2016 Vol. 40, No. 2
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2016, 40(2): 023101. doi: 10.1088/1674-1137/40/2/023101
Abstract:
In one of our previous papers, we provided general, effective Higgs interactions for the lightest Higgs boson h (SM-like) and a heavier neutral Higgs boson H based on the effective Lagrangian formulation up to the dim-6 interactions, and then proposed two sensitive processes for probing H. We showed in several examples that the resonance peak of H and its dim-6 effective coupling constants (ECC) can be detected at LHC Run 2 with reasonable integrated luminosity. In this paper, we further perform a more thorough study of the most sensitive process, pp→VH*→VVV, providing information about the relations between the 1σ,3σ,5σ statistical significance and the corresponding ranges of the Higgs ECC for an integrated luminosity of 100 fb-1. These results have two useful applications in LHC Run 2: (A) realizing the experimental determination of the ECC in the dim-6 interactions if H is found and, (B) obtaining the theoretical exclusion bounds if H is not found. Some alternative processes sensitive for certain ranges of the ECC are also analyzed.
In one of our previous papers, we provided general, effective Higgs interactions for the lightest Higgs boson h (SM-like) and a heavier neutral Higgs boson H based on the effective Lagrangian formulation up to the dim-6 interactions, and then proposed two sensitive processes for probing H. We showed in several examples that the resonance peak of H and its dim-6 effective coupling constants (ECC) can be detected at LHC Run 2 with reasonable integrated luminosity. In this paper, we further perform a more thorough study of the most sensitive process, pp→VH*→VVV, providing information about the relations between the 1σ,3σ,5σ statistical significance and the corresponding ranges of the Higgs ECC for an integrated luminosity of 100 fb-1. These results have two useful applications in LHC Run 2: (A) realizing the experimental determination of the ECC in the dim-6 interactions if H is found and, (B) obtaining the theoretical exclusion bounds if H is not found. Some alternative processes sensitive for certain ranges of the ECC are also analyzed.
2016, 40(2): 023102. doi: 10.1088/1674-1137/40/2/023102
Abstract:
The charged vector ρ mesons in the presence of external magnetic fields at finite temperature T and chemical potential μ have been investigated in the framework of the Nambu-Jona-Lasinio model. We compute the masses of charged ρ mesons numerically as a function of the magnetic field for different values of temperature and chemical potential. The self-energy of the ρ meson contains the quark-loop contribution, i.e. the leading order contribution in 1/Nc expansion. The charged ρ meson mass decreases with the magnetic field and drops to zero at a critical magnetic field eBc, which indicates that the charged vector meson condensation, i.e. the electromagnetic superconductor can be induced above the critical magnetic field. Surprisingly, it is found that the charged ρ condensation can even survive at high temperature and density. At zero temperature, the critical magnetic field just increases slightly with the chemical potential, which indicates that charged ρ condensation might occur inside compact stars. At zero density, in the temperature range 0.2-0.5 GeV, the critical magnetic field for charged ρ condensation is in the range of 0.2-0.6 GeV2, which indicates that a high temperature electromagnetic superconductor might be created at LHC.
The charged vector ρ mesons in the presence of external magnetic fields at finite temperature T and chemical potential μ have been investigated in the framework of the Nambu-Jona-Lasinio model. We compute the masses of charged ρ mesons numerically as a function of the magnetic field for different values of temperature and chemical potential. The self-energy of the ρ meson contains the quark-loop contribution, i.e. the leading order contribution in 1/Nc expansion. The charged ρ meson mass decreases with the magnetic field and drops to zero at a critical magnetic field eBc, which indicates that the charged vector meson condensation, i.e. the electromagnetic superconductor can be induced above the critical magnetic field. Surprisingly, it is found that the charged ρ condensation can even survive at high temperature and density. At zero temperature, the critical magnetic field just increases slightly with the chemical potential, which indicates that charged ρ condensation might occur inside compact stars. At zero density, in the temperature range 0.2-0.5 GeV, the critical magnetic field for charged ρ condensation is in the range of 0.2-0.6 GeV2, which indicates that a high temperature electromagnetic superconductor might be created at LHC.
2016, 40(2): 024101. doi: 10.1088/1674-1137/40/2/024101
Abstract:
The coordinate-space Hartree-Fock-Bogoliubov (HFB) approach with quasiparticle blocking has been applied to study the odd-A weakly bound nuclei 17,19B and 37Mg, in which halo structures have been reported in experiments. The Skyrme nuclear forces SLy4 and UNEDF1 have been adopted in our calculations. The results with and without blocking have been compared to demonstrate the emergence of deformed halo structures due to blocking effects. In our calculations, 19B and 37Mg have remarkable features of deformed halos.
The coordinate-space Hartree-Fock-Bogoliubov (HFB) approach with quasiparticle blocking has been applied to study the odd-A weakly bound nuclei 17,19B and 37Mg, in which halo structures have been reported in experiments. The Skyrme nuclear forces SLy4 and UNEDF1 have been adopted in our calculations. The results with and without blocking have been compared to demonstrate the emergence of deformed halo structures due to blocking effects. In our calculations, 19B and 37Mg have remarkable features of deformed halos.
2016, 40(2): 024102. doi: 10.1088/1674-1137/40/2/024102
Abstract:
The chiral geometry of multiple chiral doublet bands with identical configuration is discussed for different triaxial deformation parameters γ in the particle rotor model with π h11/2 ⊗ Vh11/2-1. The energy spectra, electromagnetic transition probabilities B(M1) and B(E2), angular momenta, and K-distributions are studied. It is demonstrated that the chirality still remains not only in the yrast and yrare bands, but also in the two higher excited bands when γ deviates from 30°. The chiral geometry relies significantly on γ, and the chiral geometry of the two higher excited partner bands is not as good as that of the yrast and yrare doublet bands.
The chiral geometry of multiple chiral doublet bands with identical configuration is discussed for different triaxial deformation parameters γ in the particle rotor model with π h11/2 ⊗ Vh11/2-1. The energy spectra, electromagnetic transition probabilities B(M1) and B(E2), angular momenta, and K-distributions are studied. It is demonstrated that the chirality still remains not only in the yrast and yrare bands, but also in the two higher excited bands when γ deviates from 30°. The chiral geometry relies significantly on γ, and the chiral geometry of the two higher excited partner bands is not as good as that of the yrast and yrare doublet bands.
2016, 40(2): 024103. doi: 10.1088/1674-1137/40/2/024103
Abstract:
A stochastic approach based on one- and two-dimensional Langevin equations is applied to calculate the pre-scission neutron multiplicity, fission probability, anisotropy of fission fragment angular distribution, fission cross section and the evaporation cross section for the compound nuclei 188Pt, 227Pa and 251Es in an intermediate range of excitation energies. The chaos weighted wall and window friction formula are used in the Langevin equations. The elongation parameter, c, is used as the first dimension and projection of the total spin of the compound nucleus onto the symmetry axis, K, considered as the second dimension in Langevin dynamical calculations. A constant dissipation coefficient of K, γ K = 0.077(MeV zs)-1/2, is used in two-dimensional calculations to reproduce the above mentioned experimental data. Comparison of the theoretical results of the pre-scission neutron multiplicity, fission probability, fission cross section and the evaporation cross section with the experimental data shows that the results of two-dimensional calculations are in better agreement with the experimental data. Furthermore, it is shown that the two-dimensional Langevin equations together with a dissipation coefficient of K, γ K = 0.077(MeV zs)-1/2, can satisfactorily reproduce the anisotropy of fission fragment angular distribution for the heavy compound nucleus 251Es. However, a larger value of γ K = 0.250(MeV zs)-1/2 is needed to reproduce the anisotropy of fission fragment angular distribution for the lighter compound nucleus 227Pa.
A stochastic approach based on one- and two-dimensional Langevin equations is applied to calculate the pre-scission neutron multiplicity, fission probability, anisotropy of fission fragment angular distribution, fission cross section and the evaporation cross section for the compound nuclei 188Pt, 227Pa and 251Es in an intermediate range of excitation energies. The chaos weighted wall and window friction formula are used in the Langevin equations. The elongation parameter, c, is used as the first dimension and projection of the total spin of the compound nucleus onto the symmetry axis, K, considered as the second dimension in Langevin dynamical calculations. A constant dissipation coefficient of K, γ K = 0.077(MeV zs)-1/2, is used in two-dimensional calculations to reproduce the above mentioned experimental data. Comparison of the theoretical results of the pre-scission neutron multiplicity, fission probability, fission cross section and the evaporation cross section with the experimental data shows that the results of two-dimensional calculations are in better agreement with the experimental data. Furthermore, it is shown that the two-dimensional Langevin equations together with a dissipation coefficient of K, γ K = 0.077(MeV zs)-1/2, can satisfactorily reproduce the anisotropy of fission fragment angular distribution for the heavy compound nucleus 251Es. However, a larger value of γ K = 0.250(MeV zs)-1/2 is needed to reproduce the anisotropy of fission fragment angular distribution for the lighter compound nucleus 227Pa.
2016, 40(2): 025101. doi: 10.1088/1674-1137/40/2/025101
Abstract:
We study a model of dark matter in which the hidden sector interacts with standard model particles via a hidden photonic portal. We investigate the effects of this new interaction on the hydrogen atom, including the Stark, Zeeman and hyperfine effects. Using the accuracy of the measurement of energy, we obtain an upper bound for the coupling constant of the model as f ≤ 10-12. We also calculate the contribution from the hidden photonic portal to the anomalous magnetic moment of the muon as au ≤ 2.2× 10-23 (for the dark particle mass scale 100 MeV), which provides an important probe of physics beyond the standard model.
We study a model of dark matter in which the hidden sector interacts with standard model particles via a hidden photonic portal. We investigate the effects of this new interaction on the hydrogen atom, including the Stark, Zeeman and hyperfine effects. Using the accuracy of the measurement of energy, we obtain an upper bound for the coupling constant of the model as f ≤ 10-12. We also calculate the contribution from the hidden photonic portal to the anomalous magnetic moment of the muon as au ≤ 2.2× 10-23 (for the dark particle mass scale 100 MeV), which provides an important probe of physics beyond the standard model.
2016, 40(2): 026001. doi: 10.1088/1674-1137/40/2/026001
Abstract:
The Jiangmen Underground Neutrino Observatory (JUNO) is an experiment proposed to determine the neutrino mass hierarchy and probe the fundamental properties of neutrino oscillation. The JUNO central detector is a spherical liquid scintillator detector with 20 kton fiducial mass. It is required to achieve a 3%/√(MeV) energy resolution with very low radioactive background, which is a big challenge to the detector design. In order to ensure the detector performance can meet the physics requirements, reliable detector simulation is necessary to provide useful information for the detector design. A simulation study of natural radioactivity backgrounds in the JUNO central detector has been performed to guide the detector design and set requirements for the radio-purity of the detector materials. The accidental background induced by natural radioactivity in the JUNO central detector is 1.1/day. The result is satisfied for the experiment.
The Jiangmen Underground Neutrino Observatory (JUNO) is an experiment proposed to determine the neutrino mass hierarchy and probe the fundamental properties of neutrino oscillation. The JUNO central detector is a spherical liquid scintillator detector with 20 kton fiducial mass. It is required to achieve a 3%/√(MeV) energy resolution with very low radioactive background, which is a big challenge to the detector design. In order to ensure the detector performance can meet the physics requirements, reliable detector simulation is necessary to provide useful information for the detector design. A simulation study of natural radioactivity backgrounds in the JUNO central detector has been performed to guide the detector design and set requirements for the radio-purity of the detector materials. The accidental background induced by natural radioactivity in the JUNO central detector is 1.1/day. The result is satisfied for the experiment.
2016, 40(2): 026002. doi: 10.1088/1674-1137/40/2/026002
Abstract:
The neutrino detector of the Jiangmen Underground Neutrino Observatory (JUNO) is designed to use 20 kilotons of liquid scintillator and approximately 16 000 20 inch photomultipliers (PMTs). One of the options is to use the 20 inch R12860 PMT with high quantum efficiency which has recently been developed by Hamamatsu Photonics. The performance of the newly developed PMT preproduction samples is evaluated. The results show that its quantum efficiency is 30% at 400 nm. Its Peak/Valley (P/V) ratio for the single photoelectron is 4.75 and the dark count rate is 27 kHz at the threshold of 3 mV while the gain is at 1×107. The transit time spread of a single photoelectron is 2.86 ns. Generally the performances of this new 20 inch PMT are improved over the old one of R3600.
The neutrino detector of the Jiangmen Underground Neutrino Observatory (JUNO) is designed to use 20 kilotons of liquid scintillator and approximately 16 000 20 inch photomultipliers (PMTs). One of the options is to use the 20 inch R12860 PMT with high quantum efficiency which has recently been developed by Hamamatsu Photonics. The performance of the newly developed PMT preproduction samples is evaluated. The results show that its quantum efficiency is 30% at 400 nm. Its Peak/Valley (P/V) ratio for the single photoelectron is 4.75 and the dark count rate is 27 kHz at the threshold of 3 mV while the gain is at 1×107. The transit time spread of a single photoelectron is 2.86 ns. Generally the performances of this new 20 inch PMT are improved over the old one of R3600.
2016, 40(2): 026201. doi: 10.1088/1674-1137/40/2/026201
Abstract:
Based on J=ψ events collected with the BESIII detector, with corresponding Monte Carlo samples, the tracking effciency and its systematic uncertainty are studied using a control sample of J/ψ→ppπ+π-. Validation methods and different factors infiuencing the tracking effciency are presented in detail. The tracking effciency and its systematic uncertainty for protons and pions with the transverse momentum and polar angle dependence are also discussed.
Based on J=ψ events collected with the BESIII detector, with corresponding Monte Carlo samples, the tracking effciency and its systematic uncertainty are studied using a control sample of J/ψ→ppπ+π-. Validation methods and different factors infiuencing the tracking effciency are presented in detail. The tracking effciency and its systematic uncertainty for protons and pions with the transverse momentum and polar angle dependence are also discussed.
2016, 40(2): 026202. doi: 10.1088/1674-1137/40/2/026202
Abstract:
Three algorithms (the Charge Comparison Method, n-γ Model Analysis and the Centroid Algorithm) have been revised to improve their accuracy and broaden the scope of applications to real-time digital n-γ discrimination. To evaluate the feasibility of the revised algorithms, a comparison between the improved and original versions of each is presented. To select an optimal real-time discrimination algorithm from these six algorithms (improved and original), the figure-of-merit (FOM), Peak-Threshold Ratio (PTR), Error Probability (EP) and Simulation Time (ST) for each were calculated to obtain a quantitatively comprehensive assessment of their performance. The results demonstrate that the improved algorithms have a higher accuracy, with an average improvement of 10% in FOM, 95% in PTR and 25% in EP, but all the STs are increased. Finally, the Adjustable Centroid Algorithm (ACA) is selected as the optimal algorithm for real-time digital n-γ discrimination.
Three algorithms (the Charge Comparison Method, n-γ Model Analysis and the Centroid Algorithm) have been revised to improve their accuracy and broaden the scope of applications to real-time digital n-γ discrimination. To evaluate the feasibility of the revised algorithms, a comparison between the improved and original versions of each is presented. To select an optimal real-time discrimination algorithm from these six algorithms (improved and original), the figure-of-merit (FOM), Peak-Threshold Ratio (PTR), Error Probability (EP) and Simulation Time (ST) for each were calculated to obtain a quantitatively comprehensive assessment of their performance. The results demonstrate that the improved algorithms have a higher accuracy, with an average improvement of 10% in FOM, 95% in PTR and 25% in EP, but all the STs are increased. Finally, the Adjustable Centroid Algorithm (ACA) is selected as the optimal algorithm for real-time digital n-γ discrimination.
2016, 40(2): 026203. doi: 10.1088/1674-1137/40/2/026203
Abstract:
During the last few years, active personal dosimeters have been developed and have replaced passive personal dosimeters in some external monitoring systems, frequently using silicon diode detectors. Incident photons interact with the constituents of the diode detector and produce electrons. These photon-induced electrons deposit energy in the detector's sensitive region and contribute to the response of diode detectors. To achieve an appropriate photon dosimetry response, the detectors are usually covered by a metallic layer with an optimum thickness. The metallic cover acts as an energy compensating shield. In this paper, a software process is performed for energy compensation. Selective data sampling based on pulse height is used to determine the photon dose equivalent. This method is applied to improve the energy response in photon dosimetry. The detector design is optimized for the response function and determination of the photon dose equivalent. Photon personal dose equivalent is determined in the energy range of 0.3-6 MeV. The error values of the calculated data for this wide energy range and measured data for 133Ba, 137Cs, 60Co and 241Am-Be sources respectively are up to 20% and 15%. Fairly good agreement is seen between simulation and dose values obtained from our process and specifications from several photon sources.
During the last few years, active personal dosimeters have been developed and have replaced passive personal dosimeters in some external monitoring systems, frequently using silicon diode detectors. Incident photons interact with the constituents of the diode detector and produce electrons. These photon-induced electrons deposit energy in the detector's sensitive region and contribute to the response of diode detectors. To achieve an appropriate photon dosimetry response, the detectors are usually covered by a metallic layer with an optimum thickness. The metallic cover acts as an energy compensating shield. In this paper, a software process is performed for energy compensation. Selective data sampling based on pulse height is used to determine the photon dose equivalent. This method is applied to improve the energy response in photon dosimetry. The detector design is optimized for the response function and determination of the photon dose equivalent. Photon personal dose equivalent is determined in the energy range of 0.3-6 MeV. The error values of the calculated data for this wide energy range and measured data for 133Ba, 137Cs, 60Co and 241Am-Be sources respectively are up to 20% and 15%. Fairly good agreement is seen between simulation and dose values obtained from our process and specifications from several photon sources.
2016, 40(2): 027001. doi: 10.1088/1674-1137/40/2/027001
Abstract:
A new generation of storage ring-based light sources, called diffraction-limited storage rings (DLSRs), with emittance approaching the diffraction limit for multi-keV photons by means of multi-bend achromat lattices, has attracted extensive studies worldwide. Among various DLSR proposals, the hybrid multi-bend achromat concept developed at the European Synchrotron Radiation Facility (ESRF) predicts an effective way of minimizing the emittance while keeping the required chromatic sextupole strengths to an achievable level. For the High Energy Photon Source planned to be built in Beijing, an ESRF-type lattice design consisting of 48 hybrid seven-bend achromats is proposed to reach emittance as low as 60 pm · rad with a circumference of about 1296 m. Sufficient dynamic aperture, allowing vertical on-axis injection, and moderate momentum acceptance are achieved simultaneously for a promising ring performance.
A new generation of storage ring-based light sources, called diffraction-limited storage rings (DLSRs), with emittance approaching the diffraction limit for multi-keV photons by means of multi-bend achromat lattices, has attracted extensive studies worldwide. Among various DLSR proposals, the hybrid multi-bend achromat concept developed at the European Synchrotron Radiation Facility (ESRF) predicts an effective way of minimizing the emittance while keeping the required chromatic sextupole strengths to an achievable level. For the High Energy Photon Source planned to be built in Beijing, an ESRF-type lattice design consisting of 48 hybrid seven-bend achromats is proposed to reach emittance as low as 60 pm · rad with a circumference of about 1296 m. Sufficient dynamic aperture, allowing vertical on-axis injection, and moderate momentum acceptance are achieved simultaneously for a promising ring performance.
2016, 40(2): 027002. doi: 10.1088/1674-1137/40/2/027002
Abstract:
Magnetic alloy (MA)-loaded cavities have been widely used in compact proton and heavy-ion synchrotrons, and the MA core is the key issue in their development. Chinese-produced MA has never yet been adopted as core material for an MA-loaded cavity. To use Chinese-produced MA as the core material, it is necessary to study its properties, and compare with MA material produced elsewhere. In this paper, the properties of several MA cores made of Chinese-produced material are measured. Based on the measured results, a schematic design is produced for a cavity which could obtain 1 kV gap voltage with less than 1.5 kW power dissipation in the frequency range of 0.5-7 MHz. The difference between resonant frequencies obtained from simulation and analytical results is less than 10%.
Magnetic alloy (MA)-loaded cavities have been widely used in compact proton and heavy-ion synchrotrons, and the MA core is the key issue in their development. Chinese-produced MA has never yet been adopted as core material for an MA-loaded cavity. To use Chinese-produced MA as the core material, it is necessary to study its properties, and compare with MA material produced elsewhere. In this paper, the properties of several MA cores made of Chinese-produced material are measured. Based on the measured results, a schematic design is produced for a cavity which could obtain 1 kV gap voltage with less than 1.5 kW power dissipation in the frequency range of 0.5-7 MHz. The difference between resonant frequencies obtained from simulation and analytical results is less than 10%.
2016, 40(2): 027003. doi: 10.1088/1674-1137/40/2/027003
Abstract:
Beam Position Monitors (BPMs) for the low-β beam of the Chinese Accelerator Driven Subcritical system (CADS) Proton linac are of the capacitive pick-up type. They provide higher output signals than that of the inductive type. This paper will describe the design and tests of the capacitive BPM system for the low-β proton linac, including the pick-ups, the test bench and the read-out electronics. The tests done with an actual proton beam show a good agreement between the measurements and the simulations in the time domain.
Beam Position Monitors (BPMs) for the low-β beam of the Chinese Accelerator Driven Subcritical system (CADS) Proton linac are of the capacitive pick-up type. They provide higher output signals than that of the inductive type. This paper will describe the design and tests of the capacitive BPM system for the low-β proton linac, including the pick-ups, the test bench and the read-out electronics. The tests done with an actual proton beam show a good agreement between the measurements and the simulations in the time domain.
2016, 40(2): 027004. doi: 10.1088/1674-1137/40/2/027004
Abstract:
The China Accelerator-Driven Sub-critical System (CADS) is a high intensity proton facility to dispose of nuclear waste and generate electric power. CADS is based on a 1.5 GeV, 10 mA CW superconducting (SC) linac as a driver. The high energy section of the linac is composed of two families of SC elliptical cavities which are designed with geometrical beta 0.63 and 0.82. In this paper, the 650 MHz β=0.63 SC elliptical cavity is studied, including cavity optimization, multipacting, high order modes (HOMs) and generator RF power calculation.
The China Accelerator-Driven Sub-critical System (CADS) is a high intensity proton facility to dispose of nuclear waste and generate electric power. CADS is based on a 1.5 GeV, 10 mA CW superconducting (SC) linac as a driver. The high energy section of the linac is composed of two families of SC elliptical cavities which are designed with geometrical beta 0.63 and 0.82. In this paper, the 650 MHz β=0.63 SC elliptical cavity is studied, including cavity optimization, multipacting, high order modes (HOMs) and generator RF power calculation.
2016, 40(2): 028201. doi: 10.1088/1674-1137/40/2/028201
Abstract:
The use of minus identity lenses with an angle-cut collimator can achieve high contrast images in high-energy proton radiography. This article presents the principles of choosing the angle-cut aperture of the collimator for different energies and objects. Numerical simulation using the Monte Carlo code Geant4 has been implemented to investigate the entire radiography for the French test object. The optimum angle-cut apertures of the collimators are also obtained for different energies.
The use of minus identity lenses with an angle-cut collimator can achieve high contrast images in high-energy proton radiography. This article presents the principles of choosing the angle-cut aperture of the collimator for different energies and objects. Numerical simulation using the Monte Carlo code Geant4 has been implemented to investigate the entire radiography for the French test object. The optimum angle-cut apertures of the collimators are also obtained for different energies.
2016, 40(2): 029001. doi: 10.1088/1674-1137/40/2/029001
Abstract:
Since the invention of Zernike phase contrast method in 1930, it has been widely used in optical microscopy and more recently in X-ray microscopy. Considering the image contrast is a mixture of absorption and phase information, we recently have proposed and demonstrated a method for quantitative phase retrieval in Zernike phase contrast X-ray microscopy. In this contribution, we analyze the performance of this method at different photon energies. Intensity images of PMMA samples are simulated at 2.5 keV and 6.2 keV, respectively, and phase retrieval is performed using the proposed method. The results demonstrate that the proposed phase retrieval method is applicable over a wide energy range. For weakly absorbing features, the optimal photon energy is 2.5 keV, from the point of view of image contrast and accuracy of phase retrieval. On the other hand, in the case of strong absorption objects, a higher photon energy is preferred to reduce the error of phase retrieval. These results can be used as guidelines to perform quantitative phase retrieval in Zernike phase contrast X-ray microscopy with the proposed method.
Since the invention of Zernike phase contrast method in 1930, it has been widely used in optical microscopy and more recently in X-ray microscopy. Considering the image contrast is a mixture of absorption and phase information, we recently have proposed and demonstrated a method for quantitative phase retrieval in Zernike phase contrast X-ray microscopy. In this contribution, we analyze the performance of this method at different photon energies. Intensity images of PMMA samples are simulated at 2.5 keV and 6.2 keV, respectively, and phase retrieval is performed using the proposed method. The results demonstrate that the proposed phase retrieval method is applicable over a wide energy range. For weakly absorbing features, the optimal photon energy is 2.5 keV, from the point of view of image contrast and accuracy of phase retrieval. On the other hand, in the case of strong absorption objects, a higher photon energy is preferred to reduce the error of phase retrieval. These results can be used as guidelines to perform quantitative phase retrieval in Zernike phase contrast X-ray microscopy with the proposed method.
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