arXiv subjects

Myung-Ki Cheoun

Publications and source records attributed to Myung-Ki Cheoun.

At least 19 recordsLinked to original sources

arXiv2026

The $ν$EYE Neutrino Telescope: Conceptual Design Report

The $\bfνEYE$ neutrino project leverages the existing large pit at Yemilab located in South Korea, to reveal the existence of sterile neutrino, the up-turn of the neutrinos from the Sun, and the first minimum of the neutrino oscillation over distances on the order of tens of kilometers for the first time. This initiative is expected to facilitate a wide range of significant scientific and technological advancements within both South Korean and international communities engaged in neutrino science and technology. The $\bfνEYE$ aims to investigate the largely unexplored sector of almost-massless lepton in the elementary particle physics in detail. The emphasis will be placed on the study of real time nuclear processes and reactions involving possible sterile neutrinos on timescales down to nanoseconds in ultra-high intense or radioactive neutrino beams for the first time in the world; the $\bfνEYE$ looks at to-be universal oscillation (``up-turn'' in the electron neutrino survival probability) of neutrinos predicted by the three neutrino oscillation paradigm. This will confirm or deny our current understanding on the particle interactions of the lepton sector; and measurement of the first oscillation minimum between the first and second neutrinos in mass.

hep-ex↗

arXiv2026

Local-nuclear-density dependent calculation of nucleon electromagnetic form factor ratios in finite nuclei

We calculate the electromagnetic form factors of nucleons bound in finite nuclei and make predictions to the ratio between the electric ($G_E^*$) and magnetic ($G_M^*$) form factors in terms of the square of the four-momentum transfer $Q^2$. We extend our previous constant-density calculations within the covariant spectator-QMC framework by incorporating the spatial nuclear density profiles of finite nuclei and quantify the deviations from the average-density approximation used in our previous applications. The impact of the medium effects can then be observed considering the ratio between $G_E^*/G_M^*$ and the ratio in free space $G_E/G_M$, that define the proton electromagnetic double ratio associated with a given nucleus. The double ratio is expected to remove some systematic uncertainties. There is the expectation that ratios $G_E^*/G_M^*$ associated with the bound protons inside the nucleus will be measured in the near future in polarization-transfer experiments $(\vec{e} A, e'\! A' \vec{p})$. Anticipating future measurements on the subject, we make predictions for the double ratios, to be compared with the average measurements on the energy states of protons bound to nuclei. We consider the nuclei $^{12}$C, $^{16}$O and $^{40}$Ca. We conclude that the form factors calculated using nuclear density profile function $ρ(r)$ are less suppressed than in the case of the results calculated using the average nuclear density. The results indicate that the relative importance of the low-density surface region increases with $Q^2$, leading to a weaker suppression than that predicted by the average-density approximation. We also make predictions for the ratios associated with neutrons bound to nuclei.

nucl-th↗

arXiv2026

From twelve to three active qubits: Ancilla-recycled rodeo filtering for trapped neutron-proton scattering

Rodeo filtering applies $R$ ancilla-assisted energy interrogations. If all measurements are deferred, a static realization requires $n_s+R$ active qubits for an $n_s$-qubit system, whereas mid-circuit measurement and reset allow one ancilla to be recycled and reduce the width to $n_s+1$ without changing the ideal filter. We demonstrate this compression for a trapped-spectrum input to model neutron--proton scattering. A static $R=10$ circuit on IonQ Forte-1 uses 12 active qubits, while a dynamic circuit on IBM Aachen uses only three, a 75\% reduction. The controlled interleaved IBM scan gives $ΔE_c=-0.017\pm0.507\keV$, comparable to the static result $-0.568\pm0.694\keV$. Mapping these centers through the finite-confinement modified effective range expansion (MERE) gives $\mathcal K_{3.7}=p\cotδ_{0,3.7} =0.13419\pm0.00020~\mathrm{fm}^{-1}$ for IonQ and $0.13435\pm0.00015~\mathrm{fm}^{-1}$ for the interleaved IBM scan, both consistent with the exact value $0.13436~\mathrm{fm}^{-1}$. Both implementations retain complete four-configuration support and therefore reproduce the exact $4\times4$ effective-space level by sample-based quantum diagonalization. Three IBM batches nevertheless expose run-dependent center variations beyond finite-shot fluctuations, while the postselection attenuation is more stable. Ancilla recycling therefore makes the rodeo width independent of $R$, freeing qubits for the nuclear register while preserving a finite-confinement scattering input, but exchanges spatial resources for mid-circuit latency and repeatability requirements.

nucl-th↗

arXiv2026

Charge-symmetry-breaking effects on displacement energies and charge radius differences in mirror nuclei

We study the effect of charge symmetry breaking (CSB) energy density function (EDF) on the mirror displacement energies (MDEs) and charge radius differences of mirror nuclei within the self-consistent Hartree-Fock-Bogolyubov (HFB) model taking Skyrme EDFs, SLy4 and SkM* as the central part of nuclear potential. We introduce the volume and the derivative terms in CSB EDF and calibrate the strength adopting four reference mirror pairs $^{34}$Ar--$^{34}$S, $^{36}$Ca--$^{36}$S, $^{38}$Ca--$^{38}$Ar, and $^{54}$Ni--$^{54}$Fe, for which experimental data of both MDEs and mirror charge-radius differences are available. We introduce a sensitivity matrix which connects two CSB terms to residuals of MDEs and mirror charge-radius differences after subtracting the effect of Coulomb interaction. By using the sensitivity matrix, we found out that the derivative term is important to reproduce both observables in a good accuracy together with the volume term, especially for the residual of mirror charge radii. The optimized CSB EDF are further applied to predict the charge radius differences of mirror pairs, $^{40}$Ti--$^{40}$Ar, $^{42}$Ti--$^{42}$Ca, $^{46}$Cr--$^{46}$Ti, and $^{50}$Fe--$^{50}$Cr. We pointed out also that the CSB effects change neutron skins of mirror proton-rich nuclei at the $10^{-2}$ fm level so that the CSB contributions must be included before charge-radius differences between mirror nuclei are used to extract neutron-skin or symmetry-energy parameters.

nucl-th↗

arXiv2026

Ground-State Energy Estimation of HeH$^{+}$, ArH$^{+}$, and H$_2$O via Sample-Based Quantum Diagonalization

Accurate ground-state energies are essential for understanding molecular structure, chemical bonding, and reaction energetics in quantum chemistry. In this work, we investigate the ground-state properties of the molecular systems HeH$^+$, ArH$^+$, and H$_2$O using Sample-Based Quantum Diagonalization (SQD), a hybrid quantum-classical framework designed for near-term quantum devices. Unlike variational approaches such as VQE, which require deep parameterized circuits and repeated expectation-value measurements, SQD reconstructs a low-energy determinant subspace directly from measured bitstrings. For the present calculations, bitstrings were generated on IBM quantum hardware using shallow local unitary cluster Jastrow (LUCJ) circuits whose parameters were constructed from the $t_1$ and $t_2$ amplitudes of coupled-cluster singles and doubles (CCSD) calculations based on restricted Hartree--Fock (RHF) references. From these samples, we compute ground-state potential-energy curves of HeH$^+$, ArH$^+$, and H$_2$O with the 6-31G and cc-pVDZ basis sets. For all three systems, the SQD results obtained with the cc-pVDZ basis closely follow the corresponding same-basis CCSD energies and reproduce the equilibrium-region trends of the potential-energy curves. HeH$^+$ and ArH$^+$ were chosen as simple yet astrophysically important molecular-ion benchmarks, while H$_2$O was included as a representative polyatomic molecule to assess the applicability of SQD beyond diatomic ionic systems. At the adopted equilibrium geometries, the deviations from the same-active-space CASCI references are 0.00, 2.51, and 6.34 mHa for HeH$^+$, ArH$^+$, and H$_2$O, respectively. These results demonstrate the feasibility of hardware-assisted SQD for the present benchmark systems and motivate further studies of its accuracy and computational scaling for larger molecular active spaces.

physics.chem-ph↗

arXiv2026

Quarkyonic Quark-Meson Coupling Model for Nuclear and Neutron Matter

We unite the dual quarkyonic model with the quark-meson coupling (QMC) model to construct a novel nuclear model based on the quark degrees of freedom, which can cover a wide range of nuclear densities, from low density to the crossover region. In the model, the relativistic, gaussian quark wavefunction is used to describe the nucleon structure. We first evaluate the energy density, chemical potential, pressure and sound velocity within the ideal Fermi gas picture. In this case, those physical quantities are discontinuous or divergent at the quark saturation density, where the quarkyonic phase emerges. To remove such singular behavior, we next introduce an infrared regulator, and combine the dual quarkyonic model and the QMC model to include the nuclear interaction -- we call it the quarkyonic quark-meson coupling (QQMC) model. In this model, the quark saturation density depends strongly on the nucleon size. For example, when $r_p = 0.6\, (0.8)$ fm, where $r_p$ is the root-mean-square radius of the proton, the quark saturation density is about $3.6\,(1.5) \times ρ_0$ in symmetric nuclear matter, where $ρ_0$ is the nuclear saturation density. Furthermore, the nuclear interaction plays an important role in considering physical quantities quantitatively. In fact, the QQMC model can produce the sound velocity which is consistent with that inferred from the observed data of several neutron stars. Furthermore, pressure in symmetric or pure neutron matter deduced from the experiments of heavy-ion collisions at high energy can be explained by the QQMC model as well. We discuss in detail the formulation for the QQMC model and the physical quantities calculated by the model.

nucl-th↗

arXiv2026

Structure of multi-$Λ$ hypernuclei with a Skyrme-type $ΛΛ$ interaction constrained by data on double-$Λ$ hypernuclei and neutron stars

We investigate multi-$Λ$ hypernuclear systems with Skyrme-type $ΛΛ$ interactions constrained by the data on double-$Λ$ hypernuclei and neutron stars. The roles of the repulsive $p$-wave and density-dependent terms in the $ΛΛ$ interaction are examined by considering the homogeneous hyperonic matter around the normal density and finite multi-$Λ$ hypernuclei within the spherical Hartree-Fock approach. In homogeneous matter, the $Λ$ chemical potential and corresponding $Λ$ drip point depend strongly on the repulsive $p$-wave term, while the effect of density-dependent term is relatively weak in the density range relevant to finite nuclei. In the multi-$Λ$ hypernuclei built on doubly closed stable cores from light to heavy systems, $Λ$ radius, separation energy and single-particle structure show a clear dependence on the repulsive $p$-wave interaction, and this dependence becomes stronger as the number of $Λ$ hyperons increases. A second and distinct effect appears near the $Λ$ drip line: when the last occupied $Λ$ orbit approaches the continuum, the repulsive $p$-wave term shifts the state upward and can produce a weakly bound state with an extended radial distribution. As a result, $Λ$ radius can increase rapidly near the threshold. This threshold effect should be distinguished from the moderate enhancement of the dependence on $p$-wave interaction with increasing number of $Λ$ hyperons. These results indicate that the multi-$Λ$ hypernuclei are particularly useful for isolating the role of $p$-wave $ΛΛ$ interacion around the normal density, whereas the density-dependent term is expected to be more important interaction in the high-density domain relevant to neutron stars.

nucl-th↗

arXiv2026

The Non-thermal Energy Window for Laser-Driven Nuclear Reactions

Laser-driven nuclear reactions proceed in non-equilibrium plasma conditions, producing ion energy distributions that are not Maxwellian. Nevertheless, fusion yields in such experiments are often interpreted using effective thermal descriptions based on the conventional Gamow window. In this work, we develop an analytical framework for evaluating nuclear reaction rates for non-thermal ions accelerated by the Target Normal Sheath Acceleration (TNSA) mechanism. Using a self-similar plasma expansion model, we derive a closed form expression for an effective reaction energy window and the corresponding fusion reactivity. The resulting effective energies differ systematically from those predicted by thermal models, indicating limitations of interpretations based on the conventional Gamow window in laser-driven environments. This framework provides a quantitative basis for analyzing fusion yields and for designing laser-driven nuclear experiments.

physics.plasm-ph↗

arXiv2026

Kaon-induced $ϕΣ$ production off the proton

We investigate the reaction mechanism of $K^-p \to ϕΣ^0$ within a hybrid Regge approach based on effective Lagrangians. The nonresonant background includes Reggeized $t$-channel $K$ and $K^*$ exchanges, together with ground-state $Σ$ and nucleon exchanges in the $s$ and $u$ channels, respectively. To describe the structures observed at $3.0 \leqslant P_{\rm Lab} \leqslant 4.5$ GeV, we include the high-mass $Σ(2620)$ and $Σ(3000)$ resonances and examine the spin-parity assignments $J^P = 1/2^\pm$, $3/2^\pm$, and $5/2^\pm$. The $K^*$-Reggeon exchange dominates the forward-angle cross sections, whereas the smaller $K$-Reggeon contribution is important for the total cross section at low energies and for the spin-density matrix elements. The nonresonant background alone is not sufficient to reproduce the local structures in the total cross section or the differential cross sections at large $-t'$. Including the two resonances, particularly the $Σ(3000)$, substantially improves the agreement with the available data. The $J^P=5/2^-$ assignment for the $Σ(3000)$ provides a reasonable overall description, although the present data do not permit a definitive determination.

nucl-th↗

arXiv2026

Electron-capture rates in the medium-mass nuclei $^{48}$Ti, $^{56}$Ni, $^{60}$Zn, and $^{64}$Ge within deformed quasiparticle random-phase approximation

Electron-capture (EC) rates in medium-mass nuclei are governed by Gamow--Teller (GT) strength distributions and provide important input for stellar weak-interaction processes. In this work, we investigate the deformation dependence of the GT strengths and stellar EC rates in selected medium-mass nuclei in and near the $pf$ shell, namely $^{48}$Ti, $^{56}$Ni, $^{60}$Zn, and $^{64}$Ge. The GT$^{(+/-)}$ strength distributions are calculated in the deformed quasiparticle random-phase approximation (DQRPA) on a single-particle basis obtained by the Skyrme SGII interaction, while the stellar EC rates are evaluated from the resulting $B(\mathrm{GT}^+)$ strengths using the standard phase-space formalism. The potential-energy curves are used to identify shape softness and possible shape coexistence in the nuclei under consideration. We find that deformation strongly modifies the GT strength distributions by changing the centroid energies, resonance splitting, and fragmentation patterns. In particular, a pronounced shape dependence of the GT$^{(+/-)}$ strengths is found for $^{56}$Ni and $^{64}$Ge, whereas $^{60}$Zn is characterized by a favoured prolate minimum and $^{48}$Ti exhibits a soft near-spherical/prolate landscape. By contrast, the corresponding EC rates are generally much less sensitive to deformation than the differential GT response itself, except at low temperatures and low densities where the low-lying GT$^+$ strength becomes decisive because of the negative EC $Q$-value in the electron phase space. Available charge-exchange data for $^{48}$Ti and $^{56}$Ni are used as benchmarks of the model predictions. The present results provide microscopic constraints on the role of deformation and shape coexistence in stellar weak rates for selected medium-mass nuclei, including proton-rich isotopes near the $N = Z$ line.

nucl-th↗

arXiv2026

Accuracy and Applicability of the Hartle-Thorne and Komatsu-Eriguchi-Hachisu Methods for Modeling Rotating Neutron Stars

Neutron stars, which are composed of extremely dense nuclear matter, serve as natural laboratories to study nuclear interactions beyond the terrestrial experiments. Recent researches have actively explored how the equation of state (EoS) can be constrained by observed neutron star masses and radii, and how nuclear interactions affect their macroscopic properties. Most of these studies, however, rely on the Tolman-Oppenheimer-Volkoff (TOV) equations, which assumed static, spherically symmetric neutron stars. Since neutron stars are rotating objects and thus axisymmetrically deformed, the TOV calculation may be insufficient to capture their realistic structure. In this work, we investigate the influence of nuclear matter properties on the physical quantities of rotating neutron stars using two approaches: the perturbative Hartle-Thorne (HT) method and fully general relativistic Komatsu-Eriguchi-Hachisu (KEH) method. For nuclear EoS parameter sets, we emamine the OMEG series, in which the slope of the symmetry energy $L$ is systematically varied. We find that rotational effects lead to a noticeable increase in the stellar radius, which depends sensitively on values of $L$. Additionally, focusing on the rotational deformation, we show that the results obtained by these two methods deviate each other even for the slowly rotating case such as $Ω=200$ Hz. These results reveal that, for detailed discussions on the internal structure and stability of rotating neutron stars, the fully general relativistic method such as KEH is indispensable.

astro-ph.HE↗

arXiv2026

Spin-Dependent Nucleon-Nucleus Interactions Constrained by Neutron Observables and Their Impact on Near-Barrier Proton Fusion

We investigate the role of spin-dependent nucleon-nucleus interactions in nuclear reactions. To this end, we use neutron spin observables to constrain the dominant central spin-spin form factors and then apply the corresponding like-channel interactions to near-barrier fusion in the $p+{}^{93}$Nb system. The interactions are constructed within a folding framework based on a finite-range effective nucleon-nucleon force and organized in terms of radial form factors associated with their spin-spin, tensor, and spin-orbit components. Neutron spin observables in the $n+{}^{27}$Al, $n+{}^{59}$Co, and $n+{}^{93}$Nb target systems are analyzed within a distorted-wave Born approximation (DWBA) framework to constrain the sign and normalization in the central spin-spin parts of the radial form factors and to examine the assembled operator conventions. The calculation reproduces the observed sign systematics of the neutron spin observables for the three targets, indicating that the essential spin-dependent structure is properly incorporated. The unlike-channel (neutron-proton) interaction constrained by neutron scattering is then reconstructed for the corresponding like-channel (proton-proton) interaction and applied to a coupled-channels description of near-barrier fusion for the $p+{}^{93}$Nb system. The resultant spin-dependent interactions lead only to a weak modification of the effective barrier and change the fusion cross section by about $0.01$-$0.03\%$ in the present calculation. These results show that the corresponding real spin-dependent correction in the like-channel is strongly suppressed in near-barrier fusion in $p+{}^{93}\mathrm{Nb}$. The present work thus connects the neutron-scattering constraints on the operator conventions with the fusion calculation in the proton channel, and quantifies the magnitude of the corresponding real spin-dependent correction in near-barrier fusion.

nucl-th↗

arXiv2026

Electric and magnetic timelike form factors of hyperons at large transfer momentum

There has been considerable progress in the study of the electromagnetic form factors of baryons in the timelike region, through electron-positron scattering reactions ($e^+ e^- \to B \bar B$), in the last two decades. Timelike experiments reveal information about the distribution of charge and magnetism inside the hyperons that cannot be obtained in spacelike experiments (electron scattering on baryons). Motivated by the novel data, we extend to the timelike region, without any further parameter fitting, a covariant quark model developed for the spacelike region that takes into account the meson cloud excitations of the baryon cores. We use the formalism to calculate the electric ($G_E$) and magnetic ($G_M$) form factors of spin 1/2 baryons in the large square transfer momentum $q^2$ region. Our calculations are compared with the available data from CLEO and BESIII above $q^2=10$ GeV$^2$. We conclude that our predictions for the effective form factors (combination between $G_E$ and $G_M$) are in good agreement with the $q^2 > 15$ GeV$^2$ data for $Λ$, $Σ^+$, $Σ^0$, $Ξ^-$ and $Ξ^0$. Upcoming data for $Σ^-$ can be used to further test our predictions. We also compare our model calculations with the available data for ratio $|G_E/G_M|$. We conclude that the present $q^2$ data range is not large enough to test our calculations, but that a more definitive test can be performed by upcoming data above $q^2=20$ GeV$^2$.

hep-ph↗

arXiv2026

Characterization of the 20-inch Photomultiplier Tubes for RENE Detector

To address the Reactor Antineutrino Anomaly (RAA) observed in neutrino experiments, the Reactor Experiment for Neutrino and Exotics (RENE) has been initiated using a liquid scintillation detector. In this study, we investigate the characteristics of two 20-inch Hamamatsu R12860 photomultiplier tubes (PMTs) intended for installation in the RENE detector. The charge and timing responses of the PMTs were evaluated at both the nominal and target gains expected during actual operation. In particular, gain non-uniformity arising from the large-diameter photocathode with a box-and-line type dynode structure was examined, and the maximum gain variation was measured. The occurrence rate, timing, and charge distributions of late pulses and afterpulses were also investigated to characterize the specific response features of the R12860 PMT. The results reported in this study will aid in the interpretation of signals from the RENE detector and serve as a reference for estimating potential systematic uncertainties in RENE data. Furthermore, these findings are expected to provide valuable information for other experiments employing the same type of PMTs.

physics.ins-det↗

arXiv2026

Effects of pair freeze-out on photon distributions in BBN epoch

We investigate the evolution of non-extensivity in the photon distribution during the Big Bang Nucleosynthesis (BBN) epoch using Tsallis statistics. Assuming a minimal deviation from the Planck distribution, we construct the perturbed Boltzmann equation for photons, including the collision terms for pair creation and annihilation processes. We analyze the possibility that these collisions could cause a slight increase in the number of high-frequency photons within the BBN era, and consequently, the primordial plasma might be temporarily placed in a state of chemical non-equilibrium. We also discuss the restoration of the photon distribution to an equilibrium state as the Universe enters the matter-dominated era. These findings, which suggest possible changes in the photon distribution during the epoch between the BBN and the recombination, offer insights that support the previously proposed ansatz solution to the primordial lithium problem in arXiv:1812.09472.

astro-ph.CO↗

arXiv2026

Phenomenological Criteria of Halo Nuclei in Ne Isotopes via Diffuseness and Helm-Model Approaches with Reaction Cross Sections

We present a systematic study of halo characteristics in the neutron-rich isotopes 28-32Ne within the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). Microscopic density distributions are analyzed in coordinate space, momentum space, and reaction observables to establish a quantitative and locally defined criterion for halo identification in medium-mass nuclei. The DRHBc densities reveal a pronounced neutron extension in 31Ne. A phenomenological analysis based on deformed Woods-Saxon fits shows a clear isotopic anomaly in the surface diffuseness parameter, with a value of about 1.1 fm for 31Ne, significantly larger than those of neighboring isotopes. The anomalously large diffuseness is therefore treated as the primary phenomenological halo signature, whereas the reduced fitted radius parameter is used only as a supporting consequence of the chosen normalization and tail-sensitive fit. Helm-model form-factor analysis demonstrates that deformation contributes to geometric smearing but does not fully account for the extended spatial structure, as reflected in the enhanced difference between microscopic and folded rms radii. Glauber reaction cross section calculations further confirm a robust relative enhancement of the interaction cross section for 31Ne that persists across reasonable nucleon-nucleon interaction prescriptions. These complementary analyses consistently identify 31Ne as the most prominent halo candidate within the 28-32Ne isotopic chain, while 32Ne exhibits intermediate features and 29Ne shows no clear halo signature. The present framework provides a practical and quantitative approach for identifying halo phenomena in deformed, neutron-rich nuclei beyond the light-mass region.

nucl-th↗

arXiv2026

A dual description of quarks and baryons: Quarkyonic matter within a relativistic quark model

We investigate quarkyonic matter within a relativistic quark model by combining the dual quarkyonic picture with the quark-meson coupling (QMC) model. Using relativistic gaussian quark wavefunctions for the nucleon, we construct the quarkyonic QMC (QQMC) model and study the properties of symmetric nuclear matter and pure neutron matter. We find that the quark saturation density depends sensitively on the nucleon size parameter and that nuclear interactions quantitatively modify the high-density behavior of the equation of state (EoS) and the sound velocity. In particular, the QQMC model yields an earlier onset of quark saturation than the noninteracting gaussian quarkyonic (GQ) model, indicating that nuclear interactions enhance the stiffening of the EoS in the quarkyonic regime.

nucl-th↗

arXiv2026

Gamow-Teller strength of $^{12,14,16}$C within deformed quasiparticle random-phase approximation

We investigate the Gamow-Teller (GT) transition strength distributions in the light carbon isotopes $^{12,14,16}$C within the framework of the deformed quasiparticle random-phase approximation (DQRPA). Nuclear deformation is explicitly incorporated through Skyrme Hartree-Fock mean-field calculations combined with the QRPA formalism. The residual particle-hole $(p-h)$ and particle-particle $(p-p)$ interactions are derived from Brückner $G$-matrix calculations based on the CD-Bonn potential, and their impact on the low-lying GT strengths is systematically examined by varying the corresponding interaction strengths. We find that nuclear deformation, associated with a reduced spin-orbit strength, plays a significant role in interpreting the GT strength distribution of $^{12}$C. In contrast, the calculated GT$^{(-)}$ strength distribution of $^{14}$C in the spherical limit reproduces the essential features of the experimental $(p,n)$ charge-exchange data. The case of $^{16}$C reveals additional high-lying GT strength associated with deformation-induced configuration mixing.

nucl-th↗