Nuclear many-body problem

Betiie, H. A., Phys. Rev. 103, 1353, "Nuclear many-body problem."... 

In the 1950s, many basic nuclear properties and phenomena were qualitatively understood in terms of single-particle and/or collective degrees of freedom. A hot topic was the study of collective excitations of nuclei such as giant dipole resonance or shape vibrations, and the state-of-the-art method was the nuclear shell model plus random phase approximation (RPA). With improved experimental precision and theoretical ambitions in the 1960s, the nuclear many-body problem was born. The importance of the ground-state correlations for the transition amplitudes to excited states was recognized. 

M. Rosina, Direct variational calculation of the two-body density matrix, in The Nuclear Marty-Body Problem Proceedings the Symposium on Present Status and Novel Developments in the Nuclear Many-Body Problem, Rome 1972, (F. Calogero and C. Ciofi degli Atti, eds.), Editrice Compositori, Bologna, 1973. 

P. Ring and Schuck, The Nuclear Many-Body Problems, (Springer-Verlag, Berlin, 1980). 

Ring, P and Schuck, P. (1980). The Nuclear Many-Body Problem (Springer, New York). 

N. N. Bogoliubov, Sov. Phys. Usp. 2, 236 (1959) M. Baranger, Carg se Lectures in Theoretical Physics (M. Levi, ed.). Benjamin, New York, 1963 P. Ring and P. Schuck, The Nuclear Many-Body Problem. Springer-Verlag, Berlin, 1980). 

J.P. Blaizot and H. Orland, Path integrals for the nuclear many-body problem, Phys. Rev. C, 24 (1981) 1740. 

The RPA, together with a simpler variant, the so-called Tamm-Dancoff Approximation, is now used in all forms of many-body theories (nuclear, solid state and molecular) in a wide variety of notations and formulations. It is an interesting exercise to consult these publications and contrast the notation and techniques used in this area with the ones used in this work. In this respect the book The nuclear many-body problem by P. Ring and P. Schuck (Springer-Verlag, 1980) might prove a useful starting point. 

Bohr O, Motelsson B (1971) Structure of atomic nucleus. Plenum, New York Ring P, Schuck P (2000) The nuclear many-body problem. Springer, Heidelberg... 

In the Brueckner approach to the nuclear many-body problem, a G-matrix is calculated which is the solution of the equation... 

The evaluation of the shell-model effective interaction between nucleons in nuclei is one of the most fundamental problems in nuclear many-body theory. Several theoretical studies have been presented throughout the last three decades, and among these studies, perturbative approaches have been much favored [1-3], though due to the exceedingly complicated character of the nuclear many-body problem, there are still many problems which need further investigation. 

One of the motivations behind the use of perturbative methods in nuclear many-body problems is the possibility of reducing the Schrodinger equation for an /4-nucleon system given by... 

Let us recall that the essence of UGA goes all the way back to 1935 when Pascual Jordan (of Nazi disrepute) used U(oo) generators to represent one- and two-body Hamiltonians [14]. In the late sixties, it was revived by Moshinsky in the context of the nuclear many-body problem [15]. Here, however, four-column irreducible representations (irreps) are required in view of the presence of both the spin and isospin. Consequently, the resulting rather complex formalism has never been implemented in actual applications for nuclei, as far as we know (see, however, [16]). 

Kumar K (1962) Perturbation theory and the nuclear many body problem. North-Holland, Amsterdam... 

Rasmussen JO (1959) Phys Rev 115 1675 Rasmussen JO (1965) Alpha decay. In Siegbahn K (ed) Alpha-, beta- and gamma-ray spectroscopy, vol 1. North-Holland, Amsterdam, p 701 Reid RV (1968) Ann Phys NY 50 411 Reines F, Cowan CL Jr (1959) Phys Rev 113 273 Reines F, Co ran CL Jr, Harrison FB, Me Guire AD, Kruse HW (1960) Phys Rev 117 159 Ring P, Schuck P (1980) The nuclear many-body problem. Springer, Berlin... 

In 1967, Brandow [69] used the Brillouin-Wigner expansion in his derivation of a multireference many-body (Rayleigh-Schrodinger) perturbation theory. In the abstract to his paper entitled Tinked-Cluster expansions for the nuclear many-body problem Brandow writes ... 

Relativistic quantum field theories with nucleons and mesons and relativistic nucleon-nucleus scattering models should also be pursued further, as such work provides important tools for dealing with the relativistic nuclear many-body problem and indicates the level at which relativistic effects might manifest themselves in nuclear systems. This work also provides an important step along the way towards a covariant description of nuclear physics. Recent work in which QCD-inspired models of NN systems and nuclear matter [We 90, Me 91, Co 91] are studied is significant and may someday provide an important link between QCD and nuclear phenomenology. 

Se 85] B.D. Serot and J.D. Walecka, The Relativistic Nuclear Many-Body Problem, Advances in Nuclear Physics, Vol. 16, eds. J.W. Negeie a E, Vogt (Plenum, New York, 1985),... 

Brillouin-Wigner perturbation theory was, however, used as a step in the development of an acceptable many-body perturbation theory most notably by Brandow [67] in his pioneering work on multi-reference formalisms for the many-body problem. In a review entitled Linked-Cluster Expansions for the Nuclear Many-Body Problem and published in 1967, B.H. Brandow writes ... 

Second, we derived the Bloch equation starting from the Brillouin-Wigner perturbation expansion, but, in contrast to the approach described by Brandow in his review [74] on Linked-Cluster Expansions for the Nuclear Many-Body Problem, we did not expand the denominator factors in order to remove the exact energy dependence. 

R. Krishnan, M. J. Frisch, and J, A. Pople, Contribution of triple substitutions to the electron correlation energy in fourth-order perturbation theory, J. Chem. Phys. 72 4244 (1980). B. H. Brandow, Linked cluster expansions for the nuclear many-body problem. Rev. Mod, Phys. 39 771 (1967). 

B. A. Brandow, Linked-cluster expansions for the nuclear many-body problem. Rev- Mod. Phys. 39 771 (1967). 

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