BRUSLIB - the Brussels Nuclear Library for Astrophysics

Ground State Properties

Single Particle Scheme

Density and Potential

Nuclear Level Density

Partition Function

E1 Strength Function

Fission Properties (90<=Z<=110)

Reaction Rates

last update: April. 30, 2015

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Ground State Properties

Data and Plot

Proton number Z:

Neutron number N:

Introduction

Ground-state properties are calculated within the Hartree-Fock-Bogoliubov (HFB) framework using an energy density function based on an extended Skyrme-type form (i.e. containing t₄ and t₅ terms), along with a delta-function pairing force derived from realistic calculations of infinite nuclear and neutron matter.

The parameter set, labelled BSkG3, is determined by a fit to essentially all experimentally known masses which at the same time is constrained to nuclear-matter properties: the corresponding rms deviation is 0.63 MeV for the 2457 masses of nuclei with N,Z ≥ 8.

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Single Particle Scheme

Data and Plot

Proton number Z:

Neutron number N:

Introduction

The force used in the Hartree-Fock-Bogoliubov (HFB) mass model is an extended Skyrme force (containing t₄ and t₅ terms), along with a 4-parameter delta-function pairing force derived from realistic calculations of infinite nuclear and neutron matter.
Pairing correlations are introduced in the framework of the Bogoliubov method. Deformations with axial and left-right symmetry are admitted.

The total binding energy is given by

E_tot= E_HFB+ E_wigner

where

E_HFBis the HFB binding energy including a cranking correction to the spurious rotational energy and a phenomenological vibration correction energy
E_wigner=V_w exp(-λ((N-Z)/A)²)+V_w|N-Z|exp(-(A/A₀)²) is a phenomenological correction for the Wigner energy.

The parameter set, labelled BSk24, is determined by constraining the nuclear-matter symmetry coefficient to J = 30 MeV and the isoscalar effective mass to M*_s/M = 0.8 and optimizing the fit to the full data set of the 2353 measured masses with N,Z ≥ 8 (both spherical and deformed) of Audi et al. [Chinese Physics C36, 1287 (2012)]: the corresponding root mean square error is 0.549 MeV for this data set.

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Density and Potential

Data and Plot

Proton number Z:

Neutron number N:

Introduction

The total binding energy is given by

E_tot= E_HFB+ E_wigner

where

E_HFBis the HFB binding energy including a cranking correction to the spurious rotational energy and a phenomenological vibration correction energy
E_wigner=V_w exp(-λ((N-Z)/A)²)+V_w|N-Z|exp(-(A/A₀)²) is a phenomenological correction for the Wigner energy.

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Nuclear Level Density

Data and Plot

Proton number Z:

Neutron number N:

Spin number:

Introduction

The NLD predictions within the combinatorial method are based on the realistic microscopic single-particle level scheme and pairing force of the Hartree-Fock-Bogolyubov model using the BSkG3 Skyrme energy density functional. The vibrational enhancement is explicitly taking into account considering phonon excitations.

More details of the nuclear level density formula can be found in

S. Hilaire, J.P. Delaroche and A.J. Koning, Nucl. Phys. A632, 417 (1998).
S. Hilaire, J.P. Delaroche and M. Girod, Eur. Phys. J. A12 (2001) 169
S. Hilaire and S. Goriely, Nucl. Phys. A779 (2006) 63
S. Goriely, S. Hilaire and A.J. Koning, Phys. Rev. C78 (2008) 064307
S. Goriely, W. Ryssens, S. Hilaire and A.J. Koning, Phys. Rev. C (2025)

The microscopic predictions of NLD (total, spin- and parity-dependent) for 7394 nuclei from Z=8 to 110 and lying between the proton and neutron drip lines are tabulated in an energy (U=0.25 to 200 MeV) and spin (the lowest 50 spins) grid. Also included in the tables is the the cumulative number of levels.

a zipped tar file including all nuclear level density tables can be downloaded HERE (70Mb).
(last update 1/12/2025)

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Partition Function

Data and Plot

Proton number Z:

Neutron number N:

Introduction

The partition functions are calculated using experimental excited spectrum whenever available (RIPL-3 database) and if not, on the basis of the nuclear level densities obtained within the HFB plus combinatorial method (Goriely et al., 2008, Phys. Rev. C78, 064307)

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E1 Strength Function

Data and Plot

Proton number Z:

Neutron number N:

Introduction

The present E1 strength functions are obtained by a large-scale calculation within the covariant-EDF framework. It is referred to as RQFAMz [1]. The ground state is calculated as a RHB state using the covariant functional DD-PC1 for the particle-hole channel and a separable pairing force. The E1 strength is then built via an axially-deformed FAM-QRPA approach. In order to obtain a dataset reproducing at the same time the low- and high-energy parts of the experimental E1 strength, a folding procedure is applied. The RQFAMz E1 strength funtion is available for all nuclei with 8 ≤ Z ≤ 110 lying between the proton and the neutron drip lines.

[1] L. González-Miret Zaragoza, J.-P. Ebran, S. Goriely, S. Hilaire, E. Khan, S. Péru, Phys Rev C 112 (2025) 044303

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Fission Properties

Data and Plot

Proton Number Z:

Neutron Number N:

Location:

Spin:

Introduction

The present tables contain the predictions of the fission properties [1] obtained within the Hartree-Fock-Bogolyubov approach based on the BSk14 Skyrme force [2], which has proven its capacity to estimate the static fission barrier height with a relatively high degree of accuracy. In particular, the barriers determined from the present HFB-14 fission path reproduce the 52 primary empirical barriers (i.e the highest barriers) of nuclei with 88 ≤ Z ≤ 96 (which are always less than 9 MeV high) with an rms deviation as low as 0.67 MeV. A similar accuracy is obtained (0.65 MeV) for the secondary barriers.

Fission properties are provided for about 1000 nuclei with 90 ≤ Z ≤ 110 lying between the valley of beta-stability and the neutron drip line.

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Astrophysical Reaction Rates

Data and Plot

Proton number Z:

Neutron number N:

Introduction

The present estimates of thermonuclear reaction rates are obtained with the reaction code called TALYS [1,2,3]. TALYS includes many state-of-the-art nuclear models to cover all main reaction mechanisms encountered in light particle-induced nuclear reactions. TALYS provides a complete description of all reaction channels and observables and in particular takes into account all types of direct, pre-equilibrium, and compound mechanisms to estimate the total reaction probability as well as the competition between the various open channels.

The code is optimized for incident projectile energies, ranging from 1 keV up to 200 MeV on target nuclei with mass numbers between 12 and 339. It includes photon, neutron, proton, deuteron, triton, ³He, and α-particles as both projectiles and ejectiles, and single-particle as well as multi-particle emissions and fission. The TALYS code was designed to calculate total and partial cross sections, residual and isomer production cross sections, discrete and continuum γ-ray production cross sections, energy spectra, angular distributions, double-differential spectra, as well as recoil cross sections. TALYS also estimates the maxwellian-averaged reaction rates [3].

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Please refer to Yi Xu, Stephane Goriely, Alain Jorissen, Guangling Chen, Marcel Arnould, Astronomy & Astrophysics 549, A106 (2013) and the specified literatures therein when using BRUSLIB.
Any comments or suggestions please send to S. Goriely % ulb.be