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L. Platter

Publications and source records attributed to L. Platter.

31 records · Page 2Linked to original sources
arXiv2007

Effective Range Corrections to Three-Body Recombination for Atoms with Large Scattering Length

Few-body systems with large scattering length a have universal properties that do not depend on the details of their interactions at short distances. The rate constant for three-body recombination of bosonic atoms of mass m into a shallow dimer scales as \hbar a^4/m times a log-periodic function of the scattering length. We calculate the leading and subleading corrections to the rate constant which are due to the effective range of the atoms and study the correlation between the rate constant and the atom-dimer scattering length. Our results are applied to 4He atoms as a test case.

cond-mat.other↗
arXiv2007

Universal Properties of the Four-Body System with Large Scattering Length

Few-body systems with large scattering length have universal properties that do not depend on the details of their interactions at short distances. We study the universal bound state properties of the four-boson system with large scattering length in an effective quantum mechanics approach. We compute the four-body binding energies using the Yakubovsky equations for positive and negative scattering length. Moreover, we study the correlation between three- and four-body energies and present a generalized Efimov plot for the four-body system. These results are useful for understanding the cluster structure of nuclei and for the creation of weakly-bound tetramers with cold atoms close to a Feshbach resonance.

nucl-th↗
arXiv2006

The Three-Nucleon System at Next-To-Next-To-Leading Order

We calculate higher order corrections for the three-nucleon system up to next-to-next-to-leading within an effective field theory with contact interactions alone. We employ a subtraction formalism previously developed and for which it has been shown that no new three-body force counterterm is needed for complete renormalization up to this order. We give results for the neutron-deuteron phaseshifts and the triton binding energy. Our results are in very good agreement with experimental results and calculations using realistic nucleon-nucleon potentials.

nucl-th↗
arXiv2006

Deuteron Matrix Elements in Chiral Effective Theory at Leading Order

We consider matrix elements of two-nucleon operators that arise in chiral effective theories of the two-nucleon system. Generically, the short-distance piece of these operators scales as 1/r^n, with r the relative separation of the two nucleons. We show that, when evaluated between the leading-order wave functions obtained in this effective theory, these two-nucleon operators are independent of the cutoff used to renormalize the two-body problem for n=1 and 2. However, for n greater than or equal to 3 general arguments about the short-distance behavior of the leading-order deuteron wave function show that the matrix element will diverge.

nucl-th↗
arXiv2006

The Three-Boson System at Next-To-Next-To-Leading Order

We discuss effective field theory treatments of the problem of three particles interacting via short-range forces (range R >> a_2, with a_2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a scattering amplitude whose low-momentum part is renormalization-group invariant up to corrections of O(R^3/a_2^3). Since corrections of O(R/a_2) and O(R^2/a_2^2) can be straightforwardly included in the integral equation's kernel, a unique solution for 1+2 scattering phase shifts and three-body bound-state energies can be obtained up to this accuracy. We use our equation to calculate the correlation between the binding energies of Helium-4 trimers and the atom-dimer scattering length. Our results are in excellent agreement with the recent three-dimensional Faddeev calculations of Roudnev and collaborators that used phenomenological inter-atomic potentials.

cond-mat.other↗
arXiv2005

Universality in the triton charge form factor

We consider the three-nucleon system within an effective theory with contact interactions at leading order in the large scattering length. We calculate the charge form factor of the triton at low momentum transfer and extract the triton charge radius. At this order, no two-body currents contribute and the calculation can be performed in the impulse approximation. We also comment on the power counting for higher orders. The requirement of a three-body force for renormalization of the three-nucleon system explains the previously observed correlation between the triton binding energy and charge radius for different model potentials.

nucl-th↗
arXiv2005

An Effective Theory for the Four-Body System with Short-Range Interactions

We discuss the application of an effective theory with contact interactions to the non-relativistic four-body system with short-range interactions. We have computed the binding energies of the 4He tetramer and the alpha-particle. A well-known linear correlation between three- and four-body binding energies can be understood as a result of the absence of a four-body force at leading order within this framework. Further, we give results for the binding energies of the four-boson system in two spatial dimensions.

nucl-th↗
arXiv2005

The Four-Boson System with Short-Range Interactions

We consider the non-relativistic four-boson system with short-range forces and large scattering length in an effective quantum mechanics approach. We construct the effective interaction potential at leading order in the large scattering length and compute the four-body binding energies using the Yakubovsky equations. Cutoff independence of the four-body binding energies does not require the introduction of a four-body force. This suggests that two- and three-body interactions are sufficient to renormalize the four-body system. We apply the equations to 4He atoms and calculate the binding energy of the 4He tetramer. We observe a correlation between the trimer and tetramer binding energies similar to the Tjon line in nuclear physics. Over the range of binding energies relevant to 4He atoms, the correlation is approximately linear.

cond-mat.other↗
arXiv2004

On the correlation between the binding energies of the triton and the alpha-particle

We consider the correlation between the binding energies of the triton and the alpha-particle which is empirically observed in calculations employing different phenomenological nucleon-nucleon interactions. Using an effective quantum mechanics approach for short-range interactions with large scattering length |a| >> l, where l is the natural low-energy length scale, we construct the effective interaction potential at leading order in l/|a|. In order to renormalize the four-nucleon system, it is sufficient to include a SU(4)-symmetric one-parameter three-nucleon interaction in addition to the S-wave nucleon-nucleon interactions. The absence of a four-nucleon force at this order explains the empirically observed correlation between the binding energies of the triton and the alpha-particle. We calculate this correlation and obtain a prediction for the alpha-particle binding energy. Corrections to our results are suppressed by l/|a|.

nucl-th↗
arXiv2004

An Effective Theory for the Four-Body System

We consider the non-relativistic four-body system with large scattering length and short-range interactions within an effective theory with contact interactions only. We compute the binding energies of the 4He tetramer and of alpha-particle. The well-known linear correlation between the three-body binding energies and the four-body binding energies of these physical systems can be understood as a consequence of the absence of a four-body force at leading order.

cond-mat.other↗
arXiv2004

Universal Properties of the Four-Boson System in Two Dimensions

We consider the nonrelativistic four-boson system in two dimensions interacting via a short-range attractive potential. For a weakly attractive potential with one shallow two-body bound state with binding energy B_2, the binding energies B_N of shallow N-body bound states are universal and thus do not depend on the details of the interaction potential. We compute the four-body binding energies in an effective quantum mechanics approach. There are exactly two bound states: the ground state with B_4^(0)=197.3(1)B_2 and one excited state with B_4^(1)=25.5(1)B_2. We compare our results to recent predictions for N-body bound states with large N>>1.

cond-mat.other↗
arXiv2002

Quasiparticle Properties in Effective Field Theory

The quasiparticle concept is an important tool for the description of many-body systems. We study the quasiparticle properties for dilute Fermi systems with short-ranged, repulsive interactions using effective field theory. We calculate the proper self-energy contributions at order (K_f/Lambda)^3, where Lambda is the short-distance scale that sets the size of the effective range parameters and K_f the Fermi momentum. The quasiparticle energy, width, and effective mass to order O(K_f/Lambda)^3 are derived from the calculated self-energy.

nucl-th↗