E-raamat: Nuclear Superfluidity: Pairing in Finite Systems

Preface		xi
Introduction		1	(32)
Pairing in nuclei, superconductors, liquid 3He and neutrons stars		1	(2)
Macroscopic wavefunction and phase rigidity		3	(3)
Broken symmetry and collective modes		6	(2)
Superfluid 4He (He II)		8	(5)
Critical velocity for superconductors		13	(1)
Pairing in nuclei		14	(5)
Superconductivity		19	(6)
Superfluidity of liquid 3He		25	(1)
Comparison of pairing in nuclei with superconductivity		26	(4)
Neutron stars		30	(3)
The pairing force and seniority		33	(19)
Evidence for pairing correlations		33	(3)
The pairing interaction		36	(3)
The δ-function nucleon--nucleon potential		39	(3)
The degenerate model and quasi-spin		42	(2)
Pairing binding energy formula		44	(1)
Quasi-spin wavefunctions		45	(2)
Pairing rotations		47	(1)
Exact solution of the pairing Hamiltonian		48	(4)
The BCS theory		52	(20)
The BCS wavefunction		52	(3)
The energy		55	(2)
Excited states and quasiparticles		57	(3)
The mean-field Hamiltonian		60	(1)
The correlation energy		61	(3)
Pairing correlations in the wavefunction		64	(1)
The degenerate model in the BCS approximation		65	(1)
Gauge invariance		66	(1)
Matrix elements of one-body operators		67	(2)
Pairing and isospin		69	(3)
Spontaneous symmetry breaking		72	(20)
General background		72	(3)
Pairing in atomic nuclei (0D systems; ξ>>R)		75	(13)
Infinite 3D neutral superconductors (ξ>>L)		88	(4)
Pairing vibrations		92	(25)
The two-level model		92	(10)
Applications		102	(6)
Multipole pairing vibrations		108	(9)
Phase transitions		117	(37)
The experimental situation		119	(3)
Static pairing correlations: the BCS theory of pairing phase transitions in strongly rotating nuclei		122	(16)
Pairing fluctuations		138	(3)
Moments of inertia		141	(3)
Condensation-induced tunnelling		144	(1)
Response function technique to calculate RPA fluctuations		145	(9)
Plastic behaviour of nuclei and other finite systems		154	(16)
Exotic decay		155	(8)
A variety of applications		163	(2)
Low-lying surface vibrations		165	(3)
Fission in metal clusters		168	(2)
Sources of pairing in nuclei		170	(34)
The bare nucleon--nucleon potential and the pairing interaction		171	(6)
Mean-field theory		177	(7)
Random phase approximation		184	(15)
Correlation energy contribution to nuclear masses		199	(5)
Beyond mean field		204	(15)
Doorway states		204	(7)
Effective mass (ω-mass)		211	(4)
The ω-mass and the induced interaction		215	(4)
Induced interaction		219	(38)
Simple estimates		219	(4)
Microscopic calculations		223	(8)
Slab model		231	(8)
Induced pairing interaction, effective mass and vertex correction processes		239	(5)
Superfluidity in the inner crust of neutron stars		244	(13)
Pairing in exotic nuclei		257	(23)
The halo nucleus 11Li		258	(17)
The halo nucleus 12Be		275	(5)
Appendix A A brief resume of second quantization		280	(12)
A.1 Fermions		280	(6)
A.2 Particles and holes		286	(2)
A.3 Bosons		288	(2)
A.4 Quasi-bosons		290	(2)
Appendix B Single particle in a non-local potential		292	(5)
B.1 Single particle in a non-local, ω-dependent potential		294	(3)
Appendix C Useful relations in the treatment of collective modes		297	(2)
C.1 Limit on the multipolarity of collective surface vibrations		297	(1)
C.2 The relation between F and α		297	(2)
Appendix D Particle-vibration coupling		299	(6)
D.1 Estimate of <lj||YL||lj>		301	(2)
D.2 A simple estimate of <R0 au/ar>		303	(2)
Appendix E Model of the single-particle strength function		305	(3)
Appendix F Simple model of Pauli principle corrections		308	(2)
Appendix G Pairing mean-field solution		310	(10)
G.1 Solution of the pairing Hamiltonian		310	(5)
G.2 Two-quasiparticle excitations		315	(2)
G.3 Minimization		317	(1)
G.4 BCS wavefunction		318	(2)
Appendix H Pairing in a single j-shell		320	(7)
H.1 BCS solution		320	(2)
H.2 Cranking moment of inertia		322	(1)
H.3 Two-particle transfer		323	(1)
H.4 Polarization effects		324	(3)
Appendix I Fluctuations and symmetry restoration		327	(8)
I.1 Conjugate variables		327	(1)
I.2 Rotation about an axis		328	(1)
I.3 Rotations in gauge space		329	(1)
I.4 Symmetry restoring fluctuations and pairing rotations		330	(5)
Appendix J RPA solution of the pairing Hamiltonian		335	(14)
J.1 Diagonalization of the H0 + Hp Hamiltonian (odd-solution)		336	(3)
J.2 Diagonalization of the H0 + Hp Hamiltonian (even-solution)		339	(4)
J.3 Diagonalization of the full Hamiltonian H = H0 + Hp + Hp		343	(6)
Appendix K Vortices in nuclei		349	(7)
K.1 Simple estimates		349	(5)
K.2 Critical velocity for the excitation of rotons		354	(1)
K.3 Critical velocity for superfluidity		355	(1)
Appendix L Josephson effect		356	(5)
References		361	(13)
Index		374

David M. Brink obtained his first degree at the University of Tasmania in 1951 and his D.Phil. at Oxford University in 1955. Between 1958 and 1993 he held academic positions in the University of Oxford, including a Fellowship at Balliol College and the Moseley Readership in Theoretical Physics and taught many branches of physics at graduate and undergraduate level. From 1993 to 1998 he was Professor of the History of Physics at the University of Trento in Italy. Professor Brink is a Fellow of the Royal Society and in 1982 was a recipient of the Rutherford Medal of the Institute of Physics. Ricardo A. Broglia earned his Ph.D. at the University of Cuyo, Argentina, in 1965. Following positions at the University of Buenos Aires, the Niels Bohr Institute and the University of Minnesota, he joined the staff of the Niels Bohr Institute in 1970, where he is now adjunct Professor. He has held visiting positions at the State University of New York at Stony Brook, Brookhaven National Laboratory, Los Alamos Scientific Laboratory and Oak Ridge National Laboratory. In 1985 he was called to occupy the chair of Nuclear Structure at the University of Milan.