arXiv subjects
Publications and source records attributed to Takashi Nakamura.
Coulomb excitation is an inelastic process in which either the target or the projectile is excited by the Coulomb interaction, which can equivalently be described as the absorption of a virtual photon. We discuss Coulomb excitation at relativistic energies, with particular emphasis on Coulomb dissociation, in which an excited projectile subsequently breaks up.
In this paper, we construct double $L$-values of negative weight that admit series representations. In our construction, we use the Thue-Morse sequence, which appears in combinatorics on words and automatic sequences.
The dineutron is a spatially compact two-neutron cluster, which is expected to appear in a low-density part of nuclei. In recent years, there has been rapid progress in experimental and theoretical research on dineutron clusters, particularly on neutron-rich rare isotopes. Experimentally, evidence for dineutron in two-neutron halo nuclei, such as $^{11}$Li, has been obtained using Coulomb breakup, measurements of charge radii, and quasi-free proton scattering. Specific unbound nuclei just beyond the neutron drip line, which decay by emitting two neutrons, are also candidates for having a dineutron correlation. For instance, the dineutron structure has recently been investigated for $^{16}$Be, focusing on its decay into the core and the two neutrons. Theoretically, it is shown that the dineutron is partially due to the admixture of different-parity configurations for the two valence neutrons. Few-body theories, including dynamical effects of the decay process, play important roles in interpreting three-body decays. We also discuss the four-neutron clusters, showing the experimental results of recent tetraneutron experiments and observation of $^{28}$O. Possible relevance of these states to dineutron correlation is discussed. Finally, we discuss future perspectives on dineutron clusters in neutron-rich nuclei and their relation to the universal features in few-body physics.
We focus on gravitational-wave events of binary black-hole mergers up to the third observing run with the minimum false alarm rate smaller than $10^{-5}\,{\rm yr}^{-1}$. These events tell us that the mass ratio of two black holes follows $m_2/m_1=0.723$ with the chance probability of 0.00301% for the chirp mass $M_{\rm chirp} > 18\,M_{\odot}$. We show that the relation of $m_2/m_1=0.723$ is consistent with the binaries originated from population III stars which are the first stars in the universe. On the other hand, it is found for ${\rm chirp} < 18 M_{\odot}$ that the mass ratio follows $m_2/m_1=0.601$ with the chance probability of 0.117% if we ignore GW190412 with $m_2/m_1\sim 0.32$. This suggests a different origin from that for $M_{\rm chirp} > 18 M_{\odot}$.
We show that central zeros of $L$-functions in the Selberg class have a probabilistic interpretation by stating an equivalence condition of the Riemann hypothesis for the $L$-functions in terms of infinitely divisible distributions.
For the Riemann zeta-function, we introduce a function such that it is a characteristic function of an infinitely divisible distribution on the real line if and only if the Riemann Hypothesis is true.
Ear EEG based driver fatigue monitoring systems have the potential to provide a seamless, efficient, and feasibly deployable alternative to existing scalp EEG based systems, which are often cumbersome and impractical. However, the feasibility of detecting the relevant delta, theta, alpha, and beta band EEG activity through the ear EEG is yet to be investigated. Through measurements of scalp and ear EEG on ten subjects during a simulated, monotonous driving experiment, this study provides statistical analysis of characteristic ear EEG changes that are associated with the transition from alert to mentally fatigued states, and subsequent testing of a machine learning based automatic fatigue detection model. Novel numerical evidence is provided to support the feasibility of detection of mental fatigue with ear EEG that is in agreement with widely reported scalp EEG findings. This study paves the way for the development of ultra-wearable and readily deployable hearables based driver fatigue monitoring systems.
Unbound states in 17C were investigated via one-neutron removal from a 18C beam at an energy of 245 MeV/nucleon on a carbon target. The energy spectrum of 17C, above the single-neutron decay threshold, was reconstructed using invariant mass spectroscopy from the measured momenta of the 16C fragment and neutron, and was found to exhibit resonances at Er=0.52(2), 0.77(2), 1.36(1), 1.91(1), 2.22(3) and 3.20(1) MeV. The resonance at Er=0.77(2) MeV [Ex=1.51(3) MeV] was provisionally assigned as the second 5/2+ state. The two resonances at Er=1.91(1) and 3.20(1) MeV [Ex=2.65(2) and 3.94(2) MeV] were identified, through comparison of the energies, cross sections and momentum distributions with shell-model and eikonal reaction calculations, as p-shell hole states with spin-parities 1/2- and 3/2-, respectively. A detailed comparison was made with the results obtained using a range of shell-model interactions. The YSOX shell-model Hamiltonian, the cross-shell part of which is based on the monopole-based universal interaction, was found to provide a very good description of the present results and those for the neighbouring odd-A carbon isotopes - in particular for the negative parity cross-shell states.
Let $a(1) >0$, $a(n) \ge 0$ for $n \ge 2$ and $a(n) = O(n^\varepsilon)$ for any $\varepsilon >0$, and put $Z(σ+ it):= \sum_{n=1}^\infty a(n) n^{-σ- it}$ where $σ, t \in {\mathbb{R}}$. In the present paper, we show that any zeta distribution whose characteristic function is defined by ${\mathcal{Z}}_σ(t) :=Z(σ+ it)/Z(σ)$ is pretended infinitely divisible if $σ>1$ is sufficiently large. Moreover, we prove that if ${\mathcal{Z}}_σ(t)$ is an infinitely divisible characteristic function for some $σ_{id} >1$, then ${\mathcal{Z}}_σ(t)$ is infinitely divisible for all $σ>1$. Note that the corresponding Lévy or quasi-Lévy measure can be given explicitly. A key of the proof is a corrected version of Theorem 11.14 in Apostol's famous textbook.
Two neutron star (NS)-black hole (BH) binaries, GW200105 and GW200115 found in the LIGO/Virgo O3b run have smaller BH mass of 6--9\,$M_{\odot}$ which is consistent with Population I and II origin. Our population synthesis simulations using $10^6$ Population I and II binaries with appropriate initial parameters show consistent binary mass, event rate, and no detection of radio pulsar (PSR) and BH binaries in our galaxy so far. Especially, we found possible progenitors of GW200105 and GW200115 which were formed at redshift $z=0.15$ and $z=1.6$ with binary mass of $(34M_{\odot},\, 9.2M_{\odot})$ and $(23.7M_{\odot},\, 10.6M_{\odot})$, respectively. The final masses of these binaries are $(6.85M_{\odot},\,2.14M_{\odot})$ and $(6.04M_{\odot},\,1.31M_{\odot})$ which look like $(9.0_{-1.7}^{+1.7}M_{\odot},\, 1.91_{-0.24}^{+0.33}M_{\odot})$ of GW200105 and $(5.9_{-2.5}^{+2.0}M_{\odot},\,1.44_{-0.29}^{+0.85}M_{\odot})$ of GW200115, respectively. We also estimate that 2.68-19.7 PSR-BH binaries in our galaxy will be observed by SKA. The existence of NS-BHs in our galaxy can be confirmed in future SKA era. Using the GW observation of NS-BH mergers and the radio observation of PSR-BHs in future, we can get more severe constraints on the NS-BH formation process.
Let $0 < a \le 1/2$ and define the quadrilateral zeta function by $2Q(s,a) := ζ(s,a) + ζ(s,1-a) + {\rm{Li}}_s (e^{2πia}) + {\rm{Li}}_s(e^{2πi(1-a)})$, where $ζ(s,a)$ is the Hurwitz zeta function and ${\rm{Li}}_s (e^{2πia})$ is the periodic zeta function. In the present paper, we show that there exists a unique real number $a_0 \in (0,1/2)$ such that $Q(σ, a_0)$ has a unique double real zero at $σ= 1/2$ when $σ\in (0,1)$, for any $a \in (a_0,1/2]$, the function $Q(σ, a)$ has no zero in the open interval $σ\in (0,1)$ and for any $a \in (0,a_0)$, the function $Q(σ, a)$ has at least two real zeros in $σ\in (0,1)$. Moreover, we prove that $Q(s,a)$ has infinitely many complex zeros in the region of absolute convergence and the critical strip when $a \in {\mathbb{Q}} \cap (0,1/2) \setminus \{1/6, 1/4, 1/3\}$. The Lerch formula, Hadamard product formula, Riemann-von Mangoldt formula for $Q(s,a)$ are also shown.
In this paper, we give Dirichlet series with periodic coefficients that have Riemann's functional equation and real zeros of Dirichlet $L$-functions. The details are as follows. Let $L(s,χ)$ be the Dirichlet $L$-function and $G(χ)$ be the Gauss sum associate with a primitive Dirichlet character $χ$ (${\rm{mod}} \,\, q$). Put $f (s,χ) := q^s L(s,χ) + i^{-κ(χ)} G(χ) L(s,\overlineχ)$, where $\overlineχ$ is the complex conjugate of $χ$ and $κ(χ) :=(1-χ(-1))/2$. Then we prove that $f (s,χ)$ satisfies Riemann's functional equation appearing in Hamburger's theorem if $χ$ is even. In addition, we show that $f (σ,χ) \ne 0$ all $σ\ge 1$. Moreover, we prove that $f(σ,χ) \ne 0$ for all $1/2 \le σ< 1$ if and only if $L(σ,χ) \ne 0$ for all $1/2 \le σ< 1$. When $χ$ is real, all zeros of $f(s,χ)$ with $\Re (s) >0$ are on the line $σ=1/2$ if and only if GRH for $L(s,χ)$ is true. However, $f (s,χ)$ has infinitely many zeros off the critical line $σ=1/2$ if $χ$ is non-real.
The probability number distribution function of binary black hole mergers observed by LIGO/Virgo O3a has double peaks as a function of chirp mass $M_c$, total mass $M_t$, primary black hole mass $M_1$ and secondary one $M_2$, respectively. The larger chirp mass peak is at $M_c \cong 30 M_{\odot}$. The distribution of $M_2$ vs. $M_1$ follows the relation of $M_2\cong 0.7M_1$. For initial mass functions of Population III stars in the form of $f(M) \propto M^{-α}$, population synthesis numerical simulations with $0\leq α\leq 1.5$ are consistent with O3a data for $M_c \gtrsim 20M_{\odot}$. The distribution of $M_2$ vs. $M_1$ for simulation data also agrees with $M_2\cong 0.7M_1$ relation of O3a data.
In this paper, we show the following; (1) The periodic zeta function ${\rm{Li}}_s (e^{2πia})$ with $0<a<1/2$ or $1/2 < a <1$ does not vanish on the real line. (2) All real zeros of $Y(s,a):=ζ(s,a) - ζ(s,1-a)$, $O(s,a) := -i {\rm{Li}}_s (e^{2πia}) + i{\rm{Li}}_s (e^{2πi(1-a)})$ and $X(s,a) := Y(s,a) + O(s,a)$ with $0 < a < 1/2$ are simple and only at the negative odd integers. (3) All real zeros of $Z(s,a):=ζ(s,a) + ζ(s,1-a)$ are simple and only at the non-positive even integers if and only if $1/4 \le a \le 1/2$. (4) All real zeros of $P(s,a):={\rm{Li}}_s (e^{2πia}) + {\rm{Li}}_s (e^{2πi(1-a)})$ are simple and only at the negative even integers if and only if $1/4 \le a \le 1/2$. Moreover, the asymptotic behavior of real zeros of $Z(s,a)$ and $P(s,a)$ are studied when $0 < a < 1/4$. In addition, the complex zeros of these zeta functions are also discussed when $0 <a <1/2$ is rational or transcendental.
For $0 < a \le 1/2$, we define the quadrilateral zeta function $Q(s,a)$ using the Hurwitz and periodic zeta functions and show that $Q(s,a)$ satisfies Riemann's functional equation studied by Hamburger, Heck and Knopp. Moreover, we prove that for any $0 < a \le 1/2$, there exist positive constants $A(a)$ and $T_0(a)$ such that the number of zeros of the quadrilateral zeta function $Q(s,a)$ on the line segment from $1/2$ to $1/2 +iT$ is greater than $A(a) T$ whenever $T \ge T_0(a)$.
In the present paper, for $s,t,u \in {\mathbb{C}}$, we show rapidly (or globally) convergent series representations of the Tornheim double zeta function $T(s,t,u)$ and (desingularized) symmetric Tornheim double zeta functions. As a corollary, we give a new a proof of known results on the values of $T(s,s,s)$ at non-positive integers and the location of the poles of $T(s,s,s)$. Furthermore, we prove that the function $T(s,s,s)$ can not be written by a polynomial in the form of $\sum_{k=1}^j c_k \prod_{r=1}^q ζ^{d_{kr}} (a_{kr} s + b_{kr})$, where $a_{kr}, b_{kr}, c_k \in {\mathbb{C}}$ and $d_{kr} \in {\mathbb{Z}}_{\ge 0}$.
We performed population synthesis simulations of Population III binary stars with Maxwellian kick velocity distribution when MGCOs (Mass Gap Compact Objects with mass 2--5$\,M_{\odot}$) are formed. We found that for eight kick velocity dispersion models of $σ_{\rm k}=0$--$500$ km/s, the mean mass of black hole (BH)-MGCO binary is $\sim (30 \,M_\odot,\,2.6 \,M_\odot)$. In numerical data of our simulations, we found the existence of BH-MGCO binary with mass $(22.9 \,M_\odot,\,2.5 \,M_\odot)$ which looks like GW190814.
In the case of zero-metal (population III or Pop III) stars, we show that the total mass of binary black holes from binary Pop III star evolution can be $\sim 150 \,M_{\odot}$, which agrees with the mass of the binary black hole GW190521 recently discovered by LIGO/Virgo. The event rate of such binary black hole mergers is estimated as 0.13--0.66$~(ρ_{\rm SFR}/(6\times10^5~M_{\odot}/{\rm Mpc}^3))~Err_{\rm sys}~{\rm yr^{-1}~Gpc^{-3}}$, where $ρ_{\rm SFR}$ and $Err_{\rm sys}$ are the cumulative comoving mass density of Pop III stars depending on star formation rate and the systematic errors depending on uncertainties in the Pop III binary parameters, respectively. The event rate in our fiducial model with $ρ_{\rm SFR}=6\times10^5~M_{\odot}/{\rm Mpc}^3$ and $ Err_{\rm sys}=1$ is 0.13--0.66$~{\rm yr^{-1}~Gpc^{-3}}$, which is consistent with the observed value of 0.02--0.43$~{\rm yr^{-1}~Gpc^{-3}}$.