arXiv subjects

T. T. S. Kuo

Publications and source records attributed to T. T. S. Kuo.

At least 55 records · Page 3Linked to original sources

arXiv2003

Counter Terms for Low Momentum Nucleon-Nucleon Interactions

There is much current interest in treating low energy nuclear physics using the renormalization group (RG) and effective field theory (EFT). Inspired by this RG-EFT approach, we study a low-momentum nucleon-nucleon (NN) interaction, V_{low-k}, obtained by integrating out the fast modes down the scale ~2fm^{-1}. Since NN experiments can only determine the effective interaction in the low momentum region, our chief purpose is to find such an interaction for complex nuclei whose typical momenta lie below this scale. In this paper we find that V_{low-k} can be satisfactorily accounted for by the counter terms corresponding to a short range effective interaction. The coefficients C_n of the power series expansion C_n*k^n for the counter terms have been accurately determined and results derived from several meson-exchange NN interaction models are compared. The counter terms are found to be important for the S, P, and D partial waves. Scaling behavior of the counter terms is also studied, and we discuss the use of these methods for computing shell model matrix elements.

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arXiv2003

Family of Hermitian Low-Momentum Nucleon Interactions with Phase Shift Equivalence

Using a Schmidt orthogonalization transformation, a family of Hermitian low-momentum NN interactions is derived from the non-Hermitian Lee-Suzuki (LS) low-momentum NN interaction. As special cases, our transformation reproduces the Hermitian interactions for Okubo and Andreozzi. Aside from their common preservation of the deuteron binding energy, these Hermitian interactions are shown to be phase shift equivalent, all preserving the empirical phase shifts up to decimation scale Lambda. Employing a solvable matrix model, the Hermitian interactions given by different orthogonalization transformations are studied; the interactions can be very different from each other particularly when there is a strong intruder state influence. However, because the parent LS low-momentum NN interaction is only slightly non-Hermitian, the Hermitian low-momentum nucleon interactions given by our transformations, including the Okubo and Andreozzi ones, are all rather similar to each other. Shell model matrix elements given by the LS and several Hermitian low-momentum interactions are compared.

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arXiv2003

Towards a Model-Independent Low Momentum Nucleon-Nucleon Interaction

We provide evidence for a high precision model-independent low momentum nucleon-nucleon interaction. Performing a momentum-space renormalization group decimation, we find that the effective interactions constructed from various high precision nucleon-nucleon interaction models, such as the Paris, Bonn, Nijmegen, Argonne, CD Bonn and Idaho potentials, are identical. This model-independent low momentum interaction, called V_{low k}, reproduces the same phase shifts and deuteron pole as the input potential models, without ambiguous assumptions on the high momentum components, which are not constrained by low energy data and lead to model-dependent results in many-body applications. V_{low k} is energy-independent and does not necessitate the calculation of the Brueckner G matrix.

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arXiv2003

Ground-state properties of closed-shell nuclei with low-momentum realistic interactions

Ground-state properties of 16O and 40Ca are calculated with a low-momentum nucleon-nucleon potential, V-low-k, derived from the chiral N3LO interaction recently constructed by Entem and Machleidt. The smooth V-low-k is used directly in a Hartree-Fock approach, avoiding the difficulties of the Brueckner-Hartree-Fock procedure. Corrections up to third order in the Goldstone expansion are evaluated, leading to results that are in very good agreement with experiment. Convergence properties of the expansion are examined.

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arXiv2003

Model-independent low momentum nucleon interaction from phase shift equivalence

We present detailed results for the model-independent low momentum nucleon-nucleon interaction V_{low k}. By introducing a cutoff in momentum space, we separate the Hilbert space into a low momentum and a high momentum part. The renormalization group is used to construct the effective interaction V_{low k} in the low momentum space, starting from various high precision potential models commonly used in nuclear many-body calculations. With a cutoff in the range of $Λ~ 2.1 fm^{-1}$, the new potential V_{low k} is independent of the input model, and reproduces the experimental phase shift data for corresponding laboratory energies below $E_{lab} ~ 350 MeV$, as well as the deuteron binding energy with similar accuracy as the realistic input potentials. The model independence of V_{low k} demonstrates that the physics of nucleons interacting at low momenta does not depend on details of the high momentum dynamics assumed in conventional potential models. V_{low k} does not have momentum components larger than the cutoff, and as a consequence is considerably softer than the high precision potentials. Therefore, when V_{low k} is used as microscopic input in the many-body problem, the high momentum effects in the particle-particle channel do not have to be addressed by performing a Brueckner ladder resummation or short-range correlation methods. By varying the cutoff, we study how the model independence of V_{low k} is reached in different partial waves. This provides numerical evidence for the separation of scales in the nuclear problem, and physical insight into the nature of the low momentum interaction.

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arXiv2002

Low-momentum Nucleon-Nucleon Potential and Hartree-Fock Calculations

A low-momentum nucleon-nucleon (NN) potential V-low-k is derived from modern realistic NN potentials by integrating out the high-momentum modes. The smooth V-low-k may be used as input for nuclear structure calculations instead of the usual Brueckner G matrix. Such an approach eliminates the energy dependence one finds in the G-matrix approach, allowing this interaction to be used directly in Hartree-Fock calculations. Bulk properties of 16O have been calculated starting from different NN potentials. Our results, obtained including up to second order contributions in the Goldstone expansion, are in good agreement with experiment.

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arXiv2002

Realistic shell-model calculations for proton particle-neutron hole nuclei around 132Sn

We have performed shell-model calculations for nuclei with proton particles and neutron holes around 132Sn using a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. For the proton-neutron channel this is explicitly done in the particle-hole formalism. The calculated results are compared with the available experimental data, particular attention being focused on the proton particle-neutron hole multiplets. A very good agreement is obtained for all the four nuclei considered, 132Sb, 130Sb, 133Te and 131Sb. We predict many low-energy states which have no experimental counterpart. This may stimulate, and be helpful to, future experiments.

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arXiv2002

Hypernuclear Weak Decay Puzzle

A general shell model formalism for the nonmesonic weak decay of the hypernuclei has been developed. It involves a partial wave expansion of the emitted nucleon waves, preserves naturally the antisymmetrization between the escaping particles and the residual core, and contains as a particular case the weak $Λ$-core coupling formalism. The Extreme Particle-Hole Model and the Quasiparticle Tamm-Dancoff Approximation are explicitly worked out. It is shown that the nuclear structure manifests itself basically through Pauli Principle, and a very simple expression is derived for the neutron and proton induced decays rates, $Γ_n$ and $Γ_p$, which does not involve the spectroscopic factors. We use the standard strangeness-changing weak $ΛN\to NN$ transition potential which comprises the exchange of the complete pseudoscalar and vector meson octets ($π,η,K,ρ,ω,K^*$), taking into account some important parity violating transition operators that are systematically omitted in the literature. The interplay between different mesons in the decay of ${^{12}_ΛC}$ is carefully analyzed. With the commonly used parametrization in the One-Meson-Exchange Model (OMEM), the calculated rate $Γ_{NM}= Γ_n+Γ_p$ is of the order of the free $Λ$ decay rate $Γ^0(Γ_{NM}^{\rm th}\cong Γ^0)$ and is consistent with experiments. Yet, the measurements of $Γ_{n/p}=Γ_n/Γ_p$ and of $Γ_p$ are not well accounted for by the theory ($Γ_{n/p}^{\rm th}\lsim 0.42; Γ_p^{\rm th}\gsim 0.60 Γ^0$). It is suggested that, unless additional degrees of freedom are incorporated, the OMEM parameters should be radically modified.

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arXiv2002

The nucleon interaction and neutron matter from the renormalization group

We show that the renormalization group decimation of modern nucleon potential models to low momenta results in a unique nucleon interaction V_{low k}. This interaction is free of short-ranged singularities and can be used directly in many-body calculations. The RG scaling properties follow directly from the invariance of the scattering phase shifts. We discuss the RG treatment of Fermi liquids. The RG equation for the scattering amplitude in the two particle-hole channels is given at zero temperature. The flow equations are simplified by retaining only the leading term in an expansion in small momentum transfers. The RG flow is illustrated by first studying a system of spin-polarized fermions in a simple model. Finally, results for neutron matter are presented by employing the unique low momentum interaction V_{low k} as initial condition of the flow. The RG approach yields the amplitude for non-forward scattering, which is of great interest for calculations of transport properties and superfluid gaps in neutron star interiors. The methods used can also be applied to condensed matter systems in the absence of long-ranged interactions.

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arXiv2002

Microscopic Nuclear Structure Based upon a Chiral NN Potential

We report on shell-model calculations employing effective interactions derived from a new realistic nucleon-nucleon (NN) potential based on chiral effective field theory. We present results for 18O, 134Te, and 210Po. Our results are in excellent agreement with experiment indicating a remarkable predictive power of the chiral NN potential for low-energy microscopic nuclear structure.

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arXiv2002

Low momentum nucleon-nucleon potentials with half-on-shell T-matrix equivalence

We study a method by which realistic nucleon-nucleon potentials V_NN can be reduced, in a physically equivalent way, to an effective low-momentum potential V-low-k confined within a cut-off momentum k-cut. Our effective potential is obtained using the folded-diagram method of Kuo, Lee and Ratcliff, and it is shown to preserve the half-on-shell T-matrix. Both the Andreozzi-Lee-Suzuki and the Andreozzi-Krenciglowa-Kuo iteration methods have been employed in carrying out the reduction. Calculations have been performed for the Bonn A and Paris NN potentials, using various choices for k-cut such as 2 fm-1. The deuteron binding energy, low-energy NN phase shifts, and the low-momentum half-on-shell T-matrix given by V_NN are all accurately reproduced by V-low-k. Possible applications of V-low-k directly to nuclear matter and nuclear structure calculations are discussed.

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arXiv2001

Modern Shell-Model Calculations

We have performed shell-model calculations starting from the CD-Bonn free nucleon-nucleon NN potential and making use of a new approach for the calculation of the effective interaction. This consists in deriving from the NN potential a low-momentum effective potential V-low-k, defined within a given cut-off momentum Lambda. Being a smooth potential it can be used directly in nuclear structure calculations. To assess the practical value of this approach, we have also performed calculations within the framework of the usual Brueckner G-matrix formalism. Comparison of the calculated results between them and with the experimental data shows that the V-low-k approach represents an advantageous alternative to the use of the G-matrix.

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arXiv2001

Renormalization Group Equation for Low Momentum Effective Nuclear Interactions

We consider two nonperturbative methods originally used to derive shell model effective interactions in nuclei. These methods have been applied to the two nucleon sector to obtain an energy independent effective interaction V_{low k}, which preserves the low momentum half-on-shell T matrix and the deuteron pole, with a sharp cutoff imposed on all intermediate state momenta. We show that V_{low k} scales with the cutoff precisely as one expects from renormalization group arguments. This result is a step towards reformulating traditional model space many-body calculations in the language of effective field theories and the renormalization group. The numerical scaling properties of V_{low k} are observed to be in excellent agreement with our exact renormalization group equation.

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arXiv2001

Two-Frequency Shell-Model Calculations for p-Shell Nuclei

We have studied p-shell nuclei using a two-frequency shell-model approach with an effective interaction derived from the Bonn-A nucleon-nucleon potential by means of a G-matrix folded-diagram method. Shell-model wave functions of two different oscillator constant are employed, one for the inner 0s core orbit and the outer valence orbits, respectively. The binding energies, energy spectra, and electromagnetic properties are calculated and compared with experiment. A quite satisfactory agreement with the experimental data is obtained, which is in some cases even better than that produced by large-basis shell-model calculations.

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arXiv2001

Low momentum nucleon-nucleon potential and shell model effective interactions

A low momentum nucleon-nucleon (NN) potential $V_{low-k}$ is derived from meson exhange potentials by integrating out the model dependent high momentum modes of $V_{NN}$. The smooth and approximately unique $V_{low-k}$ is used as input for shell model calculations instead of the usual Brueckner $G$ matrix. Such an approach eliminates the nuclear mass dependence of the input interaction one finds in the $G$ matrix approach, allowing the same input interaction to be used in different nuclear regions. Shell model calculations of $^{18}$O and $^{134}$Te using the {\bf same} input $V_{low-k}$ have been performed. For cut-off momentum $Λ$ in the vicinity of 2 $fm^{-1}$, our calculated low-lying spectra for these nuclei are in good agreement with experiments, and are weakly dependent on $Λ$.

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arXiv2001

Shell-Model Calculations with Realistic Effective Interactions

In this paper, we present some results of shell-model calculations employing effective interactions derived from the CD-Bonn free nucleon-nucleon potential. These concern 18O, 134Te, and 210Po, and are part of a comprehensive study of nuclei around doubly closed shells. Comparison of the calculated results with experimental data illustrates the degree of accuracy of modern realistic shell-model calculations.

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arXiv2001

Antikaons in nuclei and dense nuclear matter

We present recent progress on the properties of antikaons in nuclei and dense nuclear matter as obtained from two {\bar K}N interaction models: one based on the lowest-order meson-baryon chiral lagrangian and the other derived from a meson-exchange picture.

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arXiv2000

p-Shell Nuclei and Two-Frequency Shell Model with a Realistic Effective Interaction

We have studied p-shell nuclei using a two-frequency shell-model approach with an effective interaction derived from the Bonn-A nucleon-nucleon potential by means of a G-matrix folded-diagram method. First, we briefly describe our derivation of the effective interaction in a model space composed of harmonic hoscillator wave functions with two different length parameters, b_in and b_out, for the core and the valence orbits, respectively. Then we present some selected results of our calculations. We show that a good agreement with experiment is obtained, which is definitely better than that provided by a standard one-frequency calculation. A comparison with results obtained from large-basis shell-model calculations is also made.

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