A new screening function for Coulomb renormalization

We introduce a new screening function which is useful for the few-body Coulomb scattering problem in ``screening and renormalization'' scheme. The new renormalization phase factor of the screening function is analytically shown. The Yukawa type of the screening potential has been used in several decades, we modify it to make more useful. As a concrete example, we compare the proton-proton scattering phase shifts calculated from these potentials. The numerical results document that high precision calculations of the renormalization are performed by the new screening function.Comment: 4 pages, 8 figure

Quantum Computer Using Coupled Quantum Dot Molecules

We propose a method for implementation of a quantum computer using artificial molecules. The artificial molecule consists of two coupled quantum dots stacked along z direction and one single electron. One-qubit and two-qubit gates are constructed by one molecule and two coupled molecules, respectively.The ground state and the first excited state of the molecule are used to encode the |0> and |1> states of a qubit. The qubit is manipulated by a resonant electromagnetic wave that is applied directly to the qubit through a microstrip line. The coupling between two qubits in a quantum controlled NOT gate is switched on (off) by floating (grounding) the metal film electrodes. We study the operations of the gates by using a box-shaped quantum dot model and numerically solving a time-dependent Schridinger equation, and demonstrate that the quantum gates can perform the quantum computation. The operating speed of the gates is about one operation per 4ps. The reading operation of the output of the quantum computer can be performed by detecting the polarization of the qubits.Comment: 18 pages, 7 figures, submitted to Jpn. J. Appl. Phys, please send your e-mail to Nan-Jian Wu <[email protected]

Unknotting numbers and triple point cancelling numbers of torus-covering knots

It is known that any surface knot can be transformed to an unknotted surface knot or a surface knot which has a diagram with no triple points by a finite number of 1-handle additions. The minimum number of such 1-handles is called the unknotting number or the triple point cancelling number, respectively. In this paper, we give upper bounds and lower bounds of unknotting numbers and triple point cancelling numbers of torus-covering knots, which are surface knots in the form of coverings over the standard torus $T$. Upper bounds are given by using $m$-charts on $T$ presenting torus-covering knots, and lower bounds are given by using quandle colorings and quandle cocycle invariants.Comment: 26 pages, 14 figures, added Corollary 1.7, to appear in J. Knot Theory Ramification

Separability of a Low-Momentum Effective Nucleon-Nucleon Potential

A realistic nucleon-nucleon potential is transformed into a low-momentum effective one (LMNN) using the Okubo theory. The separable potentials are converted from the LMNN with a universal separable expansion method and a simple Legendre expansion. Through the calculation of the triton binding energies, the separability for the convergence of these ranks is evaluated. It is found that there is a tendency for the lower momentum cutoff parameter $\Lambda$ of LMNN to gain good separability.Comment: 6 pages, 1 tabl

Equivalent hyperon-nucleon interactions in low-momentum space

Equivalent interactions in a low-momentum space for the $\Lambda N$, $\Sigma N$ and $\Xi N$ interactions are calculated, using the SU$_6$ quark model potential as well as the Nijmegen OBEP model as the input bare interaction. Because the two-body scattering data has not been accumulated sufficiently to determine the hyperon-nucleon interactions unambiguously, the construction of the potential even in low-energy regions has to rely on a theoretical model. The equivalent interaction after removing high-momentum components is still model dependent. Because this model dependence reflects the character of the underlying potential model, it is instructive for better understanding of baryon-baryon interactions in the strangeness sector to study the low-momentum space $YN$ interactions.Comment: 9 pages, 13 figures, accepted for publication in Phys. Rev.

Contributions of 2π2\pi-exchange, 1π1\pi-exchange, and contact three-body forces in NNLO ChEFT to Λ3_\Lambda^3H

Faddeev calculations of hypertriton ($_\Lambda^3$H) separation energy are performed, incorporating all next-to-next-to-leading-order $\Lambda$NN three-body forces (3BFs) in chiral effective field theory: $2\pi$-exchange, $1\pi$-exchange, and contact interactions. The $1\pi$-exchange and contact interactions are rewritten in a form suitable for evaluating partial-wave matrix elements. The $\Lambda$-deuteron folding potentials constructed from these 3BFs are evaluated to demonstrate their contributions to \h3t. The $1\pi$-exchange interaction provides an attractive effect in which the d-state component of the deuteron wave function plays an important role. The attractive contribution tends to cancel the repulsive ones from the $2\pi$-exchange and contact 3BFs. Faddeev calculations show that the net effect of the 3BFs to the \h3t separation energy is small in a range between $-5$ to $+20$ keV, depending on the NN interaction used. Although these results are based on speculative low-energy constants, they can serve as a reference for further investigations.Comment: 6 pages, 4 figure

Faddeev Calculation of Λ3_\Lambda^3H Incorporating 2{\pi} Exchange Λ\LambdaNN Interaction

Faddeev calculations of hypertriton ($_\Lambda^3$H) separation energy are performed, incorporating $2\pi$-exchange $\Lambda$NN three-baryon force. Repulsive contributions of the three-baryon force in the order of 50 $-$ 100 keV are found, depending on the NN interactions employed. The effect is not negligible compared with the small separation-energy of $_\Lambda^3$H and is essential to gauge the two-body $\Lambda$N interactions.Comment: 6 pages, 3 Figure

Partial-wave expansion of ΛNN\Lambda NN three-baryon interactions in chiral effective field theory

An expression of partial wave expansion of three-baryon interactions in chiral effective field theory is presented. The derivation follows the method by Hebeler et al. [Phys. Rev. C{\bf 91}, 044001 (2015)], but the final expression is more general. That is, a systematic treatment of the higher-rank spin-momentum structure of the interaction becomes possible. Using the derived formula, a $\Lambda$-deuteron folding potential is evaluated. This information is valuable for inferring the possible contribution of the $\Lambda NN$ three-baryon forces to the hypertriton as the basis of further studies by sophisticated Faddeev calculations. A microscopic understanding of $\Lambda NN$ three-baryon forces together with two-body $\Lambda N$ interactions is essential for the description of hypernuclei and neutron-star matter.Comment: 7 pages, 4 figure