EPJ Web of Conferences

Effective Field Theory and the No-Core Shell Model

Ionel Stetcu

Published Jan 1, 2010• 0 citations

Abstract

In ﬁnite model space suitable for many-body calculations via the no-core shell model (NCSM), I illustrate the direct application of the eﬀective ﬁeld theory (EFT) principles to solving the many-body Schrödinger equation. Two diﬀerent avenues for ﬁxing the low-energy constants naturally arising in an EFT approach are discussed. I review results for both nuclear and trapped atomic systems, using eﬀective theories formally similar, albeit describing diﬀerent underlying physics.

DOI: 10.1051/epjconf/20100301011

Related papers

Effective Field Theory and Finite-Density Systems

R. J. Furnstahl, Gautam Rupak, Thomas Schäfer

This review gives an overview of effective field theory (EFT) as applied at finite density, with a focus on nuclear many-body systems. Uniform systems with short-range interactions illustrate the ingredients and virtues of many-body EFT; we also survey the varied frontiers of EFT for finite nuclei and nuclear matter.

arXiv:0801.0729Annual Review of Nuclear and Particle ScienceApr 17, 200831 citations

Effective theory for trapped few-fermion systems

Ionel Stetcu, BRUCE R. BARRETT, U. van Kolck +1 more

We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and four two-component fermions in a harmonic trap. In the unitary limit, we find that three-particle results are within 10% of known semianalytical values even in small model spaces. The method is very general, and can be readily extended to other regimes, more particles, different species (e.g., protons and neutrons in nuclear physics), or more-component fermions (as well as bosons). As an illustration, we present calculations of the lowest-energy three-fermion states away from the unitary limit and find a possible inversion of parity in the ground state in the limit of trap size large compared to the scattering length. Furthermore, we investigate the lowest positive-parity states for four fermions, although we are limited by the dimensions we can currently handle in this case.

arXiv:0705.4335Physical Review ADec 14, 200783 citations

Few-body physics in effective field theory

H.‐W. Hammer

Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms and nuclear physics. In particular, we will discuss the possibility of an infrared limit cycle in QCD. Recent extensions of the EFT approach to the four-body system and N-boson droplets in two spatial dimensions will also be addressed.

arXiv:nucl-th/0507060Journal of Physics G Nuclear and Particle PhysicsJul 12, 20056 citations

Few-body systems and the pionless effective field theory

Lucas Platter

The pionless effective field theory (EFT) is the appropriate low-energy EFT for short-range interactions that display a large scattering length. It has been successfully applied in atomic, nuclear and particle physics. We give an overview over recent calculations employing the pionless effective field theory and lay emphasis on applications in the three- and four-body sector where the most exciting developments have occurred.

arXiv:0910.0031Proceedings of 6th International Workshop on Chiral Dynamics — PoS(CD09)Feb 25, 20105 citations

Projection Operator Formalisms and the Nuclear Shell Model

Jennings, B K

The shell model solve the nuclear many-body problem in a restricted model space and takes into account the restricted nature of the space by using effective interactions and operators. In this paper two different methods for generating the effective interactions are considered. One is based on a partial solution of the Schrodinger equation (Bloch-Horowitz or the Feshbach projection formalism) and other on linear algebra (Lee-Suzuki). The two methods are derived in a parallel manner so that the difference and similarities become apparent. The connections with the renormalization group are also pointed out.

Apr 13, 20056 citations

Effective Field Theories for Nuclear and (Some) Atomic Physics

U. van Kolck

Abstract These lectures are a pedagogical—not comprehensive—introduction to the applications of effective field theory (EFT) in the context of nuclear and atomic physics. A common feature of these applications is the interplay between non-perturbative physics (needed at leading order to produce non-relativistic bound states and resonances) and controlled perturbative corrections (crucial for predictive power). The essential ideas are illustrated with the simplest nuclear EFT, pionless EFT, which contains only contact interactions and, with minor changes, can be adapted to certain atomic systems. This EFT exploits the two-body unitarity limit, where renormalization leads to discrete scale invariance in systems of three and more bodies. Remarkably complex structures then arise from very simple leading-order interactions. It briefly describes some of the challenges and rewards of including long-range forces—pion exchange in chiral EFT for nuclear systems or Van der Waals forces between atoms.

Apr 30, 20203 citations