Bulletin of the American Physical Society
4th Joint Meeting of the APS Division of Nuclear Physics and the Physical Society of Japan
Volume 59, Number 10
Tuesday–Saturday, October 7–11, 2014; Waikoloa, Hawaii
Session EK: Theory Related to NN and Light Nuclei |
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Sponsoring Units: DNP JPS Chair: Wayne Polyzou, University of Iowa Room: Queen's 6 |
Thursday, October 9, 2014 7:00PM - 7:15PM |
EK.00001: Nonperturbative renormalization of the chiral nucleon-nucleon interaction up to next-to-next-to-leading order Ruprecht Machleidt We study the nonperturbative renormalization of the nucleon-nucleon ($NN$) interaction at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) of chiral effective field theory. A systematic variation of the cutoff parameter is performed for values below the chiral symmetry breaking scale of about 1 GeV. The accuracy of the predictions is determined by calculating the $\chi^2$ for the reproduction of the $NN$ data for energy intervals below pion-production threshold. At NLO, $NN$ data are described well up to about 100 MeV laboratory energy and, at NNLO, up to about 200 MeV---with, essentially, cutoff independence for cutoffs between about 450 and 850 MeV. [Preview Abstract] |
Thursday, October 9, 2014 7:15PM - 7:30PM |
EK.00002: Assessing Theory Errors from Residual Cutoff Dependence Harald W. Griesshammer A recent editorial [Phys.~Rev.~A 83, 040001] emphasised the need to quantify theoretical uncertainties. Ideally, ``double-blind'' calculations would assess theory-errors based on input and method, and not by comparison to data. This is particularly important if data is absent or its consistency is checked. Effective Field Theories (EFTs) promise a well-defined scheme to provide such reproducible, objective, quantitative error estimates. But how can one validate the expansion? This is a particularly nagging question in Nuclear Physics, where a fully consistent chiral EFT is still under development since the $NN$ interaction is non-perturbative. One can indeed quantify the consistency of an EFT from the dependence of observables ${\cal O}(k;\lambda)$ at low momentum $k$ on the cutoff $\lambda$ employed in numerical calculations. The power-counting in the small, dimension-less quantity $Q\propto k$ of an EFT quanitiatively predicts $1-{\cal O}(k;\lambda_1)/{\cal O}(k;\lambda_2)\propto k^{n+1}$ for a calculation at order $Q^n$. The slope of a double-logarithmic plot of this quantity against $k$ reveals thus the order of accuracy $n$. In contradistinction to a method proposed by Lepage, this approach does not compare to data to assess uncertainties. Examples are given. [Preview Abstract] |
Thursday, October 9, 2014 7:30PM - 7:45PM |
EK.00003: Short-range part of Y$_{\mathrm{c}}$N interactions in the Quark Cluster Model Sachiko Fukino, Makoto Oka, Sachiko Takeuchi The interaction of hyperons which contain the strange quark has been studied in detail. It is interesting to extend the study to the charmed baryons and to search for their bound states to nucleus. As the basis, it is important to understand the interaction between the charmed baryon Y$_{\mathrm{c}}$ and the nucleon N. In this study, we consider the interaction between Y$_{\mathrm{c}}$ ($\Lambda_{\mathrm{c}}$, $\Sigma_{\mathrm{c}}$, $\Sigma _{\mathrm{c}}^{\mathrm{\ast }})$ and N. The phenomenological models of the Y$_{\mathrm{c}}$N interaction have been constructed on the basis of the one-boson exchange. However, the short-range parts of the interaction have not been explored well. Here we use the quark cluster model and calculate the short-range part of the Y$_{\mathrm{c}}$N interaction by treating the baryons as three-quark clusters. Due to the quark antisymmetrization, we obtain a non-local potential between Y$_{\mathrm{c}}$ and N. Comparison of the results to those in the strange baryons will be discussed in this talk. [Preview Abstract] |
Thursday, October 9, 2014 7:45PM - 8:00PM |
EK.00004: The general formalism for studying Nd scattering on the basis of configuration-space Faddeev equations Vladimir Suslov, Mikhail Braun, Igor Filikhin, Branislav Vlahovic, Ivo Slaus The known configuration-space Faddeev equations for studying proton-deuteron scattering have been derived in the context of the isotopic formalism. However, in the presence of the Coulomb interaction the isotopic formalism becomes invalid in view of proton and neutron being different particles. Appropriate modifications have been done to derive new correct Faddeev equations to study the three-nucleon system. The s-wave calculations of the elastic and breakup amplitudes for n-d and p-d scattering at Elab=14.1 MeV are performed for the Malfliet-Tjon MT I-III and AV14 potentials. Results obtained for n-d and p-d scattering are compared with our predictions [1] and those of the Los-Alamos/Iowa group [2]. \\[4pt] [1] V.M. Suslov and B. Vlahovic, Phys. Rev. C69, 044003 (2004)\\[0pt] [2] J.L. Friar, G.L. Payne, W. Gl\"ockle, D. H\"uber, and H. Witala, Phys Rev. C51, 2356 (1995) [Preview Abstract] |
Thursday, October 9, 2014 8:00PM - 8:15PM |
EK.00005: Poincar\'e invariant calculation of the three-body bound state energy and wave function M.R. Hadizadeh, Ch. Elster, W.N. Polyzou The Faddeev equation for the three-body (3B) bound state of a relativistic mass operator (rest-frame Hamiltonian) is solved directly in terms of momentum vectors without employing a partial wave decomposition. The mass operator is a Casimir operator of a dynamical unitary representation of the Poincar\'e group, which ensures the exact relativistic invariance of the theory. The input to the calculations are relativistic off-shell two-body transition matrices. They are constructed to be phase-shift equivalent to corresponding non-relativistic two-body transition matrices using the invariance principle and the first resolvent equation. Our numerical results show that relativistic effects, using the Malfliet-Tjon V interaction, reduce the 3B binding energy by about 3.3\%. We also compare the structure of the relativistic and corresponding non-relativistic wave functions as a function of the Jacobi momentum vectors. [Preview Abstract] |
Thursday, October 9, 2014 8:15PM - 8:30PM |
EK.00006: A Direct Construction of the Nuclear Effective Interaction Kenneth McElvain Traditionally the nuclear physics effective interactions problem is attacked in two steps, the encoding of phase-shift information in a rather singular ``realistic'' NN interaction $V_{NN}$, followed by a reduction of $H=T+V_{NN}$ to the included or P-space $H^{eff}$ by integrating out numerically the effects of $H$ in $Q=1-P$. Here we show that $H^{eff}$ can be determined directly in P, eliminating the need for any knowledge of $V_{NN}$ in Q. The method exploits the Haxton-Luu form of the Bloch-Horowitz equation, in which long and short-range contributions to $H^{eff}$ are separated. This decomposition allows one to build into an effective theory the correct infrared behavior, which for continuum states is governed by the energy-dependent phase shifts $\delta(E)$. The effects of $V_{NN}$ in Q can then be absorbed into a small number of nearly energy-independent low-energy constants (LECs), the coefficients of short-range operators. I show that the experimental knowledge of $\delta(E)$ that traditionally is encoded in $V_{NN}$ can instead be used directly in P to determine the LECs. The method reduces the task of finding a precise $H^{eff}$ to that of solving a self-consistent eigenvalue problem in P. [Preview Abstract] |
Thursday, October 9, 2014 8:30PM - 8:45PM |
EK.00007: Operator evolution for \textit{ab initio} theory of light nuclei Micah Schuster, Sofia Quaglioni, Calvin Johnson, Eric Jurgenson, Petr Navr\'{a}til The past two decades have seen a revolution in \textit{ab initio} calculations of nuclear properties. One key element has been the development of a rigorous effective interaction theory, applying unitary transformations to soften the nuclear Hamiltonian and hence accelerate the convergence as a function of the model space size. For consistency, however, one ought to apply the same transformation to other operators when calculating transitions and mean values from the eigenstates of the renormalized Hamiltonian. Working in a translationally invariant harmonic oscillator basis for the two- and three-nucleon systems, we evolve the Hamiltonian, square radius, and total dipole strength operators by the similarity renormalization group (SRG). The inclusion of up to three-body matrix elements in the $^4$He nucleus all but completely restores the invariance of the expectation values under the transformation. We also consider a Gaussian operator with adjustable range; short ranges have the largest absolute renormalization when including two- and three-body induced terms, while at long ranges the induced three-body contribution takes on increased relative importance. [Preview Abstract] |
Thursday, October 9, 2014 8:45PM - 9:00PM |
EK.00008: Coulomb distorted T-matrix Elements in Momentum Space V. Eremenko, L. Hlophe, N.J. Upadhyay, Ch. Elster, F.M. Nunes, I.J. Thompson, G. Arbanas, J.E. Escher Transfer $(d,p)$ reactions are an important tool to study nuclear structure. These can be connected with neutron capture, a topic of great relevance to astrophysics, as well as other applications. Usually, this problem is reduced to a three-body $n + p + A$. The most advanced Faddeev-type calculations of this kind use the screened Coulomb interaction, which is inadequate for heavy systems [1]. In [2], the Faddeev-AGS formalism is developed in the Coulomb basis, without the need to introduce screening. This Coulomb basis requires the half-shell T-matrix elements (nuclear form factor) folded with the Coulomb wavefunction $\psi_{q,l}^C (p)$. Handling the $\psi_{q,l}^C (p)$ and the computation of the integral, require care. The integral regularization technique was presented in [2]. We generalize that regularization procedure for complex form factors. The resulting form factors will be presented and discussed [3]. [1] PRC 84, 034607 (2011). [2] PRC 86, 034001 (2012). [3] PRC in press. [Preview Abstract] |
Thursday, October 9, 2014 9:00PM - 9:15PM |
EK.00009: Ab Initio NCSM/RGM for Three-Cluster Structure Systems Carolina Romero-Redondo, Sofia Quaglioni, Petr Navr\'atil, Guillaume Hupin The $ab~initio$ no-core shell model/resonating group method (NCSM/RGM) introduced in [1] is a technique able to describe both structure and reactions in light nuclear systems. This approach combines a microscopic cluster technique with the use of realistic inter-nucleon interactions and a consistent microscopic description of the nucleon clusters. In this work, we introduce the treatment of three-body cluster dynamics, making the approach suitable for the investigation of systems presenting such structure. We present results obtained for $^6$He within a $^4$He(g.s.)+$n$+$n$ basis [2]. We find a bound state in the $J^{\pi}T=0^+1$ channel, corresponding to the $^6$He ground state. On the continuum, we obtained the experimentally well-known $2^+_1$ resonance as well as the second low-lying $2_2^+$ resonance recently measured at GANIL [3]. In addition, we predict low-lying resonances in $J^{\pi}$= $1^+$, $2^-$, and $0^-$ channels. We will present initial results including core excitations through the no-core shell model with continuum coupling and for the structure of $^5$H within a $^3$H+$n$+$n$ basis.\\[4pt] [1] S.Quaglioni and P. Navr\'atil, PRL 101, 092501 (2008), [2] S. Quaglioni, C.Romero-Redondo, P. Navr\'atil, PRC 88, 034320 (2031), [3] X. Mougeot $et~al$, Phys. Lett. B 718 [Preview Abstract] |
Thursday, October 9, 2014 9:15PM - 9:30PM |
EK.00010: Double Lambda He-6 in cluster effective field theory Shung-Ichi Ando, Yongseok Oh The bound state of $^{\ \ 6}_{\Lambda\Lambda}{\rm He}$ is studied as a three-body ($\Lambda\Lambda\alpha$) cluster system in cluster effective field theory at leading order (LO). We find that the three-body contact interaction exhibits the limit cycle when the cutoff in the integral equations is sent to the asymptotic limit, and thus it should be promoted to LO. We also derive a determination equation of the limit cycle which reproduces the numerically obtained limit cycle. We then study the correlations between the double $\Lambda$ separation energy $B_{\Lambda\Lambda}^{}$ of $^{\ \ 6}_{\Lambda\Lambda}{\rm He}$ and the scattering length $a_{\Lambda\Lambda}^{}$ of the $S$-wave $\Lambda\Lambda$ scattering. The role of the scale in this approach is also discussed. [Preview Abstract] |
Thursday, October 9, 2014 9:30PM - 9:45PM |
EK.00011: Application of the absorbing boundary condition to the three-body problem with the rearrangement channels Masataka Iwasaki, Reiji Otani, Makoto Ito, Masayasu Kamimura One of the current issues in nuclear physics is the structure of the borromean three-body systems, which mainly appear around Neutron-drip lines and its dynamics of continuum states above the particle decay threshold. The borromean systems in Neutron-drip line are weak binding systems and hence, they are easily excited to unbound continuum states. Therefore, it is very important to describe the structure of the borromean systems as well as its reaction dynamics in a consistent manner. The absorbing boundary condition (ABC) method, which introduces the absorbing potential outside of a total system, is one of powerful methods to handle the continuum states in three-body systems. In the previous studies, there are several applications of ABC to the reaction problems, but its applications to precise three-body calculations are still limited. In the present study, we apply the ABC method to the three-body calculation, which takes into account the rearrangement channels completely. We assume the several types of the absorbing potentials, and the resonance parameters are calculated for the assumed absorbers. In the present report, we will discuss the optimal absorber in the three-body systems. Moreover, our calculation will be compared with the complex scaling method, which is an alternative method to handle the continuum states. [Preview Abstract] |
Thursday, October 9, 2014 9:45PM - 10:00PM |
EK.00012: Time-dependent approach to the electric dipole response of few-nucleon systems Rie Sekine, Wataru Horiuchi The electric dipole (E1) response of nucleus is often used to study nuclear resonant structure as well as the ground state properties. While there are several methods to obtain the E1 strength distribution, here we take a time-dependent approach with a basis expansion. In the basis expansion method, its matrix element can be calculated analytically, and thus it allows us to calculate the time evolution of the wave function fast and accurately. We employ the correlated Gaussian (CG) as a basis function. The CG method is an efficient way to describe many-body correlations and is easily extended to many-body systems. In addition, we extend the CG into complex-range to make the basis function more flexible. In this talk, we show the E1 strength distribution of three- and four-nucleon systems, and compare our results with experiments and other methods. [Preview Abstract] |
(Author Not Attending)
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EK.00013: Electromagnetic Nature of Nuclear Energy Bernard Schaeffer As it is known since two millenaries, there is an attraction between an electric charge and a neutral object. Coulomb found the fundamental laws of electricity two centuries ago. After one century of nuclear physics, the fundamental laws of the strong force are still ignored. It has been found that electric and magnetic Coulomb's laws alone, without any hypothetical centrifugal force, are able to predict the binding energy of the simplest bound nucleus, the deuteron $^2H$ with a precision of $4\ \%$. The nuclear potential is given by the formula: \begin{equation} U^{^2H}_{em} /A =\frac{e^2}{4\pi\epsilon_0} \left(\frac{1}{r_{np}+ a} -\frac{1}{r_{np} - a} \right) +\frac{\mu_0|\mu_n \mu_p|}{4\pi r_{np}^3}\nonumber \end{equation} This potential shows a horizontal inflection point where the electric and magnetic forces are equilibrated, coinciding with the experimental deuteron binding energy. Similar results have been obtained for the $\alpha$ particle $^4He$ where the electric attractive potential is four times larger than that of $^2H$ while the magnetic repulsion is only $1.5$ times larger and the $^4He$ binding energy six times larger than that of the deuteron. These results, prove the electromagnetic nature of the nuclear energy without the usual assumptions. [Preview Abstract] |
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