Neutron Capture Rates Research Articles

Capture rates of highly degenerate neutrons

At the low temperature and high density conditions of a neutron star crust neutrons are degenerate. In this work, we study the effect of this degeneracy on the capture rates of neutrons on neutron rich nuclei in accreted crusts. We use a statistical Hauser–Feshbach model to calculate neutron capture rates and find that neutron degeneracy can increase rates significantly. Changes increase from a factor of a few to many orders of magnitude near the neutron drip line. We also quantify uncertainties due to model inputs for masses, γ-strength functions, and level densities. We find that uncertainties increase dramatically away from stability and that degeneracy tends to increase these uncertainties further, except for cases near the neutron drip line where degeneracy leads to more robustness. As in the case of capture of classically distributed neutrons, variations in the mass model have the strongest impact. Corresponding variations in the reaction rates can be as high as 3–4 orders of magnitude, and be more than 5 times larger than under classical conditions. To ease the incorporation of neutron degeneracy in nucleosynthesis networks, we provide tabulated results of capture rates as well as analytical expressions as function of temperature and neutron chemical potential, for proton numbers between 3 ≤ Z ≤ 85, derived from fits to our numerical results. Fits are based on a new parametrization that complements previously employed power law approximations with additional Lorentzian terms that account for low energy resonances, significantly improving accuracy.

Re-analysis of temperature dependent neutron capture rates and stellar β-decay rates of 95-98Mo

The neutron capture rates and temperature dependent stellar beta decay rates of Mo isotopes are investigated within the framework of the statistical code TALYS v1.96 and the proton neutron quasi particle random phase approximation (pn-QRPA) model. The Maxwellian average cross-section (MACS) and neutron capture rates for the Mo(n,γ) Mo radiative capture process are analyzed within the framework of the statistical code TALYS v1.96 based on the phenomenological nuclear level density model and gamma strength functions. The present model-based computations for the MACS are comparable to the existing measured data. The sensitivity of stellar weak interaction rates to various densities and temperatures is investigated within the framework of the pn-QRPA model. Particular attention is paid to the impact of thermally filled excited states in the decaying nuclei ( Mo) on electron emission and positron capture rates. Furthermore, we compare the neutron capture rates and stellar beta decay rates. It is found that neutron capture rates are higher than stellar beta decay rates at both lower and higher temperatures.

The intermediate neutron capture process

Context. The observed surface abundance distributions of carbon-enhanced metal-poor (CEMP) r/s stars suggest that these stars could have been polluted by an intermediate neutron capture process (the so-called i-process) occurring at intermediate neutron densities between the r- and s-processes. Triggered by the ingestion of protons inside a convective He-burning zone, the i-process could be hosted in several sites, a promising one being the early AGB phase of low-mass, low-metallicity stars. The i-process remains affected however by many uncertainties, including those of nuclear origin, since it involves hundreds of nuclei for which reaction rates have not yet been determined experimentally. Aims. We investigate both the systematic and statistical uncertainties associated with theoretical nuclear reaction rates of relevance during the i-process and explore their impact on the i-process elemental production, and subsequently on the surface enrichment, of a low-mass, low-metallicity star during the early AGB phase. Methods. We used the TALYS reaction code to estimate both the model and parameter uncertainties affecting the photon strength function and the nuclear level densities, and hence the radiative neutron capture rates. The impact of correlated systematic uncertainties was estimated by considering different nuclear models, as was detailed in Paper II. In contrast, the uncorrelated uncertainties associated with local variation in model parameters were estimated using a variant of the backward-forward Monte Carlo method to constrain the parameter changes to experimentally known cross sections before propagating them consistently to the neutron capture rates. The STAREVOL code (Siess 2006, A&A, 448, 717) was used to determine the impact of nuclear uncertainties on the i-process nucleosynthesis in a 1 M⊙ [Fe/H] = –2.5 model star during the proton ingestion event in the early AGB phase. A large nuclear network of 1160 species coherently coupled to the transport processes was solved to follow the i-process nucleosynthesis. Results. We find that the uncorrelated parameter uncertainties lead the surface abundance uncertainties of elements with Z ≥ 40 to range between 0.5 and 1.0 dex, with odd-Z elements displaying higher uncertainties. The correlated model uncertainties are of the same order of magnitude, and both model and parameter uncertainties have an important impact on potential observable tracers such as Eu and La. We find around 125 important (n, γ) reactions impacting the surface abundances, including 28 reactions that have a medium to high impact on the surface abundance of elements that are taken as observable tracers of i-process nucleosynthesis in CEMP stars. Conclusions. Both the correlated model and uncorrelated parameter uncertainties need to be estimated coherently before being propagated to astrophysical observables through multi-zone stellar evolution models. Many reactions are found to affect the i-process predictions and will require improved nuclear models guided by experimental constraints. Priority should be given to the reactions influencing the observable tracers.

Investigation of 90,92Zr(n,γ)91,93Zr in the s-process nucleosynthesis

Abstract The neutron capture rates and Maxwellian-averaged cross-sections (MACS) for 90Zr(n,γ)91Zr and 92Zr(n,γ)93Zr processes have been computed within the framework of Talys v1.96. The effects of phenomenological nuclear level density (NLD) parameters and the gamma strength functions (GSFs) on Maxwellian-averaged cross-sections and neutron capture rates are examined both quantitatively and qualitatively. The present model-based computed data for MACS and reaction rates gives a good comparison with the existing literature. The fine-tuning of the statistical model’s nuclear properties (level density and gamma-ray strength) to reproduce experimental data will allow the detailed investigation of the s-process network.

Influence of light neutron-rich exotic nuclei in deciding abundance patterns relevant for explosive nucleosynthesis

Exotic neutron-rich nuclei play an important role in r-process nucleosynthesis. We study the effect of including proper nuclear structure to calculate neutron capture and photodisintegration rates, especially for 19C and 20N, under the aegis of post-form distorted wave Born approximation (FRDWBA). Considering a network of neutron-rich C–N–O isotopes, we show the effect on abundance calculations in a neutrino-driven wind environment of a core-collapse supernova at two critical temperatures T 9 = 3.4 and 0.62. The results are compared for nuclear physics inputs sourced from the FRDWBA, statistical estimates, and standard databases. At temperatures T 9 = 3.4, where alpha capture, or at T 9 = 0.62, where the neutron capture dominates, one can distinguish the effect of accounting for the exotic nature of the nuclei involved. Furthermore, we assess the impact of varying neutron capture and photodisintegration rates involving halo or bubble structures on the abundances within the network.

The s process in massive stars, a benchmark for neutron capture reaction rates

A clear definition of the contribution from the slow neutron-capture process (s process) to the solar abundances between Fe and the Sr-Zr region is a crucial challenge for nuclear astrophysics. Robust s-process predictions are necessary to disentangle the contribution from other stellar processes producing elements in the same mass region. Nuclear uncertainties are affecting s-process calculations, but most of the needed nuclear input are accessible to present nuclear experiments or they will be in the near future. Neutron-capture rates have a great impact on the s process in massive stars, which is a fundamental source for the solar abundances of the lighter s-process elements heavier than Fe (weak s-process component). In this work we present a new nuclear sensitivity study to explore the impact on the s process in massive stars of 86 neutron-capture rates, including all the reactions between C and Si and between Fe and Zr. We derive the impact of the rates at the end of the He-burning core and at the end of the C-burning shell, where the 22\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{22}$$\\end{document}Ne(α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document},n)25\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{25}$$\\end{document}Mg reaction is is the main neutron source. We confirm the relevance of the light isotopes capturing neutrons in competition with the Fe seeds as a crucial feature of the s process in massive stars. For heavy isotopes we study the propagation of the neutron-capture uncertainties, finding a clear difference of the impact of Fe and Co isotope rates with respect to the rates of heavier stable isotopes. The local uncertainty propagation due to the neutron-capture rates at the s-process branching points is also considered, discussing the example of 85\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{85}$$\\end{document}Kr. The complete results of our study for all the 86 neutron-capture rates are available online. Finally, we present the impact on the weak s process of the neutron-capture rates included in the new ASTRAL library (v0.2).

Enhanced symmetry energy may bear universality of r-process abundances

ABSTRACT The abundances of about half of the elements heavier than iron are subtly attuned by the rapid neutron capture process or r-process, which is intimately related to the competition between neutron capture, photo-disintegration, and β-decay rates, and ultimately depends on the binding energy of neutron-rich nuclei. The well-known Bethe–Weizsäcker semi-empirical mass formula describes the binding energy of ground states – i.e. nuclei with temperatures of T = 0 MeV – with the symmetry energy parameter converging between 23 and 27 MeV for heavy nuclei. We find an unexpected enhancement of the symmetry energy well above the ground state – at higher temperatures of T ≈ 0.7–1.0 MeV – from the available data of giant dipole resonances built on excited states. Although these are likely the temperatures where seed nuclei are created – during the cooling down of the ejecta following neutron-star mergers or collapsars – the fact that the symmetry energy remains constant between T ≈ 0.7 and 1.0 MeV, may suggest an enhanced symmetry energy at lower temperatures, where neutron-capture may start occurring. Calculations using this relatively larger symmetry energy yield a reduction of the binding energy per nucleon for heavy neutron-rich nuclei and inhibits radiative neutron-capture rates. This results in a substantial close in of the neutron drip line which may elucidate the long sought universality of heavy-element abundances through the r-process; as inferred from the similar abundances found in extremely metal-poor stars and the Sun. Sensitivity studies of r-process network calculations have been performed using more sophisticated mass models.

Impact of systematic nuclear uncertainties on composition and decay heat of dynamical and disc ejecta in compact binary mergers

ABSTRACT Theoretically predicted yields of elements created by the rapid neutron capture (r-)process carry potentially large uncertainties associated with incomplete knowledge of nuclear properties and approximative hydrodynamical modelling of the matter ejection processes. We present an in-depth study of the nuclear uncertainties by varying theoretical nuclear input models that describe the experimentally unknown neutron-rich nuclei. This includes two frameworks for calculating the radiative neutron capture rates and 14 different models for nuclear masses, β-decay rates, and fission properties. Our r-process nuclear network calculations are based on detailed hydrodynamical simulations of dynamically ejected material from NS–NS or NS–BH binary mergers plus the secular ejecta from BH–torus systems. The impact of nuclear uncertainties on the r-process abundance distribution and the early radioactive heating rate is found to be modest (within a factor of ∼20 for individual A > 90 abundances and a factor of 2 for the heating rate). However, the impact on the late-time heating rate is more significant and depends strongly on the contribution from fission. We witness significantly higher sensitivity to the nuclear physics input if only a single trajectory is used compared to considering ensembles with a much larger number of trajectories (ranging between 150 and 300), and the quantitative effects of the nuclear uncertainties strongly depend on the adopted conditions for the individual trajectory. We use the predicted Th/U ratio to estimate the cosmochronometric age of six metal-poor stars and find the impact of the nuclear uncertainties to be up to 2 Gyr.

Extracting model-independent nuclear level densities away from stability

The nuclear level density (NLD) is a fundamental measure of the complex structure of atomic nuclei at relatively high energies. Here we present the first model-independent measurement of the absolute partial NLD for a short-lived nucleus. For this purpose we adapt the recently introduced ``shape method'' for $\ensuremath{\beta}$-decay experiments, providing the shape of the $\ensuremath{\gamma}$-ray strength function for exotic nuclei. In this work, we show that combining the shape method with the $\ensuremath{\beta}$-Oslo technique allows for the extraction of the NLD of the populated states without the need for theoretical input. This development opens the way for the extraction of experimental NLDs far from stability with major implications in astrophysical and other applications. We benchmark our approach using data for the stable $^{76}\mathrm{Ge}$ nucleus, finding excellent agreement with previous experimental results. In addition, we present new experimental data and determine the absolute partial level density for the short-lived $^{88}\mathrm{Kr}$ nucleus. Our results suggest a fivefold increase in the NLD for the case of $^{88}\mathrm{Kr}$, compared to the recommended values from semimicroscopic Hartree-Fock Bogoliubov calculations recommended by the RIPL3 nuclear data library. However, our results are in good agreement with other semimicroscopic level density models. We demonstrate the impact of our method on the $^{87}\mathrm{Kr}(n,\ensuremath{\gamma}$) neutron capture rate and show that our experimental uncertainties for NLDs fulfill the requirements needed for astrophysical calculations predicting $r$-process abundances.

Synthesis of thorium and uranium in asymptotic giant branch stars

Context. The intermediate neutron capture process (i-process) operates at neutron densities between those of the slow and rapid neutron-capture processes. It is believed to be triggered by the ingestion of protons in a convective helium-burning region. One possible astrophysical site is low-mass low-metallicity asymptotic giant branch (AGB) stars. Aims. Although it has been widely believed that actinides, and most particularly Th and U, are exclusively produced by explosive r-process nucleosynthesis, we study here the possibility that actinides may also be significantly synthesized through i-process nucleosynthesis in AGB stars. Methods. We computed a 1 M⊙ model at [Fe/H] = −2.5 with the stellar evolution code STAREVOL. We used a nuclear network of 1160 species from H to Cf coupled to the transport processes. Models of various resolutions (temporal and spatial) that use different nuclear datasets are also considered for the analysis. Results. During the proton ingestion event, the neutron density in our AGB model goes up to ∼1015 cm−3 and is shown to be high enough to give rise to the production of actinides. While most of the nuclear flow cycles in the neutron-rich Pb–Bi–Po region, a non-negligible fraction leaks towards heavier elements and eventually synthesizes actinides. The surface enrichment in Th and U is subject to nuclear and astrophysical model uncertainties that could be lowered in the future, in particular by a detailed analysis of the nuclear inputs that affect the neutron capture rates of neutron-rich isotopes between Pb and Pa, along the i-process path. One stellar candidate that may confirm the production of actinides by the i-process is the carbon-enhanced metal-poor (CEMP) r/s star RAVE J094921.8−161722, which shows Th lines in its spectrum. Its surface abundance is shown to be reasonably well reproduced by our AGB model, though abundances of light N ≃ 50 elements remain underestimated. Combined with cosmochronometry, this finding opens the way to dating the i-process event and thus obtaining a lower limit for the age of CEMP-r/s stars. Such a dating is expected to be accurate only if surface abundances of Th and U can be extracted simultaneously. Conclusions. We show that actinides can be synthesized in low-metallicity low-mass AGB stars through the i-process. This astrophysical site therefore potentially contributes to the Galactic enrichment of Th and U, which demonstrates that the r-process may not be the sole mechanism for the production of U and Th.

Impact of nuclear mass measurements in the vicinity of 132Sn on the r-process nucleosynthesis

Nuclear masses are a key aspect in the modelling of nuclear reaction rates for the r-process nucleosynthesis. High precision mass measurements drastically reduce the associated uncertainties in the modelling of r-process nucleosynthesis. We investigate the impact of nuclear mass uncertainties on neutron-capture rates calculations using a Hauser – Feshbach statistical code in the vicinity of 132Sn. Finally, we study the impact of the propagated neutron-capture reaction rates uncertainties on the r-process nucleosynthesis. We find that mass measurements with uncertainties higher than 20 keV affect the calculation of reaction rates. We also note that modelling of reaction rates can differ for more than a factor of two even for experimentally known nuclear masses.

Spin distribution of the nuclear level density in a shell model approach

Nuclear level densities (NLDs) are key ingredients in calculations of neutron capture rates for neutron rich isotopes in nuclear astrophysics applications. Available experimental NLDs are limited mainly to nuclei near stability. Therefore, theoretical models are employed to predict the NLDs of neutron rich nuclei. Here we present a methodology for calculating spin- and parity- dependent NLDs using methods of statistical spectroscopy, based on the Shell Model. The spin distribution of the NLDs is predicted for nuclei in the sd and pf shells.

Neutron-capture measurement candidates for the r-process in neutron star mergers

Neutron star mergers (NSMs) are one of the astrophysical sites for the occurrence of the rapid neutron capture process (r-process). After a merger, the ejected neutron-rich matter hosts the production of radioactive heavy nuclei located far from the stability valley. Their nuclear physics properties are key inputs for r-process nucleosynthesis calculations. Here, we focus on the importance of neutron-capture rates and perform a sensitivity study for typical outflows from NSMs. We identify the rates with the highest impact on the final r-process abundance pattern and the nuclear energy release, therefore determining the nucleosynthesis in NSMs. A list of major n-capture rates affecting individual isotopes and elements production is also provided.

Shell Model Applications in Nuclear Astrophysics

In recent years, shell model studies have significantly contributed in improving the nuclear input, required in simulations of the dynamics of astrophysical objects and their associated nucleosynthesis. This review highlights a few examples such as electron capture rates and neutrino-nucleus cross sections, important for the evolution and nucleosynthesis of supernovae. For simulations of rapid neutron-capture (r-process) nucleosynthesis, shell model studies have contributed to an improved understanding of half lives of neutron-rich nuclei with magic neutron numbers and of the nuclear level densities and γ-strength functions that are both relevant for neutron capture rates.

Evaluation of cadmium ratio for conceptual design of a cyclotron-based thermal neutron radiography system

An approximate method for calculating the cadmium ratio of a cyclotron-based thermal neutron radiography system was developed. In this method, the Monte-Carlo code, MCNP6.2, was employed to calculate the neutron capture rates of Au-197, and the cadmium ratio was obtained by computing the ratio of neutron capture rates. From the simulation results, the computed cadmium ratio is reasonably acceptable, and the assumption of ignoring the fast neutron contribution to the cadmium ratio is valid.

Analysis of the impact of the 204Tl neutron capture cross section on the s-process only isotope 204Pb

In the study of the slow (s) process of nucleosynthesis branching nuclei become of particular interest. These nuclei have half-lives of the order of 1-100 years, and in the stellar environment their decay rate can compete with the neutron capture rate, which effectively leads to a split of the s-process path. Due to the dependence of the decay and the neutron capture rates on the the physical conditions -temperature and neutron density-of the nucleosynthesis environment, variations in these conditions lead to a change in the abundances of the immediately following nuclei. A very interesting branching point is the s-process only 204Tl, which decays to 204Pb. In this work we show how the capture cross section of 204Tl is a key nuclear input which, in addition to being crucial in fixing the ultimate 204Pb s-process abundance, makes the latter sensible to the temperature and neutron density of the stellar environment where the s-process takes place.

New capability for indirect neutron capture measurements: The DICER instrument at LANSCE

The Device for Indirect Capture on Radionuclides (DICER) implements a new indirect technique for (n,γ) studies in which the neutron capture rate is determined from analysis of resonance neutron transmission data. The DICER instrument and associated radionuclide production at the Isotope Production Facility (IPF), both at the Los Alamos Neutron Science Center (LANSCE), as well radioactive sample fabrication, have been under development in the last few years. First measurements on a radioactive sample (88Zr, t½=83.4 days), which was recently reported to have an extremely large thermal neutron capture cross section and resonance integral [1, 2], are planned for the winter of 2021. A performance overview, brief details on the 88Zr fabrication and proof of good operation results will be presented.

Temperature effects on neutron-capture cross sections and rates through electric dipole transitions in hot nuclei

The temperature evolution of electric dipole transition strengths of Sn isotopes is studied using self-consistent quasiparticle random phase approximation (QRPA) and finite-temperature RPA models based on a relativistic density functional. For tin isotopes lighter than $^{132}\mathrm{Sn}$, temperature only shows its effect at high values of 2 MeV, while for neutron-rich tin isotopes heavier than $^{132}\mathrm{Sn}$, the low-lying strength distributions get fragmented and spread to the lower-energy region already at temperature of 1 MeV. Using these electric dipole transition strengths as inputs for the talys code, the temperature effects on $(n,\ensuremath{\gamma})$ cross sections are studied. For tin isotopes lighter than $^{132}\mathrm{Sn}$, temperature causes an enhancement of neutron-capture cross section at high temperatures of 2 MeV, while for neutron-rich tin isotopes heavier than $^{132}\mathrm{Sn}$, the cross section is largely enhanced already at temperature $T=1.0$ MeV, and the bump of cross section caused by the pygmy dipole resonance also becomes broader. The change in neutron-capture rate can be as large as 70% for $^{136}\mathrm{Sn}$, considering the temperature effects on electric dipole transition strength in the final compound nucleus with a temperature of 0.86 MeV (corresponding to $T=10$ GK in the astrophysical environment). The change is around 20% for tin isotopes lighter than $^{132}\mathrm{Sn}$ and above 40% for those heavier than $^{132}\mathrm{Sn}$.

The intermediate neutron capture process

Context. Carbon-enhanced metal-poor (CEMP) r/s-stars show surface-abundance distributions characteristic of the so-called intermediate neutron capture process (i-process) of nucleosynthesis. We previously showed that the ingestion of protons in the convective helium-burning region of a low-mass low-metallicity star can explain the surface abundance distribution observed in CEMP r/s stars relatively well. Such an i-process requires detailed reaction network calculations involving hundreds of nuclei for which reaction rates have not yet been determined experimentally. Aims. We investigate the nuclear physics uncertainties affecting the i-process during the asymptotic giant branch (AGB) phase of low-metallicity low-mass stars by propagating the theoretical uncertainties in the radiative neutron capture cross sections, as well as the 13C(α,n)16O reaction rate, and estimating their impact on the surface-abundance distribution. Methods. We used the STAREVOL code to follow the evolution of a 1 M⊙ [Fe/H] = − 2.5 model star during the proton ingestion event occurring at the beginning of the AGB phase. In the computation, we adopt a nuclear network of 1160 species coupled to the transport processes and different sets of radiative neutron capture cross sections consistently calculated with the TALYS reaction code. Results. It is found that considering systematic uncertainties on the various nuclear ingredients affecting the radiative neutron capture rates, surface elemental abundances are typically predicted within ±0.4 dex. The 56 ≲ Z ≲ 59 region of the spectroscopically relevant heavy-s elements of Ba-La-Ce-Pr as well as the r-dominated Eu element remain relatively unaffected by nuclear uncertainties. In contrast, the inclusion of the direct capture contribution impacts the rates in the neutron-rich A ≃ 45, 100, 160, and 200 regions, and the i-process production of the Z ≃ 45 and 65–70 elements. Uncertainties in the photon strength function also impact the overabundance factors by typically 0.2–0.4 dex. Nuclear level densities tend to affect abundance predictions mainly in the Z = 74 − 79 regions. The uncertainties associated with the neutron-producing reaction 13C(α,n)16O and the unknown β-decay rates are found to have a low impact on the overall surface enrichment. Conclusions. The i-process nucleosynthesis during the early AGB phase of low-metallicity low-mass stars remains sensitive to nuclear uncertainties, substantially affecting theoretical predictions of still unknown radiative neutron capture cross sections. Improved descriptions of direct neutron capture based on shell model calculations or experimental constraints from (d, p) reactions could help to decrease the uncertainties in the estimated rates. Similarly, constraints on the photon strength functions and nuclear level densities, for example through the Oslo method, in the neutron-rich region of A ≃ 100 and 160 would increase the predictive power of the present simulations.

Effective neutron detection using vertical-type BGaN diodes

In this study, vertical-type thick BGaN PIN diodes were successfully fabricated to improve the neutron capture rate of BGaN diodes by improving the BGaN epitaxial growth technique. In this technique, 5-μm-thick epitaxial growth was achieved using trimethylboron as a B metal-organic source, which suppressed the gas-phase reaction. The α-particle energy spectrum, the neutron pulse signal, and the residual energy of particles emitted from a neutron capture reaction were measured using the fabricated BGaN diodes by performing radiation detection measurements. The detected signal position in the neutron detection signal spectrum was similar to that of 2.3 MeV α-particles. These results indicate that vertical-type BGaN diodes can be used as effective neutron detectors.