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Gogny-Hartree-Fock-Bogolyubov Nuclear Mass Models with Application to r-Process Stellar Nucleonsynthesis[量子分子动力学之家]
Gogny-Hartree-Fock-Bogolyubov Nuclear Mass Models with Application to r-Process Stellar Nucleonsynthesis
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Master's Thesis 
(mass_formula_HF.pdf) From: http://www.diva-portal.org/smash/get/diva2:684496/FULLTEXT01.pdf


Gogny-Hartree-Fock-Bogolyubov Nuclear Mass Models with Application to r-Process Stellar Nucleosynthesis


Alexander Arzhanov
November 30, 2013


Supervision:
Prof. Dr. Gabriel Martnez-Pinedo (TU Darmstadt)
Dr. Tomas R. Rodrguez (TU Darmstadt)
Dr. Chong Qi (KTH Stockholm)

------------------------------------------------


We employ the microscopic approach of Hartree-Fock-Bogolyubov (HFB) nuclear theory with an
e ective Gogny interaction in D1S and D1M parametrizations to perform a large-scale calculation
of nuclear masses from proton-drip to neutron-drip line for even-even nuclei, and compare our
results to the experimentally known masses listed in 2012 Atomic Mass Evaluation compilation.
Owing to lack of convergence for the heavier nuclear systems in a truncated working basis,
we employ and benchmark di erent energy correction techniques to extrapolated our results to
the in nite model space. We also touch on the problem of describing the odd-mass nuclear
systems with the HFB approach, and present some results of approximating such systems with
perturbative nucleon addition method. We outline some of the method's de ciencies, as well as
compare this approach with the results of a full blocking approximation. Finally, in order to
account for some of the missing correlations at the purely mean- eld level of HFB formalism,
we also introduce a number of beyond-mean- eld extensions, namely, the particle-number and
angular momentum projections, as well as the con guration-mixing method. Thereafter, we
present the results of the large-scale mean- eld mass calculations augmented with the above
mentioned beyond-mean- eld corrections.

--------------------------------------------------------

Contents
1 Introduction 11
2 Nuclear Structure Methods 13
2.1 Ab initio methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Mic-mac formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Microscopic models with e ective interactions . . . . . . . . . . . . . . . . . . . . 16
3 A Theoretical Overview 18
3.1 Microscopic Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 The Hartree-Fock approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 The Bogolyubov transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4 Perturbative nucleon addition method . . . . . . . . . . . . . . . . . . . . . . . . 23
3.5 Extensions beyond the static mean eld . . . . . . . . . . . . . . . . . . . . . . . 24
3.5.1 Particle number projection . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.5.2 Angular momentum projection . . . . . . . . . . . . . . . . . . . . . . . . 25
3.5.3 Con guration mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4 HFB Calculations with Gogny-force 27
4.1 The Gogny interaction and parametrization . . . . . . . . . . . . . . . . . . . . . 27
4.2 The gradient method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3 Spherical and deformed HO basis . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.4 Issue of convergence in a truncated basis . . . . . . . . . . . . . . . . . . . . . . . 29
4.5 Calculation overview and HFBAXIAL code . . . . . . . . . . . . . . . . . . . . . 30
5 Results 31
5.1 MVS-A Extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.1.1 The tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.1.2 Benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.1.3 Strontium isotopic chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.1.4 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.2 L2-Extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2.1 Theoretical motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2.2 Playground test. Oxygen-16 . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2.3 Benchmark. Magnesium isotopic chain . . . . . . . . . . . . . . . . . . . . 40
5.2.4 Further examinations. Medium-mass and heavy isotopic chains . . . . . . 44
5.2.5 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
9
5.3 Odd-even e ects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.3.1 Even-odd and odd-even nuclei . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.3.2 Odd-odd nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.3.3 A comparison with blocking approximation . . . . . . . . . . . . . . . . . 50
5.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.4 Large-scale drip-to-drip line HFB-D1S/D1M and BMF calculations . . . . . . . . 52
5.4.1 Quadrupole deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.4.2 Ground-state energies at the mean- eld level . . . . . . . . . . . . . . . . 54
5.4.3 The impact of the Beyond-Mean-Field corrections . . . . . . . . . . . . . 57
6 Summary and Outlook 60
Appendix A:
Astrophysical Conditions for the r-Process 62
A1 Nuclear Statistical Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
A2 Freeze-out and r-Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
A3 Astrophysical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Appendix B:
Numerical Data 67
References 99

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