Abstract
In this chapter we give explicit expression for the matrix elements of the finite-range interaction used in the second part of the book in the deformed harmonic-oscillator basis. The components of the interaction explicitly given are: the central (Gaussian) part, the spin-orbit part, a density-dependent contribution, and both the exact and Slater approximation to the Coulomb interaction.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Let us mention that using an axially deformed HO basis does not necessarily imply that nuclear shapes have to be restricted to axially symmetric ones. In fact, triaxial shapes can be described using such a basis by allowing a mixing of the orbital momentum projection quantum number Λ in the expansion of the HFB qp states, although such a mixing is convenient in practice only for relatively small triaxiality – which is generally the case along fission paths
References
Skyrme, T.H.R.: Philos. Mag. 1, 1043 (1956)
Skyrme, T.H.R.: Nucl. Phys. 9, 615 (1959)
Gogny, D.: In: Proceedings of the International Conference on Self-Consistent Fields, Trieste, p. 333. North-Holland, Amsterdam (1975)
Dechargé, J., Gogny, D.: Phys. Rev. C 21, 1568 (1980)
Stone, J.R., Reinhard, P.-G.: Prog. Part. Nucl. Phys. 58, 587 (2007)
Bender, M., Heenen, P.-H., Reinhard, P.-G.: Rev. Mod. Phys. 75, 121 (2003)
Hilaire, S., Girod, M.: Eur. Phys. J. A 33, 237 (2007)
Delaroche, J.-P., Girod, M., Libert, J., Goutte, H., Hilaire, S., Péru, S., Pillet, N., Bertsch, G.F.: Phys. Rev. 81, 014303 (2010)
Brueckner, K.A.: Phys. Rev. 97, 1353 (1955)
Day, D.A.: Rev. Mod. Phys. 39, 719 (1967)
Köhler, H.S.: Phys. Rep. 18, 217 (1975)
Côté, J., Pearson, J.M.: Nucl. Phys. A 304, 104 (1978)
Kortelainen, M., McDonnell, J., Nazarewicz, W., Reinhard, P.-G., Sarich, J., Schunck, N., Stoitsov, M.V., Wild, S.M.: Phys. Rev. C 85, 024304 (2012)
Chappert, F.: Ph.D. thesis, Université de Paris-Sud. Faculté des Sciences d’Orsay (Essonne) (2007)
Goriely, S., Hilaire, S., Girod, M., Péru, S.: Phys. Rev. Lett. 102, 242501 (2009)
Péru, S., Martini, M.: Eur. Phys. J. A 50, 88 (2014)
Younes, W.: Comput. Phys. Commun. 180, 1013 (2009)
Schunck, N., Robledo, L.M.: arXiv:1511.07517v2, submitted to Rep. Prog. Phys. (2016)
Flocard, H., Quentin, P., Kerman, A.K., Vautherin, D.: Nucl. Phys. A 203, 433 (1973)
Girod, M., Grammaticos, B.: Phys. Rev. C 27, 2317 (1983)
Egido, J.L., Robledo, L.M., Chasman, R.R.: Phys. Lett. B 393, 13 (1997)
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1972)
Vautherin, D., Brink, D.M.: Phys. Rev. C 5, 626 (1972)
Ring, P., Schuck, P.: The Nuclear Many-Body Problem. Springer, Heidelberg (1980)
Slater, J.C.: Phys. Rev. 81, 385 (1951)
Acknowledgements
This chapter was prepared by a contractor of the U.S. Government under contract number DE-AC52-06NA27344. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Younes, W., Gogny, D.M., Berger, JF. (2019). Matrix Elements of the Finite-Range Interaction. In: A Microscopic Theory of Fission Dynamics Based on the Generator Coordinate Method. Lecture Notes in Physics, vol 950. Springer, Cham. https://doi.org/10.1007/978-3-030-04424-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-04424-4_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-04422-0
Online ISBN: 978-3-030-04424-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)