nucl. Phys.

(1979)

C. Ko et al.

Nucl. Phys.

(1974)

F. Tondeur

Nucl. Phys.

(1978)

J.M. Cavedon et al.

Phys. Rev. Lett.

(1987)

M.M. Sharma et al.

Nucl. Phys.

(1989)

F. Tondeur et al.

Z. Phys.

(1986)

B. ter Haar et al.

Phys. Rev. Lett.

(1987)

H.A. Bethe et al.

Nucl. Phys.

(1979)

B. Friedman et al.

Nucl. Phys.

(1981)

J. Cugnon et al.

Z. Phys.

(1987)

M. Farine et al.

Nucl. Phys.

(1978)

M. Farine et al.

Phys. Rev.

(1981)

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^☆: Supported by NSERC (Canada) and FCAR (Québec).

¹: Present address: School of Physics, Devi Ahilya University, Indore, 452001 India.

²: On leave from: Dept. of Physics, Khallikote College, Berhampur, 760001 India.

³: Present address: Laboratoire de Spectroscopie Nucléaire, Université de Nantes, 44072 Nantes, France.

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Thomas-Fermi approach to nuclear mass formula: (III). Force fitting and construction of mass table☆

Abstract

Nucl. Phys.

Nucl. Phys.

Ann of Phys.

Ann of Phys.

At. Data Nucl. Data Tables

Nucl. Phys.

Ann. of Phys.

Nucl. Phys.

Phys. Reports

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys

Nucl. Phys.

Phys. Lett.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Phys. Rev. Lett.

Nucl. Phys.

Z. Phys.

Phys. Rev. Lett.

Nucl. Phys.

Nucl. Phys.

Z. Phys.

Nucl. Phys.

Phys. Rev.