“Functionals

INTRODUCTION

Code is based on Density Functional Theory [Fiolhais, Nogueira, and Marques (2003), Magierski (2019), Bulgac (2013)]. It is using Skyrme Hartree-Fock approach, for general overview we refer to review article [Klüpfel and Reinhard (2007)] and references therein.

The Skyrme force is an effective interaction depending on a limited number of parameters:

V_{12} = t_0\left(1+x_0P_\sigma\right)\delta \\ + \tfrac{1}{2}t_1\left(1+x_1P_\sigma\right) \left(\boldsymbol{k}^{\prime2}\delta+\delta\boldsymbol{k}^2\right)\\ + t_2(1+x_2P_\sigma)\boldsymbol{k}^\prime\cdot \delta\boldsymbol{k} \\ + \tfrac{1}{6}t_3\left(1+x_3P_\sigma\right)\rho^\gamma \delta\\ + iW_0\left(\boldsymbol{\sigma}_1 + \boldsymbol{\sigma}_2\right) \cdot \left(\boldsymbol{k}^\prime\times\delta\boldsymbol{k}\right)

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PARAMETRIZATION

NAME	PAPER	t0	t1	t2	t3	x0	x1	x2	x3	gamma	W0	J^2	Implemented
SIII	[Beiner et al. (1975)]	-1128.75	395.0	-95.0	14000.0	0.45	0.0	0.0	1.0	1.0	130	No	No
SkM*	[Bartel et al. (1982)]	-2645.0	410.0	-135.0	15595.0	0.09	0.0	0.0	0.0	1/6	120	No	Yes
SLy4	[Chabanat et al. (1998)]	-2488.913	486.818	-546.395	13777.0	0.834	-0.344	-1.0	1.354	1/6	123	Yes	Yes
SLy4d	[Kim, Otsuka, and Bonche (1997)]	-2479.662	473.216	-333.654	13487.0	0.8122	-0.7228	-1.0	1.398	1/6	128	—	No
SLy5	[Chabanat et al. (1998)]	-2484.88	483.13	-549.4	13763.0	0.778	-0.328	-1.0	1.267	1/6	126	Yes	No
SLy6	[Chabanat et al. (1998)]	-2479.5	462.18	-448.61	13673.0	0.825	-0.465	-1.0	1.355	1/6	122	—	Yes
SLy7	[Chabanat et al. (1998)]	-2482.41	457.97	-419.85	13677.0	0.846	-0.511	-1.0	1.391	1/6	126	Yes	No
SkP	[Dobaczewski, Flocard, and Treiner (1984)]	-2931.696	320.6182	-337.4091	18708.96	0.29215	0.65318	-0.53732	0.18103	1/6	100	Yes	Yes

TODO: SKa, SGI, SkOP1, SkOP2, SLy family, SkX, SeaLL1, SKMP, SkI phd thesis

Bartel, J, Ph Quentin, Matthias Brack, C Guet, and H-B Håkansson. 1982. “Towards a Better Parametrisation of Skyrme-Like Effective Forces: A Critical Study of the SkM Force.” Nuclear Physics A 386 (1): 79–100.

Beiner, M, H Flocard, Nguyen Van Giai, and Phu Quentin. 1975. “Nuclear Ground-State Properties and Self-Consistent Calculations with the Skyrme Interaction:(i). Spherical Description.” Nuclear Physics A 238 (1): 29–69.

Bulgac, Aurel. 2013. “Time-Dependent Density Functional Theory and the Real-Time Dynamics of Fermi Superfluids.” Annual Review of Nuclear and Particle Science 63: 97–121.

Chabanat, E, P Bonche, P Haensel, J Meyer, and R Schaeffer. 1998. “A Skyrme Parametrization from Subnuclear to Neutron Star Densities Part II. Nuclei Far from Stabilities.” Nuclear Physics A 635 (1-2): 231–56.

Dobaczewski, J, H Flocard, and J Treiner. 1984. “Hartree-Fock-Bogolyubov Description of Nuclei Near the Neutron-Drip Line.” Nuclear Physics A 422 (1): 103–39.

Fiolhais, Carlos, Fernando Nogueira, and Miguel AL Marques. 2003. A Primer in Density Functional Theory. Vol. 620. Springer Science & Business Media.

Kim, Ka-Hae, Takaharu Otsuka, and Paul Bonche. 1997. “Three-Dimensional TDHF Calculations for Reactions of Unstable Nuclei.” Journal of Physics G: Nuclear and Particle Physics 23 (10): 1267.

Klüpfel, P, and P-G Reinhard. 2007. “Self-Consistent Mean-Field Models for Nuclear Structure and Dynamics.” International Journal of Modern Physics E 16 (04): 1009–19.

Magierski, Piotr. 2019. “Nuclear Reactions and Superfluid Time Dependent Density Functional Theory.” Progress of Time-Dependent Nuclear Reaction Theory 2: 57–71.