arXiv subjects

Shin Watanabe

Publications and source records attributed to Shin Watanabe.

At least 19 recordsLinked to original sources

arXiv2026

Rotational Feshbach resonances in the deformed halo nucleus $^{31}$Ne

Background: The deformed halo nucleus $^{31}$Ne exhibits unique structural properties arising from the interplay between its halo neutron and the deformation of the $^{30}$Ne core. While previous studies have established the nature of its weakly-bound ground state through reaction cross sections and inclusive breakup measurements, the structure of its excited states in the low-energy continuum, which are expected to appear as resonances, remains largely unexplored. Purpose: We investigate the structure of these resonant states and clarify their rotational nature and formation mechanism. Method: The structure of $^{31}$Ne is described using the particle rotor model (PRM), which explicitly treats the coupling between core excitation and single-particle motion in both bound and continuum states. Results: The calculations predict the emergence of unbound rotational states in the low-energy continuum of $^{31}$Ne, which form a rotational sequence built on the weakly-bound Nilsson [321 3/2] configuration. As the total angular momentum increases along the rotational band, the intrinsic Nilsson structure is largely preserved, whereas the dominant core-spin component shifts to higher spins. These resonances are stabilized through the combined effects of coupling to higher-lying closed core-excited channels and reduced effective neutron relative energies, and can therefore be interpreted as rotational Feshbach resonances. Conclusion: The present study elucidates the formation mechanism of rotational Feshbach resonances in $^{31}$Ne. This mechanism is expected to be a general feature of weakly-bound deformed nuclei. Exclusive breakup measurements with coincident detection of $\gamma$ rays from the de-exciting core will provide crucial tests of the proposed formation mechanism of rotational Feshbach resonances.

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arXiv2026

Low-Noise SiPM Light Readout and ASIC-Based Charge Readout of a Liquid Argon Time Projection Chamber for MeV Gamma-Ray Measurements

We have developed a compact liquid argon time projection chamber (LArTPC), NanoGRAMS, as a technology demonstrator for the Gamma-Ray and AntiMatter Survey (GRAMS). LArTPCs have the potential to enable Compton cameras with unprecedented effective area in the MeV gamma-ray band. NanoGRAMS has an active volume of $5.12 \times 5.12 \times 10~\mathrm{cm^3}$ and is equipped with a low-noise scintillation and charge readout system. The scintillation light is detected by an array of 16 SiPMs ($6 \times 6~\mathrm{mm^2}$ each), whose signals are summed and amplified by a low-noise transimpedance amplifier operable at liquid argon temperature. Ionization electrons are read out with $3.2\,\mathrm{mm}$-pitch pixels and processed by VATA-SGD ASICs, with synchronization provided by an FPGA-based data acquisition system. We irradiated the detector with a $^{60}\mathrm{Co}$ source (1173 and $1332\,\mathrm{keV}$) and successfully detected both 1-hit and 2-hit events. The collected charge was converted to deposited energy using a phenomenological recombination model, and the detector response was evaluated with a Geant4-based Monte Carlo simulation. The reconstructed energy spectrum shows Compton edges at 963 and $1118\,keV$, consistent with the expected values. For 2-hit events, the sequence of interactions was identified, and the reconstructed back-projection image agrees with the source position. These results demonstrate the feasibility of NanoGRAMS as a Compton camera for MeV gamma-ray imaging spectroscopy.

astro-ph.IM↗

arXiv2026

The line modulations of H-like Fe, Ca, Ar, and S observed with $XRISM$/Resolve in Cyg X-3

Cygnus X-3, hosting a Wolf-Rayet (WR) star whose dense wind produces various spectral lines due to photoionization by X-rays from a compact object, provides an ideal laboratory for studying wind dynamics and density structure. We measured the orbital modulations of the Fe, Ca, Ar, and S Ly$\alpha$ lines observed with the X-ray microcalorimeter (Resolve) onboard the $XRISM$, taking account of both emission and absorption lines of the Ly$\alpha$ complexes. The modulations of Doppler shifts of the Fe, Ca, Ar, and S Ly$\alpha$ lines showed amplitudes of 500 km s$^{-1}$ and phase offsets of 0.04, 0.09, 0.11, and 0.17, respectively, in units of an orbital period (4.8 hours) relative to the orbital motion of the compact object. This result indicated that H-like Fe most closely follows the compact object's motion. The line widths ranged from 400 to 1000 km s$^{-1}$. The intensities of both emission and absorption lines reached their minima around orbital phase 0.0 and their maxima around phase 0.5. The absorption peaks, however, did not align exactly with phase 0.5, suggesting the inhomogeneous structures such as an accretion wake and/or a bow shock. We compared the observed modulations with calculations based on a stellar wind model, accelerated by ultraviolet radiation from the WR star. One of the calculations qualitatively reproduced the observed trend that H-like Fe ions were concentrated near the compact object, whereas H-like S was distributed across the binary system, with H-like Ca and Ar showing intermediate spatial distributions. From this comparison, we estimated that a mass-loss rate of the stellar wind was approximately $5 \times 10^{-6}$-$1 \times 10^{-5}\ M_{\odot}\ {\rm yr}^{-1}$.

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arXiv2026

SpaceWire-based Data Acquisition Network for the Solar Flare Sounding Rocket Experiment FOXSI-4 and FOXSI-5

We developed a SpaceWire-based data acquisition (DAQ) system for the FOXSI-4 and FOXSI-5 sounding rocket experiments, which aim to observe solar flares with high sensitivity and dynamic range using direct X-ray focusing optics. The FOXSI-4 mission, launched on April 17, 2024, achieved the first direct focusing observation of a GOES M1.6 class solar flare with imaging spectroscopy capabilities in the soft and hard X-ray energy ranges, using a suite of advanced detectors, including two CMOS sensors, four CdTe double-sided strip detectors (CdTe-DSDs), and a Quad-Timepix3 detector. To accommodate the high photon flux from a solar flare and these diverse detector types, a modular DAQ network architecture was implemented based on SpaceWire and the Remote Memory Access Protocol (RMAP). This modular architecture enabled fast, reliable, and scalable communication among various onboard components, including detectors, readout boards, onboard computers, and telemetry systems. In addition, by standardizing the communication interface and modularizing each detector unit and its associated electronics, the architecture also supported distributed development among collaborating institutions, simplifying integration and reducing overall complexity. To realize this architecture, we developed FPGA-based readout boards (SPMU-001 and SPMU-002) that support SpaceWire communication for high-speed data transfer and flexible instrument control. In addition, a real-time ground support system was developed to handle telemetry and command operations during flight, enabling live monitoring and adaptive configuration of onboard instruments in response to the properties of the observed solar flare. The same architecture is being adopted for the upcoming FOXSI-5 mission, scheduled for launch in 2026.

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arXiv2025

First-principles response simulation of wide-gap CdTe-DSDs for the FOXSI solar sounding rocket experiment

We have developed a wide-gap CdTe double-sided strip detector (CdTe-DSD) for the fourth and fifth flights of the Focusing Optics X-ray Solar Imager sounding rocket experiment (FOXSI-4/FOXSI-5). This detector features a 30 um strip width and a variable gap width from 30 um to 70 um, enabling position resolution finer than the strip pitch by inducing charge sharing across adjacent strip electrodes and utilizing this shared energy information for position reconstruction. However, this wide-gap configuration introduces complex detector responses, such as charge loss in the gap regions and electric field distortion near the electrodes, requiring a more advanced modeling approach for interpreting observation results in FOXSI-4/FOXSI-5 and for further optimization of future detector design. To address these complexities, we have constructed a first-principles simulation framework to model the detector response. The simulation integrates Geant4-based Monte Carlo simulations of energy deposition, finite element calculations of electric and weighting fields using COMSOL Multiphysics, charge transport modeling incorporating trapping and diffusion, and calculation of the induced charge on the electrodes based on the Shockley-Ramo theorem. By introducing a surface conductive layer, which causes electric field distortion, the model successfully reproduces the experimentally observed charge loss on the cathode side. In addition, the model reproduces the distinct charge sharing behavior on the cathode and anode sides. These results validate the effectiveness of the model in characterizing the wide-gap CdTe-DSD.

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arXiv2025

XRISM Spectroscopy of the Stellar-Mass Black Hole 4U 1630-472 in Outburst

We report on XRISM/Resolve spectroscopy of the recurrent transient and well-known black hole candidate 4U 1630$-$472 during its 2024 outburst. The source was captured at the end of a disk-dominated high/soft state, at an Eddington fraction of $\lambda_\mathrm{Edd} \sim 0.05~(10 M_{\odot}/M_\mathrm{BH})$. A variable absorption spectrum with unprecedented complexity is revealed with the Resolve calorimeter. This marks one of the lowest Eddington fractions at which highly ionized absorption has been detected in an X-ray binary. The strongest lines are fully resolved, with He-like Fe XXV separated into resonance and intercombination components, and H-like Fe XXVI seen as a spin-orbit doublet. The depth of some absorption lines varied by almost an order of magnitude, far more than expected based on a 10% variation in apparent X-ray flux and ionization parameter. The velocity of some absorption components also changed significantly. Jointly modeling two flux segments with a consistent model including four photoionization zones, the spectrum can be described in terms of highly ionized but likely failed winds that sometimes show red-shifts, variable obscuration that may signal asymmetric structures in the middle and outer accretion disk, and a tentative very fast outflow ($v = 0.026-0.033c$). We discuss the impact of these findings on our understanding of accretion and winds in stellar-mass black holes, and potential consequences for future studies.

astro-ph.HE↗

arXiv2025

Verification of the Timing System for the X-ray Imaging and Spectroscopy Mission in the GPS Unsynchronized Mode

We report the results from the ground and on-orbit verifications of the XRISM timing system when the satellite clock is not synchronized to the GPS time. In this case, the time is determined by a free-run quartz oscillator of the clock, whose frequency changes depending on its temperature. In the thermal vacuum test performed in 2022, we obtained the GPS unsynchronized mode data and the temperature-versus-clock frequency trend. Comparing the time values calculated from the data and the true GPS times when the data were obtained, we confirmed that the requirement (within a 350 $\mu$s error in the absolute time, accounting for both the spacecraft bus system and the ground system) was satisfied in the temperature conditions of the thermal vacuum test. We also simulated the variation of the timing accuracy in the on-orbit temperature conditions using the Hitomi on-orbit temperature data and found that the error remained within the requirement over $\sim 3 \times 10^{5}$ s. The on-orbit tests were conducted in 2023 September and October as part of the bus system checkout. The temperature versus clock frequency trend remained unchanged from that obtained in the thermal vacuum test and the observed time drift was consistent with that expected from the trend.

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arXiv2025

XRISM spectroscopy on orbital modulation of Fe Ly$\alpha$ lines in Cygnus X-3

To understand physical processes such as mass transfer and binary evolution in X-ray binaries, the orbital parameters of the system are fundamental and crucial information. Cygnus X-3 is a high-mass X-ray binary composed of a compact object of unknown nature and a Wolf-Rayet star, which is of great interest in the context of wind-fed mass accretion and binary evolution. Here we present XRISM/Resolve high-resolution spectroscopy focusing on the Fe Ly$\alpha$ lines in its hypersoft state. We perform an orbital phase-resolved spectral analysis of the lines to study the orbital modulation of the emission and absorption lines. It is found that the emission lines reflect the orbital motion of the compact object whose estimated velocity amplitude is $430^{~~+150}_{~~-140}~~\mathrm{km\,s^{~-1}}$, while the absorption lines show a variation that can be interpreted as originating from the stellar wind. We discuss possible mass ranges for the binary components using the mass function with the estimated value of the velocity amplitude in this work, combined with the relation between the mass loss rate and the orbital period derivative and the empirical mass and mass loss rate relation for Galactic Wolf-Rayet stars. They are constrained to be $(1.3\text{-}5.1)\,M_\odot$ and $(9.3\text{-}12)\,M_\odot$ for the assumed inclination angle of $i = 25$ deg, which becomes more relaxed to $(1.3\text{-}24)\,M_\odot$ and $(9.3\text{-}16)\,M_\odot$ for $i = 35$ deg, respectively. Thus, it remains unclear whether the system harbors a black hole or a neutron star.

astro-ph.HE↗

arXiv2025

Development of the Timing System for the X-Ray Imaging and Spectroscopy Mission

This paper describes the development, design, ground verification, and in-orbit verification, performance measurement, and calibration of the timing system for the X-Ray Imaging and Spectroscopy Mission (XRISM). The scientific goals of the mission require an absolute timing accuracy of 1.0~ms. All components of the timing system were designed and verified to be within the timing error budgets, which were assigned by component to meet the requirements. After the launch of XRISM, the timing capability of the ground-tuned timing system was verified using the millisecond pulsar PSR~B1937+21 during the commissioning period, and the timing jitter of the bus and the ground component were found to be below $15~\mu$s compared to the NICER (Neutron star Interior Composition ExploreR) profile. During the performance verification and calibration period, simultaneous observations of the Crab pulsar by XRISM, NuSTAR (Nuclear Spectroscopic Telescope Array), and NICER were made to measure the absolute timing offset of the system, showing that the arrival time of the main pulse with XRISM was aligned with that of NICER and NuSTAR to within $200~\mu$s. In conclusion, the absolute timing accuracy of the bus and the ground component of the XRISM timing system meets the timing error budget of $500~\mu$s.

astro-ph.IM↗

arXiv2025

Imaging and Spectral Performance of a Wide-gap CdTe Double-Sided Strip Detector

The fourth flight of the Focusing Optics X-ray Solar Imager sounding rocket experiment (FOXSI-4) aimed to achieve the first imaging spectroscopic observations of mid-to-large class ( >= GOES C5 class) solar flares, in contrast to the previous three flights that targeted relatively quiet regions of the Sun. To meet the emerging requirements for hard X-ray focal plane detectors for providing simultaneous diagnostics of spectrally (<1 keV FWHM) and spatially (<50 um) separated coronal and chromospheric emissions from solar flares, we developed a new strip-configuration detector called the wide-gap CdTe semiconductor double-sided strip detector (CdTe-DSD). The wide-gap CdTe-DSD employs a unique design principle to enhance position resolution. This enhancement is realized by expanding the gaps between electrodes to induce charge-sharing across adjacent strip electrodes and using this sharing energy information for position reconstruction to a level finer than the strip-pitch. However, the detector response becomes complex and requires consideration of various factors, such as the charge loss due to wider gaps and the dependence on the depth of photon interaction. Thus, we developed an energy reconstruction method that fully leverages the energy information between adjacent strips and from both the cathode and anode sides, achieving an energy resolution of 0.75 keV (FWHM) at 14 keV. Furthermore, we conducted an X-ray scanning experiment using a synchrotron beam at Spring-8 to evaluate the detector response with a fine scale of 10 um. Based on these results, we established a sub-strip position reconstruction method, demonstrating that X-rays interacting at the center of the gap can be determined with an accuracy of 20 um, and even those at the strip center can be determined with an accuracy of 50 um.

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arXiv2024

Deformation and core$+n$ decoupling in the spectrum of $^{17}$C

The coexistence of various structures, such as diverse shapes and cluster structures, is a fundamental property of atomic nuclei. In neutron-rich nuclei, a core$+n$ structure can compete with nuclear deformation due to the small neutron separation energy. A neutron-rich carbon isotope, $^{17}$C, exemplifies the appearance of the deformation and the core+$n$ decoupling in its spectrum, which is desirable for a deeper understanding of the coexistence phenomena in neutron-rich nuclei. We aim to describe and understand this coexistence phenomenon in the low-lying levels of $^{17}$C in a unified manner considering explicitly the degrees of freedom of both the quadrupole deformation and the relative motion between a $^{16}$C core and a valence neutron. We adopt the generator coordinate method (GCM) with the antisymmetrized molecular dynamics (AMD) to describe various configurations. We superpose various basis wave functions generated by the energy variation by imposing two types of constraints: one incorporating the degree of the quadrupole deformation and the other taking care of the relative motion between a $^{16}$C core and a valence neutron. We find that the experimental energy level is well reproduced by the present method, including both deformed and $^{16}$C+$n$ configurations. The ground $3/2^{+}$ and second excited $5/2^{+}$ states exhibit a triaxially deformed shape, while the main component of the first excited $1/2^{+}$ state is a $^{16}$C($0^{+}$) core plus an $s$-wave neutron configuration. The tail of the valence neutron is significantly improved by including the $^{16}$C+$n$ basis functions explicitly. The explicit inclusion of both the quadrupole deformation and the relative motion between a core and a valence neutron is essential to describe the coexistence phenomena observed in neutron-rich nuclei in the AMD+GCM framework.

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arXiv2024

Nonspherical Pauli-forbidden states in deformed halo nuclei: Impact on the ${}^7\mathrm{Be}+p$ resonant states in the particle rotor model

Background: An important aspect of reducing nuclear many-body problems to few-body models is the presence of Pauli forbidden (PF) states, which are excluded in fully antisymmetrized calculations. Insufficient treatments of PF states in deformed halo nuclei underscore the need for model refinement. Purpose: We propose a new method utilizing Nilsson states as PF states in the orthogonality condition model, and investigate the impact of PF states on the properties of resonant states. Method: We investigate the scattering states of ${}^8\mathrm{B}$ within the Particle Rotor Model (PRM) framework based on a deformed ${}^7\mathrm{Be}$ core and $p$ two-body model. We compare several methods for eliminating PF states and test them with the experimental data. Results: Our model successfully reproduces the experimental excitation function for elastic scattering cross section by properly eliminating PF states. The same calculation predicts the presence of a low-energy bump in the inelastic scattering excitation function, although its position is overestimated by about 1 MeV compared to experimental data. Conclusion: This study extends the applicability of the PRM, offering a comprehensive approach for exploring structures and reactions of loosely bound nuclei like ${}^8$B. Future integration with the continuum discretized coupled channels (CDCC) method promises to further advance the research.

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arXiv2024

FOXSI-2: Upgrades of the Focusing Optics X-ray Solar Imager for its Second Flight

The Focusing Optics X-ray Solar Imager (FOXSI) sounding rocket payload flew for the second time on 2014 December 11. To enable direct Hard X-Ray (HXR) imaging spectroscopy, FOXSI makes use of grazing-incidence replicated focusing optics combined with fine-pitch solid-state detectors. FOXSI's first flight provided the first HXR focused images of the Sun. For FOXSI's second flight several updates were made to the instrument including updating the optics and detectors as well as adding a new Solar Aspect and Alignment System (SAAS). This paper provides an overview of these updates as well as a discussion of their measured performance.

astro-ph.IM↗

arXiv2024

Investigation of the determination of nuclear deformation using high-energy heavy-ion scattering

Background: Nuclear deformation provides a crucial characteristic of nuclear structure. Conventionally, the quadrupole deformation length of a nucleus, $\delta_{2}$, has often been determined based on a macroscopic model through a deformed nuclear potential with the deformation length $\delta^{\rm (pot)}_{2}$, which is determined to reproduce the nuclear scattering data. This approach assumes $\delta_{2}=\delta^{\rm (pot)}_{2}$ although there is no theoretical foundation. Purpose: We clarify the relationship between $\delta_{2}$ and $\delta^{\rm (pot)}_{2}$ for high-energy heavy-ion scattering systematically to evaluate the validity of the conventional approach to determine the nuclear deformation. Method: The deformation lengths for the $^{12}$C inelastic scattering by $^{12}$C, $^{16}$O, $^{40}$Ca, and $^{208}$Pb targets at $E/A$ = 50--400 MeV are examined. First, we perform microscopic coupled-channel (CC) calculations to relate $\delta_{2}$ of the deformed density into the inelastic scattering cross section. Second, we use the deformed potential model to determine $\delta^{\rm (pot)}_{2}$ so as to reproduce the microscopic CC result. We then compare $\delta^{\rm (pot)}_{2}$ with $\delta_{2}$. Results: We find that $\delta^{\rm (pot)}_{2}$ is about 20--40 \% smaller than presumed $\delta_{2}$, showing strong energy and target dependence. Further analysis, which considers higher-order deformation effects beyond the derivative model, reveals that $\delta^{\rm (pot)}_{2}$ is still about 15--35 \% smaller than $\delta_{2}$. Conclusion: Our results suggest that one needs to be careful when the deformed potential model for the high-energy heavy-ion scattering is used to extract the nuclear deformation. The conventional approach may underestimate the deformation length $\delta_2$ systematically.

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arXiv2024

Uncovering the sign of nuclear deformations: Determination of prolate or oblate shape via low-energy $\alpha$ inelastic scattering

Background: Understanding nuclear shape is a crucial problem in nuclear physics. In particular, determining the sign of quadrupole deformation, i.e., whether prolate or oblate, remains a challenging problem. Purpose: Our aim is to propose a method for determining the sign of quadrupole deformation using $\alpha$ inelastic scattering data and to demonstrate its effectiveness. Method: Our approach is the standard coupled-channel method based on the macroscopic model. We utilize the nuclear reorientation effect, a phenomenon associated with the self coupling of excited states, as a probe sensitive to the sign of deformation. Results: We first provide an overview of how the reorientation effect influences inelastic scattering cross sections, and numerically confirm its validity in realistic cases. We then demonstrate that the sign of deformation can be uniquely determined from inelastic scattering cross section data. Conclusion: Our technique offers a systematic approach for determining the sign of deformation in both stable and unstable nuclei. The broad applicability of $\alpha$ inelastic scattering will make it a valuable tool to study shape of nuclei, especially unstable nuclei.

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arXiv2023

2-mm-Thick Large-Area CdTe Double-sided Strip Detectors for High-Resolution Spectroscopic Imaging of X-ray and Gamma-ray with Depth-Of-Interaction Sensing

We developed a 2-mm-thick CdTe double-sided strip detector (CdTe-DSD) with a 250 um strip pitch, which has high spatial resolution with a uniform large imaging area of 10 cm$^2$ and high energy resolution with high detection efficiency in tens to hundreds keV. The detector can be employed in a wide variety of fields for quantitative observations of hard X-ray and soft gamma-ray with spectroscopic imaging, for example, space observation, nuclear medicine, and non-destructive elemental analysis. This detector is thicker than the 0.75-mm-thick one previously developed by a factor of $\sim$2.7, thus providing better detection efficiency for hard X-rays and soft gamma rays. The increased thickness could potentially enhance bias-induced polarization if we do not apply sufficient bias and if we do not operate at a low temperature, but the polarization is not evident in our detector when a high voltage of 500 V is applied to the CdTe diode and the temperature is maintained at -20 $^\circ$C during one-day experiments. The ''Depth Of Interaction'' (DOI) dependence due to the CdTe diode's poor carrier-transport property is also more significant, resulting in much DOI information while complicated detector responses such as charge sharings or low-energy tails that exacerbate the loss in the energy resolution. In this paper, we developed 2-mm-thick CdTe-DSDs, studied their response, and evaluated their energy resolution, spatial resolution, and uniformity. We also constructed a theoretical model to understand the detector response theoretically, resulting in reconstructing the DOI with an accuracy of 100 um while estimating the carrier-transport property. We realized the detector that has high energy resolution and high 3D spatial resolution with a uniform large imaging area.

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arXiv2023

Offline Skill Generalization via Task and Motion Planning

This paper presents a novel approach to generalizing robot manipulation skills by combining a sampling-based task-and-motion planner with an offline reinforcement learning algorithm. Starting with a small library of scripted primitive skills (e.g. Push) and object-centric symbolic predicates (e.g. On(block, plate)), the planner autonomously generates a demonstration dataset of manipulation skills in the context of a long-horizon task. An offline reinforcement learning algorithm then extracts a policy from the dataset without further interactions with the environment and replaces the scripted skill in the existing library. Refining the skill library improves the robustness of the planner, which in turn facilitates data collection for more complex manipulation skills. We validate our approach in simulation, on a block-pushing task. We show that the proposed method requires less training data than conventional reinforcement learning methods. Furthermore, interaction with the environment is collision-free because of the use of planner demonstrations, making the approach more amenable to persistent robot learning in the real world.

cs.RO↗

arXiv2023

Systematic analysis of $t$ and $^3$He breakup reactions

Systematic measurement of $t$ and $^3$He knockout processes is planned. The weakly-bound nature of these nuclei may affect the interpretation of forthcoming knockout reaction data. Purpose: We aim at clarifying breakup properties of $t$ and $^3$He by investigating their elastic and breakup cross sections. We employ the four-body continuum-discretized coupled-channels method with the eikonal approximation to describe the $t$ and $^3$He reactions. The breakup cross section of $t$ is found to be almost the same as that of $^3$He and is about one-third of that of $d$. Coulomb breakup plays negligible role in the breakup of $t$ and $^3$He, in contrast to in the deuteron breakup reaction. It is found that $t$ and $^3$He tend to breakup into three nucleons rather than $d$ and a nucleon. It is shown that the breakup cross sections of $t$ and $^3$He are not as large as those of d but non-negligible. Because about 80% of them corresponds to the three-nucleon breakup process, a four-body breakup reaction model is necessary to quantitatively describe the breakup of $t$ and $^3$He.

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