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The Nuclear Many-Body Problem de Peter Ring

The Nuclear Many-Body Problem: Theoretical and Mathematical Physics

Autor Peter Ring, Peter Schuck
en Limba Engleză Paperback – 25 mar 2004

Găsim în această lucrare, The Nuclear Many-Body Problem, o abordare riguroasă a metodologiilor teoretice esențiale pentru înțelegerea nucleului atomic. Autorii Peter Ring și Peter Schuck au ales o structură dictată de metodele matematice și tehnice — de la teoria Hartree-Fock dependentă de timp la coordonatele generatoare și expansiunile bozonice — oferind astfel un instrument de lucru analitic, nu doar o trecere în revistă a fenomenelor fizice. Această ediție, un reprint al volumului de referință din 1980, rămâne fundamentală prin modul în care tratează sistematic problemele de rotație, vibrație și mișcare colectivă de mare amplitudine.

Progresia materialului este logică: se pornește de la Modelul Picăturii de Lichid și stabilitatea la fisiune, continuând cu Modelul de Pături și corecțiile Strutinski, până la modelele microscopice complexe. Cititorii familiarizați cu Shapes and Shells in Nuclear Structure de Ingemar Ragnarsson vor aprecia aici accentul pus pe formalismul matematic avansat și pe teoriile moderne care, la data primei apariții, erau rar documentate în manuale. În timp ce alte lucrări se concentrează pe date experimentale, acest volum prioritizează rigoarea derivărilor teoretice.

Această monografie se încadrează în traiectoria academică a autorilor, completând cercetările lor ulterioare din Extended Density Functionals in Nuclear Structure Physics, unde aplică aceste baze teoretice asupra nucleelor aflate departe de valea stabilității beta. Deși este o lucrare densă de 740 de pagini, claritatea expunerii o face accesibilă pentru studenții din ultimii ani de licență și cercetătorii care au nevoie de un fundament teoretic solid în fizica nucleară matematică.

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Specificații

ISBN-13: 9783540212065
ISBN-10: 354021206X
Pagini: 740
Ilustrații: XVIII, 718 p. 4 illus.
Dimensiuni: 155 x 235 x 45 mm
Greutate: 1.08 kg
Ediția:Softcover reprint of the original 1st ed. 1980
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Theoretical and Mathematical Physics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Lower undergraduate

De ce să citești această carte

Recomandăm această carte ca fiind „biblia” teoretică a problemei celor mai multe corpuri în fizica nucleară. Cititorul câștigă o înțelegere profundă a tehnicilor de calcul și a modelelor matematice (Hartree-Fock, RPA) necesare pentru a modela structura nucleului. Este o investiție esențială pentru oricine dorește să treacă de la descrieri calitative la rigoarea formalismului microscopic utilizat în cercetarea modernă.

Despre autor

Peter Ring și Peter Schuck sunt figuri proeminente în comunitatea științifică internațională, recunoscuți pentru contribuțiile lor fundamentale în fizica nucleară teoretică. Peter Ring, profesor emerit, s-a specializat în modelele microscopice ale structurii nucleare, în timp ce Peter Schuck este cunoscut pentru expertiza sa în sistemele finite de fermioni și metodele semiclasice. Împreună, au creat în The Nuclear Many-Body Problem un standard academic utilizat de decenii în universitățile de elită. Lucrările lor ulterioare, inclusiv cele despre funcționalele de densitate, continuă să exploreze limitele stabilității materiei nucleare, fundamentate pe principiile riguroase stabilite în acest volum de referință publicat de Springer.

Descriere scurtă

It is the aim of this book to describe in concise form our present theoretical understanding of the nuclear many-body problem. The presen­ tation of the enormous amount of material that has accumulated in this field over the last few decades may be divided into two broad categories: One can either concentrate on the physical phenomena, such as the single-particle excitations, rotations, vibrations, or large-amplitude collec­ tive motion, and treat each of them using a variety of theoretical methods; or one may stress the methodology and technical aspects of the different theories that have been used to describe the nucleus. We have chosen the second avenue. The structure of this book is thus dictated by the different methods used-Hartree-Fock theory, time-dependent Hartree-Fock the­ ory, generator coordinates, boson expansions, etc. -rather than by the physical subjects. Many of the present theories have, of course, already been presented in other textbooks. In order to be able to give a more rounded picture, we shall either briefly review such topics (as in the case of the liquid drop or the shell model) or try to give more updated versions (as in the cases of rotations or the random phase approximation). Our essential aim, however, is to present the more modern theories-such as boson expansions, genera­ tor coordinates, time-dependent Hartree-Fock, semiclassical theories, etc. -which have either never been seen, or at best had little detailed treat­ ment in, book form.

Cuprins

1 The Liquid Drop Model.- 1.1 Introduction.- 1.2 The Semi-empirical Mass Formula.- 1.3 Deformation Parameters.- 1.4 Surface Oscillations About a Spherical Shape.- 1.5 Rotations and Vibrations for Deformed Shapes.- 1.6 Nuclear Fission.- 1.7 Stability of Rotating Liquid Drops.- 2 The Shell Model.- 2.1 Introduction and General Considerations.- 2.2 Experimental Evidence for Shell Effects.- 2.3 The Average Potential of the Nucleus.- 2.4 Spin Orbit Coupling.- 2.5 The Shell Model Approach to the Many-Body Problem.- 2.6 Symmetry Properties.- 2.7 Comparison with Experiment.- 2.8 Deformed Shell Model.- 2.9 Shell Corrections to the Liquid Drop Model and the Strutinski Method.- 3 Rotation and Single-Particle Motion.- 3.1 Introduction.- 3.2 General Survey.- 3.3 The Particle-plus-Rotor Model.- 3.4 The Cranking Model.- 4 Nuclear Forces.- 4.1 Introduction.- 4.2 The Bare Nucleon-Nucleon Force.- 4.3 Microscopic Effective Interactions.- 4.4 Phenomenological Effective Interactions.- 4.5 Concluding Remarks.- 5 The Hartree-Fock Method.- 5.1 Introduction.- 5.2 The General Variational Principle.- 5.3 The Derivation of the Hartree-Fock Equation.- 5.4 The Hartree-Fock Method in a Simple Solvable Model.- 5.5 The Hartree-Fock Method and Symmetries.- 5.6 Hartree-Fock with Density Dependent Forces.- 5.7 Concluding Remarks.- 6 Pairing Correlations and Superfluid Nuclei.- 6.1 Introduction and Experimental Survey.- 6.2 The Seniority Scheme.- 6.3 The BCS Model.- 7 The Generalized Single-Particle Model (HFB Theory).- 7.1 Introduction.- 7.2 The General Bogoliubov Transformation.- 7.3 The Hartree-Fock-Bogoliubov Equations.- 7.4 The Pairing-plus-Quadrupole Model.- 7.5 Applications of the HFB Theory for Ground State Properties.- 7.6 Constrained Hartree-Fock Theory (CHF).- 7.7 HFB Theory in the Rotating Frame(SCC).- 8 Harmonic Vibrations.- 8.1 Introduction.- 8.2 Tamm-Dancoff Method.- 8.3 General Considerations for Collective Modes.- 8.4 Particle-Hole Theory with Ground State Correlations (RPA).- 8.5 Linear Response Theory.- 8.6 Applications and Comparison with Experiment.- 8.7 Sum Rules.- 8.8 Particle-Particle RPA.- 8.9 Quasi-particle RPA.- 9 Boson Expansion Methods.- 9.1 Introduction.- 9.2 Boson Representations in Even-Even Nuclei.- 9.3 Odd Mass Nuclei and Particle Vibration Coupling.- 10 The Generator Coordinate Method.- 10.1 Introduction.- 10.2 The General Concept.- 10.3 The Lipkin Model as an Example.- 10.4 The Generator Coordinate Method and Boson Expansions.- 10.5 The One-Dimensional Harmonic Oscillator.- 10.6 Complex Generator Coordinates.- 10.7 Derivation of a Collective Hamiltonian.- 10.8 The Choice of the Collective Coordinate.- 10.9 Application of the Generator Coordinate Method for Bound States.- 11 Restoration of Broken Symmetries.- 11.1 Introduction.- 11.2 Symmetry Violation in the Mean Field Theory.- 11.3 Transformation to an Intrinsic System.- 11.4 Projection Methods.- 12 The Time Dependent Hartree-Fock Method (TDHF).- 12.1 Introduction.- 12.2 The Full Time-Dependent Hartree-Fock Theory.- 12.3 Adiabatic Time-Dependent Hartree-Fock Theory (ATDHF).- 13 Semiclassical Methods in Nuclear Physics.- 13.1 Introduction.- 13.2 The Static Case.- 13.3 The Dynamic Case.- Appendices.- A Angular Momentum Algebra in the Laboratory and the Body-Fixed System.- B Electromagnetic Moments and Transitions.- B.l The General Form of the Hamiltonian.- B.2 Static Multipole Moments.- B.3 The Multipole Expansion of the Radiation Field.- B.4 Multipole Transitions.- B.5 Single-Particle Matrix Elements in a Spherical Basis.- B.6 Translational Invariance and Electromagnetic Transitions.-B.7 The Cross Section for the Absorption of Dipole Radiation.- C Second Quantization.- C.1 Creation and Annihilation Operators.- C.2 Field Operators in the Coordinate Space.- C.3 Representation of Operators.- C.4 Wick’s Theorem.- D Density Matrices.- D.l Normal Densities.- D.2 Densities of Slater Determinants.- D.3 Densities of BCS and HFB States.- D.4 The Wigner Transformation of the Density Matrix.- E Theorems Concerning Product Wave Functions.- E.l The Bloch-Messiah Theorem [BM 62].- E.2 Operators in the Quasi-particle Space.- E.3 Thouless’ Theorem.- E.4 The Onishi Formula.- E.5 Bogoliubov Transformations for Bosons.- F Many-Body Green’s Functions.- F.l Single-Particle Green’s Function and Dyson’s Equation.- F.2 Perturbation Theory.- F.3 Skeleton Expansion.- F.4 Factorization and Brückner-Hartree-Fock.- F.5 Hartree-Fock-Bogoliubov Equations.- F.6 The Bethe-Salpeter Equation and Effective Forces.- Author Index.

Recenzii

From the reviews:
"The monography by Peter Ring and Peter Schuck covers the techniques used to solve the nuclear many-body problem … . is recognized as a reference by the nuclear physics community. Theoretical developments are explained pedagogically, with a constant rigour, are well documented and are illustrated with suitably chosen examples. The book contains a lot of references … . It is served by a concise style. By its scope and rigour, it has no real rival and will expectedly remain a familiar introductory text in nuclear structure theory for many years." (Joseph Cugnon, Physicalia, Vol. 57 (3), 2005)
"In many ways, the 1950s through to the 1970s may be seen as a golden period for the development of nuclear physics, both experimental and theoretical. … The book contains an excellent description of many basic theoretical methods, which continue to be relevant today, it is still of value to specialist students of nuclear theory." (J. P. Elliott, Contemporary Physics, Vol. 46 (6), 2005)

Textul de pe ultima copertă

This long-standing introductory text thoroughly describes
nuclear many-body theory, with an emphasis on methodology
and the technical aspects of the theories that have been
used to describe the nucleus. Now available in a more
affordable softcover edition, the original contents of
"The Nuclear Many-Body Problem” presented here is intended
for students with basic knowledge of quantum mechanics and
some understanding of nuclear phenomena.
From the reviews –
"Its scope and complexity are suitable for easy reading
by beginning students of nuclear theory. With a crisp and
concise style, the authors quickly develop the shell-model
approach to the nuclear many-body problem and subsequently
devote more than a third of the text to Hartree-Fock and
related models…”
- Physics Today